Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate-using decision-making by a large population of quorum sensing bacteria-that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.

Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.

MOTIVATION: Understanding the encoding and propagation of information by biochemical reaction networks and the relationship of such information processing properties to modular network structure is of fundamental importance in the study of cell signalling and regulation. However, a rigorous, automated approach for general biochemical networks has not been available, and high-throughput analysis has therefore been out of reach. RESULTS: Modularization Identification by Dynamic Independence Algorithms (MIDIA) is a user-friendly, extensible R package that performs automated analysis of how information is processed by biochemical networks. An important component is the algorithm's ability to identify exact network decompositions based on both the mass action kinetics and informational properties of the network. These modularizations are visualized using a tree structure from which important dynamic conditional independence properties can be directly read. Only partial stoichiometric information needs to be used as input to MIDIA, and neither simulations nor knowledge of rate parameters are required. When applied to a signalling network, for example, the method identifies the routes and species involved in the sequential propagation of information between its multiple inputs and outputs. These routes correspond to the relevant paths in the tree structure and may be further visualized using the Input-Output Path Matrix tool. MIDIA remains computationally feasible for the largest network reconstructions currently available and is straightforward to use with models written in Systems Biology Markup Language (SBML). AVAILABILITY: The package is distributed under the GNU General Public License and is available, together with a link to browsable Supplementary Material, at http://code.google.com/p/midia. Further information is at www.maths.bris.ac.uk/~macgb/Software.html.