Correlation Resonance Generated by Coupled Enzymatic Processing

Abstract

A major challenge for systems biology is to deduce the molecular interactions that underlie correlations observed between concentrations of different intracellular molecules. Although direct explanations such as coupled transcription or direct protein-protein interactions are often considered, potential indirect sources of coupling have received much less attention. Here we show how correlations can arise generically from a posttranslational coupling mechanism involving the processing of multiple protein species by a common enzyme. By observing a connection between a stochastic model and a multiclass queue, we obtain a closed form expression for the steady-state distribution of the numbers of molecules of each protein species. Upon deriving explicit analytic expressions for moments and correlations associated with this distribution, we discover a striking phenomenon that we call correlation resonance: for small dilution rate, correlations peak near the balance-point where the total rate of influx of proteins into the system is equal to the maximum processing capacity of the enzyme. Given the limited number of many important catalytic molecules, our results may lead to new insights into the origin of correlated behavior on a global scale.

A queueing approach to multi-site enzyme kinetics

“…In this article, we extend a prior investigation [22] of ClpXP proteolytic kinetics. ClpXP is a well-studied protease in Escherichia coli that is responsible for degrading mistranslated proteins and (in healthy conditions) certain stress response factors [26][27][28].…”

“…Given the distribution in equation (4.2), many results follow [22,24]. For example, it is easy to show that, for a definite number of substrate molecules, the frequency of substrate classes is multi-nomial.…”

“…In the limit of large substrate count, where the concentration of substrate does not change appreciably on the time scale of enzyme kinetics, we predict that this approximation will be valid. It is worth noting that simpler models for multi-class enzyme kinetics have already been analysed in detail outside of the quasi-steady-state assumption [22], in which case free substrate can exhibit strongly correlated behaviour.…”

“…operations research, suggests that some biologically motivated questions tied to queueing may already have been answered in a different context. Pursuit of the queueing approach to biological problems has indeed been fruitful thus far, leading to progress in gene networks [15][16][17][18][19], metabolic networks [20,21], degradation pathways [22], signalling [23,24] and translational cross talk [25].…”

Noise in biology

“…A prototypical queueing model of enzymatic correlation was considered by Mather et al (2010). A system with m protein species X 1 , …, X m is governed by the following set of biochemical reactions.…”