BiomodelReaction Networks Electrophysiology

Rule-based Modeling

Mesoscopic Processes

Cell Motility

Model Analysis

MovingBoundary

Solver

Langevin Solver

NFSim

Sloppy Cell,COPASI

Biophysics to Software TR&D 3

BiomodelReaction Networks Electrophysiology

Rule-based Modeling

Mesoscopic Processes

Cell Motility

Model Analysis

MovingBoundary

Solver

Langevin Solver

NFSim

Sloppy Cell,COPASI

Aim1 : Modeling Framework for Cell Motility

(DBPs: Pollard, Mogilner, Haugh)

Simulation of actin polymerization around a tubule of cell membrane with two rings of nucleation-promoting factors. XZ cross-section of 3D geometry; extracellular space is white. Density of F-actin (pseudo-color) and its velocities (arrows) correspond to 20 seconds into patch formation.

Simulation of a migrating cell (zero-stress model)Myosin concentration (pseudo-color) and the actin velocities (arrows) corresponding to steady migration of a polarized cell.

Pollard DBPendocytosis

Mogilner DBPcell migration of fish keratocytes

Approach• Cell Motility is driven by microscopic cellular mechanochemical processes

• Models of macroscopically observable cell motion and mechanics require selection of a consistent description of bulk properties, constitutive equations and boundary conditions which incorporate the microscopic processes and result in a solvable system of equations.

• At the level of VCell applications, we will couple the mechanics to the cellular geometry and support a choice of consistent course grained (macroscopic) approximations resulting in systems of equations which can be simulated within VCell. We will take advantage of simplified, limiting approximations where we can leverage existing solvers in cases where boundaries don’t move (fixed shape with a moving frame of reference) or nonspatial approximations can be used (e.g. for cell volume control).

• As always, the modeler is free to use our solvers by directly specifying their constitutive equations within our mathematical description language.

Aim 1: New Modeling Concepts

• Physiology: – polymers as abstract dynamic one-dimensional structures.– force sensitive binding– force generation from polymerization and motors directed

along polymers

• Application: – Choices of continuum mechanics approximations– mapping physiology cellular structures to material

properties (e.g. viscoelastic description)– mapping cellular processes into internal forces.

Aim 1: Optimal use of solvers

• Most cases will require our new moving boundary solver (TR&D 2).

• Existing fixed boundary solvers when possible – truly stationary cells– motile cells without shape change,– small regions far from membranes using boundary conditions– small regions very close to ‘planar’ membrane using membrane

as frame of reference.• Lumped parameter descriptions of cell mechanics for ODE

or DAE solvers.• Interoperability with COMSOL Multiphysics.

BiomodelReaction Networks Electrophysiology

Rule-based Modeling

Mesoscopic Processes

Cell Motility

Model Analysis

MovingBoundary

Solver

Langevin Solver

NFSim

Sloppy Cell,COPASI

Aim 2: Modeling framework for rule-based models(DBPs: Rosen, Mayer, Tyson, Ruan, Posner, Gladfelter)

Simulation of models with combinatorial complexity

Precise description of biological information

Receptor reversibly binds ligand with the same affinity, provided receptor is in a monomeric form

and not bound to another ligand. The state of intracellular sites of a receptor, as well as whether

receptor is bound to something inside membrane, is irelevant for ligand-receptor binding.

Problems

• Need rule-based support for spatial modeling (Rosen, Mayer)

• Too different from Virtual Cell modeling approach & steep learning curve:– Too technical to define– Too many details may be required to specify rule-based model

• Generated clusters are difficult to analyze (Rosen, Ruan) • New types of data (site specific) are required (Ruan,

Bader)

Enhance rule-based modeling capabilities

• Compartmental modeling (deterministic and stochastic rule-based applications)

• Spatial rule-based simulations (PDE and Smoldyn)– Boundary conditions, diffusion coefficients, advection by

species patterns.

• Statistics and visualization of large complexes

Define rule-based models while avoiding technical details of rules and patterns.

• Specify biological processes that define sites, rules and interactions:

– Phosphorylation => site with two states => unimolecular rule => observable

– Binding => site that bind itself => biomolecular rule => observable

• This extra informational layer will be used for searching and reusability.

Provide useful integration with pathway databases: link sites, molecules, rules, species and observables to database entities.

BiomodelReaction Networks Electrophysiology

Rule-based Modeling

Mesoscopic Processes

Cell Motility

Model Analysis

MovingBoundary

Solver

Langevin Solver

NFSim

Sloppy Cell,COPASI

Aim 3: Modeling framework for mesoscopic processes(DBPs: Rosen, Mayer, Tyson, Ruan, Dodge-Kafka, Gladfelter)

Spatial rule-based molecular modeling

- Defined using rules operating on the set of sites- Provides complete spatial and orientational information.- Excluded volume accounts for protein sizes and steric hindrance.- Captures exact dynamics, including reduced diffusion of larger

clusters.

4.2 nm2.4 nm

Functional Domains (BioNetGen)

Molecular Geometry (Langevin)

Problems

• Computationally expensive (not as MD, but more than network-free)

• Model specification is separated from rule-based framework

• Simulation results are a new type of data not used by VCell.

• Need molecular geometry information.

Optimize simulator and provide rule-based capable interface

• Introduce Langevin application as an extension of rule-

based model with molecular geometry details with user-

interface compatible with the VCell rule-based

framework.

• Integrate Langevin Dynamic Simulator as a simulation

option by implementing efficient C++ code for parallel

simulations on VCell server clusters.

• Enable model visualization to be used for molecules with

and without molecular geometry.

Develop a scalable Infrastructure for statistical analysis of multiple-run spatial stochastic simulations.

• Multiple VCell simulators (Smoldyn, Smoldyn/PDE hybrid, Gibson, and Langevin solvers) generate spatial distribution.

• Analysis of spatial properties (molecular composition, clustering, density, phase transitions, etc).

Provide integration with pathway and protein structures databases.

BiomodelReaction Networks Electrophysiology

Rule-based Modeling

Mesoscopic Processes

Cell Motility

Model Analysis

MovingBoundary

Solver

Langevin Solver

NFSim

Sloppy Cell,COPASI

Aim 4: Model Analysis Tools (DBP: Hansen, Bader, Fournier)

Aim 4: Model Analysis Tools (DBPs: Gary Bader, Kevin Claffey, Marcia Fournier, Marc Hansen, Bruce Mayer, Richard Posner)

• Aim 4.1. – Model structure– Problem: uncertainty and/or phenotypic variation in large(r) models regarding

connectivity/topology (interactions, species)– Problem: target selection(s) in large(r) models for specific qualitative changes (targeted

interventions for altering phenotype)– Solution: framework for simulating “model ensembles”

• Aim 4.2. – Model parameters– Problem: uncertainty in large(r) models regarding quantitative parameters (rates,

concentrations)– Problem: insufficient constraint(s) in large(r) models provided by experimental data– Solution: framework for “sloppy models”

• Aim 4.3. (maybe not…) – Model consistency– Extended mass conservation analysis, thermodynamic constraints, etc.

• Related developments (Core1)– Steady-state solving of ODE systems– Cytoscape connection (via BioPAX)– SloppyCell connection (via SBML)– Visualization of 6D data

Model Ensembles

Sloppy Models