A quantum model for controlled enzymic reactions

A quantum model for the general enzymic reaction,E+S ⇌ ES → P, is presented, starting with the assumptions that any chemical substanceS, which may be a substrate for a particularE _(S)-enzyme is a microphysical system and any enzymeE-molecule, capable of interacting with anS-substrate is a “measuring system” which will “measure” one or more of theS-observables. According to the above assumptions a stochastic model of the reaction is constructed and a computer simulation of the steady state performed. The results thus obtained predicted fluctuations in the enzymic reaction rate, function of the substrate “perturbation”. On an experimental basis it is demonstrated that the irradiation of an enzymic substrate with low energies results in the inducement of a dose-dependent oscillatory behavior in the corresponding enzymic reaction rate. In the reaction type, the oscillations thus induced in theE-activity by the corresponding substrates are out-of-phase, realizing a biochemical discriminating net. Likewise, in an reaction type, the oscillations induced by the irradiatedS-substrate in the activities of the respective enzyme, realize a biochemical switching net.     

A theoretical model for the control mechanisms in biochemical reactions

A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ _f of a mappingf: A→B in the stimulated Φ¹ and unstimulated state Φ⁰. Likewise, the range of τ is formed by the set δ={f ^o ,f ¹} wheref ¹ means the mappingf in its stimulated state andf ^o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ _f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.     

METANNOGEN: compiling features of biochemical reactions needed for the reconstruction of metabolic networks

Background  

One central goal of computational systems biology is the mathematical modelling of complex metabolic reaction networks. The first and most time-consuming step in the development of such models consists in the stoichiometric reconstruction of the network, i. e. compilation of all metabolites, reactions and transport processes relevant to the considered network and their assignment to the various cellular compartments. Therefore an information system is required to collect and manage data from different databases and scientific literature in order to generate a metabolic network of biochemical reactions that can be subjected to further computational analyses.     

Graphical approach to model reduction for nonlinear biochemical networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a "concentration-clamp" procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β(1)-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal "kinetic biomarkers" of the overall β(1)-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems.     

A probabilistic approach to compact steady-state kinetic equations for enzymic reactions

We describe a method for deriving kinetic equations based on the simplification of a complex graphical scheme of steady-state enzymic reactions to one that is comprised of an unbranched pathway. It entails compressing unbranched multi-step sequences into one step, and fusing some graph nodes into a single node. The final form of the equations is compact and well structured, and it simplifies the choice of independent kinetic parameters. The approach is illustrated by an analysis of representative two- and three-substrate reactions.     

RMBNToolbox: random models for biochemical networks

Background  

There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models.     

Condor-COPASI: high-throughput computing for biochemical networks

ABSTRACT: BACKGROUND: Mathematical modelling has become a standard technique to improve our understanding of complex biological systems. As models become larger and more complex, simulations and analyses require increasing amounts of computational power. Clusters of computers in a high-throughput computing environment can help to provide the resources required for computationally expensive model analysis. However, exploiting such a system can be difficult for users without the necessary expertise. RESULTS: We present Condor-COPASI, a server-based software tool that integrates COPASI, a biological pathway simulation tool, with Condor, a high-throughput computing environment. Condor-COPASI provides a web-based interface, which makes it extremely easy for a user to run a number of model simulation and analysis tasks in parallel. Tasks are transparently split into smaller parts, and and submitted for execution on a Condor pool. Result output is presented to the user in a number of formats, including tables and interactive graphical displays. CONCLUSIONS: Condor-COPASI can effectively use a Condor high-throughput computing environment to provide significant gains in performance for a number of model simulation and analysis tasks. Condor-COPASI is free, open source software, released under the Artistic License 2.0, and is suitable for use by any institution with access to a Condor pool. Source code is freely available for download at http://code.google.com/p/condor-copasi/, along with full instructions on deployment and usage.     

Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks

Background  

Mathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand.     

Quantum-like behavior without quantum physics II. A quantum-like model of neural network dynamics

In earlier work, we laid out the foundation for explaining the quantum-like behavior of neural systems in the basic kinematic case of clusters of neuron-like units. Here we extend this approach to networks and begin developing a dynamical theory for them. Our approach provides a novel mathematical foundation for neural dynamics and computation which abstracts away from lower-level biophysical details in favor of information-processing features of neural activity. The theory makes predictions concerning such pathologies as schizophrenia, dementias, and epilepsy, for which some evidence has accrued. It also suggests a model of memory retrieval mechanisms. As further proof of principle, we analyze certain energy-like eigenstates of the 13 three-neuron motif classes according to our theory and argue that their quantum-like superpositional nature has a bearing on their observed structural integrity.     

A new kinetic model for biochemical oscillations: Graph-theoretical analysis

A graphical analysis demonstrates the ability of slow substrate activation and certain types of cooperativity between the two enzyme active sites to generate sustained oscillations. The analysis allows us to estimate kinetic parameter values for which oscillations exist. The scheme analyzed can explain the cyclical changes in functioning of various motor enzymes. Moreover, this scheme does not generate bistability for any parameter values. The graphical analysis presented is simple and visually clarifies the regulatory role of the details in the kinetic schemes.