ATP production optimization in biochemical mass action models with protein turnover

We introduce a simple approach to account for the ATP consumption and production in the case of mass action models of metabolic pathways including protein turnover. Under some simplifying assumptions, the method makes it possible to characterize the optimal rate of enzyme synthesis if the substrate concentrations and other rate constants are known. Furthermore we demonstrate that the proposed approach is capable of the comparison of the efficiency of different feedback laws in dynamic environment, considering time-varying substrate concentration. Copyright © 2013 IFAC

Model predictive control for the hybrid primary circuit dynamics of a pressurized water nuclear power plant^1

In this paper, a model predictive controller is developed for controlling the main primary circuit dynamics of pressurized water nuclear power plants during load-change transients. The hybrid model of the plant is successfully embedded into a non-hybrid discrete time LPV form. The designed controller is able to handle the hard constraints for the state and input variables while keeping the plant stable and producing satisfactory time-domain behavior

Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions

summary:In this paper a novel method is proposed for the structural identifiability analysis of nonlinear time delayed systems. It is assumed that all the nonlinearities are analytic functions and the time delays are constant. We consider the joint structural identifiability of models with respect to the ordinary system parameters and time delays by including delays into a unified parameter set. We employ the Volterra series representation of nonlinear dynamical systems and make use of the frequency domain representations of the Volterra kernels, i. e. the Generalized Frequency Response Functions (GFRFs), in order to test the unique computability of the parameters. The advantage of representing nonlinear systems with their GFRFs is that in the frequency domain representation the time delay parameters appear explicitly in the exponents of complex exponential functions from which they can be easily extracted. Since the GFRFs can be symmetrized to be unique, they provide us with an exhaustive summary of the underlying model structure. We use the GFRFs to derive equations for testing structural identifiability. Unique solution of the composed equations with respect to the parameters provides sufficient conditions for structural identifiability. Our method is illustrated on non-linear dynamical system models of different degrees of non-linearities and multiple time delayed terms. Since Volterra series representation can be applied for input-output models, it is also shown that after differential algebraic elimination of unobserved state variables, the proposed method can be suitable for identifiability analysis of a more general class of non-linear time delayed state space models

Computing different realizations of linear dynamical systems with embedding eigenvalue assignment

In this paper we investigate realizability of discrete time linear dynamical systems (LDSs) in fixed state space dimension. We examine whether there exist different Θ = (A,B,C,D) state space realizations of a given Markov parameter sequence Y with fixed B, C and D state space realization matrices. Full observation is assumed in terms of the invertibility of output mapping matrix C. We prove that the set of feasible state transition matrices associated to a Markov parameter sequence Y is convex, provided that the state space realization matrices B, C and D are known and fixed. Under the same conditions we also show that the set of feasible Metzler-type state transition matrices forms a convex subset. Regarding the set of Metzler-type state transition matrices we prove the existence of a structurally unique realization having maximal number of non-zero off-diagonal entries. Using an eigenvalue assignment procedure we propose linear programming based algorithms capable of computing different state space realizations. By using the convexity of the feasible set of Metzler-type state transition matrices and results from the theory of non-negative polynomial systems, we provide algorithms to determine structurally different realization. Computational examples are provided to illustrate structural non-uniqueness of network-based LDSs

On the Verification and Correction of Large-Scale Kinetic Models in Systems Biology

14 páginasIn this paper we consider the problem of verification of large dynamic models of biological systems. We present syntactical criteria based on biochemical kinetics to ensure the plausibility of a model and the positivity of its solution. These criteria include the positivity of the rate functions, their kinetic type dependence on the reactant species concentrations, and the absence of the negative cross-effects that together guarantee the nonnegativity of the dynamics. Further, the stoichiometric matrix of the truncated reaction system is checked against conservation using its algebraic properties. Algorithmic procedures are then proposed for checking these criteria with emphasis on good scaling up properties. In addition to these verification procedures, we also provide, for certain typical errors, model correcting methods. The capabilities and usefulness of these procedures are illustrated on biochemical models taken from the Biomodels database. In particular, a set of 11 kinetic models related with E. coli are checked, finding two with deficiencies. Correcting actions for these models are proposed.Peer reviewe