## StochSim

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

** Abstract** StochSim is a stochastic simulator for biological processes
[(bio)chemical reactions]. The particles are represented as individual
software objects which react according to probabilities derived from
concentrations and rate constants.

In version 1.4 of StochSim simple two-dimensional spatial structures have been implemented, in which nearest-neighbor interactions of molecules can be simulated.

It was developed as part of a study of bacterial chemotaxis as a more realistic way to represent the stochastic features of this 'signaling pathway' and also as a means to handle the large numbers of individual reactions encountered.

The program now provides a general purpose 'biochemical simulator' in which individual molecules or molecular complexes are represented as individual software objects (as stated above). Reactions between molecules occur stochastically, according to probabilities derived from known rate constants.

An important feature of the program is its ability to represent multiple post-translational modifications (PTMs) and conformational states of protein molecules.

StochSim consists of a platform-independent core 'simulation engine' encapsulating the algorithm described below and a separate graphical user interface.

Description of the algorithm --

Each molecule is represented as a separate software object in StochSim, and the simulation also includes dummy molecules, or "pseudo-molecules", used in the simulation of unimolecular reactions.

Time is quantized into a series of discrete, independent time-slices, the size of which is determined by the most rapid reaction in the system. At the start of the simulation, the user assigns the maximum number of molecules, N, the system will use.

In each time-slice, one molecule (Not a pseudo-molecule) is selected at random from N possibilities (the probability of selection of each molecule is 1/N). Then, another object, either a molecule or a pseudo- molecule, is selected at random from N possibilities.

If two molecules are selected, any reaction that occurs will be bimolecular, whereas if one molecule and a pseudo-molecule are selected, it will be unimolecular. Another random number is then generated and used to see if a reaction occurs.

The probability of a reaction is retrieved from a look-up table and if the probability exceeds the random number, the particles do Not react. On the other hand, if the probability is less than the random number, the particles react, and the system is updated accordingly.

The next time-slice then begins with another pair of molecules being selected.

Spatial representation --

The original version of StochSim (1.0) treated the entire reaction system as a uniformly mixed solution. Although this is clearly Not how molecules are arranged within living cells, the omission of spatial heterogeneity has been the norm in biochemical simulations because it greatly facilitates modeling and reduces the computational load of simulation.

However, as the resolution of our understanding of biochemical processes increases, it is becoming clear that even in bacteria, the simplest of cells, the spatial organization of molecules often plays an important role.

The manufacturer has therefore extended StochSim to incorporate explicit spatial representation.

In versions of StochSim later than 1.2, a simple two-dimensional spatial structure is implemented, in which nearest-neighbor interactions of molecules (such as clustered receptors on a membrane) can be simulated.

The original implementation of this spatial structure only allowed geometries composed of square units with four nearest neighbors, but as of version 1.4, two (2) additional geometries, one composed of triangles and the other of hexagons, are supported.

These three are the only three regular tessellations which can cover a two-dimensional surface. The new geometries can be used, for example, to reflect the recent prediction of the structural arrangement of the chemotaxis receptor complex (Shimizu et al., 2000).

The primary purpose of this spatial structure implementation so far has been to study various properties of complex arrays of fixed size and geometry. The binding of other complexes in the reaction system to complexes within the complex array is permitted, but does Not alter the geometry of the array.

Each node of the complex array has exactly one complex, and three to six nearest-neighbor nodes.

The geometry of the array can therefore be triangular, rectangular or hexagonal, and real or toroidal boundaries can be used.

StochSim accuracy --

The simulation proceeds in a series of small time steps, dt, and as with any method of numerical integration, this introduces inaccuracies. Small errors can arise in StochSim because the program can simulate at most one reaction event in each interval, dt, whereas in reality molecular events occur at random times.

However, the errors are as often positive and negative and therefore Not cumulative. Moreover, they can be made as small as required by reducing the size of the time steps.

*System Requirements*

Contact manufacturer.

*Manufacturer*

- Department of Physiology, Development and Neuroscience
- University of Cambridge
- Anatomy School
- Downing Street
- Cambridge CB2 3DY
- UK
- Tel: +44 1223 333750
- Fax: +44 1223 333840

** Manufacturer Web Site**
StochSim

** Price** Contact manufacturer.

** G6G Abstract Number** 20468

** G6G Manufacturer Number** 104065