Computing Linearly Conjugate Weakly Reversible Kinetic Structures Using Optimization and Graph Theory

A graph-theory-based algorithm is given in this paper for computing dense weakly reversible linearly conjugate realizations of kinetic systems using a fixed set of complexes. The algorithm is also able to decide whether such a realization exists or not. To prove the correctness of the method, it is shown that weakly reversible linearly conjugate chemical reaction network realizations containing the maximum number of directed edges form a unique super-structure among all linearly conjugate weakly reversible realizations. An illustrative example taken from the literature is used to show the operation of the algorithm

Computing Core Reactions of Uncertain Polynomial Kinetic Systems

Kinetic systems form a wide nonlinear system class with good descriptive power that can efficiently be used for the dynamical modeling of non-negative models emerging not only in (bio)chemistry but in other important scientific and engineering fields as well. The directed graph structure assigned to kinetic models give us important information about the qualitative dynamical properties of the system. In this paper we extend the previous results for computing structurally invariant directed edges (called core reactions) for uncertain kinetic polynomial models, where the uncertainty is represented as a multi-dimensional interval in the space of monomial coefficients. We show that the computation can be put into the framework of linear programming. Using illustrative examples we demonstrate the properties of the computed structures and the potential application of the method in the support of structural identification of biochemical networks

Analysis-based Parameter Estimation of an in vitro Transcription-Translation System

Recent advances in measurement technology pro- vide us with rich source of data for estimating parameters in biomolecular circuit models, particularly in simplified in vitro transcription-translation systems, so-called molecular “bread- boards”. In this paper, we elaborate on a mass action type dynamic model for such an in vitro system and detail a parameter estimation procedure that may be used with time series data containing information about both transcriptional and translational stages of gene expression. The identification process is supported by structural identifiability analysis to ensure proper model structure. Statistical analysis and vali- dation of the estimated parameter set help us to understand the characteristics of point estimation results