SABRE

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

Abstract SABRE is a tool for Stochastic Analysis of Biochemical REaction networks.

SABRE implements Fast Adaptive Uniformization (FAU), a direct numerical approximation algorithm for computing transient solutions of biochemical reaction networks.

Biochemical reactions networks represent biological systems studied at a molecular level and these reactions can be modeled as transitions of a Markov chain.

SABRE accepts as input the formalism of guarded commands, which it interprets either as continuous-time or as discrete-time Markov chains.

Besides operating in a stochastic mode, SABRE may also perform a deterministic analysis by directly computing a mean-field approximation of the system under study.

SABRE is a tool for the transient analysis of Markov population models. In other words, SABRE analyzes discrete time, or continuous-time Markov processes that have a structured discrete state space and state-depended rate functions.

SABRE offers both stochastic and deterministic analysis of population models. For stochastic analysis, SABRE implements three (3) algorithms: standard uniformization, fast adaptive uniformization and Runge-Kutta fourth order method.

Fast Adaptive Uniformization method --

The focus of the tool is on the fast adaptive uniformization method, while the remaining methods are given for completeness and comparison.

Fast adaptive uniformization is a variant of the uniformization method which is, an efficient method to compute probability distributions if the number of states of the Markov process is manageable. However, the size of a Markov process that represents a biochemical reaction network is usually far beyond what is feasible.

Fast adaptive uniformization improves the original uniformization method at the cost of a small approximation error.

The main ideas for this improvement are the on-the-fly construction of the state space and the restriction imposed on the state space to contain only states with significant probabilities, e.g. states that have a probability larger than 10 to the -15.

Even though fast adaptive uniformization can treat larger models than the previous uniformization methods could, as expected, models with remarkably high expected populations remain unsolvable and should be studied using deterministic analysis of simulation tools.

A second down side of fast adaptive uniformization is that, due to the approximation error, it can overlook rare events of the model, e.g. events that occur with a very small probability.

Stochastic and Deterministic analysis --

SABRE performs a transient analysis of the input system, that is, SABRE computes the state of the system at time t given the state of the system at time 0.

SABRE may execute either a stochastic analysis or a deterministic analysis of the input system; and in the first case the state of the system at time t is actually given as a probability distribution over the discrete states of the system.

The second type of analysis --the deterministic analysis-- is done over a continuous state space, and its result is a single state of this continuous space.

The result of the deterministic analysis, also known as ‘mean field analysis’, is an approximation of the expectation of the stochastic analysis.

SABRE Tool Interface --

From the tool’s interface, the user has several ways of selecting a model for analysis. One can load an existing model, upload a System Biology Markup Language (SBML) file or introduce a GCM text description of the system to analyze.

Guarded-command models (GCM) are the input formalism of SABRE. GCMs are a textual description of processes and are given in the style of Dijkstra’s guarded-command language.

SBML is a standardized format for representing models of biological processes, such as metabolism or cell signaling and is the input to SABRE’s core program.

GCMs that have update functions with constant increment (or decrement) have a straight forward translation to SBML.

Once the model is chosen, the user chooses a configuration of the analysis by choosing the semantics, the mode and, if needed, the type of stochastic solution. Finally, one chooses a time horizon, or the number of steps for which one wants the system to run.

The program computes the intermediates and the final results which are then dynamically plotted for each species, as the computation runs.

If the uniformization method is selected, the user also needs to provide an estimate of the maximal exit rate over all reachable states. If the estimate is too small, the computation needs to be restarted, and if the estimate is too large, the computation is likely to take longer.

It is standard uniformization which is especially touched, by choosing too large an upper bound on the maximal exit rate. Estimating this upper bound by heuristics such as those used for the ‘sliding window’ algorithm is an on going work.

SABRE Software Architecture --

SABRE is available on line (web-based). The core of the manufacturer's tool is implemented in C++, while the website that hosts it is implemented using PHP and JavaScript.

The user provides the desired input through the web interface, than a query is generated to the Linux machine on which SABRE is installed. The server sends back to the user intermediate results which are then plotted.

Note: An offline SABRE version release is planned for the future. For completeness and comparison, SABRE also performs deterministic analysis of the input (model) system.

System Requirements

Web-based.

Manufacturer

Manufacturer Web Site SABRE

Price Contact manufacturer.

G6G Abstract Number 20611

G6G Manufacturer Number 104211