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20080516 Spontaneous separation of bi-stable biochemical systems
 

20080516 Spontaneous separation of bi-stable biochemical systems

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2008 Journal Club

2008 Journal Club

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  • lengthy abstract, disguises main point, that the supplementary material (which I will be going into) describes the next subvolume stochastic simulation method, this is implemented in MesoRD...
  • blood cells lines ODEs
  • David S. Goodsell
  • Rate matrix is sum of reactant rates (r) and diffusion rates (s), used to load the dice which is rolled to determine whether reaction or diffusion happens at this step.
  • Spontaneous domain separation requires that a localised part of the system jumps from an attractor in phase to an attractor out of phase with the surroundings. For this to happen, the size of the part of the system that jumps out of phase must be big enough so that it is not invaded by neighbouring molecules. At the same time, the size must be small enough so that the local escape from the original attractor does not take too long. It is only when there exists a local volume size for which invasion by diffusion takes a longer time than attractor escape, that spatial domains become sufficiently decoupled from their surroundings to allow for spontaneous domain separation. Accordingly, systems in tube-like or flat geometries display domain separation much more easily than do their spherical or cubic equivalents.
  • similar program from Luis Serrano’s laboratory, used Next Reaction Method (Gibson and Bruck) but switched to NSM because of overhead [quoth. MesoRD]

20080516 Spontaneous separation of bi-stable biochemical systems 20080516 Spontaneous separation of bi-stable biochemical systems Presentation Transcript

  • Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases Johan Elf and Måns Ehrenberg Presented by Jonathan Blakes Computational Foundations of Nanoscience Journal Club 2008-05-16
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  • Outline
    • Introduction: Bi-stable chemical systems
    • Well-mixed assumptions violated even in bacteria
    • The Next Subvolume Method
      • Implementation
      • Ideas for Multi-Compartmental Gillespie
    • Influence of Diffusion
    • Specifying Geometries
    • Influence of Geometry
    • Conclusions
  • Bi-stable chemical systems
    • Biochemical systems can be in different, self-perpetuating states depending on previous stimuli: loss of ‘potency’ when stem cells differentiate, switching on and off of genes in quorum sensing, etc.
    • Bi-stable chemical systems have two reasonably steady states and switch between these unpredictably due to the underlying stochasticity of the system.
    • Stochasticity arises from small numbers of a particular molecular species in the system and slow reactions .
    • Stochastic simulation algorithms based on Gillespie Direct Method allow us to sample trajectories of the Markov process corresponding to the Chemical Master Equation (CME).
  • Assumptions violated
    • “ Bistability can vanish due to spatial localised fluctuations for inorganic catalysts, and thus invalidate any macroscopic description of the kinetics.”
    • ‘ Macroscopic’ in this case could mean a bacterial cell.
    • Our model of quorum sensing in P. aeruginosa treats each bacteria as an single volume because they are defined by a single membrane and very small (rod shaped ~ 0.3-0.8 μ m wide 1.0-1.2 μ m long ≈ 0.311 μ m 3 ).
    • We use a version of the Gillespie algorithm to determine which reactions in our system will happen next.
    • Because Gillespie samples CME it assumes a homogenous (well-mixed) system, where diffusion of reactants in the system occurs on a much faster timescale than the reactions; i.e. no patches of higher or lower reactant concentrations (domain separation).
    • However, diffusion of molecules in vivo is much slower than in vitro , due to intracellular organisation like the actin cytoskeleton and genome (next slide)
    • Cells often have non-uniform shapes : macrophages, budding yeast; domain separation should be expected, and is in fact crucial for functioning.
  • Macrophage and Bacterium 2,000,000X 2002 Watercolor by David S. Goodsell
  • Next Subvolume Method (NSM)
    • Partition large volumes (cell) into many smaller volumes, where each subvolume small enough relative to rate of diffusion that it can be considered well-mixed.
    • As well a rate constant for each reaction,
    • each reactant has diffusion constant D , which
    • summarises the intracellular congestion.
    The authors tool MesoRD has been used to model the stochastic contribution to different mutant phenotypes in the Min-system in E. coli . Visualisation of a stochastic simulation of a wild type E. coli cell: MinD on the cell membrane and MinE in complex with MinD.
  • Implementation
    • Connectivity matrix defines
    • neighbours and therefore geometry
    • (boundaries is connection to self)
    • Configuration is a multiset
    • Q is order in event queue
    • Heap structure
    • Scales logarithmically
    • with number of
    • subvolumes
    • Could equally be used for storing next compartment in multi-compartmental Gillespie algorithm...
    Implementation
  • Multi-Compartmental Gillespie
  • Influence of Diffusion
    • A and B inhibit the production
    • of each other at identical rates
    • Slower diffusion (upper) leads to domain separation, while
    • faster diffusion (lower) does not, ascribed to faster transitioning between attractors, however this is not so at boundary (corners).
  • Specifying Geometries
    • Shape achieved in MesoRD using Constructive Solid Geometry (CSG)
    • Describe shape by extending
    • SBML:
  • Influence of Geometry
    • Domain separation in tube and plane, but not for cube, as mixing time shorter in cube.
    • Shape determines domains as much as diffusion rate.
  • Conclusions
    • Localisation of molecules within even small volumes can affect behaviour of system, dependent on diffusion rates of species and geometry.
    • Next Subvolume Method is a scalable algorithm for modelling these affects.
    • NSM could be used in our simulator as next level down of multiscale approach for 3D (cytoplasm) and 2D (membrane) volumes, not having this facility could mean our models cannot reproduce observed phenomena.
    • Constructive Solid Geometry of cytoplasm would define membrane shape.
    • Heap may be better way of finding next reaction in multiple compartments.
    • That’s it, thanks for listening.
  • References
    • Elf, J. and Ehrenberg, M. Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases Syst. Biol. 2004 1(2): 230-236
    • Hattne, J., Fange, D. and Elf, J. Stochastic reaction-diffusion simulation with MesoRD Bioinformatics 2005 21(12) 2923—2924
    • Fange, D. and Elf, J. Noise induced Min phenotypes in E. coli . PLoS Comp. Biol. 2006 2(6): 637-648
    • M. Ander et al. SmartCell, a framework to simulate cellular processes that combines stochastic approximation with diffusion and localisation: analysis of simple networks Syst. Biol. 2004 1: 129-138
    • Lemerle, C., Di Ventura, B. and Serrano, L. Space as the final frontier in stochastic simulations of biological systems FEBS Letters 2005 579: 1789-1794
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