How to reveal various aspects of regulation in grouptransfer pathways.

AbstractFor an ‘ideal’ metabolic pathway, genetic modulation of the enzyme concentration and titration with different types of specific inhibitor all leads to the determination of the same quantitative indicator of the extent to which an enzyme controls the flux and metabolite concentrations: the control coefficient with respect to the enzyme concentration. By contrast, for a group-transfer pathway these methods reveal various modes of the control exerted by an enzyme on the flux and on the concentrations of pathway components. Modulation of gene expression allows one to determine the (classical) control coefficient with respect to the enzyme concentration. Titration with inhibitors (competitive or uncompetitive) that do not bind to enzyme-enzyme complexes leads to information on the classical control coefficient of the inhibited enzyme and on the relative concentrations of its different forms. Should such inhibitors be irreversible, the classical control coefficients can be measured directly. Titration with a purely non-competitive inhibitor (binding to all the complexes of the target enzyme) reveals the impact control coefficient, a measure of the total kinetic effect of that enzyme on the system. Combined approaches applied to intact systems will detect an expected variety of control properties that cannot be measured after the system has been disassembled

Rate limitation within a single enzyme is directly related to enzyme intermediate levels.

AbstractThe extents to which different rate constants limit the steady-state rate of an isolated enzyme can be quantified as the control coefficients of those constants and elemental steps. We have found that the sum of the control coefficients of rate constants characterising unidirectional rates depleting a particular enzyme intermediate is equal to the concentration of that enzyme intermediate as a fraction of the total enzyme concentration. Together with simple measurements this powerful relation may be used (i) to estimate certain enzyme intermediate levels, in particular the free enzyme concentration, and (ii) to estimate the control coefficients of rate constants and steps

Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law

A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control Analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient, cannot be applied to spatially separated protein networks. The present paper unravels the principles that govern the control over the fluxes and intermediate concentrations in spatially heterogeneous reaction networks. Our main results are two types of the control summation theorems. The first type is a non-trivial generalization of the classical theorems to systems with spatially and temporally varying concentrations. In this generalization, the process of diffusion, which enters as the result of spatial concentration gradients, plays a role similar to other processes such as chemical reactions and membrane transport. The second summation theorem is completely novel. It states that the control by the membrane transport, the diffusion control coefficient multiplied by two, and a newly introduced control coefficient associated with changes in the spatial size of a system (e.g., cell), all add up to one and zero for the control over flux and concentration. Using a simple example of a kinase/phosphatase system in a spherical cell, we speculate that unless active mechanisms of intracellular transport are involved, the threshold cell size is limited by the diffusion control, when it is beginning to exceed the spatial control coefficient significantly

Analysis of signalling pathways using continuous time Markov chains

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

The Attributed Pi Calculus with Priorities

International audienceWe present the attributed $\pi$-calculus for modeling concurrent systems with interaction constraints depending on the values of attributes of processes. The $\pi$-calculus serves as a constraint language underlying the $\pi$-calculus. Interaction constraints subsume priorities, by which to express global aspects of populations. We present a nondeterministic and a stochastic semantics for the attributed $\pi$-calculus. We show how to encode the $\pi$-calculus with priorities and polyadic synchronization $\pi$@ and thus dynamic compartments, as well as the stochastic $\pi$-calculus with concurrent objects spico. We illustrate the usefulness of the attributed $\pi$-calculus for modeling biological systems at two particular examples: Euglena’s spatial movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda. Furthermore, population-based model is supported beside individual-based modeling. A stochastic simulation algorithm for the attributed $\pi$-calculus is derived from its stochastic semantics. We have implemented a simulator and present experimental results, that confirm the practical relevance of our approach

How do external parameters control fluxes and concentrations of metabolites? An additional relationship in the theory of metabolic control

AbstractThe flux through a metabolic pathway can be controlled by external signals from the environment. These signals are formally described as changes in external parameters, such as concentrations of external metabolites (substrates or effectors) or physical parameters, e.g. temperature, pH, ionic strength. It was proved that the response coefficient of the flux (or of the concentration) to a change in an external parameter is the weighted average of external elasticities of pathway enzymes towards this parameter; weight factors are the control coefficients of corresponding enzymes. As compared with the previously known relationships these ones are applicable to the more common case of parameters acting on more than one enzyme. Along with other applications, the use of the obtained relationships for control analysis of moiety-conserved cycles is considered