Multiscale Methods for Stochastic Dynamical Systems in Biology

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Multiscale Methods for Stochastic Dynamical Systems in Biology

 Feb 29 - Mar 04, 2016
 ICMS, 15 South College Street Edinburgh

Scientific Organisers:

  • Mark Chaplain, University of St Andrews

  • Radek Erban, University of Oxford

  • Yannis Kevrekidis, University of Princeton

  • Ben Leimkuhler, University of Edinburgh

  • Kevin Painter, Heriot-Watt University

This workshop was part of the Stochastic Dynamical Systems in Biology: Numerical Methods and Applications programme.

The three main objectives were:

  • To increase participation of researchers from the north of the UK in the INI programme

  • To introduce both main themes of the INI programme (spatial and non-spatial models)

  • To discuss the most recent advances in multiscale modelling

The speakers of this Satellite Workshop dealt with issues relating to multiple temporal and spatial scales. In particular, this workshop covered the two main themes of the INI programme and was a dedicated research workshop, and an introduction to the INI programme. The participants of the workshop were encouraged to contribute to the programme by working on research topics investigated by Cambridge-based research participants.


  •  Alexandra Jilkine, University of Notre Dame - The Role of Cell Location and Spatial Gradients in the Evolutionary Dynamics of the Intestinal Cryp
  • Gerhard Hummer, Max Planck Institute of Biophysics - Molecular Simulation and Stochastic Dynamical Modeling of Protein Function
  • Tim Elston, University of North Carolina - Multiscale Modeling of Gradient Sensing
  • Mark Chaplain, University of St Andrews - Spatial Stochastic Modelling of Gene Regulatory Networks
  • Garegin Papoian, University of Maryland - Molecular Simulations of Acto-Myosin Network Dynamics
  • Mariya Ptashnyk, University of Dundee - Stochastic Homogenization of a Model of Plant Biomechanics and the Keller-Segel Chemotaxis System
  • Per Lotstedt, Uppsala University - Diffusion, Subdiffusion, Reactions, and Internal States in Mesoscopic Models
  • Andreas Deutsch, Technische Universität Dresden - Cellular Automaton Modelling of Cancer Growth and Invasion
  • Thomas Hillen, University of Alberta - Stochastic Modelling of the Normal Tissue Complication Probability in Radiation Treatment of Cancer
  • Daan Frenkel, University of Cambridge - Towards Addressable Self-Assembly
  • Assyr Abdulle, École Polytechnique Fédérale de Lausanne - Numerical Techniques for Stiff and Ergodic Stochastic Differential Equations 
  • Hye-Won Kang, University of Maryland - Multiscale Stochastic Reaction-Diffusion Algorithms Combining Markov Chain Models with SPDEs  
  • Jonathan Chapman, University of Oxford - Model Reduction for Slow-Fast Stochastic Systems with Metastable Behaviour
  • Anastasios Matzavinos, Brown University - Mesoscopic Modeling of DNA Transport in an Array of Entropic Barriers 
  • Radek Erban, University of Oxford - Mathematical Methods for Multiscale Modelling of Intracellular Processes
  • Franziska Matthaeus, Heidelberg University - Stochastic Modeling of Collective Cancer Cell Migration
  • Wilhelm Huisinga, Potsdam - Hybrid Stochastic-Deterministic Solution of the Chemical Master Equation
  • Sarah Harris, University of Leeds - Fluctuating Finite Element Analysis
  • Giovanni Samaey, KU Leuven - Variance-Reduced Simulation of Stochastic Agent-Based Models in Biological Applications
  • Ben Leimkuhler, University of Edinburgh - Enhanced Sampling of Biomolecular Systems Using Extended Dynamics
  • Pep Espanol, Universidad Nacional de Educación a Distancia -  Thermal Blobs
  • Kevin Painter, Heriot-Watt University - Navigating the Flow
  • John Chodera, Memorial Sloan-Kettering Cancer Center - Stochastic Modeling of Biomolecular Conformational Dynamics with Markov State Models

  • Konstantinos Zygalakis, University of Edinburgh - Hybrid Modelling of Stochastic Chemical Kinetics

This Satellite Workshop at ICMS is jointly funded by the INI programme and the ICMS.


Zygalakis1, Konstantinos
Hybrid modelling of stochastic chemical kinetics
View Abstract
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.


Assyr, AbdulleÉcole Polytechnique Fédérale de Lausanne
David, AndersonUniversity of Wisconsin - Madison
Sandesh, Athni HiremathTU Kaiserslautern
Casper, BeentjesUniversity of Oxford
Jamie, BennettHeriot-Watt University
Mark, ChaplainUniversity of St Andrews
Jon, ChapmanUniversity of Oxford
Mohammed, CherkaouiUniversity of Nottingham
John, ChoderaMemorial Sloan-Kettering Cancer Center
Claudia, CianciUniversity of Florence
Diana-Patricia, DanciuUniversity of Heidelberg - Institute of Applied Mathematics and BioQuant
Justine, DattaniImperial College London
Andreas, DeutschTechnische Universität Dresden
Andrew, DuncanImperial College London
Tim, ElstonUniversity of North Carolina at Chapel Hill
Radek, ErbanUniversity of Oxford
Pep, EspanolUniversidad Nacional de Educación a Distancia
Núria, Folguera-BlascoCentre de Recerca Matemàtica (CRM)
Daan, FrenkelUniversity of Cambridge
Sarah, HarrisUniversity of Leeds
Jan, HaskovecKing Abdullah University of Science and Technology
Thomas, HillenUniversity of Alberta
David, HolcmanENS
Wilhelm, HuisingaPotsdam
Gerhard, HummerMax Planck Institute of Biophysics
Samuel, IsaacsonBoston University
Alexandra, JilkineUniversity of Notre Dame
Hye-Won, KangUniversity of Maryland,
Ben, LeimkuhlerUniversity of Edinburgh
Christopher, LesterOxford University
Shuohao, LiaoUniversity of Oxford
Yen Ting, LinThe University of Manchester
Karen, LipkowBabraham Institute, Cambridge
Gabriel, LordHeriot-Watt University
Per, LotstedtUppsala University
Franziska, MatthaeusBIOMS/IWR, Heidelberg University
Anastasios, MatzavinosBrown University
Bence, MélykútiUniversity of Freiburg
Eleni, MorakiHeriot-Watt University
Kevin, PainterHeriot-Watt University
Garegin, PapoianUniversity of Maryland
Fabio, PeruzzoUniversity of Leeds
Duong, PhamLuxembourg Centre for Systems Biomedicine
Tomislav, PlesaUniversity of Oxford
Mariya, PtashnykUniversity of Dundee
Edward, RollsUniversity of Oxford
Giovanni, SamaeyKU Leuven
Markus, SchmuckHWU
Xiaocheng, ShangUniversity of Edinburgh
Stephen, SmithUniversity of Edinburgh
Yongzheng, SunChina University of Mining and Technology
Eleanor, TannerMIGSAA (Heriot-Watt University and University of Edinburgh)
Dumitru, TrucuUniversity of Dundee
Romain, YvinecINRA
Kostas, ZygalakisUniversity of Edinburgh