Deviant effects in molecular reaction pathways

Abstract

In biological networks, any manifestations of behaviors substantially 'deviant' from the predictions of continuousdeterministic classical chemical kinetics (CCK) are typically ascribed to systems with complex dynamics and/or a small number of molecules. Here we show that in certain cases such restrictions are not obligatory for CCK to be largely incorrect. By systematically identifying properties that may cause significant divergences between CCK and the more accurate discrete-stochastic chemical master equation (CME) system descriptions, we comprehensively characterize potential CCK failure patterns in biological settings, including consequences of the assertion that CCK is closer to the 'mode' rather than the 'average' of stochastic reaction dynamics, as generally perceived. We demonstrate that mechanisms underlying such nonclassical effects can be very simple, are common in cellular networks and result in often unintuitive system behaviors. This highlights the importance of deviant effects in biotechnologically or biomedically relevant applications, and suggests some approaches to diagnosing them in situ.Although the temporal evolution of a spatially homogeneous molecular system subject to a set of (bio)chemical reactions is often described macroscopically via the classical chemical kinetics (CCK) formalism through a set of deterministic differential equations (ODEs) 1 -otherwise referred to as 'reaction rate equations' or 'mass action kinetics'-this approach does not substantially reflect the fundamentally random and discrete nature of individual molecular interactions. The latter is well described by the chemical master equation (CME) 2-4 . Although this makes CME an intrinsically much more accurate description of biological or chemical molecular system dynamics, CCK is significantly more efficient computationally and could be viewed as derived from CME via a set of limiting approximations 5 .The conditions under which these approximations hold are often considered to be broadly valid for biological and/or simple chemical systems. However, as shown here, neither is guaranteed to be the case. Breakdowns in the limiting approximations can occur in some of the most basic processes owing to mechanisms that are particularly common in biological systems. These breakdowns then manifest themselves as various 'deviant nonclassical effects'-distinctive behaviors not accounted for by the classical molecular kinetic description-whereby the discrete and/or stochastic nature of reaction events conspires to drive the characteristic behavior of the system substantially away from that predicted by classical kinetics.Notably, we demonstrate that although deviant effects may be stochastic in origin, this is by no means a requirement. The behavior of the system might be accurately characterized by a deterministic formalism, albeit not by CCK. In particular, although CCK dynamics is at times casually interpreted as describing the evolution of CME averages-this is only strictly accurate for purely linear (unimolecular and consta...

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