Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species' Concentrations.

The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.

Stability analysis of the coexistence equilibrium of a balanced metapopulation model.

We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle's invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.

Stability analysis of the Michaelis-Menten approximation of a mixed mechanism of a phosphorylation system.

In this paper, we consider a mixed mechanism of a n-site phosphorylation system in which the mechanism of phosphorylation is distributive and that of dephosphorylation is processive. It is assumed that the concentrations of the substrates are much higher than those of the enzymes and their intermediate complexes. This assumption enables us to reduce the system using the steady-state approach to a Michaelis-Menten approximation of the system. It is proved that the resulting system of nonlinear ordinary differential equations admits a unique positive equilibrium in every positive stoichiometric compatibility class using the theory of quadratic equations. We then consider two special cases. In the first case, we assume that the Michaelis constants associated with the different substrates in the phosphorylation reactions are equal and construct a Lyapunov function to prove asymptotic stability of the system. In the second case, we assume that there are just two sites of phosphorylation and dephoshorylation and prove that the resulting system is asymptotically stable using Poincare´ Bendixson theorem.

Global stability of a class of futile cycles.

In this paper, we prove the global asymptotic stability of a class of mass action futile cycle networks which includes a model of processive multisite phosphorylation networks. The proof consists of two parts. In the first part, we prove that there is a unique equilibrium in every positive compatibility class. In the second part, we make use of a piecewise linear in rates Lyapunov function in order to prove the global asymptotic stability of the unique equilibrium corresponding to a given initial concentration vector. The main novelty of the paper is the use of a simple algebraic approach based on the intermediate value property of continuous functions in order to prove the uniqueness of equilibrium in every positive compatibility class.

The short-chain fatty acid uptake fluxes by mice on a guar gum supplemented diet associate with amelioration of major biomarkers of the metabolic syndrome.

Studies with dietary supplementation of various types of fibers have shown beneficial effects on symptoms of the metabolic syndrome. Short-chain fatty acids (SCFAs), the main products of intestinal bacterial fermentation of dietary fiber, have been suggested to play a key role. Whether the concentration of SCFAs or their metabolism drives these beneficial effects is not yet clear. In this study we investigated the SCFA concentrations and in vivo host uptake fluxes in the absence or presence of the dietary fiber guar gum. C57Bl/6J mice were fed a high-fat diet supplemented with 0%, 5%, 7.5% or 10% of the fiber guar gum. To determine the effect on SCFA metabolism, 13C-labeled acetate, propionate or butyrate were infused into the cecum of mice for 6 h and the isotopic enrichment of cecal SCFAs was measured. The in vivo production, uptake and bacterial interconversion of acetate, propionate and butyrate were calculated by combining the data from the three infusion experiments in a single steady-state isotope model. Guar gum treatment decreased markers of the metabolic syndrome (body weight, adipose weight, triglycerides, glucose and insulin levels and HOMA-IR) in a dose-dependent manner. In addition, hepatic mRNA expression of genes involved in gluconeogenesis and fatty acid synthesis decreased dose-dependently by guar gum treatment. Cecal SCFA concentrations were increased compared to the control group, but no differences were observed between the different guar gum doses. Thus, no significant correlation was found between cecal SCFA concentrations and metabolic markers. In contrast, in vivo SCFA uptake fluxes by the host correlated linearly with metabolic markers. We argue that in vivo SCFA fluxes, and not concentrations, govern the protection from the metabolic syndrome by dietary fibers.

A model reduction method for biochemical reaction networks.

BACKGROUND: In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model. RESULTS: We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%. CONCLUSIONS: The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

A novel energy-efficient rotational variable stiffness actuator.

This paper presents the working principle, the design and realization of a novel rotational variable stiffness actuator, whose stiffness can be varied independently of its output angular position. This actuator is energy-efficient, meaning that the stiffness of the actuator can be varied by keeping constant the internal stored energy of the actuator. The principle of the actuator is an extension of the principle of translational energy-efficient actuator vsaUT. A prototype based on the principle has been designed, in which ball-bearings and linear slide guides have been used in order to reduce losses due to friction.

Stiffness and position control of a prosthetic wrist by means of an EMG interface.

In this paper, we present a novel approach for decoding electromyographic signals from an amputee and for interfacing them with a prosthetic wrist. The model for the interface makes use of electromyographic signals from electrodes placed in agonistic and antagonistic sides of the forearm. The model decodes these signals in order to control both the position and the stiffness of the wrist.