Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

Abstract

Stochastic effects in biomolecular systems have now been recognized as a major physiologically and evolutionarily important factor in the development and function of many living organisms. Nevertheless, they are often thought of as providing only moderate refinements to the behaviors otherwise predicted by the classical deterministic system description. In this work we show by using both analytical and numerical investigation that at least in one ubiquitous class of (bio)chemical-reaction mechanisms, enzymatic futile cycles, the external noise may induce a bistable oscillatory (dynamic switching) behavior that is both quantitatively and qualitatively different from what is predicted or possible deterministically. We further demonstrate that the noise required to produce these distinct properties can itself be caused by a set of auxiliary chemical reactions, making it feasible for biological systems of sufficient complexity to generate such behavior internally. This new stochastic dynamics then serves to confer additional functional modalities on the enzymatic futile cycle mechanism that include stochastic amplification and signaling, the characteristics of which could be controlled by both the type and parameters of the driving noise. Hence, such noise-induced phenomena may, among other roles, potentially offer a novel type of control mechanism in pathways that contain these cycles and the like units. In particular, observations of endogenous or externally driven noiseinduced dynamics in regulatory networks may thus provide additional insight into their topology, structure, and kinetics.network motif ͉ signal transduction ͉ chemical reaction ͉ synthetic biology ͉ systems biology

Deviant effects in molecular reaction pathways

“…Importantly, as local dynamics can then propagate through biomolecular networks-for example, via signal transduction pathways [26][27][28][29][30][31] , potentially expressing themselves in species that are otherwise directly involved only in strictly classical kinetics-the presence of just one such mechanism within a larger biological process may lead to a variety of system-wide nonclassical behavior modes 22,[32][33][34][35][36][37][38][39][40] . Given such potentially global implications of locally deviant pathway dynamics, we hope that this work may offer biologists involved with kinetic analysis or molecular modeling additional tools and intuition to help decide whether their work requires the use of discrete and stochastic chemical master equation-based methods or whether the simpler classical chemical kinetics framework is sufficient.…”

“…Namely, the futile cycle always exhibits monostable substrate/product levels if stationary behavior of the enzymes is described using CCK (distribution modes). However, if it is examined using nonclassical analysis (whether Langevin or CME), this mechanism could be observed to display stochastic oscillations in product/substrate levels-doing so without any additional feedback/ forward mechanisms and manifestly due to the enzyme activity being stochastically governed by a (unimodal) probability distribution, rather than fixed at the mode 22 .…”

Amplification and Detection of Single-Molecule Conformational Fluctuation through a Protein Interaction Network with Bimodal Distributions

“…[29,37,41,42,43,44,45] In eukaryotic transcription, a gene may be turned on and off through binding and dissociation of a regulating protein, which may result in bimodal distribution of the expressed protein level. The process is mathematically equivalent to the problem we discussed here.…”

“…Therefore, in this limit one can represent overall concentration of the enzymes as (cf. with equation S8 in [29])…”

“…(7). Hence, only when the switching rates α and β are fast (i.e., no dynamic disorder) the white noise approximation used in reference [29] is expected to work well, since in this case exponential decay of the correlation function can be safely replaced by δ-function. Recently Warmflash et .al also discussed the legitimacy of using the δ-function approximation [39].…”