A Linear Framework for Time-Scale Separation in Nonlinear Biochemical Systems

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level

Relationship between nucleotide binding and ion channel gating in cystic fibrosis transmembrane conductance regulator

We have employed rate-equilibrium free energy relationship (REFER) analysis to characterize the dynamic events involved in the allosteric regulation of cystic fibrosis transmembrane conductance regulator (CFTR) function. A wide range of different hydrolysable and poorly hydrolysable nucleoside triphosphates were used to elucidate the role of ATP hydrolysis in CFTR function. The linearity of the REFER plots and Φ values near unity for all ligands tested implies that CFTR channel gating is a reversible thermally driven process with all structural reorganization in the binding site(s) completed prior to channel opening. This is consistent with the requirement for nucleotide binding for channel opening. However, the channel structural transition from the open to the closed state occurs independently of any events in the binding sites. Similar results were obtained on substitution of amino acids at coupling joints between both nucleotide binding domains (NBD) and cytoplasmic loops (CL) in opposite halves of the protein, indicating that any structural reorganization there also had occurred in the channel closed state. The fact that fractional Φ values were not observed in either of these distant sites suggests that there may not be a deterministic ‘lever-arm’ mechanism acting between nucleotide binding sites and the channel gate. These findings favour a stochastic coupling between binding and gating in which all structural transitions are thermally driven processes. We speculate that increase of channel open state probability is due to reduction of the number of the closed state configurations available after physical interaction between ligand bound NBDs and the channel