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We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current method, unlike some of the graphical approaches proposed in the literature, uses the values of the experimental measurements only relative to the geometry of the biochemical reactions under the assumption that the underlying reaction network is the same for all the experiments. The proposed approach utilizes algebraic statistical methods in order to parametrize the set of possible reactions so as to identify the most likely network structure, and is easily scalable to very complicated biochemical systems involving a large number of species and reactions. The method is illustrated with a numerical example of a hypothetical network arising form a mass transfer-type model.
We present herein an extension of an algebraic statistical method for inferring biochemical reaction networks from experimental data, proposed recently in [3]. This extension allows us to analyze reaction networks that are not necessarily full-dimens
We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular co
It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this paper, we consider the following related question: supposing that the initial
We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast vari
Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to a