The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation—by orders of magnitude for some observables.
Intracellular populations of genes, RNA and proteins are often described by continuous-time, discrete-state Markov processes. As such, the time-varying probability distributions of these systems evolve according to the large or infinite dimensional linear ordinary differential equation known as the chemical master equation (CME). Unfortunately, the large dimension of the CME means that numerical integration and stochastic simulation are often impossible or time consuming. To enable useful integration of computational and experimental studies, new approximations are needed to improve this efficiency. In this paper, we introduce new methods to project the full CME onto a lower dimensional space, while retaining the transient and equilibrium statistics of the original process. First, we investigate three complementary sets of simple coarsegraining rules: (i) We use the previously described finite state projection approach to remove unlikely states from the Markov process; (ii) We modify an existing coarse-graining approach in order to reduce the system dimension while capturing the equilibrium distribution of the process; and (iii) We introduce small correction terms to the timescales of the reduced process in order to capture the transient dynamics of the original system. Next, we explore four different iterative algorithms that automatically adapt the projection resolution and thereby improve both accuracy and effidenc.y of the CME solution. We test the resulting projection rules and refinement strategies on a number of one-, two-, and three-species gene regulatory processes, and we select the most efficient and most accurate combination of coarse-graining rules and refinement strategies.
BackgroundMechanistic models that describe the dynamical behaviors of biochemical systems are common in computational systems biology, especially in the realm of cellular signaling. The development of families of such models, either by a single research group or by different groups working within the same area, presents significant challenges that range from identifying structural similarities and differences between models to understanding how these differences affect system dynamics.ResultsWe present the development and features of an interactive model exploration system, MOSBIE, which provides utilities for identifying similarities and differences between models within a family. Models are clustered using a custom similarity metric, and a visual interface is provided that allows a researcher to interactively compare the structures of pairs of models as well as view simulation results.ConclusionsWe illustrate the usefulness of MOSBIE via two case studies in the cell signaling domain. We also present feedback provided by domain experts and discuss the benefits, as well as the limitations, of the approach.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2105-15-316) contains supplementary material, which is available to authorized users.
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