NRCAM Virtual Cell

Category Cross-Omics>Agent-Based Modeling/Simulation/Tools

Abstract The Virtual Cell is a software modeling environment for quantitative cell biological research. Users can create simple or complex multi-layered models with a Java web-based interface.

Distinct biological and mathematical frameworks exist within a single graphical interface designed for experimental 'cell biologists' or theoretical biophysicists.

The biologically oriented user interface allows experimentalists to create models, define cellular geometry, specify simulations and analyze the simulation results. The results are run and stored on a remote server and can be reviewed in the software and/or exported in a variety of popular formats.

The design of the biological to mathematical mapping allows for separate use of biological and math components, and includes automatic mathematical simplification using pseudo-steady approximations and mass conservation relationships. This allows for direct specification of mathematical problems, performing simulations and analysis on those systems.

The stand alone mathematics user interface is also an advanced tool for modeling reaction-diffusion systems.

A transparent general purpose solver is used to translate the initial biological description into a set of concise mathematical problems.

The solver is transparent to the average user, but is accessible to the theorist as the 'Math Editor' component.

The Virtual Cell software is composed of three (3) main components:

1) Modeling Framework - The modeling framework represents the physiological models of the Virtual Cell and allows for persistence and database support (See below...).

2) Mathematics Framework - The mathematics framework transparently solves an important class of mathematical problems encountered in cellular modeling (See below...).

3) WWW Interface-Biological Oriented Interface with Integrated Math Editor - The WWW accessible graphical user interface provides access to the technology mentioned above. The user interface has been developed using Java 2 Applets (See below...).

Modeling Process -- It begins with the physiological model being defined in terms of species, structures, reactions, fluxes, and currents. The model is associated with the application component, which allows you to isolate simulation specific assumptions from the rest of the model.

This involves mapping the structures to sub-domains, which are the image regions defined in either, the analytical or experimental geometry, and defining initial conditions, boundary conditions, fast reactions, diffusion protocols and electrical mapping.

Once the application is created, a detailed math description of the model and application is automatically and transparently generated by the software. One can then run a simulation which will include additional model details such as model parameters, mesh size and solver options.

The simulation results can provide information regarding time response, sensitivities and steady state. Such results can be used for analysis, further modeling and for redefining the experimental protocol.

External resources such as pathway databases and information from existing literature are being introduced into the Virtual Cell software. Currently reactions from the KEGG Reaction Database can be entered into the Virtual Cell.

1) Modeling Framework --

Purpose - The goal of the modeling framework is to provide the biological abstractions necessary to represent models of cellular physiology. This framework, in turn, uses the services of the Mathematics Framework for the simulation of its models.

System Level Interface -

Modeling Language - A declarative modeling language has been developed to concisely describe a class of physiological models that has been encountered in the Virtual Cell project. This language defines molecular species, cellular structures, biochemical reactions, and cellular geometry.

Testability - A substantial advantage of separating the 'math framework' from the modeling framework is the improved ability to verify the correctness of the two frameworks from high level system interfaces. The Modeling Framework can be tested by specifying simple physiological models, requesting a specific simulation, and observing the resulting mathematical description generated.

Framework Design - The current implementation of the cell model description involves the manipulation of abstract modeling objects that reside in the Modeling Framework as Java objects.

These modeling objects can be edited, viewed, stored in a remote database, and analyzed using the WWW-based user interface section. These objects are categorized as Models, Geometry, and Application objects. This adopts the naming convention used in the current Modeling Framework software.

2) Math Framework --

Purpose - The goal of the math framework is to provide a general purpose solver for the mathematical problems in the application domain of computational cellular physiology. These problems include the steady, unsteady solutions of non-linear PDE/ODE/Algebraic systems, including sensitivity analysis and parameter optimization.

This framework exposes a very high level system interface that allows a mathematical problem to be posed in a concise and implementation independent way, and for the solution to be made available in an appropriate format. This framework represents an application specific implementation of a Problem Solving Environment (PSE).

System Level Interface -

Math Language - A declarative mathematics language has been developed to concisely describe the class of mathematical systems that has been encountered in the Virtual Cell project.

This language defines parameters, independent variables, differential/algebraic systems defined over complex geometry including discontinuous solutions, membrane boundaries, and the description of the task to perform on such a system.

Testability - A substantial advantage of separating the mathematics framework from the biological modeling software is the improved ability to verify the correctness of the frameworks mathematical capabilities from a high level system interface.

Framework Design -

PDE Solver Library - The PDE Solver Library is a rigorously validated and highly extensible C++ class library that computes numerical solutions to the ordinary and partial differential equations (ODE/PDE) and algebraic equations associated with physiological modeling.

The modular design of this library allows the coordination of an almost arbitrary collection of variables, equations, solvers, parallel processing schemes, and meshing techniques.

Note: The Mathematics Framework automatically generates the appropriate C++ code to define a particular model, and links this with the library for a fully compiled simulation code.

Interpreted ODE Solver - The ODE solver is a well tested Java package that computes the solution of a system of ODE's. This solver can be executed within the client software (web browser) or on the server.

Local Sensitivity Analysis - The Local Sensitivity Analysis is computed at the nominal trajectory of the ODE system and uses exact Jacobian's and Rate Sensitivities (symbolic).

It computes a direct solution of all sensitivities of a single parameter and displays normalized (log) sensitivities as function of time. The state trajectory is extrapolated for small parameter changes.

Testing - The mathematics framework is charged with the responsibility of generating efficient and accurate solutions to the problems posed.

Mathematical Simplifications -

Stoichiometry Analysis - Conserved moieties from the stoichiometry are identified and a reduced order system is automatically determined. This results in a minimum number of differential equations.

Pseudo-Steady Approximations - Very fast reactions are considered to always be in equilibrium and they are incorporated as a nonlinear system of algebraic equations and linear constraints. This results in faster computation time, when the ratio of time scales is greater than 100.

Region Approximation - Very fast diffusion (or conduction) is considered in order to eliminate gradients and it is incorporated as a single variable per region (ODE with spatial integral in RHS). This takes place as a Laplacian Equation (elliptic PDE) for non-neuronal cells.

3) User Interface -- Virtual Cell Biologically Oriented Interface -

Purpose - The Virtual Cell, designed to be accessible to the experimental biologist, is a fully modular computational framework that provides a general approach to modeling the spatially organized and interdependent chemical events that underlie dynamic cellular processes.

A Java biological interface allows experimentalists to input specific geometry, in the form of experimental images, specify compartment topology, define and assign species, chemical reactions and transport kinetics, and computational mesh.

The user interface for the Virtual Cell allows full interaction from the WWW. This interface facilitates the creation and analysis of abstract models, generation of specific simulations, control and monitoring of simulations, and data analysis. This interface aims to present the physiology of chemical and structural phenomena and mechanisms in a natural and consistent manner.

Current Implementation - The current Virtual Cell application utilizes a newly designed system-level architecture based on the unified modeling language (UML). The system is decomposed into an application framework and system services. The application framework is the Modeling Framework. (See above…)

The system services are the Database Service, the Simulation Control Service (which encapsulates the Simulation Library), and the Simulation Data Service. The architecture is designed such that the location of the user interface and the corresponding back end services are transparent to the majority of the application.

The typical configuration is a Java applet running in a WWW browser, with the Database, Simulation Control, and Simulation Data services executing on a remote machine (WWW server). Alternatively, the software may be executed as a standalone application on a local machine with the requirement that the Java Runtime Environment and a C++ compiler are installed.

System Requirements

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G6G Abstract Number 20440

G6G Manufacturer Number 104069