MBI Videos

Videos by Workshop 2: Stochastic Processes in Cell and Population Biology

  • Recombination dynamics and ancestral recombination trees
    Ellen Baake
    I will start with an overview over various models for the dynamics of the genetic composition of populations evolving under recombination. For the deterministic treatment that applies in the infinite-population limit, one has large, nonlinear dynamical systems; for the stochastic treatment required for finite populations, the Moran, or Wright-Fisher model is appropriate.
  • Bridging Scales in Molecular Motor Models: From Single to Multiple Motor Systems
    Peter Kramer
    Recent years have seen increasing attention to the subtle effects on intracellular transport caused when multiple molecular motors bind to a common cargo. We develop and examine a coarse-grained model which resolves the spatial configuration as well as the thermal fluctuations of the molecular motors and the cargo. This intermediate model can accept as inputs either common...
  • Bridging Scales in Molecular Motor Models: From Diffusing Heads to Multiple Steps
    John Fricks
    A stochastic model for variable-length stepping of kinesins engineered with extended neck linkers is developed. This requires consideration of the separation in microtubule binding sites between the heads of the motor at the beginning of a step. It can be shown that the separation is a stationary Markov process and can be included in the calculation of standard experimenta...
  • Cell-free synthetic biology in nanofabricated reaction devices
    David Karig
    The growing field of synthetic biology aims to forward engineer biology both for applications such as energy production, drug production, and bioremediation, as well as for the purpose of furthering the fundamental understanding of natural systems. However, engineering living cells is notoriously difficult due to issues such as mutation, epigenetic variation, fitness effec...
  • Population persistence in the face of demographic and environmental uncertainty
    Sebastian Schreiber
    Populations, whether they be viral particles, bio-chemicals, plants or animals, are subject to intrinsic and extrinsic sources of stochasticity. This stochasticity in conjunction with nonlinear interactions between individuals determines to what extinct populations are able to persist in the long-term. Understanding the precise nature of these interactive effects is a cent...
  • Large-scale behaviour of the spatial Lambda-Fleming-Viot process
    Amandine Veber
    The SLFV process is a population model in which individuals live in a continuous space. Each of them also carries some heritable type or allele. We shall describe the long-term behaviour of this measure-valued process and that of the corresponding genealogical process of a sample of individuals in two cases : one that mimics the evolution of nearest-neighbour voter model (...
  • Impacts of genetics, environment and noise on virus growth
    John Yin
    The dynamics of a virus infection within its host is governed at its earliest stages by processes at the molecular and cellular scale. We are developing cell-culture measurements and computational models to better understand how these and other processes contribute to the early dynamics of virus growth and infection spread. As a model system we study vesicular stomatitis v...
  • Effective population sizes and the canonical equation of adaptive dynamics
    Johan (=Hans) Metz
    Deterministic population dynamical models connect to reality through their interpretation as limits for systems size going to infinity of stochastic processes in which individuals are represented as discrete entities. In structured population models individuals may be born in different states (e.g. locations in space) after which they proceed through their h(eterogeneity)-...
  • Pathogen Extinction in Stochastic Models of Epidemics and Viral Dynamics
    Linda Allen
    In deterministic epidemic models, pathogen extinction in a population is determined by the magnitude of the basic reproduction number R0. In stochastic epidemic models, the probability of pathogen extinction depends on R0, the size of the population and the number of infectious individuals. For example, in the SIS Markov chain epidemic model, if the basic reproduction numb...
  • Kinetic equations in spatial quantitative genetics
    Judith Miller
    We derive kinetic differential or integrodifference equations for the mean and variance or of a quantitative trait as a function of space and time, in some cases recovering known equations and in some cases obtaining new ones that capture effects, such as nonmonotonicity of traveling waves, that can be seen in stochastic simulations. We then reanalyze kinetic equations due...
  • Simple, very simple, and not so simple models of populations lingering around a carrying capacity, and allowing evolutionary branching
    Peter Jagers
    In a toy model of binary splitting branching processes with population size dependence (supercritical below and subcritical above a threshhold, the carrying capacity) the chance of a little population establishing itself in the sense of reaching a band around the carrying capacity is determined, and so is the persistence time of the population. Mutations and competition be...
  • Computational methods for stochastically modeled biochemical reaction networks
    David Anderson
    I will focus on computational methods for stochastically modeled biochemical reaction networks. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. I will show how different computational methods can be...
  • Stochastic processes in the adiabatic limit: applications to biochemistry and population genetics
    Ilya Nemenman
    Stochastic biochemical systems and population genetics models are described by similar mathematical equations, and hence similar phenomena should be observed in both systems. Here we focus on stochastic kinetics with time scale separation. We show how to integrate out the fast degrees of freedom, while rigorously preserving their effects on the fluctuations of slower varia...

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