Propensity approach to nonequilibrium thermodynamics of a chemical reaction network: controlling single E-coli β-galactosidase enzyme catalysis through the elementary reaction steps.
26 Dec 2013-Journal of Chemical Physics (American Institute of Physics)-Vol. 139, Iss: 24, pp 244104-244104
TL;DR: This work develops an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the elementary reaction propensities, and thoroughly analyzes the temporal as well as the steady state behavior of various thermodynamic quantities for each elementary reaction.
Abstract: In this work, we develop an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the elementary reaction propensities. The method is akin to the microscopic formulation of the dissipation function in terms of the Kullback-Leibler distance of phase space trajectories in Hamiltonian system. The formalism is applied to a single oligomeric enzyme kinetics at chemiostatic condition that leads the reaction system to a nonequilibrium steady state, characterized by a positive total entropy production rate. Analytical expressions are derived, relating the individual reaction contributions towards the total entropy production rate with experimentally measurable reaction velocity. Taking a real case of Escherichia coli β-galactosidase enzyme obeying Michaelis-Menten kinetics, we thoroughly analyze the temporal as well as the steady state behavior of various thermodynamic quantities for each elementary reaction. This gives a useful insight in the relative magnitudes of various energy terms and the dissipated heat to sustain a steady state of the reaction system operating far-from-equilibrium. It is also observed that, the reaction is entropy-driven at low substrate concentration and becomes energy-driven as the substrate concentration rises.
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TL;DR: A simple theory is developed which predicts that certain classes of enzyme pathways can be distinguished by studying the turnover rate, V, as a function of substrate concentration, [S], and it is found to depend sensitively on the manner in which substrate molecules in the bath are replenished.
Abstract: The ability to dynamically probe single enzymes allows the experimental investigation of enzyme kinetics with unprecedented resolution. In this paper we develop a simple theory which predicts that certain classes of enzyme pathways can be distinguished by studying the turnover rate, V, as a function of substrate concentration, [S]. In particular, we study the steady state of a single enzyme interacting with a bath of substrate molecules, and analyse it as a stochastic process. The V([S]) relation is found to depend sensitively on the manner in which substrate molecules in the bath are replenished. We focus on a gedanken experiment in which the average substrate concentration is kept fixed by allowing molecules to enter the bath at a constant rate. We derive the exact relationship between V and [S], which has a relatively simple form, though different to that of the Michaelis–Menten (MM) equation. Interestingly, the MM equation is exactly recovered if the substrate concentration is instantaneously maintained with molecular precision. We examine the new V([S]) relation for a number of enzyme pathways and find that it differentiates between enzyme reactions involving one or many intermediate enzyme–substrate complexes. This, in principle, allows one to probe the internal conformations of enzymes by careful measurement of V([S]) curves in appropriately designed single enzyme experiments.
19 citations
TL;DR: Dissipation plays a guiding role in the optimization of the catalytic rate in the tRNA selection network of protein synthesis, and the network tends to maximize both the EPR and catalytic rates, but not the accuracy.
Abstract: Major biological polymerization processes achieve remarkable accuracy while operating out of thermodynamic equilibrium by utilizing the mechanism known as kinetic proofreading. Here, we study the interplay of the thermodynamic and kinetic aspects of proofreading by exploring the dissipation and catalytic rate, respectively, under the realistic constraint of fixed chemical potential difference. Theoretical analyses reveal no-monotonic variations of the catalytic rate and total entropy production rate (EPR), the latter quantifying the dissipation, at steady state. Applying this finding to a tRNA selection network in protein synthesis, we observe that the network tends to maximize both the EPR and catalytic rate, but not the accuracy. Simultaneously, the system tries to minimize the ratio of the EPRs due to the proofreading steps and the catalytic steps. Therefore, dissipation plays a guiding role in the optimization of the catalytic rate in the tRNA selection network of protein synthesis.
6 citations
TL;DR: Using some special properties of the Legendre transformation, here, a relation between the fluctuations of fluxes and dissipation rates is provided, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuations in the dissipation rate is yet to be characterized for small systems.
Abstract: In the framework of large deviation theory, we have characterized nonequilibrium turnover statistics of enzyme catalysis in a chemiostatic flow with externally controllable parameters, like substrate injection rate and mechanical force. In the kinetics of the process, we have shown the fluctuation theorems in terms of the symmetry of the scaled cumulant generating function (SCGF) in the transient and steady state regime and a similar symmetry rule is reflected in a large deviation rate function (LDRF) as a property of the dissipation rate through boundaries. Large deviation theory also gives the thermodynamic force of a nonequilibrium steady state, as is usually recorded experimentally by a single molecule technique, which plays a key role responsible for the dynamical symmetry of the SCGF and LDRF. Using some special properties of the Legendre transformation, here, we have provided a relation between the fluctuations of fluxes and dissipation rates, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuation in the dissipation rate is yet to be characterized for small systems. Such an enzymatic reaction flow system can be a very good testing ground to systematically understand the rare events from the large deviation theory which is beyond fluctuation theorem and central limit theorem.
3 citations
03 Sep 2015
TL;DR: In this paper, an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of individual elementary reactions and corresponding reverse reactions is introduced.
Abstract: We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction.
2 citations
TL;DR: In this article, entropy change along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium entropy, and the total entropy change obeys an integral fluctuation theorem and a class of further exact relations.
Abstract: Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the surrounding medium. Within a Langevin dynamics, a unique identification of these two contributions is possible. The total entropy change obeys an integral fluctuation theorem and a class of further exact relations, which we prove for arbitrarily coupled slow degrees of freedom including hydrodynamic interactions. These theoretical results can therefore also be applied to driven colloidal systems. For transitions between different internal conformations of a biomolecule involving unbalanced chemical reactions, we provide a thermodynamically consistent formulation and identify again the two sources of entropy production, which obey similar exact relations. We clarify the particular role degenerate states have in such a description.
1 citations
References
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TL;DR: The results show that it is possible successfully to study non-viral protein crystals with unit cell dimensions in excess of 500 Å and with relative molecular masses in the region of 2,000K per asymmetric unit and non-crystallographic symmetry averaging proved to be a very powerful tool in the structure determination.
Abstract: The beta-galactosidase from Escherichia coli was instrumental in the development of the operon model, and today is one of the most commonly used enzymes in molecular biology. Here we report the structure of this protein and show that it is a tetramer with 222-point symmetry. The 1,023-amino-acid polypeptide chain folds into five sequential domains, with an extended segment at the amino terminus. The participation of this amino-terminal segment in a subunit interface, coupled with the observation that each active site is made up of elements from two different subunits, provides a structural rationale for the phenomenon of alpha-complementation. The structure represents the longest polypeptide chain for which an atomic structure has been determined. Our results show that it is possible successfully to study non-viral protein crystals with unit cell dimensions in excess of 500 A and with relative molecular masses in the region of 2,000K per asymmetric unit. Non-crystallographic symmetry averaging proved to be a very powerful tool in the structure determination, as has been shown in other contexts.
557 citations
TL;DR: It is shown that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by =W-DeltaF=kTD(rho||rho[ over ])=kT, where rho and rho[over ] are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process.
Abstract: We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by $⟨{W}_{\mathrm{diss}}⟩=⟨W⟩\ensuremath{-}\ensuremath{\Delta}F=kTD(\ensuremath{\rho}\ensuremath{\parallel}\stackrel{\texttildelow{}}{\ensuremath{\rho}})=kT⟨\mathrm{ln} (\ensuremath{\rho}/\stackrel{\texttildelow{}}{\ensuremath{\rho}})⟩$, where $\ensuremath{\rho}$ and $\stackrel{\texttildelow{}}{\ensuremath{\rho}}$ are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. $D(\ensuremath{\rho}\ensuremath{\parallel}\stackrel{\texttildelow{}}{\ensuremath{\rho}})$ is the relative entropy of $\ensuremath{\rho}$ versus $\stackrel{\texttildelow{}}{\ensuremath{\rho}}$. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations.
410 citations
TL;DR: It is shown that each of them, the total, the adiabatic, and the nonadiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.
Abstract: The total entropy production of a trajectory can be split into an adiabatic and a nonadiabatic contribution, deriving, respectively, from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic, and the nonadiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.
364 citations
TL;DR: A formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints and furthermore driven by external time-dependent forces is proposed, leading to a splitting of the second law leading to three second-law-like relations.
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TL;DR: This review presents an overview of a statistical thermodynamic treatment for such systems, with examples from several key components in cellular signal transduction from open-system nonequilibrium steady-state (NESS) models.
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270 citations