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Timetable (SDBW04)

Spatially distributed stochastic dynamical systems in biology

Monday 20th June 2016 to Friday 24th June 2016

Monday 20th June 2016
09:00 to 09:20 Registration
09:20 to 09:30 Welcome from Christie Marr (INI Deputy Director)
09:30 to 09:45 Programme Summary by Radek Erban INI 1
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).
10:30 to 11:00 Morning Coffee
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.
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.
12:30 to 13:30 Lunch @ Wolfson Court
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.

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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.

[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)

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15:30 to 16:00 Afternoon Tea
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.

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16:45 to 18:00 Welcome Wine Reception and Poster Session
Tuesday 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
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.
10:30 to 11:00 Morning Coffee
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.

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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.

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12:30 to 13:30 Lunch @ Wolfson Court
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. 
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.
15:30 to 16:00 Afternoon Tea
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.
17:00 to 18:00 Reception
Wednesday 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.

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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.
10:30 to 11:00 Morning Coffee
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.

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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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12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 17:00 Free Afternoon
19:30 to 22:00 Formal Dinner at Emmanuel College
Thursday 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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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.

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10:30 to 11:00 Morning Coffee
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.
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.
12:30 to 13:30 Lunch @ Wolfson Court
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. 
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.
15:30 to 16:00 Afternoon Tea
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 ( 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. 

Friday 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.
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.  
10:30 to 11:00 Morning Coffee
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.
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.

12:30 to 13:30 Lunch @ Wolfson Court
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons