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Seminars (SDB)

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Event When Speaker Title Presentation Material
SDB 12th January 2016
15:00 to 16:00
Ulrich Dobramysl Role and dynamics of cytoskeletal actin bundles
SDB 13th January 2016
15:00 to 16:00
Karen Lipkow Cellular Systems Biology of Chromosome Dynamics
SDBW01 18th January 2016
11:45 to 12:30
Radek Erban, David Holcman, Samuel Isaacson, Konstantinos Zygalakis Eight Open Problems
SDBW01 18th January 2016
13:30 to 14:15
Jasmine Foo Field cancerization and recurrence in head and neck squamous cell carcinoma
Co-authors: Kevin Leder (University of Minnesota), Marc Ryser (Duke University), Walter Lee (Duke University)

The accumulation and spatial spread of mutations during carcinogenesis leads to the production of premalignant 'fields' in many epithelial cancers. I will discuss a spatial stochastic model of this process, based on the biased voter model, and analysis of the extent and geometry of these fields. We apply this model to head and neck squamous cell carcinoma and use it to understand population-level incidence and recurrence patterns.
SDBW01 18th January 2016
14:15 to 15:00
Blerta Shtylla Mathematical modeling of cellular nano machines
The generation of directed movement of cellular components frequently requires the rectification of Brownian motion. In this talk, we discuss mathematical models that track bias generation by nano machine constructs. These dynamic constructs work during cell division and their efficient operation requires specific interactions with dynamic bio polymers. We use first passage techniques to derive mesoscale properties for these motor constructs using microscale rates and reactions. 
SDBW01 18th January 2016
15:30 to 16:15
Des Higham Efficiency of Stochastic Simulations
Co-authors: David F. Anderson (University of Wisconsin-Madison), Yu Sun (University of Wisconsin-Madison)

I will analyze and compare the computational complexity of different simulation strategies for continuous time Markov chains. I consider the task of approximating the expected value of some functional of the state of the system over a compact time interval. This task is a bottleneck in many large-scale computations arising in biochemical kinetics and cell biology. In this context, the terms 'Gillespie's method', 'The Stochastic Simulation Algorithm' and 'The Next Reaction Method' are widely used to describe exact simulation methods. For example, Google Scholar records more than 6,000 citations to Gillespie's seminal 1977 paper. I will look at the use of standard Monte Carlo when samples are produced by exact simulation and by approximation with tau-leaping or an Euler-Maruyama discretization of a diffusion approximation. In particular, I will point out some possible pitfalls when computational complexity is analysed. Appropriate modifications o f recently proposed multilevel Monte Carlo algorithms will then be studied for the tau-leaping and Euler-Maruyama approaches. I will pay particular attention to a parameterization of the problem that, in the mass action chemical kinetics setting, corresponds to the classical system size scaling.

Related Links
SDBW01 19th January 2016
09:00 to 09:45
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (non-spatial models)
SDBW01 19th January 2016
09:45 to 10:30
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (non-spatial models)
SDBW01 19th January 2016
11:00 to 11:45
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (non-spatial models)
SDBW01 19th January 2016
11:45 to 12:30
Darren Wilkinson Linking stochastic dynamic biological models to data: Bayesian inference for parameters and structure
Within the field of systems biology there is increasing interest in developing computational models which simulate the dynamics of intra-cellular biochemical reaction networks and incorporate the stochasticity inherent in such processes. These models can often be represented as nonlinear multivariate Markov processes. Analysing such models, comparing competing models and fitting model parameters to experimental data are all challenging problems. This talk will provide an overview of a Bayesian approach to the problem. Since the models are typically intractable, use is often made of algorithms exploiting forward simulation from the model in order to render the analysis "likelihood free". There have been a number of recent developments in the literature relevant to this problem, involving a mixture of sequential and Markov chain Monte Carlo methods. Particular emphasis will be placed on the problem of Bayesian parameter inference for the rate constants of stochastic b iochemical network models, using noisy, partial high-resolution time course data, such as that obtained from single-cell fluorescence microscopy studies.
SDBW01 19th January 2016
13:30 to 14:15
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (non-spatial models)
SDBW01 19th January 2016
14:15 to 15:00
Linda Petzold A Spatial Stochastic Model of Cell Polarization
Co-authors: Brian Drawert (UC Santa Barbara), Michael Lawson (Uppsala University), Tau-Mu Yi (UC Santa Barbara), Mustafa Khammash (ETH Zurich), Otger Campas (UC Santa Barbara), Michael Trogdon (UC Santa Barbara) AbstractPolarization is an essential behavior of living cells, yet the dynamics of this symmetry-breaking process are not fully understood. Previously, noise was thought to interfere with this process; however, we show that stochastic dynamics plan an essential role in robust cell polarization and the dynamic response to changing cues. 

To further our understanding of polarization, we have developed a spatial stochastic model of cellular polarization during mating of Saccharomyces cerevisiae. Specifically we investigate the ability of yeast cells to sense a spatial gradient of mating pheromone and respond by forming a projection in the direction of the mating partner. Our mechanistic model integrates three components of the polarization process: the G-protein cycle activated by pheromone bound receptors, the focusing of a Cdc42 polarization cap, and the formation of the tight localization of proteins on the membrane known as the polarisome. 

Our results demonstrate that higher levels of stochastic noise result in increased robustness, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function. Additionally, our simulations predict that two positive feedback loops are required to generate the spatial amplification to produce focal polarization. We combined our modeling with experiments to explore the critical role of the polarisome scaffold protein Spa2 during yeast mating, and as a result, have characterized a novel positive feedback loop critical to focal polarization via the stabilization of actin cables. 
SDBW01 19th January 2016
15:30 to 16:15
Peter Swain Identifying sources of variation in biochemical networks
Co-authors: Clive Bowsher (), Margaritis Voliotis (University of Bristol)

To understand how cells control and exploit biochemical fluctuations, we must identify the sources of stochasticity, quantify their effects, and distinguish informative variation from confounding "noise". I will present an analysis that allows fluctuations of biochemical networks to be decomposed into multiple components, gives conditions for the design of experimental reporters to measure all components, and provides a technique to predict the magnitude of these components from models. Further, I will identify a particular component of variation that can be used to quantify the efficacy of information flow through a biochemical network. 
SDBW01 20th January 2016
09:00 to 09:45
Johan Paulsson Exploiting single-cell fluctuations
All intracellular processes involve components present in low numbers, creating spontaneous fluctuations that in turn can enslave the components present in high numbers. The mechanisms often appear complex, with reaction rates that depend nonlinearly on concentrations, indirect feedback loops, and distributed delays. Most systems are also sparsely characterized, with a few steps known in detail but many important interactions not even identified. In the first half of the talk, I will discuss mathematical approaches that exploit natural fluctuations to more reliably analyze data and to make predictions about what complex biological networks cannot do. In the second half I will discuss some of our recent experimental results on the role of fluctuations in cells, e.g. in the segregation of mitochondria, oscillations of synthetic genetic networks, bacterial cell fate decisions, and DNA repair.
SDBW01 20th January 2016
09:45 to 10:30
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models)
SDBW01 20th January 2016
11:00 to 11:45
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models)
SDBW01 20th January 2016
11:45 to 12:30
Raymond Goldstein The Stochastic Nonlinear Dynamics of Eukaryotic Flagella
In nearly all of the contexts in biology in which groups of cilia or flagella are found they exhibit some form of synchronized behaviour. Since the experimental observations of Lord Rothschild in the late 1940s and G.I. Taylor’s celebrated waving-sheet model, it has been a working hypothesis that synchrony is due in large part to hydrodynamic interactions between beating filaments. But it is only in the last few years that suitable methods have been developed to test this hypothesis. Those methods have led to the discovery of significant intrinsic biochemical noise in the beating of eukaryotic flagella. This stochasticity occurs at the level of individual beats, with interesting variations within the cycle, and is correlated and even recurrent, with memory extending to hundreds of beats. Possible biological origins of this behaviour will be discussed.
SDBW01 20th January 2016
13:30 to 14:15
Christof Schuette Modelling Cellular Reaction-Diffusion Kinetics
Accurate modeling of reaction kinetics is important for understanding the functionality of biological cells. Depending on the particle concentrations and on the relation between particle mobility and reaction rate constants, different mathematical models are appropriate. In the limit of slow diffusion and small concentrations, both discrete particle numbers and spatial inhomogeneity must be taken into account. The most detailed model consists of particle-based reaction-diffusion dynamics, where all individual particles are explicitly resolved in time and space, and particle positions are propagated by diffusion equations, and reaction events may occur only when reactive species are adjacent. For rapid diffusion or large concentrations, the model may be coarse-grained in different ways. Rapid diffusion leads to mixing and implies that spatial resolution is not needed below a certain length scale. This permits the system to be modeled via a spatiotemporal chemical Master equation (STCME), i.e. a coupled set of chemical Master equations acting on spatial sub-volumes. The talk will discuss these different models; in particular, we will see how the STCME description can be derived from particle-based reaction-diffusion dynamics.

Joint work with Stefanie Winkelmann (FU Berlin) 
SDBW01 20th January 2016
14:15 to 15:00
Ben Simons Tracing the cellular basis of epidermal maintenance and cancer
In adult, tissues are maintained and repaired by stem cells, which divide and differentiate to generate more specialized progeny. The mechanisms that control the balance between proliferation and differentiation promise fundamental insights into the origin and design of multi-cellular organisms. Using epidermis as a model system, we show how the combination of genetic lineage tracing assays in transgenic mouse models with simple ideas from non-equilibrium statistical physics provide a quantitative platform to resolve the stochastic fate behaviour of stem cells and their progeny in both healthy and diseased states. Furthermore, we describe how these methods can be adapted to address exome deep-sequening data, providing a new and general method to resolve the pattern of normal stem cell fate, and detect and characterize the mutational signature of rare field transformations in human tissues, with implications for the early detection of preneoplasia.
SDBW01 20th January 2016
15:30 to 16:15
Scott McKinley Anomalous Diffusion and Random Encounters in Biological Fluids
The last twenty years have seen a revolution in tracking data of biological agents across unprecedented spatial and temporal scales. An important observation from these studies is that path trajectories of living organisms can appear random, but are often poorly described by classical Brownian motion. The analysis of this data can be controversial because practitioners tend to rely on summary statistics that can be produced by multiple, distinct stochastic process models. Furthermore, these summary statistics inappropriately compress the data, destroying details of non-Brownian characteristics that contain vital clues to mechanisms of transport and interaction. In this talk, I will survey the mathematical and statistical challenges that have arisen from recent work on the movement of foreign agents, including viruses, antibodies, and synthetic microparticle probes, in human mucus. 
SDBW01 21st January 2016
09:00 to 09:45
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models)
SDBW01 21st January 2016
09:45 to 10:30
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models)
SDBW01 21st January 2016
11:00 to 11:45
David Holcman Advanced Lecture1 (Part I): Narrow escape theory, first passage time to a small hole and applications to modelling cell biology processes
This is a fast 45 minutes tutorial of the passage time and narrow escape theory with various application in cell biology.
Asymptotic method for the Laplace equation, boundary layer analysis, Dire strait time and Brownian motion in cusp geometry.
SDBW01 21st January 2016
11:45 to 12:30
Rachel Kuske Noise-generated mixed-mode oscillations
Abstract Over the last decade or so, there has been an increased focus on the appearance of mixed-mode oscillations in a variety of applications, including cell dynamics and the environment. Taking a broad definition of mixed-mode oscillations, the talk will cover a number of biological phenonema that have mixed-mode oscillations as their basis.These include more familiar dynamics related to canards and coherence resonance, as well as new mechanisms appearing in systems with delays and nonsmooth dynamics. We concentrate on applications in which these mixed mode oscillations are in fact noise-induced, and discuss how the fundamental mechanisms in these examples appear broadly. These ideas point to a number of opportunities in transfering ideas between different areas of life sciences, as well as bringing new ideas to biological modeling from other areas of science and engineering. 
SDBW01 21st January 2016
13:30 to 14:15
Ruth Baker Multi-level Monte Carlo: adaptive algorithms and distribution estimation
Co-authors: Christopher Lester (University of Oxford), Christian Yates (University of Bath), Daniel Wilson (University of Oxford)

Discrete-state, continuous-time Markov models are widely used to model biochemical reaction networks. Their complexity generally precludes analytic solution, and so we rely on Monte Carlo simulation to estimate system statistics of interest. The most widely used method is the Gillespie algorithm. This algorithm is exact but computationally complex. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Sample paths are generated by taking leaps of length tau through time and using an approximate method to generate reactions within leaps. However, tau must be relatively small to avoid significant estimator bias and this significantly impacts on potential computational advantages of the method.

The multi-level method of Anderson and Higham tackles this problem by employing a variance reduction approach that involves generating sample paths with different accuracies in order to estimate statistics. A base estimator is computed using many (cheap) paths at low accuracy. The bias inherent in this estimator is then reduced using a number of correction estimators. Each correction term is estimated using a collection of (increasingly expensive) paired sample paths where one path of each pair is generated at a higher accuracy compared to the other. By sharing randomness between these paired sample paths a relatively small number of paired paths are required to calculate each correction term.

This talk will outline two main extensions to the multi-level method. First, I will discuss how to extend the multi-level method to use an adaptive time-stepping approach. This enables use of the method to explore systems where the reaction activity changes significantly over the timescale of interest. Second, I will discuss how to harness the multi-level approach to estimate probability distributions of species of interest, giving examples of the utility of this approach by applying it to systems that exhibit bistable behaviour.  
SDBW01 21st January 2016
14:15 to 15:00
Neil Dalchau Performing computation with DNA
The development of technology to read and write DNA quickly and cheaply is enabling new opportunities for programming biological systems. One example of this is DNA computing, a field devoted to implementing computation in purely biological materials. The hope is that this would enable computation to be performed inside cells, which could pave the way for so-called “smart therapeutics”. Naturally, what we have learned in computer science can be applied to DNA computing systems, and has enabled the implementation of a wide variety of examples of performing computation. Examples include DNA circuits for computing a square root, implementing artificial neural networks, and a general scheme for describing arbitrary chemical reaction networks (CRNs), which itself can be thought of as a compiler.

We have used such a CRN compiler of DNA circuitry to implement the approximate majority (AM) algorithm, which seeks to determine the initial majority of a population of agents holding different beliefs. In its simplest form, the algorithm can be described by three chemical reactions. In this talk, I will describe how we implemented, characterized and modelled a purely DNA implementation of the AM reactions. Along the way, I will demonstrate our software platform for programming biological computation. The platform brings together a variety of stochastic methods that are relevant for both programming and understanding biochemical systems, including stochastic simulation, integration of the chemical master equation, a linear noise approximation, and Markov chain Monte Carlo methods for parameter inference. I will also show preliminary work on synthesizing CRNs with specified probabilistic behaviours.

Related Links
SDBW01 21st January 2016
15:30 to 16:15
Stefan Klumpp Aspects of bacterial persistence
Bacterial persistence is probably the best-established example of a system where noisy gene expression provides a fitness benefit. By inducing switching between two phenotypes, one well-adapted to growth-promoting conditions and one adapted to survival in hostile conditions, noise allows provides a mechanism that allows a population to deal with unpredictable environmental conditions. In the talk I will discuss the gene circuits and feedback underlying persistence, aspects of the evolution of these circuits as well as how such heterogeneity of the population can be advantageous for the spreading of a population in space.

Related Links
SDBW01 22nd January 2016
09:00 to 09:45
David Holcman Advanced Lecture 1 (Part II): Narrow escape theory, first passage time to a small hole: analytical theory of chemical reactions
This is a fast 45 minutes tutorial about modeling of stochatic chemical-reaction theory using Markov chains.

SDBW01 22nd January 2016
09:45 to 10:30
David Holcman Advanced Lecture 2-3: Narrow escape theory application to the analysis of super-resolution single particle trajectories,
This lecture follows Part 1 of (Lecture 1/3)
SDBW01 22nd January 2016
11:00 to 11:45
David Holcman Tutorial C: Narrow escape theory, first passage time to a small hole and applications to modelling cell biology processes
SDBW01 22nd January 2016
11:45 to 12:30
Mike Giles Multilevel Monte Carlo methods
The multilevel Monte Carlo (MLMC) method was developed by the author for Brownian diffusion SDEs, and then adapted for continuous-time Markov processes by David Anderson and Des Higham. In this talk I will review the ideas behind MLMC, and discuss some extensions such as adaptive time-stepping and alternative couplings between coarse and fine simulations.

Related Links
SDB 26th January 2016
15:00 to 16:00
Grant Lythe Stochastic modelling and immunology
SDB 27th January 2016
15:00 to 16:00
Steve Andrews Open problems in stochastic cell biology: information transfer, macromolecular crowding, and filament simulation
SDB 29th January 2016
14:30 to 17:00
David Holcman Lecture 1: Stochastic modeling, asymptotics, simulations and data analysis of super-resolution trajectories: application to cellular biology
Introduction to various escape problems and presentation of the futures lectures.
-Ito calculus,
-stochatic integral and
-The Langevin equation. 
(D. Holcman)




SDB 2nd February 2016
15:00 to 16:00
Pietro Cicuta Subdiffusive fluctuations in bacterial chromosomes
SDB 3rd February 2016
15:00 to 16:00
Konstantinos Zygalakis Hybrid modelling of stochastic chemical kinetics
It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be adequately modelled by Markov processes and, for such systems, methods such as Gillespie's algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarse grained schemes, where the ``fast'' reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating well-mixed stochastic kinetics, using Gillepsie--type dynamics to simulate the network in regions of low reactant concentration, and chemical langevin dynamics when the concentrations of all species is large. These two regimes are coupled via an intermediate region in which a ``blended'' jump-diffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cell-cycle model are simulated, using the exact and hybrid scheme, and compared, both in terms weak error, as well as computational cost.  
SDB 5th February 2016
14:30 to 17:00
David Holcman Lecture 2: Introduction to the stochastic integral and Ito calculus,
Lecture 2 is a continuation of lecture 1, (D. Holcman).



SDB 9th February 2016
15:00 to 16:00
Yongzheng Sun Influence of noise and time delay on the collective behavior of self-propelled particles system
Collective animal behaviour is often modelled by individual-based models which assume that each individual alters its behaviour according to signals in its neighborhoods. Basic self-propelled particle models can successfully explain some experimentally observed group-level properties, but additional conjectures have to be hypothesized at the individual-level to fully explain experimental data .  In this talk, we will discuss the influence of time delay and noise on the collective  behavior of self-propelled particles system. Firstly, we consider the directional switching of a self-driven particle model with constant, time-varying and random delay times, respectively. The presented analytical and numerical results have demonstrated that time delay can facilitate coherence in self-driven interacting particle systems. Then we discuss the effect of noise on the convergence speed of a stochastic  Cucker-Smale system. We show that noise can accelerate the emergence of flocking.  
SDB 10th February 2016
15:00 to 16:00
Bence Mélykúti Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks
Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus–response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulatory mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules.
SDB 12th February 2016
14:30 to 17:00
David Holcman Stochastic modeling, asymptotics, simulations and data analysis of super-resolution trajectories: application to cellular biology
SDB 16th February 2016
15:00 to 16:00
Framework for Construction of Caricature Chemical Reaction Systems
SDB 17th February 2016
15:00 to 16:00
Omer Dushek A novel biophysical method for the study of tethered signalling reactions
Many signalling reactions depend on the signalling protein first localising near its substrate before catalysing a reaction. A common example is the binding of cytosolic enzymes to the unstructured cytoplasmic tails of immune receptors. The tethering (binding) of these enzymes to the tails of immune receptors influences the local concentration of substrate that they experience. In contrast to cytosolic reactions, we currently do not have experimental tools to study tethered signalling reactions. In this work-in-progress talk, I will present an experimental assay that we have been using to study tethered signalling. I will show that the PDE model fails to fit the data (which is averaged over moles of protein) whereas the equivalent stochastic simulation can fit the data. We derived a modified PDE model based on a pair density formalism that can fit the data and the stochastic simulation. Ultimately, we are able to recover 4 parameters that characterise a tethered signalling reaction from the data: binding rates, catalytic rate, and a parameter that determines the properties of the tether.
SDB 23rd February 2016
15:00 to 16:00
Grant Lythe Stochastic modelling and immunology
SDB 24th February 2016
15:00 to 16:00
Krasimira Tsaneva Modelling gonadotrophin-releasing hormone signalling: dynamics, noise and reliability
SDB 26th February 2016
14:30 to 17:00
David Holcman Lecture 4
SDB 4th March 2016
14:30 to 17:00
David Holcman Lecture 5: (U. of Cambridge): Activation escape through a potential well.
Asymptotic computation for the escape time through a barrier. 
Singular perturbation of the second order operator.
D. Holcman



SDB 8th March 2016
15:00 to 16:00
Mark Flegg Stochastic simulation of high order molecular interactions with spatial resolution and individual molecule detail: A generalised Smoluchowski theory
In biology, intracellular molecular systems are elaborate. Systems biology and bioinformatics are examples of whole areas of research which exist to make sense of these types of complex systems. As technology inevitably marches forward it has offered a tool for which complex systems may be investigated; simulation. Simulating a whole human cell at the level of individual molecules and proteins is an ambitious goal for mathematicians and computer scientists. There are multiple approaches to simulating stochastic intracellular molecular systems with spatial resolution. One of the most common approaches, due to its relative conceptual simplicity, utilises Smoluchowski reaction kinetics. The primary characteristic of these approaches is the abstract reduction of the chemical reaction to a rule that states that reactions may occur when two reactants are within a particular distance of each other. The critical distance that is used in the simulation is a parameter which controls the macroscopic reaction rate. One of the greatest problems with these types of approaches is that they are only applicable to bimolecular reactions. In this presentation, I hope to demonstrate that overcoming this limitation is critical to accurate Smoluchowski-like simulation of diffusion-limited chemical systems which contain catalytic reactions. Often exploited in mathematics, catalytic reactions may usually be approximated by high order reactions (reactions that involve three or more reactants). I will present a generalised Smoluchowski theory for diffusion-limited reaction kinetics of any order, N.
SDB 9th March 2016
15:00 to 16:00
Andreas Hellander PyURDME, MOLNs and StochSS — from new algorithms for spatial stochastic simulation to large-scale distributed computational experiments in “the cloud"
SDB 11th March 2016
14:30 to 17:00
David Holcman No lecture
SDB 15th March 2016
15:00 to 16:00
Shuohao Liao Tensor Methods for Parameter Estimation and Bifurcation Analysis of Stochastic Reaction Networks
Intracellular networks of interacting bio-molecules carry out many essential functions in living cells, but the molecular events underlying the functioning of such networks are ubiquitously random. Stochastic modelling provides an indispensable tool for understanding how cells control, exploit and tolerant the biological noise. A common challenge of stochastic modelling is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviours of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviours (bifurcation). One fundamental reason for these challenges is that the existing computational approaches are susceptible to the curse of dimensionality, i.e., the exponential growth in memory and computational requirements in the dimension (number of species and parameters). Herein, we have developed a tensor-based computational framew  ork to address this computational challenge. It is based on recently proposed low-parametric, separable tensor-structured representations of classical matrices and vectors. The framework covers the whole process from solving the underlying equations to automated parametric analysis of the stochastic models such that the high cost of working in high dimensions is avoided. One notable advantage of the proposed approach lies in its ability to capture all probabilistic information of stochastic models all over the parameter space into one single tensor-formatted solution, in a way that allows linear scaling of basic operations with respect to the number of dimensions. Within such framework, the existing algorithms commonly used in the deterministic framework can be directly used in stochastic models, including parameter inference, robustness analysis, sensitivity analysis, and stochastic bifurcation analysis.
SDB 16th March 2016
15:00 to 16:00
Romain Yvinec Stochastic coagulation-fragmentation models for the study of protein aggregation phenomena
This work is motivated by protein aggregation phenomena   in neurodegenerative  diseases. A key observation of \textit{in-vitro}   polymerization experiments of prion protein is the large variability   of the so-called 'nucleation time',  which is experimentally defined   as the lag time before the polymerization of proteins trully starts.     In this context, we study a stochastic version of a well-known   nucleation model in physics, namely the Becker-D\"oring model.   In this model, aggregates may increase or decrease their size   one-by-one, by capturing or shedding a single particle. I will   present numerical and analytical investigation of the   nucleation time as a first passage time problem.   I also will present limit theorem techniques to study the link   from the discrete size Becker-D\"oring model to a continuous size version (the Lifshitz-Slyozov model) and (numerically observed) large deviations from the mean-field limit.   Finally, I will present state-of-the art studies of more   general stochastic coagulation-fragmentation models.
SDB 18th March 2016
14:30 to 17:00
David Holcman Lecture 7: (U. of Cambridge): Additive property of the MFPT, Fokker-Planck with a killing term, Non-Poissonnian escape
Using Green’s function, we  study the additive properties of the MFPT. We use path-integral approach to study Fokker-Planck with a killing term. We introduce a non Poissonian stochastic escape from a limit cycle (part I).D. Holcman



SDB 21st March 2016
14:00 to 15:00
Stefan Hellander Reaction rates for nearest-neighbor reactions in the reaction-diffusion master equation
SDB 22nd March 2016
15:00 to 16:00
Julius Kirkegaard Stochastic Aspects of Choanoflagellates
SDB 29th March 2016
15:00 to 16:00
Peter Roland Kramer Stochastic Fluctuations in Suspensions of Swimming Microorganisms
SDB 30th March 2016
15:00 to 16:00
Sandro Azaele Stochastic Modeling of Species-Rich Ecosystems
SDBW03 4th April 2016
09:30 to 10:15
Thomas Kurtz Approximations for Markov chain models
Co-author: David F. Anderson (Univ of Wisconsin - Madison)

The talk will begin by reviewing methods of specifying continuous-time Markov chains and classical limit theorems that arise naturally for chemical network models. Since models arising in molecular biology frequently exhibit multiple state and time scales, analogous limit theorems for these models will be illustrated through simple examples.

Related Links
SDBW03 4th April 2016
10:15 to 11:00
James Faeder Towards large scale models of biochemical networks
Co-authors: Jose Juan Tapia (University of Pittsburgh), John Sekar (University of Pittsburgh)

In this talk I will address some of the challenges faced in developing detailed models of biochemical networks, which encompass large numbers of interacting components. Although simpler coarse-grained models are often useful for gaining insight into biological mechanisms, such detailed models are necessary to understand how molecular components work in the network context and essential to developing the ability to manipulate such networks for practical benefits. The rule-based modeling (RBM) approach, in which biological molecules can be represented as structured objects whose interactions are governed by rules that describe their biochemical interactions, is the basis for addressing multiple scaling issues that arise in the development of large scale models. Currently available software tools for RBM, such as BioNetGen, Kappa, and Simmune, enable the specification and simulation of large scale models, and these tools are in widespread use by the modeling community. I will re view some of the developments that gave rise to those capabilities, and then I will describe our current efforts broaden the appeal of these tools as well as to better enable collaborative development of models through re-use of existing models and improving visual representations of models.

Related Links
  • http://bionetgen.org - For more information about rule-based modeling tools described in this talk.
SDBW03 4th April 2016
11:30 to 12:15
Simon Cotter A constrained approach to the simulation and analysis of stochastic multiscale chemical kinetics
Co-authors: Radek Erban (University of Oxford), Ioannis Kevrekidis (Princeton), Konstantinos Zygalakis (University of Southampton)

In many applications in cell biology, the inherent underlying stochasticity and discrete nature of individual reactions can play a very important part in the dynamics. The Gillespie algorithm has been around since the 1970s, which allows us to simulate trajectories from these systems, by simulating in turn each reaction, giving us a Markov jump process. However, in multiscale systems, where there are some reactions which are occurring many times on a timescale for which others are unlikely to happen at all, this approach can be computationally intractable. Several approaches exist for the efficient approximation of the dynamics of the “slow” reactions, some of which rely on the “quasi-steady state assumption” (QSSA). In this talk, we will present the Constrained Multiscale Algorithm, a method based on the equation free approach, which was first used to construct diffusion approximations of the slowly changing quantities in the system. We will compare this method with other methods which rely on the QSSA to compute the effective drift and diffusion of the approximating SDE. We will then show how this method can be used, back in the discrete setting, to approximate an effective Markov jump generator for the slow variables in the system, and quantify the errors in that approximation. If time permits, we will show how these generators can then be used to sample approximate paths conditioned on the values of their endpoints.
SDBW03 4th April 2016
14:00 to 14:45
Raul Fidel Tempone Efficient Simulation and Inference for Stochastic Reaction Networks
Co-authors: CHRISTIAN BAYER (WIAS, BERLIN), CHIHEB BEN HAMMOUDA (KAUST, THUWAL), ALVARO MORAES (ARAMCO, DAMMAM), FABRIZIO RUGGERI (IMATI, MILAN), PEDRO VILANOVA (KAUST, THUWAL) 

Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 

This talk is focused on novel fast simulation algorithms and statistical inference methods for SRNs. 

Regarding simulation, our novel Multi-level Monte Carlo (MLMC) hybrid methods provide accurate estimates of expected values of a given observable at a prescribed final time. They control the global approximation error up to a user-selected accuracy and up to a certain confidence level, with near optimal computational work. 

With respect to statistical inference, we first present a multi-scale approach, where we introduce a deterministic systematic way of using up-scaled likelihoods for parameter estimation. In a second approach, we derive a new forward-reverse representation for simulating stochastic bridges between consecutive observations. This allows us to use the well-known EM Algorithm to infer the reaction rates. 
SDBW03 4th April 2016
14:45 to 15:30
Erkki Somersalo tba
SDBW03 5th April 2016
09:00 to 09:45
Rosalind Allen Inherent variability in the kinetics of amyloid fibril formation
Co-authors: Juraj Szavits-Nossan, Kym Eden, Ryan Morris, Martin Evans and Cait MacPhee

In small volumes, the kinetics of filamentous protein self-assembly is expected to show significant variability, arising from intrinsic molecular noise. We introduce a simple stochastic model including nucleation and autocatalytic growth via elongation and fragmentation, which allows us to predict the effects of molecular noise on the kinetics of autocatalytic self-assembly. We derive an analytic expression for the lag-time distribution, which agrees well with experimental results for the fibrillation of bovine insulin. Our analysis shows that significant lag-time variability can arise from both primary nucleation and from autocatalytic growth and should provide a way to extract mechanistic information on early-stage aggregation from small-volume experiments.
SDBW03 5th April 2016
09:45 to 10:30
Muruhan Rathinam Analysis of Monte Carlo estimators for parametric sensitivities in stochastic chemical kinetics
Co-author: Ting Wang (University of Delaware)

We provide an overview of some of the major Monte Carlo approaches for parametric sensitivities in stochastic chemical systems. The efficiency of a Monte Carlo approach depends in part on the variance of the estimator. It has been numerically observed that in several examples, that the finite difference (FD) and the (regularized) pathwise differentiation (RPD) methods tend to have lower variance than the Girsanov Tranformation (GT) estimator while the latter has the advantage of being unbiased. We present a theoretical explanation in terms of system volume asymptotics for the larger variance of the GT approach when compared to the FD methods. We also present an analysis of efficiency of the FD and GT methods in terms of desired error and system volume.
SDBW03 5th April 2016
11:00 to 11:45
David Doty "No We Can't": Impossibility of efficient leader election by chemical reactions
Co-author: David Soloveichik (University of Texas, Austin)

Suppose a chemical system requires a single molecule of a certain species $L$. Preparing a solution with just a single copy of $L$ is a difficult task to achieve with imprecise pipettors. Could we engineer artificial reactions (a chemical election algorithm, so to speak) that whittle down an initially large count of $L$ to 1? Yes, with the reaction $L+L \to L+F$: whenever two candidate leaders encounter each other, one drops out of the race. In volume $v$ convergence to a single $L$ requires expected time proportional to $v$; the final reaction --- two lone $L$'s seeking each other in the vast expanse of volume $v$ --- dominates the whole expected time.

One might hope that more cleverly designed reactions could elect a leader more quickly. We dash this hope: $L+L \to L+F$, despite its sloth, is the fastest chemical algorithm for leader election there is (subject to some reasonable constraints on the reactions). The techniques generalize to establish lower bounds on the time required to do other computational tasks, such as computing which of two species $X$ or $Y$ holds an initial majority.


Democracy works... but it's painstakingly slow.

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SDBW03 5th April 2016
11:45 to 12:30
Jay Newby First-passage time to clear the way for receptor-ligand binding in a crowded environment
I will present theoretical support for a hypothesis about cell-cell contact, which plays a critical role in immune function. A fundamental question for all cell-cell interfaces is how receptors and ligands come into contact, despite being separated by large molecules, the extracellular fluid, and other structures in the glycocalyx. The cell membrane is a crowded domain filled with large glycoproteins that impair interactions between smaller pairs of molecules, such as the T cell receptor and its ligand, which is a key step in immunological information processing and decision-making. A first passage time problem allows us to gauge whether a reaction zone can be cleared of large molecules through passive diffusion on biologically relevant timescales. I combine numerical and asymptotic approaches to obtain a complete picture of the first passage time, which shows that passive diffusion alone would take far too long to account for experimentally observed cell-cell contact format ion times. The result suggests that cell-cell contact formation may involve previously unknown active mechanical processes.
SDBW03 5th April 2016
14:00 to 14:45
John Albeck Linking dynamic signaling events within the same cell
In intracellular signaling pathways, biochemical activation events are transmitted from one node within the signaling network to another.  Recent work examining the information capacity of signaling pathways has concluded that most signaling pathways have limited abilities to resolve different strengths of inputs.  However, these studies are based on data in which only a single signal is measured in each cell, in response to a given cell, with the limitation that transmission of a signal from one signaling node to another cannot be directly observed.  Other published data suggest that single cells may have a much higher capacity to transmit quantitative information, which is obscured by population heterogeneity.  To better understand the properties of information transmission through biochemical cascades in individual cells, we have developed a panel of live-cell reporters to monitor multiple signaling events in the cell proliferation and growth network (CPGN).  These reporters include activity biosensors for the kinases ERK, Akt, mTOR, and AMPK, and CRISPR-based reporters for ERK target gene expression.  Experimental analysis with these tools reveals the temporal and quantitative linkage properties between nodes of the CPGN.  I will discuss two studies currently underway in our lab.  The first examines the how the CPGN manages the interplay between ATP-producing and ATP-consuming processes during cell proliferation; we find that loss of Akt signaling results in unstable levels of ATP and NADH in proliferating cells.  The second project focuses on how variations in amplitude and duration of ERK activity control the expression of the target gene Fra-1, which is involved in metastasis; here, we show that cancer therapeutics directed at inhibiting this pathway create strikingly different kinetics of ERK activity at the single-cell level, with distinct effects on Fra-1 expression.



SDBW03 5th April 2016
14:45 to 15:30
Aleksandra Walczak tba
SDBW03 5th April 2016
16:00 to 16:45
Vahid Shahrezaei Inference of size dependence of transcription parameters from single cell data using multi-scale models of gene expression
Co-authors: Anthony Bowman (Imperial College London), Xi-Ming Sun (MRC CSC), Samuel Marguerat (MRC CSC)

Gene expression is affected by both random timing of reactions (intrinsic noise) and interaction with global stochastic systems in the cells (extrinsic noise). A challenge in inferring parameters of gene expression using models of stochastic gene expression is that these models usually only inlcude intrinsic noise. However, experimental distributions of transcripts are strongly influenced by extrinsic effects including cell cycle and cell division. Here, we present a multi-scale approach in stochastic gene expression to deal with this problem. We apply our methodology to data obtained using single molecule Fish technique in fission yeast. The data suggests cell size influences transcription parameters. We use Approximate Bayesian Computation (ABC) along with sequential Monte Carlo to infer the dependence of gene expression parameters on cell size. Our analysis reveals a linear increase of transcription burst size during the cell cycle.
SDBW03 6th April 2016
09:00 to 09:45
Omer Dushek Cellular signalling in T cells is captured by a tractable modular phenotypic model
T cells initiate adaptive immune responses when their T cell antigen receptors (TCRs) recognise antigenic peptides bound to major histocompatibility complexes (pMHC). The binding of pMHC ligands to the TCR can trigger a large signal transduction cascade leading to T cell activation, as measured by the secretion effector cytokines/chemokines. Although the signalling proteins involved have been identified, it is still not understood how the cellular signalling network that they form converts the dose and affinity of pMHC into T cell activation. Here we use a holistic method to infer the signalling architecture from T cell activation data generated by stimulating T cells with a 100,000-fold variation in pMHC affinity/dose. We observe bell-shape dose-response curves and a different optimal pMHC affinity at different pMHC doses. We show that this can be explained by a unique, tractable, and modular phenotypic model of signalling that includes kinetic proofreading with limited sign alling coupled to incoherent feedforward but not negative feedback. The work provides a complementary approach for studying cellular signalling that does not require full details of biochemical pathways.

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SDBW03 6th April 2016
09:45 to 10:30
Eric Deeds tba
SDBW03 6th April 2016
11:00 to 11:45
Carlos Lopez Intracellular signaling processes and cell decisions using stochastic algorithms
Cancer cells within a tumor environment exhibit a complex and adaptive nature whereby genetically and epigenetically distinct subpopulations compete for resources. The probabilistic nature of gene expression and intracellular molecular interactions confer a significant amount of stochasticity in cell fate decisions. This cellular heterogeneity is believed to underlie cases of cancer recurrence, acquired drug resistance, and so-called exceptional responders. From a population dynamics perspective, clonal heterogeneity and cell-fate stochasticity are distinct sources of noise, the former arising from genetic mutations and/or epigenetic transitions, extrinsic to the fate decision signaling pathways and the latter being intrinsic to biochemical reaction networks. Here, we present our results and ongoing work of a kinetic modeling study based on experimental time course data for EGFR-addicted non-small cell lung cancer (PC9) cells in both parental and isolated sublines. When PC9 c ells are treated with erlotinib, an EGFR inhibitor, a complex array of division and death cell decisions arise within a given population in response to treatment. Although deterministic (ODE) simulations capture the effects of clonal heterogeneity and describe the overall trends of experimentally treated tumor cell populations, these are not capable of explaining the observed variability of drug response trajectories, including response magnitude and time to rebound. Our stochastic simulations, instead, capture the effects of intrinsically noisy cell fate decisions that cause significant variability in cell population trajectories. These findings indicate that stochastic simulations are necessary to distinguish the contribution of extrinsic (clonal heterogeneity) and intrinsic (cell fate decisions) noise to understand the variability of cancer-cell response treatment. Furthermore, they suggest that, whereas tumors with distinct clon-al structures are expected to behave differently in response. 
SDBW03 6th April 2016
11:45 to 12:30
Tomas Vejchodsky Tensor methods for higher-dimensional Fokker-Planck equation
In order to analyse stochastic chemical systems, we solve the corresponding Fokker-Planck equation numerically. The dimension of this problem corresponds to the number of chemical species and the standard numerical methods fail for systems with already four or more chemical species due to the so called curse of dimensionality. Using tensor methods we succeeded to solve realistic problems in up to seven dimensions and an academic example of a reaction chain of 20 chemical species.

In the talk we will present the Fokker-Planck equation and discuss its well-posedness. We will describe its discretization based on the finite difference method and we will explain the curse of dimensionality. Then we provide the main idea of tensor methods. We will identify several types of errors of the presented numerical scheme, namely the modelling error, the domain truncation error, discretization error, tensor truncation error, and the algebraic error. We will present an idea that equilibration of these errors based on a posteriori error estimates yields considerable savings of the computational time.
SDBW03 7th April 2016
09:00 to 09:45
Pieter Rein ten Wolde Fundamental limits to transcriptional regulatory control
Gene expression is typically regulated by gene regulatory proteins that bind to the DNA. Experiments have shown that these proteins find their DNA target site via a combination of 3D diffusion in the cytoplasm and 1D diffusion along the DNA. This stochastic transport sets a fundamental limit on the precision of gene regulation. We derive this limit analytically and show by particle-based GFRD simulations that our expression is highly accurate under biologically relevant conditions.
SDBW03 7th April 2016
09:45 to 10:30
Andrew Duncan Hybrid modelling of stochastic chemical kinetics
Co-authors: Radek Erban (University of Oxford), Kostantinos Zygalakis (University of Edinburgh)

It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be adequately modelled by Markov processes and, for such systems, methods such as Gillespie's algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarse grained schemes, where the "fast" reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating well-mixed stochastic kinetics, using Gillepsie-type dynamics to simulate the network in regions of low reactant concentration, and chemical Langevin dynamics when the concentrations of all species is large. These two regimes are coupled via an intermediate region in which a "blended"' jump-diffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cell-cycle model are simulated, using the exact and hybrid scheme, and compared, both in terms weak error, as well as computational cost.
SDBW03 7th April 2016
11:00 to 11:45
Kevin Burrage Sampling Methods for Exploring Between Subject Variability in Cardiac Electrophysiology Experiments
Co-authors: C. C. Drovandi (QUT), N. Cusimano (QUT), S. Psaltis (QUT), A. N. Pettitt (QUT), P. Burrage (QUT)

Between-subject and within-subject variability is ubiquitous in biology and physiology and understanding and dealing with this is one of the biggest challenges in medicine. At the same time it is difficult to investigate this variability by experiments alone. A recent modelling and simulation approach, known as population of models (POM), allows this exploration to take place by building a mathematical model consisting of multiple parameter sets calibrated against experimental data. However, finding such sets within a high-dimensional parameter space of complex electrophysiological models is computationally challenging. By placing the POM approach within a statistical framework, we develop a novel and efficient algorithm based on sequential Monte Carlo (SMC). We compare the SMC approach with Latin hypercube sampling (LHS), a method commonly adopted in the literature for obtaining the POM, in terms of efficiency and output variability in the presence of a drug block through an in-depth investigation via the Beeler-Reuter cardiac electrophysiological model. We show improved efficiency via SMC and that it produces similar responses to LHS when making out-of-sample predictions in the presence of a simulated drug block.
SDBW03 7th April 2016
11:45 to 12:30
Vikram Sunkara Insights into the dynamics of Hybrid Methods through a range of biological examples. A hands on approach
Biological systems can emerge complexity from simple yet multitude of interactions. Capturing such biological phenomenon mathematically for predictions and inference is being actively researched. Computing systems where the interacting components are inherently stochastic demands large amounts of computational power. Recently, splitting the dynamics of the system into deterministic and stochastic components has been a new strategy for computing biological networks. This hybrid strategy drastically reduces the number of equations to solve, however, the new equations are naturally stiff and nonlinear. Hybrid models are a strong candidate as a numerical method for probing large biological networks with intrinsic stochasticity. In this talk we will take on a new mathematical and numerical perspective of hybrid models. Through many biological examples, we will aim to gain insight into the benefits and stumbling blocks of the hybrid framework.

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SDBW03 7th April 2016
14:00 to 14:45
Carmen Molina-Paris A stochastic story of two receptors and two ligands
In this talk, I will introduce the role of the co-receptors CD28 and CTLA-4 in the immune system. Both CD28 and CTLA-4 molecules are expressed on the membrane of T cells and can bind CD80 and CD86 ligand molecules, expressed on the membrane of antigen presenting cells. Classical immunology has identified CD28 co-receptor as enhancing the signal received by T cells from their T cell receptors (TCRs), and CTLA-4 as suppressing TCR signals. New experimental work is supporting a different role for the CTLA-4 molecule. In this talk, I will describe work in progress by our group, to model as  a multi-variate stochastic process the system of two receptors and two ligands. 
SDBW03 7th April 2016
14:45 to 15:30
Ankit Gupta Stability properties of stochastic biomolecular reaction networks: Analysis and Applications
Co-author: Mustafa Khammash (ETH Zurich)

The internal dynamics of a living cell is generally very noisy. An important source of this noise is the intermittency of reactions among various molecular species in the cell. The role of this noise is commonly studied using stochastic models for reaction networks, where the dynamics is described by a continuous-time Markov chain whose states represent the molecular counts of various species. In this talk we will discuss how the long-term behavior of such Markov chains can be assessed using a blend of ideas from probability theory, linear algebra and optimisation theory. In particular we will describe how many biomolecular networks can be viewed as generalised birth-death networks, which leads to a simple computational framework for determining their stability properties such as ergodicity and convergence of moments. We demonstrate the wide-applicability of our framework using many examples from Systems and Synthetic Biology. We also discuss how our results can hel p in analysing regulatory circuits within cells and in understanding the entrainment properties of noisy biomolecular oscillators.
SDBW03 7th April 2016
16:00 to 16:45
Mustafa Khammash Subtle is the noise, but malicious it is not: dynamic exploits of intracellular noise
Co-authors: Ankit Gupta (ETH Zürich), Corentin Briat (ETH Zürich)

Using homeostasic regulation and oscillatory entrainment as examples, I demonstrate how novel and beneficial functional features can emerge from exquisite interactions between intracellular noise and network dynamics. While it is well appreciated that negative feedback can be used to achieve homeostasis when networks behave deterministically, the effect of noise on their regulatory function is not understood. Combining ideas from probability and control theory, we have developed a theoretical framework for biological regulation that explicitly takes into account intracellular noise. Using this framework, I will introduce a new regulatory motif that exploits stochastic noise, using it to achieve precise regulation and perfect adaptation in scenarios where similar deterministic regulation fails. Next I propose a novel role of intracellular noise in the entrainment of decoupled biological oscillators. I will show that while intrinsic noise may inhibit oscillatory activity in ind ividual oscillators, it can actually induce the entrainment of a population of such oscillators. Thus in both regulation and oscillatory entrainment, beneficial dynamic features exist not just in spite of the noise, but rather because of it.
SDBW03 8th April 2016
09:00 to 09:45
Yiannis Kaznessis Closure Scheme for Chemical Master Equations - Is the Gibbs entropy maximum for stochastic reaction networks at steady state?
Stochasticity is a defining feature of biochemical reaction networks, with molecular fluctuations influencing cell physiology. In principle, master probability equations completely govern the dynamic and steady state behavior of stochastic reaction networks. In practice, a solution had been elusive for decades, when there are second or higher order reactions. A large community of scientists has then reverted to merely sampling the probability distribution of biological networks with stochastic simulation algorithms. Consequently, master equations, for all their promise, have not inspired biological discovery.

We recently presented a closure scheme that solves chemical master equations of nonlinear reaction networks [1]. The zero-information closure (ZI-closure) scheme is founded on the observation that although higher order probability moments are not numerically negligible, they contain little information to reconstruct the master probability [2]. Higher order moments are then related to lower order ones by maximizing the entropy of the network. Using several examples, we show that moment-closure techniques may afford the quick and accurate calculation of steady-state distributions of arbitrary reaction networks.

With the ZI-closure scheme, the stability of the systems around steady states can be quantitatively assessed computing eigenvalues of the moment Jacobian [3]. This is analogous to Lyapunov’s stability analysis of deterministic dynamics and it paves the way for a stability theory and the design of controllers of stochastic reacting systems [4, 5].

In this seminar, we will present the ZI-closure scheme, the calculation of steady state probability distributions, and discuss the stability of stochastic systems.

1. Smadbeck P, Kaznessis YN. A closure scheme for chemical master equations. Proc Natl Acad Sci U S A. 2013 Aug 27;110(35):14261-5.

2. Smadbeck P, Kaznessis YN. Efficient moment matrix generation for arbitrary chemical networks, Chem Eng Sci, 20
SDBW03 8th April 2016
09:45 to 10:30
Darren Wilkinson Scalable algorithms for Markov process parameter inference
Inferring the parameters of continuous-time Markov process models using partial discrete-time observations is an important practical problem in many fields of scientific research. Such models are very often "intractable", in the sense that the transition kernel of the process cannot be described in closed form, and is difficult to approximate well. Nevertheless, it is often possible to forward simulate realisations of trajectories of the process using stochastic simulation. There have been a number of recent developments in the literature relevant to the parameter estimation problem, involving a mixture of approximate, sequential and Markov chain Monte Carlo methods. This talk will compare some of the different "likelihood free" algorithms that have been proposed, including sequential ABC and particle marginal Metropolis Hastings, paying particular attention to how well they scale with model complexity. Emphasis will be placed on the problem of Bayesian pa rameter inference for the rate constants of stochastic biochemical network models, using noisy, partial high-resolution time course data.
SDBW03 8th April 2016
11:00 to 11:45
Christian Ray Lineage as a conception of space in compartmental stochastic processes across cellular populations
Co-author: Arnab Bandyopadhyay (University of Kansas)

Cytoplasmic regulatory networks often approximate well-mixed reaction kinetics in single cells, but with variability from cell to cell. As a result, inheritance dynamics and kin correlations have been implicated in effects on cell cycle, regulatory networks, and modulation of population growth rate. Based on an experimental result in our lab suggesting lineage correlations in bacterial growth arrest, we developed a cellular stochastic simulation framework to analyse the role of lineage in bacterial cells regulating growth rate by means of an intracellular molecular network. The simulation framework thus models both intrinsic and inherited noise sources while maintaining lineage data between cell agents assigned individual unique identifiers.

Our initial application of the framework demonstrates the role of lineage in the probability of bacterial growth arrest controlled by an endogenous toxin from a toxin-antitoxin system. These systems have tight binding between toxin and antitoxin, so that there is a discrete critical threshold in the toxin:antitoxin ratio below which a cell is essentially toxin-free and growth is unrestricted, and above which toxin rapidly slows the growth rate. The subset of high-toxin cells crossing into the growth arrested state are associated with antibiotic persistence. Our implementation of a simple toxin-antitoxin system in the simulation framework revealed the statistical dependence of growth arrest on cellular lineage: after several generations of growth, the probability of cellular growth arrest began to depend on lineage distance. Clusters of closely related cell agents had a high probability of transitioning into growth arrest, while the rest of the lineage continued to grow withou t restriction.

We consider various quantities of interest in multiscale lineage simulations, and conclude that growth transitions in a cellular colony cannot be fully understood without quantitative knowledge of its lineage.
SDBW03 8th April 2016
11:45 to 12:30
Ramon Grima The system-size expansion of the chemical master equation: developments in the past 5 years
Co-author: Philipp Thomas (Imperial College London)

The system-size expansion of the master equation, first developed by van Kampen, is a well known approximation technique for deterministically monostable systems. Its use has been mostly restricted to the lowest order terms of this expansion which lead to the deterministic rate equations and the linear-noise approximation (LNA). I will here describe recent developments concerning the system-size expansion, including (i) its use to obtain a general non-Gaussian expression for the probability distribution solution of the chemical master equation; (ii) clarification of the meaning of higher-order terms beyond the LNA and their use in stochastic models of intracellular biochemistry; (iii) the convergence of the expansion, at a fixed system-size, as one considers an increasing number of terms; (iv) extension of the expansion to describe gene-regulatory systems which exhibit noise-induced multimodality; (v) the conditions under which the LNA is exact up to second-order moments; (v i) the relationship between the system-size expansion, the chemical Fokker-Planck equation and moment-closure approximations.

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SDB 12th April 2016
15:00 to 16:00
Yiannis Kaznessis Multiscale Models for New Antibiotic Technologies
Antibiotic-resistant bacterial infections are significant causes of morbidity and mortality worldwide. These infections kill over 700,000 people globally every year. Because of the paucity of new antibiotics, this number may increase to over 10 million by 2050, surpassing deaths from cancer and diabetes combined (http://amr-review.org/). Using synthetic biology techniques, we engineer probiotic bacteria to produce antimicrobial peptides (AMPs) and deliver the potent antibiotic proteins in the gastrointestinal tract of hosts. We test this new technology and demonstrate that it safely reduces multi-drug resistant pathogenic bacteria in the gut of animals [1,2]. At the heart of biological engineering efforts are multiscale models that guide explanations and predictions of the antagonistic activity of recombinant LAB against pathogenic strains [3]. Models are developed to quantify how AMPs kill bacteria at distinct but tied scales. Using atomistic simulations the various interaction steps between peptides and cell membranes are explored. Mesoscopic models are developed to study ion transport and depolarization of membranes treated with AMPs [4]. Stochastic kinetic models are developed to quantify the strength of synthetic promoters and AMPs expression [5]. In this presentation, we will discuss how modeling facilitates biological engineering and stress important theoretical and numerical challenges.
References
  1. Volzing K, Borrero J, Sadowsky MJ, Kaznessis YN. “Antimicrobial Peptides Targeting Gram-negative Pathogens, Produced and Delivered by Lactic Acid Bacteria.” ACS Synth Biol. 2013. 15;2(11):643-50. doi: 10.1021/sb4000367 .
  2. Geldart K., Borrero J., Kaznessis Y.N., “A Chloride-Inducible Expression Vector for Delivery of Antimicrobial Peptides Against Antibiotic-Resistant Enterococcus faecium”, Applied and Environmental Microbiology, 2015 81:11 3889-3897.3.
  3. Kaznessis Y, “Multiscale Models of Antibiotic Probiotics”, Curr Opin Chem Eng, 2014, 1;6:18-24
  4. Bolintineanu D, Kaznessis YN. "Computational studies of protegrin antimicrobial peptides: a review." Peptides. 2011 Jan;32(1):188-201
  5. Kaznessis YN. Computational methods in synthetic biology. Biotechnol J. 2009 Oct;4(10):1392-405. doi: 10.1002/biot.200900163. 
SDB 13th April 2016
15:00 to 16:00
James Rothman On the Structural Biochemical Mechanism of Synaptic Neurotransmission in the Brain
Neurotransmitters stored in synaptic vesicles at nerve endings are synchronously released in less than one millisecond after the action potential arrives and calcium ions secondarily enter the pre-synaptic cytoplasm.  This is by far the fastest membrane fusion mechanism in nature, as is required for all thought and action.  Yet, neurotransmission relies on the same SNAREpin zippering mechanism that powers more leisurely and less coherent hormone release and vesicle trafficking within the cell.  How can the same molecular machine provide for such action on time scales differing by up to a factor of 10,000?  Answers are emerging from mechanistic studies of the two key elements of synaptic regulatory machinery that together allow many SNAREpins to synchronize spatially and temporally.  The calcium sensor, Synaptotagmin, assembles into rings that can impede fusion until they disassemble upon binding calcium ions.  The rod-like Complexin molecule can organize two layers of SNAREpins into zig-zag arrays while at the same time impeding completion of zippering.
SDB 15th April 2016
14:30 to 17:00
David Holcman Lecture 8: (U. of Cambridge): Oscillatory escape: a Non-Poissonnian escape process
This lecture introduces novel concepts in asymptotic of second order PDE. It is a continuation of lecture 7. The motivation is coming from noisy dynamical systems, modelling neuronal networks with synaptic properties. The lecture presents a novel matched asymptotic, based on Mobius conformal mapping, Hopf normal form, to estimate the distribution of exit times and exit points (concentrated at one boundary point). The spectrum of the Fokker-Planck non-selfadjoint operator is computed. The role of the second eigenvalue is explained and generated the oscillation escape.



SDB 19th April 2016
15:00 to 16:00
Bob Eisenberg Mathematics and physiology
SDB 22nd April 2016
14:30 to 17:00
David Holcman Lecture 9: (U. of Cambridge): Oscillatory escape: a Non-Poissonnian escape process
This lecture continues lecture 8 (asymptotics of second order PDEs) and escape through a limit cycle.  The second part introduces the Stochastic Narrow Escape theory. D. Holcman.



SDB 26th April 2016
15:00 to 16:00
André Leier The use of delays in modelling and simulation of biochemical reaction systems and exact model reduction
Delay differential equations have become an integral part of mathematical modelling, in particular when representing biological processes such as population dynamics, epidemiology, or gene regulation and cell signalling. With increased interest in stochastic dynamics, delays have also been introduced into stochastic simulation algorithms.
In my talk I will review such developments over the last ten years, introduce the Delay Chemical Master Equation (DCME), show examples of when the DCME can be solved exactly, and discuss recent developments in the use of delays in model reduction of chemical reaction systems and incorporation of spatial aspects into purely temporal models
SDB 27th April 2016
15:00 to 16:00
Jay Newby Metastable dynamics: rare events in cell biology
I will discuss an emerging framework where the extensive and powerful toolbox of deterministic dynamical systems can be used to study an important class of noise induced stochastic phenomena, called metastable dynamics. Consider two trajectories: one deterministic and one perturbed by weak noise, each having the same initial conditions. A single fluctuation is very unlikely to perturb the stochastic trajectory very far from the deterministic trajectory, and on short time scales the two remain close. On long time scales, both trajectories approach a stable steady state.  Given enough time, it is possible for a rare sequence of fluctuations to perturb the stochastic trajectory far enough that it moves toward a different steady state. Hence, a stable steady state for a deterministic system becomes a metastable state under the influence of weak noise. I will discuss two applications in biology.   1. The first application is epigenetic switching in gene circuits, the biological problem that first motivated my research. It has been known for decades that gene expression is strongly influenced by random forces within the cell. Rare events driven by noise can cause a dramatic shift in the way a gene is expressed, which can radically alter the state of a cell. One example is an altered state that imparts antibiotic resistance to e-coli bacteria. I will show that diffusion approximations, widely used to study gene expression systems, are inaccurate and unreliable for metastable phenomena. As an alternative, I will propose a far more accurate direct method that eliminates the need for a diffusion approximation.   2. The second application is spontaneous neural activity. Intrinsic noise from molecular fluctuations of voltage-gated ion channels cause spontaneous activity that propagates into and affects local network function.  A spontaneous action potential is a physical example of a new type of first-exit-time problem: the random time to initiate an excitable event in an excitable system with a single fixed point. Using a metastable phase plane analysis, I will show how noise induced excitable events in the stochastic Morris-Leccar model are initiated through a predictable sequence of events. In other words, a single mechanism explains how spontaneous activity is generated. Moreover, the generating mechanism contradicts the current understanding of this phenomena.  It is widely believed that spontaneous activity in most neurons is driven primarily by fast sodium channels, because these channels govern the fast initiation stage of an action potential. Potassium channels respond much more slowly and are responsible for reseting the membrane voltage at the final stage of the action potential. Contrary to the standard paradigm, metastable dynamics predicts that the primary driving force behind spontaneous initiation is the slow potassium channel noise.
SDB 28th April 2016
11:00 to 12:00
Colin Gillespie Efficient construction of optimal designs for stochastic kinetic models
Stochastic kinetic models are discrete valued continuous time Markov processes and are often used to describe biological and ecological systems. In recent years there has been interest in the construction of Bayes optimal experimental designs for these models. Unfortunately standard methods such as that by Muller (1999) are computationally intensive even for relatively simple models. However progress can be made by using a sequence of Muller algorithms, where each one has an increasing power of the expected utility function as its marginal distribution. At each stage efficient proposals in the design dimension can be made using the results from the previous stages. In this talk we outline this algorithm, investigate some computational efficiency gains made using parallel computing and illustrate the results with an example.
SDB 29th April 2016
14:30 to 17:00
David Holcman Lecture 10: (U. of Cambridge): Escape through a cusp. Applications to diffusion in a crowded membrane
This lecture introduces asymptotic computations to estimate the escape time through a cusp. The method uses conformal mapping in novel banana shaped domain.  The second part of the lecture concerns the computation of  the effective diffusion coefficient of a crowded membrane. D. Holcman.



SDB 4th May 2016
15:00 to 16:00
Chuan Xue Multiscale Modeling of Axonal Cytoskeleton Dynamics in Disease
The shape and function of an axon is dependent on its cytoskeleton, including microtubules, neurofilaments and actin. Neurofilaments accumulate abnormally in axons in many neurological disorders including ALS. In many situations, an early event of such accumulation is a striking radial segregation of microtubules and neurofilaments. This phenomenon has been observed for over 30 years now, but the underlying mechanism is still poorly understood. To address this problem, we developed a stochastic multiscale model for the cross-sectional cytoskeleton dynamics in an axon. The model successfully explained the cytoskeletal segregation and generated testable predictions. Based on the insights obtained using the stochastic model, we extracted a heuristic nonlocal PDE model that has led to further insights into this problem through mathematical analysis and fast computation. These modeling efforts have motivated new experiments in Dr. Anthony Brown’s lab from Dept. of Neuroscience at the Ohio State University.
SDB 5th May 2016
16:00 to 17:00
Tatiana T Marquez Lago Spatial stochastic models of cell polarity and personalized medicine
SDB 6th May 2016
14:30 to 17:00
David Holcman Lecture 11: (U. of Cambridge): statistics and analysis of super-resolution Single Particle trajectories.
  This lecture presents a stochastic process approach to a statistical analysis of super-resolution Single Particle trajectories. Extraction of the drift, diffusion tensor and removing the position noise.
D. Holcman.



SDB 10th May 2016
15:00 to 16:00
German A. Enciso Absolute robustness in deterministic and stochastic chemical reaction networks
SDB 11th May 2016
10:00 to 13:00
Steve Andrews Smoldyn Tutorial
SDB 11th May 2016
15:00 to 16:00
Ralf Metzler Anomalous diffusion in biological membranes and their mathematical description
I will present results from Molecular Dynamics simulations of pure andcrowded lipid bilayer systems, giving evidence of anomalous diffusion.While in the pure lipid bilayer this anomaly is very short ranged, theaddition of colesterols or the passage to the gel phase leads to exten-ded anomalous diffusion.  The character of the dynamics corresponds tothat of the fractional Brownian motion in the dilute bilayer, changingto non-Gaussian motion when the bilayer is crowded with proteins. Realbiological membranes show macroscopic anomalous diffusion, which is ev-idenced from superresolution microscopy experiments. In particular themotion becomes non-ergodic and ageing.
SDB 13th May 2016
11:00 to 12:00
John Fricks Time Series Analysis of Diffusion with Transient Binding
In living cellls, Brownian forces play a dominant role in the movement of small and not so small particles, such as vesicles, organelles, etc. However, proteins and other macromolecules bind to one another, altering the underlying Brownian dynamics.  In this talk, classical approaches in the biophysical literature to time series which switch between bound and unbound states will be presented, and an alternative approach using stochastic expectation-maximization algorithm (EM) combined with particle filters will be proposed along with extensions for non-quadratic potentials when the particle is bound.  As an example system, molecular motors, such as kinesin, switch between weakly and strongly bound states, as well as directed transport.
SDB 13th May 2016
14:30 to 15:30
David Holcman Lecture 12: (U. of Cambridge): Stochastic chemical reactions: modelling and analysis
This lecture presents models and coarse-graining analysis of stochastic chemical reactions. The first time that k Brownian particles are bound is computed using Markov chains (Mean time to Threshold) . The conditional mean time and splitting probability are computed using certain paths in two dimensional Markov chains. D. Holcman.



SDB 17th May 2016
15:00 to 16:00
Jürgen Reingruber Modeling and stochastic analysis of autoregulation of the Krox20 transcription factor driving cellular diversification and hindbrain patterning
I will present the molecular implementation and function of the autoregulatory loop that amplifies and maintains the expression of Krox20, a transcription factor governing vertebrate hindbrain segmentation. By combining data analysis, biophysical modeling, stochastic analysis and simulations, I dissect the autoregulation process as a function of an initiation signal that leads to promoter activation and subsequent mRNA and protein production. Autoregulation generates a bistable switch that turns a transient initiation signal into a persistent cell fate. The duration and strength of the input signal controls  patterning by modulating the distribution between the cell fates.
SDB 18th May 2016
15:00 to 16:00
Kevin Burrage What we have been doing while at INI for the last 5 weeks: a mathematical study on anomalous diffusion
The field of anomalous diffusion can be very polarising, with some saying that there is little basis for such studies in biology to those saying most of spatial crowding effects lead to these ideas.  This presentation  will be mainly extempore and off the top of my head but I will try to put some of these ideas in context, warts and all.  I will then branch off into such esoteric fields as fractional differential equations, fractional stochastic differential equations, Poisson tau leap with memory, fractional Poisson processes, Mittag Leffler waiting times and finish with a new Poisson tau leap method for anomalous diffusive effects. This will be very much seat of the pants and I hope there is lots of discussion.
SDB 19th May 2016
16:00 to 17:00
Daniel Coombs Particle tracking to elucidate cell surface receptor motion and signalling
SDB 20th May 2016
14:30 to 17:00
David Holcman Lecture 13: (U. of Cambridge): Stochastic biology: stochastic telomere model and Rouse polymer model.
This lecture presents the final computation of the mean time to threshold. The second part concerns modeling telomere length during cell division (computation of the shortest telomere and comparison with the second shortest). The last introduce Rouse and the beta polymer model.



SDB 25th May 2016
15:00 to 16:00
John Tyson Getting Things Right in a Noisy Milieu: Stochastic Models of Cell Cycle Dynamics in Budding Yeast and Bacteria
SDB 27th May 2016
14:30 to 17:00
David Holcman Lecture 14: (U. of Cambridge): Anomalous diffusion for a monomer, mean time for a polymer to loop.
This lecture presents recent methods to study the anomalous exponent of a monomer from a polymer (Rouse and beta). The second part is about asymptotic estimations of the mean first looping time using high dimensional perturbation method of the Laplace operator when removing a tubular neighbourhood of a low dimensional submanifold.



SDB 31st May 2016
15:00 to 16:00
Stephen Smith Four arguments against the reaction-diffusion master equation (and one in its favour).
The reaction-diffusion master equation (RDME) is a well-established and popular lattice-based mathematical description of spatial stochastic chemical systems. A well-known argument against the RDME is that it gives absurd results in the limit of small lattice spacing: this fact has led researchers to develop modified RDMEs which avoid this problem. In this talk, I will offer three further scenarios in which the RDME cannot be considered an accurate description of the underlying physical process. I subsequently argue that there is only a tiny class of problems for which the RDME is the most appropriate route to a solution. I will conclude by offering a beautiful problem from this tiny class to which the RDME provides a remarkable and counterintuitive solution.

SDB 1st June 2016
15:00 to 16:00
Garegin Papoian Stochastic Mechanochemistry of the Eukaryotic Cytoskeleton
SDB 6th June 2016
15:00 to 16:00
Vahid Shahrezaei Multi-scale modelling of stochastic gene expression
Genetically identical cells exhibit variability in gene expression due to inherent stochasticity in biochemical reactions. In this seminar, I describe a multi-scale approach that includes modelling cell growth, division and proliferation in addition to stochastic gene expression inside individual cells. I then discuss three short stories that uses this approach. Firstly, how cell growth rate regulates gene expression noise, secondly, how does expression of fitness inducing gene is shaped by proliferation and finally how to infer parameters of gene expression from single cell data.
SDB 7th June 2016
15:00 to 16:00
André Leier Stochastic membrane processes in biomedicine
SDB 8th June 2016
15:00 to 16:00
David Schnoerr Cox process representation and inference for stochastic reaction-diffusion processes
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from systems biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. On the other hand, spatio-temporal point processes offer several computational advantages from the statistical perspective. In this talk, I will show how the Poisson representation of the Chemical Master Equation can be used to derive a novel connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes. This connection allows us to naturally define an approximate likelihood, which can be optimised with respect to the kinetic parameters of the model. We show on several examples from systems biology and epidemiology that the method yields consistently accurate parameter estimates, and can be used effectively for model selection.
SDB 9th June 2016
16:00 to 17:00
Tuomas Knowles Kinetics of filamentous protein self-assembly
SDB 10th June 2016
11:00 to 12:00
Jonathan Mattingly Scaling limits of a model for selection at two scales Joint with Shishi Luo
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval [0,1] with dependence on a single parameter, λ. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on λ and the behavior of the initial data around 1. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.
SDB 13th June 2016
15:00 to 16:00
Justine Dattani Stochastic models of gene transcription with upstream drives: Exact solution and sample path characterisation
Gene transcription is a highly stochastic, dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. I will present a framework to model gene transcription in populations of cells with time-varying (stochastic or deterministic) transcription and degradation rates. Such rates can be understood as upstream cellular drives representing the effect of different aspects of the cellular environment, e.g. external signalling, circadian rhythms, or chromatin remodelling. I will show that the full solution of the generic master equation for gene transcription contains two components: a model-specific, upstream effective drive, which encapsulates the effect of the cellular drives (e.g., entrainment, periodicity or promoter randomness), and a downstream transcriptional Poissonian part, which is common to all models. This analytical framework allows us to treat cell-to-cell and dynamic variability consistently, unifying several approaches in the literature.   Our general solution confers to us two broad advantages. The first is pragmatic: the theory provides us with new approaches for solving non-stationary gene transcription models, analysing single-cell snapshot and time-course data, and reducing the computational cost of sampling solutions via stochastic simulation. The second advantage is conceptual: studying the solution of a broad class of models in generality provides us with physical intuition for the sources of noise and their characteristics, and the ability to deduce which models are analytically solvable (along with the form and structure of their solutions). I will demonstrate some such benefits by applying our solution to several biologically-relevant examples.
SDB 14th June 2016
11:00 to 12:00
Ben O'Shaughnessy Mechanics of cell division by the actomyosin contractile ring
SDB 14th June 2016
15:00 to 16:00
Markos A. Katsoulakis Path-space information metrics for uncertainty quantification and coarse-graining of molecular systems
We present path-space, information theory-based, sensitivity analysis, uncertainty quantification and variational inference methods for complex high-dimensional stochastic dynamics, including chemical reaction networks with hundreds of parameters, Langevin-type equations and lattice kinetic Monte Carlo. We establish their connections with goal-oriented methods in terms of new, sharp, uncertainty quantification inequalities that scale appropriately at both long times and for high dimensional state and parameter space.   The combination of proposed methodologies is capable to (a) tackle non-equilibrium processes, typically associated with coupled physicochemical mechanisms or boundary conditions, such as reaction-diffusion problems, and where even steady states are unknown altogether, e.g. do not have a Gibbs structure. The path-wise information theory tools,  (b) yield a surprisingly simple, tractable and easy-to-implement approach to quantify and rank parameter sensitivities, as well as  (c) provide reliable parameterizations for coarse-grained molecular systems based on fine-scale data, and rational model selection through path-space (dynamics-based) variational inference methods.
SDB 15th June 2016
15:00 to 16:00
Kevin Lin An analysis of implicit samplers in the small-noise limit
Weighted direct samplers, also known as importance samplers, are Monte Carlo algorithms for generating independent, weighted samples from a given target probability distribution.  Such algorithms have a variety of applications in, e.g., data assimilation, state estimation for stochastic and chaotic dynamics, and computational statistical mechanics.  One challenge in designing and implementing weighted samplers is to ensure the variance of the weights, and that of the resulting estimator, are well-behaved.  Recently, Chorin, Tu, Morzfeld, and coworkers have introduced a class of novel weighted samplers called implcit samplers, which have been shown to possess a number of nice properties.  In this talk, I will report on an analysis of the variance of implicit samplers in the small-noise limit and describe a simple method (suggested by the analysis) to obtain a higher-order implicit sampler. Time permitting, I will also discuss how these methods can be applied to numerical discretizations of SDEs.  This is joint work with Jonathan Goodman, Andrew Leach, and Matthias Morzfeld.
SDB 16th June 2016
11:00 to 12:00
Bence Mélykúti Cross-contamination rate estimation for digital PCR in lab-on-a-chip microfluidic devices
In the bond percolation model on a lattice, we colour vertices with n_c colours independently at random according to Bernoulli distributions. A vertex can receive multiple colours and each of these colours is individually observable. The colours colour the entire component into which they fall. Our goal is to estimate the n_c +1
parameters of the model: the probabilities of colouring of single vertices and the probability with which an edge is open. The input data is the configuration of colours once the complete components have been coloured, without the information which vertices were originally coloured or which edges are open.

We use a Monte Carlo method, the method of simulated moments to achieve this goal. We prove that this method is a strongly consistent estimator by proving a strong law of large numbers for the vertices' weakly dependent colour values. We evaluate the method in computer tests. The motivating application is cross-contamination rate estimation for digital PCR in lab-on-a-chip microfluidic devices.
SDB 17th June 2016
14:15 to 17:00
David Holcman Lecture 15 (University of Cambrdige). Polymer model, mean looping time and interpretation of Hi-C data (Enounter frequencies data)
In this talk, I will present the computation of the mean time for a Rouse polymer  to loop in free and confined domains. The results are used to extract information (such the radius of confinement) from Hi-C data for the chromatin organization. The methods is based on the asymptotic analysis of the Fokker-Planck equation.  
SDBW04 20th June 2016
09:45 to 10:30
Daniel Coombs Interpretation and modelling with super-resolution microscopy
Co-authors: Libin Abraham (University of British Columbia), Alejandra Herrera (University of British Columbia), Michael R Gold (University of British Columbia), Keng Chou (University of British Columbia), Reza Tafteh (University of British Columbia), Joshua Scurll (University of British Columbia), Henry Lu (University of British Columbia), Ki Woong Sung (University of British Columbia)

I will describe recent progress in interpretation and modelling of B cell signalling based on super-resolution light microscopy (primarily, STORM imaging and single particle tracking).
SDBW04 20th June 2016
11:00 to 11:45
Nathanael Hoze Recovering a stochastic process from super-resolution noisy ensembles of single particle trajectories
Co-author: David Holcman (ENS Paris)

Recovering a stochastic process from noisy ensembles of single particle trajectories is resolved here using the Langevin equation as a model. The massive redundancy contained in single particle trajectories allows recovering local parameters of the underlying physical model. However, point localization is perturbed by instrumental noise, which, although of the order of ~10 nanometers, affects the estimation of biophysical parameters such as the drift and diffusion of the motion. Moreover, even if the acquisition frequency of modern tracking algorithm is very high, it is not instantaneous, and this biases parameter estimation. Here, we use several parametric and non-parametric estimators to compute the first and second moment of the process and to recover the local drift, its derivative and the diffusion tensor, in diffusion processes whose observation is perturbed by instrumental noise and non-instantaneous sampling rate. Using a local asymptotic expansion of the estimators and computing the empirical transition probability function, we develop here a method to deconvolve the instrumental from the physical noise. We use numerical simulations to explore the range of validity for the estimators. The present analysis allows characterizing what can exactly be recovered from the statistics of super-resolution microscopy trajectories used in molecular tracking and underlying cellular function.
SDBW04 20th June 2016
11:45 to 12:30
Maria Bruna Diffusion of finite-size particles and application to heterogeneous domains
Co-author: Jonathan Chapman (University of Oxford)

We discuss nonlinear Fokker-Planck models describing diffusion processes with particle interactions. These models are motivated by the study of many particle systems in biology, and arise as the population-level description of a stochastic particle-based model. In particular, we consider a system of impenetrable diffusing spheres and use the method of matched asymptotic expansions to obtain a systematic model reduction. In the second part of the talk, we discuss how this method can be used to derive an effective transport equation in heterogeneous domains, such as porous media or crowded environments. A nice feature of this approach is that it can easily account for macroscopic gradients in porosity or crowding.
SDBW04 20th June 2016
14:00 to 14:45
Stefan Engblom Stability and strong convergence in multiscale methods for spatial stochastic kinetics
Co-authors: Pavol Bauer (Uppsala university), Augustin Chevallier (ENS Cachan), Stefan Widgren (National Veterinary Institute)

Recent progress in spatial stochastic modeling within the reaction-transport framework will be reviewed. I will first look at the issues with guaranteeing well-posedness of the involved mathematical and numerical models. Armed with this and the Lax-principle, I will then present an analysis of split-step methods and multiscale approximations, all performed in a pathwise, or "strong" sense. These analytical techniques hint at how effective (i.e. parallel) numerical implementations can be designed.

Some fairly large-scale simulations will serve as illustrations of the inherent flexibility of the modeling framework. While much of the initial motivation for this work came from problems in cell biology, I will also highlight examples from epidemics and neuroscience.

Related Links
SDBW04 20th June 2016
14:45 to 15:30
Radek Erban From molecular dynamics to Brownian dynamics
I will discuss methods for spatio-temporal modelling in molecular and cell biology, including all-atom and coarse-grained molecular dynamics (MD) and stochastic reaction-diffusion models, with the aim of developing and analysing multiscale methods which use MD simulations in parts of the computational domain and (less-detailed) stochastic reaction-diffusion approaches in the remainder of the domain. The main goal of this multiscale methodology is to use a detailed modelling approach in localized regions of particular interest (in which accuracy and microscopic details are important) and a less detailed model in other regions in which accuracy may be traded for simulation efficiency. Applications using all-atom MD include intracellular dynamics of ions and ion channels. Applications using coarse-grained MD include protein binding to receptors on the cellular membrane, where modern stochastic reaction-diffusion simulators of intracellular processes can be used in the bulk and a ccurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.

References:
[1] Radek Erban, "Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics", Proceedings of the Royal Society A, Volume 472, Number 2186, 20150556 (2016)
[2] Radek Erban, "From molecular dynamics to Brownian dynamics", Proceedings of the Royal Society A, Volume 470, Number 2167, 20140036 (2014)

Related Links
SDBW04 20th June 2016
16:00 to 16:45
Ramon Grima Exact and approximate solutions for spatial stochastic models of biochemical systems
Co-authors: Claudia Cianci (University of Edinburgh), Stephen Smith (University of Edinburgh)

Stochastic effects in chemical reaction systems have been mostly studied via the chemical master equation, a non-spatial discrete stochastic formulation of chemical kinetics which assumes well-mixing and point-like interactions between molecules. These assumptions are in direct contrast with what experiments tells us about the nature of the intracellular environment, namely that diffusion plays a fundamental role in intracellular dynamics and that the environment itself is highly non-dilute (or crowded). I will here describe our recent work on obtaining (i) exact expressions for the solution of the reaction-diffusion master equation (RDME) and its crowded counterpart (cRDME) in equilibrium conditions and (ii) approximate expressions for the moments in non-equilibrium conditions. The solutions portray an emerging picture of the combined influence of diffusion and crowding on the stochastic properties of chemical reaction networks.

Related Links
SDBW04 21st June 2016
09:00 to 09:45
Aleksandar Donev Fast Reactive Brownian Dynamics
I will describe a particle-based algorithm for reaction-diffusion problems that combines Brownian dynamics with a Markov reaction process. The microscopic model simulated by our Split Reactive Brownian Dynamics (SRBD) algorithm is based on the Doi or volume-reactivity model. This model applies only to reactions with at most two reactants, which is physically realistic. Let us consider the simple reaction A+B->product. In the Doi model, particles are independent spherical Brownian walkers (this can be relaxed to account for hydrodynamic interactions), and while an A and a B particle overlap, there is a Poisson process with a given microscopic reaction rate for the two particles to react and give a product. Our goal is to simulate this complex Markov process in dense systems of many particles, in the presence of multiple reaction channels.

Our algorithm is inspired by the Isotropic Direct Simulation Monte Carlo (I-DSMC) method and the next subvolume method. Strang splitting is used to separate diffusion and reaction; this is the only approximation made in our method. In order to process reactions without approximations, with the particles frozen in place, we use an event-driven algorithm. We divide the system into a grid of cells such that only particles in neighboring cells can react. Each cell schedules the next potential reaction to happen involving a particle in that cell and a particle in one of the neighboring cells, and an event queue is used to select the next cell in which a reaction may happen.

Note that, while a grid of cells is used to make the algorithm efficient, the results obtained by the SRBD method are grid-independent and thus free of grid artifacts, such as loss of Galilean invariance and sensitivity of the results to the grid spacing. I will compare our SRBD method with grid-based methods, such as (C)RDME and a variant of RDME that we call Split Brownian Dynamics with Reaction Master Equation (S-BD-RME), on a problem involving the spontaneous f
SDBW04 21st June 2016
09:45 to 10:30
Konstantinos Spiliopoulos Metastability and Monte Carlo Methods for Multiscale Problems
Rare events, metastability and Monte Carlo methods for stochastic dynamical systems have been of central scientific interest for many years now. In this article we focus on rough energy landscapes, that are modeled as multiscale stochastic dynamical systems perturbed by small noise. Large deviations deals with the estimation of rare events. Depending on the type of interaction of the fast scales with the strength of the noise we get different behavior, both for the large deviations and for the corresponding Monte Carlo methods. We describe how to design asymptotically provably efficient importance sampling schemes for the estimation of associated rare event probabilities, such as exit probabilities,hitting probabilities, hitting times, and expectations of functionals of interest. Standard Monte Carlo methods perform poorly in these kind of problems in the small noise limit. In the presence of multiple scales one faces additional difficulties and straightforward adaptation of importance sampling schemes for standard small noise diffusions will not produce efficient schemes. Theoretical results are supplemented by numerical simulation studies.
SDBW04 21st June 2016
11:00 to 11:45
Frank Noe Interacting-Particle Reaction-Diffusion Simulations: Endocytosis
We have introduced interacting-particle reaction-diffusion (iPRD) simulations as a hybrid between molecular dynamics simulations and particle-based reaction-diffusion simulations. iPRD is a suitable modeling framework for many cellular signaling processes, especially such processes involving dense protein mixtures, supramolecular architectures or protein scaffolds at membranes. I will introduce to the theory behind iPRD and present computational algorithms.

One of our key application areas is clathrin-mediated endocytosis in neurons, and I will briefly elude to simulations of protein recruitment to clathrin-coated pits and the interplay between membrane-associated proteins and membrane deformation in endocytosis.

Related Links
SDBW04 21st June 2016
11:45 to 12:30
Avrama Blackwell Computationally efficient simulation of signaling pathways underlying synaptic plasticity
Co-authors: Jedrzejewski-Szmek, Zbigniew (George Mason University), Jedrzejewska-Szmek, Joanna (George Mason University)

Long-lasting forms of long term potentiation (LTP) represent one of the major cellular mechanisms underlying learning and memory. The degree to which neuromodulatory systems, e.g. beta-adrenergic receptors or dopamine receptors, modify LTP and memory is still unclear. Computational modeling of the signaling pathways activated by neuromodulatory and cortical inputs is one approach for investigating these issues. Cortical inputs are spatially specific, often synapse onto spines and produce changes in small numbers of molecules. In contrast, neuromodulatory inputs tend to to be spatially dispersed. The interaction between these two inputs can lead to changes lasting minutes to hours. Because of the heavy computational cost of performing simulations at these diverse spatial and temporal scales, we have developed an asynchronous, adaptive tau-leaping algorithm for reaction-diffusion systems. For every reaction and diffusion channel at each step of the simulation the more efficien t of an exact stochastic event or a tau-leap is implemented from the priority queue. This new approach removes the inherent tradeoff between speed and accuracy in stiff systems which was present in all tau-leaping methods by allowing each reaction channel to proceed at its own pace. We use our computational efficient tau leaping algorithm to investigate how activation of neuromodulatory systems interacts with cortical inputs to modify the development of synaptic plasticity.

Related Links
SDBW04 21st June 2016
14:00 to 14:45
Andrew Rutenberg Models of Microtubule Acetylation
Microtubule (MT) acetylation is done post-translationally in the MT lumen by the acetyltransferase alpha-TAT1. A simple picture is that alpha-TAT1 enters the lumen at the open ends of MT, and diffuses inside while acetylating. Complicating this picture, alpha-TAT1 is approximately half the luminal diameter --- indicating that it may undergo single-file diffusion (SFD). Computationally, we explore the consequences of SFD in this system. Experimentally, in collaboration with the group of Guillaume Montagnac (Institut Gustave Roussy), immunofluorescence techniques allows us to measure the acetylation pattern of individual MT. We try to reconcile the computational and experimental approaches, and highlight open questions. 
SDBW04 21st June 2016
14:45 to 15:30
Kevin Sanft Spatial simulation and analysis of actin filament dynamics and wave propagation
Co-authors: Hans Othmer (University of Minnesota), Yougan Cheng (University of Minnesota)

Actin filaments play an important role in many cellular processes, including cell motility. We present a stochastic model of actin filament dynamics in a three-dimensional Cartesian domain. Actin monomers bind to nucleation sites on the membrane and polymerize to form filaments (F-actin). F-actin polymers interact with membrane-bound nucleation promoting factors via a positive feedback loop. The resulting model produces waves of actin filaments that propagate along the membrane. Simulating polymer growth presents challenges to traditional Gillespie-type simulations. We describe a rule-based simulation approach to handle the many states of actin filament growth. Finally, we discuss techniques for managing the simulation output data.
SDBW04 21st June 2016
16:00 to 17:00
Yannis Kevrekidis Rothschild Lecture: Mathematics for data-driven modeling - The science of crystal balls
In mathematical modeling one typically progresses from observations of the world (and some serious thinking!) to equations for a model, and then to the analysis of the model to make predictions. Good mathematical models give good predictions (and inaccurate ones do not) > - but the computational tools for analyzing them are the same: algorithms that are typically based on closed form equations. While the skeleton of the process remains the same, today we witness the development of mathematical techniques that operate directly on observations -data-, and "circumvent" the serious thinking that goes into selecting variables and parameters and writing equations. The process then may appear to the user a little like making predictions by  "looking into a crystal ball". Yet the "serious thinking" is still there and uses the same -and some new- mathematics: it goes into building algorithms that "jump directly" from data to the analysis of the model (which is never available in closed form) so as to make predictions. I will present a couple of efforts that illustrate this new path from data to predictions. It really is the same old path, but it is travelled by new means.
SDBW04 22nd June 2016
09:00 to 09:45
Tom Chou Path integral-based Bayesian inference of bond energy and mobility

Co-authors: Josh Chang (NIH), Pak-Wing Fok (Univ. of Delaware)

A Bayesian interpretation is given for regularization terms for
parameter functions in inverse problems. Fluctuations about the
extremal solution depend on the regularization terms - which encode
prior knowledge - provide quantification of uncertainty. After
reviewing a general path-integral framework, we set up a number of
applications that arise in biophysics. The inference of bond energies
and bond coordinate mobilities from dynamic force spectroscopy
experiments are worked out in detail.

Related Links http://faculty.biomath.ucla.edu/tchou/
SDBW04 22nd June 2016
09:45 to 10:30
Zaida Luthey-Schulten Simulations of Cellular Processes: From Single Cells to Colonies
Co-authors: Michael J. Hallock (University of Illinois at Urbana-Champaign), Joseph R. Peterson (University of Illinois at Urbana-Champaign), John A. Cole (University of Illinois at Urbana-Champaign), Tyler M. Earnest (University of Illinois at Urbana-Champaign), John E. Stone (University of Illinois at Urbana-Champaign)

High-performance computing now allows integration of data from cryoelectron tomography, super resolution imaging, various –omics, and systems biology reaction studies into coherent computational models of cells and cellular processes functioning under in vivo conditions. Here we analyze the stochastic reaction-diffusion dynamics of ribosome biogenesis in slow growing bacterial cells undergoing DNA replication and probe the metabolic reprogramming that occurs within dense colonies of Escherichia coli cells over periods of hours. Using our GPU-based Lattice Microbe software, the some 1300 reactions and 250 species involved in transcription, translation and ribosome assembly are described in terms of reaction-diffusion master equations and simulated over a cell cycle of two hours. The ribosome biogenesis simulations account for DNA replication that takes place within the cell cycle, and the results are compared to super resolution imaging results. In the case of the c ell colony simulations, reaction-diffusion kinetics of the surrounding medium are coupled with the cellular metabolic networks to demonstrate how small colonies of interacting bacterial cells differentially respond to the competition for resources according to their position in the colony. The predicted metabolic reprogramming has been observed experimentally. Finally we will report on the progress we have achieved to date and how supercomputers will provide us a window into cellular dynamics within bacterial and eukaryotic cells.
SDBW04 22nd June 2016
11:00 to 11:45
Kit Yates Developing PDE-compartment hybrid frameworks for modeling stochastic reaction-diffusion processes
Co-author: Mark Flegg (University of Monash)

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biology. The modelling technique most commonly adopted is systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, the simulation of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems.

The specific stochastic models with which we shall be concerned in this talk are referred to as `compartment-based' or `on-lattice'. These models are characterised by a discretisation of the computational domain into a grid/lattice of `compartments'. Within each compartment particles are assumed to be well-mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments.

In this work we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: `how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully re-defining the continuous PDE concentration as a probability distribution. Whilst this first algorithm shows very strong convergence to analytic solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of the first, it is derived in the continuum limit over the PDE region alone. We test our hybrid methods for functionality and accuracy in a variety of different scenarios by comparing the averaged simulations to analytic solutions of PDEs for mean concentrations.

Related Links
SDBW04 22nd June 2016
11:45 to 12:30
Erik De Schutter Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations
Co-authors: Hepburn, Iain (OIST), Chen, Weiliang (OIST)

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either by particle tracking or voxel-based methods, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers. GPU parallel implementations have been described for particle tracking methods [1,2] and for voxel-based methods [3], where good parallel performance gain up to 2 order of magnitude have been demonstrated but this depends strongly on model specificity. MPI parallel implementations have gained less attention than GPU implementations to date but offer several advantages including a greater range of platform support from personal computers to advanced supercomputer clusters. An initial MPI implementation for irregular grids has been described and almost ideal speedup demonstrated but only up to 4 cores [4], which indicates the potential for good scalability of such implementations.

We describe an operator splitting implementation for irregular grids with a novel method to improve accuracy over Lie-Trotter splitting that is somewhat comparable to tau-reduction but without the performance cost. We systematically investigate parallel performance for a range of models and mesh partitionings using the STEPS simulation platform [5]. Finally we introduce a whole cell parallel simulation of a published reaction-diffusion model [6] within a detailed, complete neuron morphology and demonstrate a speedup of 3 orders of magnitude over serial computations. 

[1] L Dematte 2012. IEEE/ACM Trans. Comput. Biol. Bioinf. 9: 655-667 [2] DV Gladkov et al. 2011. Proc. 19th High Perf. Comp. Symp. 151-158 [3] E Roberts, JE Stone, Z Luthey-Schulten 2013. J. Comp. Chem. 34: 245–255 [4] A Hellander et al. 2014. J. Comput. Phys. 266: 89-100 [5] I Hepburn et al. 2012. BMC Syst. Biol. 6:36 [6] H Anwar et al. 2013. J. Neurosci. 33: 15848-15867

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SDBW04 23rd June 2016
09:00 to 09:45
Jun Allard Clustering of cell surface receptors: Simulating the mesoscale between reaction-diffusion and atomistic scales
Co-author: Omer Dushek (Oxford)

Many biological molecules, including cell surface receptors, form densely-packed clusters that are weakly bound, mechanically soft, and have volumes on the same order as the volumes of the proteins they interact with. Preventing the formation of clusters dramatically attenuates proper cell function in many examples (including T cell activation and allergen activation in Mast cells), but for unknown reason. Therefore, receptor clusters involve biology hidden at the mesoscale between individual protein structure (~0.1nm) and the cell-scale signaling pathways of populations of diffusing protein (~1000nm). In some parameter regimes, clusters comprise 10-100 molecules tied to fixed locations on the cell surface by molecular tethers. The Dushek Lab is developing an in vitro setup that mimics this regime, and find that the time courses of binding and enzymatic reactions are non-trivial and cannot be fit to simple ODE models. On the other hand, fitting to explicitly spatial simulatio ns with volume exclusion is prohibitively slow. Here we present a fast algorithm for tethered reactions with volume exclusion. The algorithm exploits, first, the spatially-fixed tethers, allowing us to construct a single nearest-neighbor tree, and, second, a separation of timescales between the fast diffusion of molecular domains and slow binding and catalytic reactions. This allows use of a hybrid Metropolis-Gillespie algorithm: on the fast timescale of domain motion, efficient equilibrium algorithms that include volume exclusion provide the effective concentrations for the slow timescale of binding and catalysis, which are simulated using a maximally-fast next-event algorithm. Crucially, we employ dynamic connected-set-discovery subroutines to simulate the minimal subset of molecules each time step. The algorithm has computational time scaling approximately with the number of molecules and can reproduce the non-trivial time courses observed experimentally.

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SDBW04 23rd June 2016
09:45 to 10:30
Denis Grebenkov Rigorous results on first-passage times for surface-mediated diffusion
Co-authors: Jean-Francois Rupprecht (National University of Singapore, Singapore), Olivier Bénichou (CNRS - UPMC, France), Raphael Voituriez (CNRS - UPMC, France)

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Explicit solutions are provided for normal and biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface. As a consequence, an intermittent exploration process may enhance search and reaction, as compared to pure surface diffusion or pure bulk diffusion. Our method is applicable to extended targets of arbitrary size (i.e., beyond the narrow escape limit). Higher-order moments and the probability distribution of the first-passage time can also be derived.

Related Links
SDBW04 23rd June 2016
11:00 to 11:45
Scott McKinley Anomalous Diffusion and Random Encounters in Living Systems
Due to the rapid growth of animal movement data obtained by GPS, radio tracking collars and other means, there is a growing recognition that classical models of encounter rates among animal populations should be revisited. Recent theoretical investigations have demonstrated that biologically relevant modifications to classical assumptions about individual behavior can bring about non-trivial changes in the formulation of population-scale dynamical systems. In particular, the combination of tracking data with habitat information has revealed the substantial impact that environmental factors have on animal movement and sociality. In this talk, I will review some of the existing conventional wisdom that supports the use of so-called “Levy flight” models that seek to describe animal movement in the absence of environmental cues. However, through a few examples, I will make the case that animal movement patterns should not be separated from the spatial environmental features that shape them. In fact, animal sensing and decision-making are “leading-order” effects, and their study gives rise to new ecological observations and novel mathematical challenges.
SDBW04 23rd June 2016
11:45 to 12:30
Ruth Baker tbaCell biology processes: model building and validation using quantitative data
Cell biology processes such as motility, proliferation and death are essential to a host of phenomena such as development, wound healing and tumour invasion, and a huge number of different modelling approaches have been applied to study them. In this talk I will explore a suite of related models for the growth and invasion of cell populations. These models take into account different levels of detail on the spatial locations of cells and, as a result, their predictions can differ depending on the relative magnitudes of the various model parameters. To this end, I will discuss how one might determine the applicability of each of these models, and the extent to which inference techniques can be used to estimate their parameters, using both cell- and population-level quantitative data.
SDBW04 23rd June 2016
14:00 to 14:45
Julien Berro Quantitative approaches to unravel the molecular mechanisms of clathrin-mediated endocytosis
Eukaryotic cells ubiquitously use clathrin-mediated endocytosis to internalize nutrients, receptors and recycle plasma membrane. Defects in endocytosis are implicated in multiple diseases such as cancer, neuropathies, metabolic syndromes, and the endocytic machinery can be hijacked by some pathogens to infect cells. During clathrin-mediated endocytosis, the endocytic machinery shapes a ~50-nm diameter vesicle from the flat plasma membrane in less than 20 seconds. When membrane tension is high, a dynamic actin cytoskeleton is necessary for endocytosis to proceed. Despite intensive studies on most of the endocytic proteins, it remains unknown how the actin network produces the forces necessary to deform the plasma membrane during endocytosis.

In this talk, we will show how the development of new quantitative methods can be key to unravel the molecular mechanisms of complex biological processes such as endocytosis. We will focus on new methods to measure the temporal evolution of a) the number of molecules of endocytic proteins, b) their residence times in the endocytic structure, c) the nanometer-scale deformations of the endocytic structure, and d) methods to increase the quality and the temporal resolution of noisy datasets. We will also show how these data are invaluable to constrain mathematical models that we have developed to test hypotheses and make experimentally testable predictions. 
SDBW04 23rd June 2016
14:45 to 15:30
Lei Zhang Noise Attenuation during the Development of Spatial Pattern
Co-author: Qing Nie (UC Irvine)

Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. In this talk, I will present a novel noise attenuation mechanism during the development of spatial pattern. First, we investigate the boundary sharpening in the zebrafish hindbrain. Computational analyses of spatial stochastic models show, surprisingly, that a combination of noise in RA concentration and noise in hoxb1a/krox20 expression promotes sharpening of boundaries between adjacent segments. Second, we integrate spatial and temporal noise attenuation in the BMP-FGF signaling network in the dorsal telencephalon. We demonstrate that perturbing FGF signaling transiently will lead to a noisier boundary with loss of boundary s harpness and a global delay in development.
SDBW04 23rd June 2016
16:00 to 16:45
Jonathan Wattis Dynamics of DNA base-pair breathing, telomere loss and telomere clustering
We start by analysing a model of base-pair breathing in DNA using a system of stochastic ordinary differential equations to describe the distances between bases in a sequence of bases that contains a defect.  We describe how the parameters in the SODE model are obtained from  all-atom MD simulations (AMBER) using a maximum likelihood algorithm.  The result is a model which explains how base-pair breathing depends on the twist of the double helix.  This work is in collaboration with Cipri Duduiala, Ian Dryden and Charlie Laughton (Phys Rev E, 80, 061906, 2009 and Physica D 240, 1254-1261, 2011). 

Telomeres are sequences of bases at the ends of chromosomes.  During replication, they are shortened due to imperfect replication of the DNA.  We present a variety of models of telomere loss, using an evolving distribution of telomere lengths, and analyse this mechanism of aging in cell populations using a combination of theoretical and analytical techniques. This work formed part of the PhD thesis of Qi Qi, cosupervised by Helen Byrne (http://eprints.nottingham.ac.uk/12258 and Bull Math Biol 76, 1241, 2014).

Finally, we  outline ongoing work modelling (in collaboration with David Holcman) on the formation of protein-telomere clusters in yeast cells, using coagulation-fragmentation equations to describe the cluster size and composition. 


SDBW04 24th June 2016
09:00 to 09:45
Paul Bressloff Diffusion in randomly switching environments
In this talk we review recent work with Sean Lawley on diffusion in randomly switching environments. One of the fundamental transport processes in biological cells is the exchange of ions, proteins and other macromolecules between subcellular domains, or between the interior and exterior of the cell, via stochastically gated membrane pores and channels. For example, the nucleus of eukaryotes is surrounded by a protective nuclear envelope within which are embedded nuclear pore complexes (NPCs). The NPCs are the sole mediators of exchange between the nucleus and cytoplasm, which requires the formation of complexes with chaperone molecules known as karyopherins. Other examples include the membrane transport of particles via voltage-gated and ligand-gated ion channels, and intercellular gap-junction coupling. One example at the more macroscopic level is the passive diffusion of oxygen during insect respiration. We show how each of these systems can be modeled in terms of diffusio n in a bounded domain with (partially) switching boundaries, and use a combination of PDE theory and probabilistic methods to determine statistical properties of the system. We highlight important differences between cases where the diffusing particles switch conformational state and cases where the boundary physically switches.
SDBW04 24th June 2016
09:45 to 10:30
Heinz Koeppl Statistical inference of single-cell and single-molecule dynamics
Single-cell and single-molecule experimental techniques expose the randomness of cellular processes and invite a stochastic description. In this talk I will present our efforts to solve inverse problems related to stochastic cellular dynamics. First, we provide a inference framework that accounts for extrinsic and intrinsic noise contributions present in single-cell measurements. For that, we show that stochastic components of a cellular process can be marginalised exactly such that the inference remains tractable. Second, we present single-molecule experimental data to study transcriptional kinetics in live yeast cells. A stochastic models for the system is presented and biophysical parameters such elongation speed, termination rate etc are inferred from single transcription-site intensities. Moreover, optimal filtering or state estimation is performed to reconstruct the most likely position of single RNAP molecules on the gene.  
SDBW04 24th June 2016
11:00 to 11:45
Assaf Amitai Changes in local chromatin structure during homology search: effects of local contacts on search time
Co-authors: Andrew Seeber (Friedrich Miescher Institute for Biomedical Research), Susan M. Gasser (Friedrich Miescher Institute for Biomedical Research), David Holcman (Ecole Normale Supérieure)

Double-strand break (DSB) repair by homologous recombination (HR) requires an efficient and timely search for a homologous template. Here we developed a statistical method of analysis based on single-particle trajectory data which allows us to extract forces acting on chromatin at DSBs. We can differentiate between extrinsic forces from the actin cytoskeleton and intrinsic alterations on the nucleosomal level at the cleaved MAT locus in budding yeast. Using polymer models we show that reduced tethering forces lead to local decondensation near DSBs, which reduces the mean first encounter time by two orders of magnitude. Local decondensation, likely stems from loss of internal mechanical constraints and a local redistribution of nucleosomes that depends on chromatin remodelers. Simulations verify that local changes in inter-nucleosomal contacts near DSBs would shorten drastically the time required for a long-range homology search.
SDBW04 24th June 2016
11:45 to 12:30
David Holcman Advanced Lecture (U. of Cambridge): Analysis of electrodiffusion in dendritic spines for synaptic transmission
This lecture presents recent methods to study electro-diffusion and the Poisson-Nernst-Planck equation (PNP) in bounded domains. The methods are used to interpret and deconvolve  voltage dye (Arclight) signal from dendritic spine and to extract the I-V relation. The geometry of the spine plays a crucial roles in defining this relation.




University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons