Clusters of reaction rates and concentrations in protein networks such as the phosphotransferase system

To understand the functioning of living cells, it is often helpful or even necessary to exploit inherent timescale disparities and focus on long-term dynamic behaviour. In the present study, we explore this type of behaviour for the biochemical network of the phosphotransferase system. We show that, during the slow phase that follows a fast initial transient, the network reaction rates are partitioned into clusters corresponding to connected parts of the reaction network. Rates within any of these clusters assume essentially the same value: differences within each cluster are vastly smaller than that from one cluster to another. This rate clustering induces an analogous clustering of the reactive compounds: only the molecular concentrations on the interface between these clusters are produced and consumed at substantially different rates and hence change considerably during the slow phase. The remaining concentrations essentially assume their steady-state values already by the end of the transient phase. Further, we find that this clustering phenomenon occurs for a large number of parameter values and also for models with different topologies; to each of these models, there corresponds a particular network partitioning. Our results show that, in spite of its complexity, the phosphotransferase system tends to behave in a rather simple (yet versatile) way. The persistence of clustering for the perturbed models we examined suggests that it is likely to be encountered in various environmental conditions, as well as in other signal transduction pathways with network structures similar to that of the phosphotransferase system.