## MesoRD

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

** Abstract** MesoRD (Mesoscopic Reaction Diffusion Simulator) is a tool for stochastic and deterministic simulation of chemical reactions and diffusion in 3D space.

In particular, it is an implementation of the Next Subvolume Method, which is an exact method to simulate the Markov process corresponding to the reaction-diffusion master equation (see below...).

Since version 0.2.0, MesoRD also supports mean-field simulations.

The description of the system that you want to simulate is written in the Systems Biology Markup Language (SBML) file format.

The SBML file contains all information about the species, reactions, reactions rates, compartment geometries, diffusion constants, etc.

In addition to the SBML file, MesoRD will require information about how the simulation should be executed, such as spatial discretization of the reaction volume, duration of the simulation, visualization and output options, and for deterministic simulations, the choice of integration method.

These parameters are given through the MesoRD user interface.

The output files from MesoRD are intended for external data analysis and visualization packages, for instance, the freely distributed MesoRD MATLAB toolbox available at the MesoRD website.

MesoRD MATLAB toolbox - The MesoRD Toolbox is a set of scripts for MATLAB that allows easy viewing of the simulation data generated by MesoRD.

In both the deterministic and the stochastic mode of simulation is the reaction volume which is discretized into a large number of small subvolumes and the state of the system is given by the number of molecules per subvolume.

In the stochastic simulation the number of molecules per subvolume is discrete.

Furthermore, the reaction and diffusion events that change the number of molecules are probabilistic, in the sense that the next event in the system is sampled from the distribution function.

In the deterministic simulation, the state is assumed to be continuous and the change in the number of molecules per time unit is given by the average change as defined by the stochastic model.

Reaction-diffusion master equation info and Introduction to MesoRD --

Chemical reactions are stochastic event(s), meaning that it is Not possible to know when and where the next reaction will occur.

The probabilities for the reaction events can however be modeled and the time evolution of the system can therefore be described probabilistically.

Stochastic reaction-diffusion kinetics is commonly modeled by the reaction-diffusion master equation (RDME).

Stochastic reactions-diffusion kinetics can be modeled in many other ways and at different levels of detail. The stochastic simulations performed by MesoRD do however represent the RDME level.

In the RDME the total system volume is divided into a number of virtual subvolumes that are small enough to be considered homogenized by diffusion on the time-scale of the chemical reaction.

The state of the system is defined by the copy number of each species in each subvolume. This state is changed by chemical reactions within the subvolumes or diffusion jumps of single molecules between neighboring subvolumes.

The rates of the chemical reactions depend on the local concentrations of the molecules within each subvolume.

The rates of diffusion events are modeled as first order reactions, defined in the subvolume where the jump originates. Given the state description and the rates for the different events, the RDME describes the time evolution of the probability of each possible state of the system.

Due to the exceptionally high dimension of the state space, neither analytical nor direct numerical solutions of the RDME are possible for interesting biochemical systems.

The natural escape route is the Monte Carlo simulation of individual realizations of the Markov processes described by the RDME.

However, the manufacturers were interested in chemical reactions in structured geometries in three dimensions, which may require millions of subvolumes to be correctly discretized.

Specialized simulation methods must be used to obtain reasonable execution times for these systems.

One such method is the Next Subvolume Method (NSM).

The algorithm behind NSM takes advantage of the special structure of the RDME, and generates trajectories that are equivalent to those from the Gillespie’s method.

Efficient and flexible implementation of the NSM is finicky, which is why the manufacturers created MesoRD.

Running MesoRD --

A simulation starts once the SBML file has been parsed, the neighbor relationships among the subvolumes have been defined and the initial number of molecules has been distributed.

While simulating, MesoRD divides the workload into three (3) threads:

1) The simulation thread, which samples the time to the next reaction or diffusion event from the state dependent probability density functions and updates the state of the system accordingly.

2) The optional visualization thread, which runs a three-dimensional OpenGL viewer of the simulation.

3) The status thread, which displays the progress to the user and handles requests to terminate simulation.

At user-specified intervals, the full state of the system is written to a file for statistical post-processing.

Geometry in MesoRD --

In MesoRD, the geometry of each compartment is described using constructive solid geometry (CSG).

This means that each compartment is defined by differences, intersections or unions of a number of geometric primitives (boxes, cones, cylinders and spheres).

Any primitive, or combination of primitives, can be rotated, scaled and translated. Periodic boundary conditions can be used for boxes and cylinders.

Expression evaluation --

Rate expressions are specified for each reaction in the SBML model definition.

MesoRD handles units explicitly and converts the rates into the number of events per time and subvolume.

MesoRD represents general mathematical expressions in Abstract Syntax Trees (ASTs). Recursive traversal of such trees can easily turn into a performance bottleneck.

MesoRD attempts to restructure ASTs into sums of products that can be evaluated iteratively. For instance, rate expressions derived from the law of mass action can be simplified in this way.

Furthermore, the outcome of any evaluation is cached, so that a subsequent computation of the same rate expression for the same configuration of reactant molecules need Not involve any evaluation at all.

The cache should yield an acceptable hit rate when the number of reactant molecule configurations is reasonably low.

In many cases this is expected to be true; if the number of subvolumes is larger than the number of molecules, and the number of molecules of each species within a subvolume is low.

Note: The use of MesoRD is Not limited to the realm of molecular biology. Its efficiency for systems with millions of subvolumes and molecules makes it generally useful in physical chemistry.

MesoRD can also be used for testing approximations of the RDME based on renormalization group approaches and for comparison of RDME descriptions with simulations based on discretization in time instead of space.

*System Requirements*

Contact manufacturer.

*Manufacturer*

- Department of Cell and Molecular Biology
- Biomedical Center
- Uppsala University
- 75124 Uppsala, Sweden

** Manufacturer Web Site**
MesoRD

** Price** Contact manufacturer.

** G6G Abstract Number** 20625

** G6G Manufacturer Number** 104225