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Register a new userAlgebraic Methods for Inferring Biochemical Networks: a Maximum Likelihood Approach
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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.
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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-dimensional, i.e., the dimension of their stoichiometric space is smaller than the number of species. Specifically, we propose to augment the original algebraic-statistical algorithm for network inference with a preprocessing step that identifies the subspace spanned by the correct reaction vectors, within the space spanned by the species. This dimension reduction step is based on principal component analysis of the input data and its relationship with various subspaces generated by sets of candidate reaction vectors. Simulated examples are provided to illustrate the main ideas involved in implementing this method, and to asses its performance.
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 components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.
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 distribution of a stochastically modeled reaction network is a product of Poissons, under what conditions will the distribution remain a product of Poissons for all time? By drawing inspiration from Crispin Gardiners Poisson representation for the solution to the chemical master equation, we provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical complex-balancing for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). We term this new condition the dynamical and restricted complex balance condition (DR for short).
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 variables are made, or necessary.We apply the theoretical results to chemical reaction networks with mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems there exist canonical parameterizations of the variety of stationary points, hence the theory is applicable in a natural manner. In particular we obtain a closed form expression for the reduced system when the fast subsystem admits complex balanced steady states.
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 adequately describe this complex process. In this paper, we investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher-order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments as well as the global features of actomyosin networks. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight on the heterogeneous morphologies of actomyosin networks at a global level. We find that ABPs with a valency greater than two promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosin-like motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosin detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.
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