Category Cross-Omics>Pathway Analysis/Gene Regulatory/Networks/Tools and Cross-Omics>Agent-Based Modeling/Simulation/Tools

Abstract GridCell is a stochastic particle-based biological system simulator.

It was developed as a three-dimensional simulation environment for investigating the behavior of biochemical networks under a variety of spatial influences including crowding, recruitment, and localization.

GridCell enables the tracking and characterization of individual particles, leading to insights on the behavior of low ‘copy number’ molecules participating in signaling networks.

The simulation space is divided into a discrete 3D grid that provides ideal support for particle collisions without distance calculation and particle search.

Systems Biology Markup Language (SBML) support enables existing networks to be simulated and visualized. The user interface provides intuitive navigation that facilitates insights into species behavior across spatial and temporal dimensions.

GridCell Background --

The manufacturer's developed GridCell to simulate biological models with specific consideration for stochasticity, locality, and collision. GridCell is based on a simplified model for molecular movement and interaction.

It uses a discrete three-dimensional cubic grid based on the D3Q27 model often used in the application of the Lattice-Boltzmann Method (LBM).

Each voxel has access to itself and its 26 neighbors and is independent of voxels outside this immediate surrounding. The integer-addressed 3D grid avoids floating-point computation and distance calculations, resulting in an efficient implementation.

Molecules are represented as particles that move and react stochastically within discrete volumes in discrete time-steps. Collisions and molecular crowding are enforced since only one particle can occupy a given location at any time.

GridCell stores the coordinates of all the particles on the 3D grid at every turn, thereby enabling particle tracking in both space and time.

GridCell Implementation --

Algorithm - The simulation employs a two-phase process in which particles 1) attempt to move and then 2) attempt to react to every turn.

Movement Phase - A particle can move at most, once per time-step. Since a particle only has access to its immediate surrounding, a particle can only move in one of 27 nearest locations, including the current location.

The selection of the movement direction is made randomly; therefore the particles follow a Brownian random walk.

In GridCell, any particle attempting to move to an occupied location will generate a collision. A collision prevents the particle attempting to move from moving during that turn and does Not affect the other particle.

Reaction Phase - A particle may react only once per turn and only with its immediate surrounding. The reaction phase is completely independent from the movement phase, therefore it does Not matter if a particle previously moved or collided with another particle.

Common interactions include aggregation events such as molecular complex formation/dissolution or conversion events such as chemical reactions.

Only the simplest reactions involving 3 or less particles are directly supported. Complex reactions involving more than 3 particles are decomposed into several elementary reactions.

The probability of reaction per time-step is derived from the overall rate of reaction and is very similar to the approach taken by ChemCell (see G6G Abstract Number 20621).

GridCell User Interface Features --

GridCell's user interface consists of:

1) A menu system;

2) An interactive 3D simulation space;

3) A species panel;

4) A 2D plot of concentration versus time: and

5) A 2D plot of concentration versus space.

The menu system provides the ability to load SBML models, set parameters, and control the simulation.

User-designated simulation parameters include the number of times to run the simulation, the time-step, the total simulation time, the sampling rate which is the frequency that the 2D graphs are updated and the results saved to file, and the frame rate which designates the frequency of updating the 3D visualization.

GridCell computes the means and the standard deviations of the concentration over time if the user chooses to run multiple iterations of the simulation. These preferences may be saved and used later in any simulation.

GridCell saves the particle concentrations and the 2D surface plot data in user-specified tab-delimited files. Spatial information such as specific compartment geometries or co-localization of particles is specified in an optional configuration file.

A key feature of the GridCell user interface is the ability to interact with the three-dimensional simulation volume. Users can navigate in the 3D scene with mouse and keyboard controls to rotate, pan and zoom.

Buttons are present to:

The species panel contains the current amount of each species, and allows species selection for the visualization plots.

A second column specifies which species to render in the 2D surface plot of concentration versus space. Particle colors are automatically selected from a predefined color palette.

Finally, two plots to summarize particle concentrations with respect to time and space are provided in real-time. The 2D spatial plot displays increasing concentration with increasing brightness along a selected Cartesian axis.

Michaelis-Menten reaction -- The Michaelis-Menten equations are used to describe most enzymatic reactions.

Crowding --

According to the manufacturer's, one of the main differences between GridCell and other simulators is its ability to simulate particle crowding.

Molecular crowding occurs when particle density affects movement and reactivity. Crowding is typically ignored in most models since kinetics are often based on controlled, in vitro conditions that are Not crowded.

In addition, simulators do Not typically support this feature since it is computationally expensive to keep track of all particle positions and their excluded volume, and to implement collision-detection algorithms.

Some simulators (e.g. Smoldyn - see G6G Abstract Number 20619) have shown crowding effects by explicitly introducing ‘cubic obstacles’ in the model.

In contrast, GridCell implicitly exhibits molecular crowding effects by allowing inter-particle collisions.

The manufacturers demonstrate the effect of crowding by adding inert particles to a Michaelis-Menten system. Inert particles do Not react with other molecules but reduce their movement and affect the overall number of reactions.

System Requirements

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Manufacturer Web Site GridCell

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G6G Abstract Number 20623

G6G Manufacturer Number 104223