Finding weakly reversible realizations of chemical reaction networks using optimization

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem statement can be traced back at least 30 years ago. The algorithm uses standard linear and mixed integer linear programming, and it is based on elementary graph theory and important former results on the dense realizations of CRNs. The proposed method is also capable of determining if no dynamically equivalent weakly reversible structure exists for a given reaction network with a previously fixed complex set.Comment: 18 pages, 9 figure

Checking Dynamic Consistency of Conditional Hyper Temporal Networks via Mean Payoff Games (Hardness and (pseudo) Singly-Exponential Time Algorithm)

In this work we introduce the \emph{Conditional Hyper Temporal Network (CHyTN)} model, which is a natural extension and generalization of both the \CSTN and the \HTN model. Our contribution goes as follows. We show that deciding whether a given \CSTN or CHyTN is dynamically consistent is \coNP-hard. Then, we offer a proof that deciding whether a given CHyTN is dynamically consistent is \PSPACE-hard, provided that the input instances are allowed to include both multi-head and multi-tail hyperarcs. In light of this, we continue our study by focusing on CHyTNs that allow only multi-head or only multi-tail hyperarcs, and we offer the first deterministic (pseudo) singly-exponential time algorithm for the problem of checking the dynamic-consistency of such CHyTNs, also producing a dynamic execution strategy whenever the input CHyTN is dynamically consistent. Since \CSTN{s} are a special case of CHyTNs, this provides as a byproduct the first sound-and-complete (pseudo) singly-exponential time algorithm for checking dynamic-consistency in CSTNs. The proposed algorithm is based on a novel connection between CSTN{s}/CHyTN{s} and Mean Payoff Games. The presentation of the connection between \CSTN{s}/CHyTNs and \MPG{s} is mediated by the \HTN model. In order to analyze the algorithm, we introduce a refined notion of dynamic-consistency, named $\epsilon$-dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction time $\hat{\varepsilon}$ where a \CSTN/CHyTN transits from being, to not being, dynamically consistent. The proof technique introduced in this analysis of $\hat{\varepsilon}$ is applicable more generally when dealing with linear difference constraints which include strict inequalities.Comment: arXiv admin note: text overlap with arXiv:1505.0082

Statistical analysis of a dynamical multifragmentation path

A microcanonical multifragmentation model (MMM) is used for investigating whether equilibration really occurs in the dynamical evolution of two heavy ion collisions simulated via a stochastic mean field approach (SMF). The standard deviation function between the dynamically obtained freeze-out fragment distributions corresponding to the reaction $^{129}$Xe+$^{119}$Sn at 32 MeV/u and the MMM ones corresponding to a wide range of mass, excitation energy, freeze-out volume and nuclear level density cut-off parameter shows a unique minimum. A distinct statistically equilibrated stage is identified in the dynamical evolution of the system.Comment: 5 pages, 3 figure

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biolog

Thermodynamic modelling of synthetic communities predicts minimum free energy requirements for sulfate reduction and methanogenesis

Microbial communities are complex dynamical systems harbouring many species interacting together to implement higher-level functions. Among these higher-level functions, conversion of organic matter into simpler building blocks by microbial communities underpins biogeochemical cycles and animal and plant nutrition, and is exploited in biotechnology. A prerequisite to predicting the dynamics and stability of community-mediated metabolic conversions is the development and calibration of appropriate mathematical models. Here, we present a generic, extendable thermodynamic model for community dynamics and calibrate a key parameter of this thermodynamic model, the minimum energy requirement associated with growth-supporting metabolic pathways, using experimental population dynamics data from synthetic communities composed of a sulfate reducer and two methanogens. Our findings show that accounting for thermodynamics is necessary in capturing the experimental population dynamics of these synthetic communities that feature relevant species using low energy growth pathways. Furthermore, they provide the first estimates for minimum energy requirements of methanogenesis (in the range of −30 kJ mol−1) and elaborate on previous estimates of lactate fermentation by sulfate reducers (in the range of −30 to −17 kJ mol−1 depending on the culture conditions). The open-source nature of the developed model and demonstration of its use for estimating a key thermodynamic parameter should facilitate further thermodynamic modelling of microbial communities