Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics

The mathematical theory of nonequilibrium steady state (NESS) has a natural application in open biochemical systems which have sustained source(s) and sink(s) in terms of a difference in their chemical potentials. After a brief introduction in Section 1, in Part II of this review, we present the widely studied biochemical enzyme kinetics, the workhorse of biochemical dynamic modeling, in terms of the theory of NESS (Section 2.1). We then show that several phenomena in enzyme kinetics, including a newly discovered activation-inhibition switching (Section 2.2) and the well-known non-Michaelis-Menten-cooperativity (Section 2.3) and kinetic proofreading (Section 2.4), are all consequences of the NESS of driven biochemical systems with associated cycle fluxes. Section 3 is focused on nonlinear and nonequilibrium systems of biochemical reactions. We use the phosphorylation-dephosphorylation cycle (PdPC), one of the most important biochemical signaling networks, as an example (Section 3.1). It starts with a brief introduction of the Delbrück-Gillespie process approach to mesoscopic biochemical kinetics (Sections 3.2 and 3.3). We shall discuss the zeroth-order ultrasensitivity of PdPC in terms of a new concept — the temporal cooperativity (Sections 3.4 and 3.5), as well as PdPC with feedback which leads to biochemical nonlinear bistability (Section 3.6). Also, both are nonequilibrium phenomena. PdPC with a nonlinear feedback is kinetically isomorphic to a self-regulating gene expression network, hence the theory of NESS discussed here could have wide applications to many other biochemical systems.     

Billion‐Fold Enhancement in Sensitivity of Nuclear Magnetic Resonance Spectroscopy for Magnesium Ions in Solution

β‐nuclear magnetic resonance (NMR) spectroscopy is highly sensitive compared to conventional NMR spectroscopy, and may be applied for several elements across the periodic table. β‐NMR has previously been successfully applied in the fields of nuclear and solid‐state physics. In this work, β‐NMR is applied, for the first time, to record an NMR spectrum for a species in solution. ³¹Mg β‐NMR spectra are measured for as few as 10⁷ magnesium ions in ionic liquid (EMIM‐Ac) within minutes, as a prototypical test case. Resonances are observed at 3882.9 and 3887.2 kHz in an external field of 0.3 T. The key achievement of the current work is to demonstrate that β‐NMR is applicable for the analysis of species in solution, and thus represents a novel spectroscopic technique for use in general chemistry and potentially in biochemistry.     

Threshold Sensing through a Synthetic Enzymatic Reaction–Diffusion Network

A wet stamping method to precisely control concentrations of enzymes and inhibitors in place and time inside layered gels is reported. By combining enzymatic reactions such as autocatalysis and inhibition with spatial delivery of components through soft lithographic techniques, a biochemical reaction network capable of recognizing the spatial distribution of an enzyme was constructed. The experimental method can be used to assess fundamental principles of spatiotemporal order formation in chemical reaction networks.