Despite the arsenal of technologies employed to control foodborne nontyphoidal Salmonella (NTS), infections have not declined in decades. Poultry is the primary source of NTS outbreaks, as well as the fastest growing meat sector worldwide. With recent FDA rules for phasing-out antibiotics in animal production, pressure is mounting to develop new pathogen reduction strategies. We report on a technology to reduce Salmonella enteritidis in poultry. We engineered probiotic E. coli Nissle 1917, to express and secrete the antimicrobial peptide, Microcin J25. Using in vitro experiments and an animal model of 300 turkeys, we establish the efficacy of this technology. Salmonella more rapidly clear the ceca of birds administered the modified probiotic than other treatment groups. Approximately 97% lower Salmonella carriage is measured in a treated group, 14 days post-Salmonella challenge. Probiotic bacteria are generally regarded as safe to consume, are bile-resistant and can plausibly be modified to produce a panoply of antimicrobial peptides now known. The reported systems may provide a foundation for platforms to launch antimicrobials against gastrointestinal tract pathogens, including ones that are multi-drug resistant.
Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CMEbased approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CMEbased modeling formalisms, especially in the context of synthetic biology efforts.
Deterministic and stochastic models of chemical reaction kinetics can give starkly different results when the deterministic model exhibits more than one stable solution. For example, in the stochastic Schlögl model, the bimodal stationary probability distribution collapses to a unimodal distribution when the system size increases, even for kinetic constant values that result in two distinct stable solutions in the deterministic Schlögl model. Using zero-information (ZI) closure scheme, an algorithm for solving chemical master equations, we compute stationary probability distributions for varying system sizes of the Schlögl model. With ZI-closure, system sizes can be studied that have been previously unattainable by stochastic simulation algorithms. We observe and quantify paradoxical discrepancies between stochastic and deterministic models and explain this behavior by postulating that the entropy of non-equilibrium steady states (NESS) is maximum.
The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the time evolution of stochastic reaction networks. Based on the assumption that the entropy of the reaction network is maximum, Lagrange multipliers are introduced. The proposed method derives equations that model the time derivatives of these Lagrange multipliers. We present detailed steps to transform moment equations to Lagrange multiplier equations. In order to demonstrate the method, we present examples of non-linear stochastic reaction networks of varying degrees of complexity, including multistable and oscillatory systems. We find that the new approach is as accurate and significantly more efficient than Gillespie’s original exact algorithm for systems with small number of interacting species. This work is a step towards solving stochastic reaction networks accurately and efficiently.
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