Approximation of Event Probabilities in Noisy Cellular Processes

Abstract

Abstract. Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.

Fast Adaptive Uniformization of the Chemical Master Equation

“…a given accuracy may yield a smaller right truncation point compared to the truncation in Eq. (6). Hence, fewer matrix-vector multiplications have to be carried out.…”

“…Therefore, statistical estimation procedures such as Monte Carlo simulation are widely used to circumvent the problem of state space explosion. Recent work, however, indicates that numerical approximation methods for the CME can be used to compute the transient state probabilities more accurately and, in particular, with shorter running times [6]. Especially if the probabilities of interest are small, numerical approximations turn out to be superior to Monte Carlo simulation.…”

Symmetry-Based Model Reduction for Approximate Stochastic Analysis

“…Various methods for approximate stochastic analysis have been suggested: Monte Carlo sampling of probability density functions of species' counts over time, known as Gillespie's algorithm [11]; approximations of this sampling [4,19]; explicit treatment of fluctuations with stochastic differential equations [12]; consideration of subspace of system states with highest probability mass [6,24]; aggregation of states [17]. Moment closure (MC) is a promising method for approximate analysis of the behavior of stochastic systems.…”

A hybrid factored frontier algorithm for dynamic Bayesian network models of biopathways

“…As might be expected, the exact inferencing problem for large CTMCs is computationally infeasible. Analysis methods based on Monte Carlo simulations [8,9,12,14] as well as numerically solving the Chemical Master Equation describing a CTMC [7,13] are being developed. In these studies the CTMCs are presented implicitly while our DBNs are available explicitly.…”