The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Results of atomistic molecular dynamics simulations of dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylglycerol monolayers at the air/water interface are presented. Dipalmitoylphosphatidylcholine is zwitterionic and dipalmitoylphosphatidylglycerol is anionic at physiological pH. NaCl and CaCl2 water subphases are simulated. The simulations are carried out at different surface densities, and a simulation cell geometry is chosen that greatly facilitates the investigation of phospholipid monolayer properties. Ensemble average monolayer properties calculated from simulation are in agreement with experimental measurements. The dependence of the properties of the monolayers on the surface density, the type of the headgroup, and the ionic environment are explained in terms of atomistically detailed pair distribution functions and electron density profiles, demonstrating the strength of simulations in investigating complex, multicomponent systems of biological importance.

Convergent gene pairs with head-to-head configurations are widespread in both eukaryotic and prokaryotic genomes and are speculated to be involved in gene regulation. Here we present a unique mechanism of gene regulation due to convergent transcription from the antagonistic prgX/prgQ operon in Enterococcus faecalis controlling conjugative transfer of the antibiotic resistance plasmid pCF10 from donor cells to recipient cells. Using mathematical modeling and experimentation, we demonstrate that convergent transcription in the prgX/prgQ operon endows the system with the properties of a robust genetic switch through premature termination of elongating transcripts due to collisions between RNA polymerases (RNAPs) transcribing from opposite directions and antisense regulation between complementary counter-transcripts. Evidence is provided for the presence of truncated RNAs resulting from convergent transcription from both the promoters that are capable of sense-antisense interactions. A mathematical model predicts that both RNAP collision and antisense regulation are essential for a robust bistable switch behavior in the control of conjugation initiation by prgX/prgQ operons. Moreover, given that convergent transcription is conserved across species, the mechanism of coupling RNAP collision and antisense interaction is likely to have a significant regulatory role in gene expression.inverse expression | overlapping DNA | gene-regulatory network

We conducted over 150 ns of simulation of a protegrin-1 octamer pore in a lipid bilayer composed of palmitoyloleoyl-phosphatidylethanolamine (POPE) and palmitoyloleoyl-phosphatidylglycerol (POPG) lipids mimicking the inner membrane of a bacterial cell. The simulations improve on a model of a pore proposed from recent NMR experiments and provide a coherent understanding of the molecular mechanism of antimicrobial activity. Although lipids tilt somewhat toward the peptides, the simulated protegrin-1 pore more closely follows the barrel-stave model than the toroidal-pore model. The movement of ions is investigated through the pore. The pore selectively allows negatively charged chloride ions to pass through at an average rate of one ion every two nanoseconds. Only two events are observed of sodium ions crossing through the pore. The potential of mean force is calculated for the water and both ion types. It is determined that the chloride ions move through the pore with ease, similarly to the water molecules with the exception of a zone of restricted movement midway through the pore. In bacteria, ions moving through the pore will compromise the integrity of the transmembrane potential. Without the transmembrane potential as a countermeasure, water will readily flow inside the higher osmolality cytoplasm. We determine that the diffusivity of water through a single PG-1 pore is sufficient to cause fast cell death by osmotic lysis.

Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higherorder moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time.stochastic models | information theory | entropy maximization | statistical mechanics T he fabric of all things living is discrete and noisy, individual molecules in perpetual random motion. However, humans, in our effort to understand and manipulate the biological cosmos, have historically perceived and modeled nature as large collections of molecules with behaviors not far from an expected average. Mathematical models, founded on such determinism, may be excellent approximations of reality when the number of molecules is very large, approaching the limit of an infinitely sized molecular population (1-5). Of course, the size of biomolecular systems is far from infinite. And we know that the behavior of a few molecules fluctuating from the average in unexpected ways may forever seal the fate of a living organism. It has thus been commonly recognized that models of small, evolving molecular populations better account for the noisy, probabilistic nature of outcomes (6-8).The most complete model of stochastically evolving molecular populations is one based on the master probability equation (9). The "master" in the name reflects the all-encompassing nature of an equation that purports to govern all possible outcomes for all time. Because of its ambitious character, the master equation has remained unsolved for all but the simplest of molecular interaction networks, even though it is now over seven decades since the first master equations were set up for chemical systems (10,11). Herein we ...