Complex Biochemical Reaction Networks Research Articles

Computational multiple steady states for enzymic production of l-DOPA in an isothermal CSTR

The capacity of computational multiple steady states in a complex biochemical reaction networks, consisting of nine non-linear ordinary differential equations, was investigated. The system involved the production of l-DOPA (L-3,4-dihydroxyphenylalanine) using l-tyrosine as a substrate and using the enzyme tyrosinase as the biocatalyst operating in an isothermal continuous stirred tank reactor (CSTR). A Deficiency One Algorithm and a Subnetwork Analysis were applied to determine the steady state multiplicity. A set of rate constants and two corresponding steady states were constructed for three cases. The phenomena of hysteresis and bifurcation were discussed. Two sets of signatures of multiple steady states were provided, which could be used to identify reaction mechanism if steady states of some species had been measured. The capacity of multiple steady states was extended to its family members.

Reconstructing metabolic flux vectors from extreme pathways: defining the α-spectrum

The move towards genome-scale analysis of cellular functions has necessitated the development of analytical ( in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the α-spectrum. The α-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the α-spectrum. The α-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

BioMOL: a computer-assisted biological modeling tool for complex chemical mixtures and biological processes at the molecular level.

A chemical engineering approach for the rigorous construction, solution, and optimization of detailed kinetic models for biological processes is described. This modeling capability addresses the required technical components of detailed kinetic modeling, namely, the modeling of reactant structure and composition, the building of the reaction network, the organization of model parameters, the solution of the kinetic model, and the optimization of the model. Even though this modeling approach has enjoyed successful application in the petroleum industry, its application to biomedical research has just begun. We propose to expand the horizons on classic pharmacokinetics and physiologically based pharmacokinetics (PBPK), where human or animal bodies were often described by a few compartments, by integrating PBPK with reaction network modeling described in this article. If one draws a parallel between an oil refinery, where the application of this modeling approach has been very successful, and a human body, the individual processing units in the oil refinery may be considered equivalent to the vital organs of the human body. Even though the cell or organ may be much more complicated, the complex biochemical reaction networks in each organ may be similarly modeled and linked in much the same way as the modeling of the entire oil refinery through linkage of the individual processing units. The integrated chemical engineering software package described in this article, BioMOL, denotes the biological application of molecular-oriented lumping. BioMOL can build a detailed model in 1-1,000 CPU sec using standard desktop hardware. The models solve and optimize using standard and widely available hardware and software and can be presented in the context of a user-friendly interface. We believe this is an engineering tool with great promise in its application to complex biological reaction networks.