Opening workshop
Monday 18th January 2016 to Friday 22nd January 2016
11:00 to 11:35  Registration & Morning Coffee  
11:35 to 11:45  Welcome from Christie Marr (INI Deputy Director)  
11:45 to 12:30 
Radek Erban ; David Holcman ; Samuel Isaacson ; Konstantinos Zygalakis Eight Open Problems 
INI 1  
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Jasmine Foo Field cancerization and recurrence in head and neck squamous cell carcinoma
Coauthors: 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 populationlevel incidence and recurrence patterns. 
INI 1  
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.

INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 16:15 
Des Higham Efficiency of Stochastic Simulations
Coauthors: David F. Anderson (University of WisconsinMadison), Yu Sun (University of WisconsinMadison) 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 largescale 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 tauleaping or an EulerMaruyama 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 tauleaping and EulerMaruyama 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 
INI 1  
16:15 to 17:00  Poster Session  
17:00 to 18:00  Welcome Wine Reception 
09:00 to 09:45 
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (nonspatial models) 
INI 1  
09:45 to 10:30 
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (nonspatial models) 
INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (nonspatial models) 
INI 1  
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 intracellular
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 highresolution time course data, such as that obtained
from singlecell fluorescence microscopy studies.

INI 1  
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
David Anderson Tutorial A: Stochastic Simulation of Models Arising in the Life Sciences I (nonspatial models) 
INI 1  
14:15 to 15:00 
Linda Petzold A Spatial Stochastic Model of Cell Polarization
Coauthors: Brian Drawert (UC Santa Barbara), Michael Lawson (Uppsala University), TauMu 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 symmetrybreaking 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 Gprotein 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. 
INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 16:15 
Peter Swain Identifying sources of variation in biochemical networks
Coauthors: 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. 
INI 1  
16:15 to 17:00  Discussion (SC)  INI 1 
09:00 to 09:45 
Johan Paulsson Exploiting singlecell 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.

INI 1  
09:45 to 10:30 
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models) 
INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models) 
INI 1  
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 wavingsheet 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.

INI 1  
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Christof Schuette Modelling Cellular ReactionDiffusion 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 particlebased reactiondiffusion 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 coarsegrained 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 subvolumes.
The talk will discuss these different models;
in particular, we will see how the STCME description can
be derived from particlebased reactiondiffusion dynamics.
Joint work with Stefanie Winkelmann (FU Berlin) 
INI 1  
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 multicellular 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 nonequilibrium 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 deepsequening 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.

INI 1  
15:00 to 15:30  Afternoon Tea  
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 nonBrownian 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.

INI 1  
16:15 to 17:00  Discussion (BM)  INI 1  
19:30 to 22:00  Conference Dinner at Trinity College 
09:00 to 09:45 
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models) 
INI 1  
09:45 to 10:30 
Samuel Isaacson Tutorial B: Stochastic Simulation of Models Arising in the Life Sciences II (spatial models) 
INI 1  
10:30 to 11:00  Morning Coffee  
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. 
INI 1  
11:45 to 12:30 
Rachel Kuske Noisegenerated mixedmode oscillations
Abstract
Over the last decade or so, there has been an increased focus on the
appearance of mixedmode oscillations in a variety of applications, including
cell dynamics and the environment. Taking a broad definition of mixedmode
oscillations, the talk will cover a number of biological phenonema that have
mixedmode 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 noiseinduced, 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.

INI 1  
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Ruth Baker Multilevel Monte Carlo: adaptive algorithms and distribution estimation
Coauthors: Christopher Lester (University of
Oxford), Christian Yates (University of Bath), Daniel Wilson
(University of Oxford) Discretestate, continuoustime 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 tauleap 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 multilevel 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 multilevel method. First, I will discuss how to extend the multilevel method to use an adaptive timestepping 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 multilevel 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. 
INI 1  
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 socalled “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

INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 16:15 
Stefan Klumpp Aspects of bacterial persistence
Bacterial persistence is probably the bestestablished example of a system
where noisy gene expression provides a fitness benefit. By inducing switching
between two phenotypes, one welladapted to growthpromoting 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

INI 1  
16:15 to 17:00  Discussion (PK)  INI 1 
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 chemicalreaction theory using Markov chains. 
INI 1  
09:45 to 10:30 
David Holcman Advanced Lecture 23: Narrow escape theory application to the analysis of superresolution single particle trajectories,
This lecture follows Part 1 of (Lecture 1/3) 
INI 1  
10:30 to 11:00  Morning Coffee  
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 
INI 1  
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 continuoustime 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 timestepping and alternative
couplings between coarse and fine simulations.
Related Links

INI 1  
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15  Summary and Discussion (KZ)  INI 1 