Biological Implications of Dynamical Phases in Non-equilibrium Networks

Abstract

Biology achieves novel functions like error correction, ultra-sensitivity and accurate concentration measurement at the expense of free energy through Maxwell Demon-like mechanisms. The design principles and free energy trade-offs have been studied for a variety of such mechanisms. In this review, we emphasize a perspective based on dynamical phases that can explain commonalities shared by these mechanisms. Dynamical phases are defined by typical trajectories executed by nonequilibrium systems in the space of internal states. We find that coexistence of dynamical phases can have dramatic consequences for function vs free energy cost trade-offs. Dynamical phases can also provide an intuitive picture of the design principles behind such biological Maxwell Demons.

Topologically protected modes in non-equilibrium stochastic systems

“…An intuitive way to understand proofreading is through localization (Fig. 6); despite substrates R and W having very similar kinetics when binding with an enzyme E , reactions with desired substrate R should be localized near products, while reactions with W should be localized near reactants1425. In contrast, our results on topological protection provide a simple necessary and sufficient condition for efficient proofreading.…”

“…An intuitive way to understand proofreading is through localization (Fig. 6); despite substrates R and W having very similar kinetics when binding with an enzyme E, reactions with desired substrate R should be localized near products while reactions with W should be localized near reactants [12,20]. Previous literature has investigated many differing models and assumptions on the kinetics of R and W and driving forces that lead to differing localization and hence proofreading [1,12,21,22].…”

Topological localization in out-of-equilibrium dissipative systems

“…As discussed in Ref. [23], the spatial connectivity and structure of this Markov state network resembles that of networks routinely used to study adaptation [4], kinetic proofreading [26,27], and cell signal sensing [28]. These and other Markov state representations of biophysical processes can often be decomposed into bulk like subgraphs stitched together by interfaces as indicated in Fig.…”

Reaction-Path Statistical Mechanics of Enzymatic Kinetics

“…where |p(t) = p S (t) |S + p C (t) |C + p P (t) |P involves all possible stochastic paths in the time interval (0, τ obs ). Therefore, we can decompose the propagator into the operators of conditional probabilities for unbinding events K, U(τ obs ) = K P(K|τ obs ), and the corre- Recent studies have reported that the probability density of dynamic events may show a multi-modal behavior, which signifies more than two dynamical phases in systems exhibiting heterogeneous or glassy dynamics [8][9][10][11][12][13][14][15][16]43 . Similarly, the Michaelis-Menten mechanism displays heterogeneous kinetics in its unbinding events and results in the inactive (unbinding-poor)…”

“…This idea provides a concrete theoretical framework that is beneficial for considering numerous systems under equilibrium or near-equilibrium conditions, whereas the thermodynamic ensemble approach is potentially invalid in far-from-equilibrium systems in which Boltzmann's postulate of ergodicity does not hold 4,5 . However, the recent advances in nonequilibrium statistical mechanics introduced a framework 3,6,7 , which poses a significant potential for enabling a comprehensive understanding of out-of-equilibrium systems via the same mathematical formalism as the thermodynamic ensemble approach [7][8][9][10][11][12][13][14][15][16] . The construction of the dynamic ensemble as a collection of nonequilibrium trajectories (or paths) enables the calculation of out-of-equilibrium properties such as the number of dynamic events in a given system, for instance, glass-forming liquids 9,10 , spin-facilitated systems 8,12,17,18 , kinetic networks 13,14 , and protein-folding pathways 11 .…”