1. Information Theoretic Projection of Cytoskeleton Dynamics onto Surrogate Cellular Motility Models Sorin Mitran 1 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA Information Theoretic Projection of Cytoskeleton Dynamics onto Surrogate Cellular Motility Models Sorin Mitran 1 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA Surrogate models RESULTS & DISCUSSION CONCLUSIONS INTRODUCTION – Biological Background Cytoskeleton dynamics determined by interaction of: Cell nucleus: rigid Microtubules: stiff, 5 mm persist.L, 25 nm diameter, 8 nm step Actin filaments: flexible, 0.2 mm persist.L, 7 nm diameter, 37 nm step Cytosol: Newtonian fluid Cellular adhesion complexes Objective is to describe: Porous diffusion of biochemical network factors (Arp2/3, Cap, …) Range of time scales: symmetry breakdown G-actin polymerization filament-bead attachment/detachment Range of space scales: G-actin monomer size bead size ‘comet’ tail Stochastic ODE model MODELING – Multiscale approach Research goal: Extract from detailed mechanical descriptions of individual components a reduced cytoskeleton model that captures essential features of cellular motility Motility phases: a)Protrusion b)Attachment c)Contraction d)Detachment First stage: Listeria monocytogenes Bacterium that disrupts normal cytoskeletal actin polymerization Allows focus on actin dynamics Activated bead Listeria monocytogenes model: bead with actin polymerization activator (WASP-VCA) Placed in actin solution Observed behavior: Quasi-spherical actin mesh forms around bead Symmetry breakdown after 3-25 min Bead motion observed upon symmetry breakdown Observed behavior is non-trivial, with distinct regimes for steady/oscillatory bead motion (Bernheim-Groswasser et al. Biophys.J. 2005), Levy flight behavior (one of the simplest natural systems to exhibit such behavior) Model: Includes F-actin attach/detach to bead, F-actin depolymerization G-actin polymerization Cap, Arp2/3, Mg advection-diffusion Reproduces symmetry breakdown, Levy flight behavior Model provides extensive, detailed information How to extract meaning from the simulation informationç Construct reduced-order model: Includes F-actin attach/detach to bead, F-actin depolymerization G-actin polymerization Cap, Arp2/3, Mg advection-diffusion Reproduces symmetry breakdown, Levy flight behavior Model provides extensive, detailed information How to extract meaning from the simulation information? Information geometry Basic idea: Introduce statistical model Random vector characterizes system state Concentrations of Cap, Arp2/3, Mg, G-actin F-actin lengths, attachment density Consider parametric PDF Information geometry approach: Consider geometric structure induced by parametrization Small-dimensional models obtained by projection Projection carried out by transport along geodesics Some parametric expansions lead to Euclidean geometry (e.g., Karhunen-Loeve) Other parametric expansions lead to non-Euclidean geometry (e.g. exponential families), and non-trivial geodesics Differential geometry Manifold of PDFs Metric Geodesic equation Information theory PDF encapsulates known information about system: Information Relative information Infinitesimal relative entropy (Fisher metric) Gaussian PDF models Gaussian PDF manifold Metric Hyperbolic geometry in plane Geodesics: vertical lines and semiellipses Weibull, Levy PDFs Weibull distribution, suitable for rupture, parameter corresponds to failure decrease, constancy, increase over time Levy distribution, exhibits long tails to capture super-diffusive behavior ç Approach: Take data from multiscale stochastic model Fit Weibull model to capture symmetry breaking Fit Levy model to capture ‘flight-forage’ behavior Weibull model Collapse stochastic simulation data onto Weibull model to predict actin mesh rupture Levy model Collapse stochastic simulation bead motion data onto Levy model Detailed, stochastic mathematical models of biological motility can reproduce observed behavior Data from detailed models can be compactly represented through reduced-order statistical models (“surrogate models”) Information geometry provides a rigorous technique to obtain reduced- order models Projection by geodesic transport more efficiently captures nonlinear features of the model