Effects of nonproductive binding on the kinetics of enzymatic reactions with patterned substrates

Existing models of ligand-receptor binding kinetics suggest that clustering surface-associated molecules tends to decrease the rates with which solution phase molecules associate and dissociate. Here, the authors use kinetic Monte Carlo simulations to study the case of an enzyme catalyzing the turnover of substrate molecules immobilized on a surface. The simulations reveal a crossover in the overall reaction rates for randomly distributed and clustered substrate molecules as the enzyme unbinding rate is varied. Approximate expressions for the effective kinetic parameters are introduced, and they show that the observed behavior derives from sequestration of the enzyme in the strong-sticking limit.     

Entropic estimate of cooperative binding of substrate on a single oligomeric enzyme: an index of cooperativity

Here we have systematically studied the cooperative binding of substrate molecules on the active sites of a single oligomeric enzyme in a chemiostatic condition. The average number of bound substrate and the net velocity of the enzyme catalyzed reaction are studied by the formulation of stochastic master equation for the cooperative binding classified here as spatial and temporal. We have estimated the entropy production for the cooperative binding schemes based on single trajectory analysis using a kinetic Monte Carlo technique. It is found that the total as well as the medium entropy production shows the same generic diagnostic signature for detecting the cooperativity, usually characterized in terms of the net velocity of the reaction. This feature is also found to be valid for the total entropy production rate at the non-equilibrium steady state. We have introduced an index of cooperativity, C, defined in terms of the ratio of the surprisals or equivalently, the stochastic system entropy associated with the fully bound state of the cooperative and non-cooperative cases. The criteria of cooperativity in terms of C is compared with that of the Hill coefficient of some relevant experimental result and gives a microscopic insight on the mechanism of cooperative binding of substrate on a single oligomeric enzyme which is usually estimated from the macroscopic reaction rate.     

The effective concentration of unbound ink anchors at the molecular printboard

Self-assembled monolayers terminating in beta-cyclodextrin cavities can be used to bind ink molecules and so provide a molecular printboard for nanopatterning applications. Multivalent or multisite binding strengthens the attachment of large inks and provides more robust patterns. In the present work we use computer simulations to probe the behavior of functionalized dendrimer inks at the printboard. We performed a series of long 10 ns fully atomistic molecular dynamics (MD) simulations to measure the effective local concentration of unbound ink anchor groups at the printboard for a variety of binding modes and also for the partial unbinding prerequisite for ink diffusion on the printboard. These simulations allow us to describe the conformational space occupied by partially bound inks and estimate the likelihood of an additional binding interaction. Furthermore, by simulating the shift from a divalent to monovalent binding mode we show that the released anchor quickly moves to the periphery of the dendrimer binding hemisphere but then reapproaches the printboard and remains in the vicinity of alternative binding sites. Secondary electrostatic interactions between the protonated dendrimer core and hydroxyl groups at the entrance to the beta-cyclodextrin cavities give "flattened" dendrimer binding orientations and may aid dendrimer diffusion on the printboard, allowing the dendrimer to "walk" along the printboard by switching between different partially bound states and minimizing complete unbinding to bulk solution, crucial for the application of the printboard in, for example, medical diagnostics.     

An analytical approach to solutions of master equations for stochastic nonlinear reactions

In this paper we consider a class of nonlinear reactions which are important in stochastic reaction networks. We find the exact solution of the chemical master equation for a class of irreversible and reversible nonlinear reactions. We also present the explicit form of the equilibrium probability solution of the reactions. The results can be used for analyzing stochastic dynamics of important reactions such as binding/unbinding reaction and protein dimerization.     

Stochastic dynamics of complexation reaction in the limit of small numbers

We study stochastic dynamics of the non-linear bimolecular reaction A + B?AB. These reactions are common in several bio-molecular systems such as binding, complexation, protein multimerization to name a few. We use master equation to compute the full distribution of several stochastic equilibrium properties such as number of complexes formed (N(c)), equilibrium constant (K). We provide exact analytical and simpler approximate expression for equilibrium fluctuation quantities to quickly estimate the amount of noise as a function of reactant molecules and rates. We construct the phase diagram for a fluctuational quantity f, defined as the ratio of standard deviation to average (f=√(ΔN(c))(2)/N(c)), as a function of different number of reactant molecules and reaction rates. One of the striking result is, it is possible to have f as high as 45% or higher in significant regions of the phase diagram even when number of reactants involved are around 20-40, typical in biology. Our finding indicates studying averages alone using mass action law needs careful scrutiny. We also outline possible application of our findings in gene expression. Furthermore, we compute average and fluctuation properties of time dependent quantities and derive equations of motion for different moments such as N(c)(t) and N(c)(t)(2). While mean-field mass action law fails to reproduce the exact time dependence, approximate solutions of coupled equations of motions for different moments, capturing fluctuation, is in good agreement with exact results. This may be a way to compute time development of averages and fluctuations in such non-linear systems where mass action law breaks down. Moreover, for this reaction, we outline connection to variational principle of maximum caliber and other more traditional approaches such as chemical Langevin equation. We derive noise statistics for the equivalent Langevin equation and show possible departure from Gaussian white noise. We believe quantitative estimates of phase diagrams for noise, time dependent quantities, and simple analytical expression for equilibrium quantities will be particularly useful to guide experiments involving such non-linear reactions with small numbers of reactants that are often encountered in biology.     

Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.     

Stereoselection in the diels–alderase ribozyme: A molecular dynamics study

The Diels‐Alderase ribozyme is an in vitro‐evolved ribonucleic acid enzyme that catalyzes a [4 + 2] cycloaddition reaction between an anthracene diene and a maleimide dienophile. The ribozyme can in principle be used to selectively synthesize only one product enantiomer, depending on which of the two entrances to the catalytic pocket, “front” or “back”, the substrate is permitted to use. Here, we investigate stereoselection and substrate recognition in the ribozyme by means of multiple molecular dynamics simulations, performed on each of the two substrates individually in the pocket, on the reactant state, and on the product state. The results are consistent with a binding mechanism in which the maleimide likely binds first followed by the anthracene, which enters preferentially through the front door. The free energy profiles for anthracene binding indicate that the pre‐(R,R)‐enantiomer conformation is slightly preferred, in agreement with the experimentally observed small enantiomeric excess of the (R,R)‐enantiomer of the product. The reactant state is stabilized by the simultaneous presence of both substrates bound to their binding sites in the hydrophobic pocket as well as by stacking interactions between them. © 2012 Wiley Periodicals, Inc.     

苯磺酰胺从碳酸酐酶II中脱离过程的分子动力学模拟

综合运用分子动力学模拟和自由能计算方法研究了苯磺酰胺分子从碳酸酐酶II (CA II)的活性位点脱离过程中底物与酶之间的动态相互作用. 脱离过程的平均力势(PMF)显示, 底物脱离时存在一个特殊的结合状态. 其中, 静电相互作用占据了主导地位. 轨迹分析显示, 除了金属离子的配位作用之外, 底物脱离路径上的关键残基Leu198、Thr199和Thr200通过与底物磺胺基的氢键作用阻碍了底物从酶中的脱离. 当前的研究对于深入认识磺胺类药物与CA II的详细结合过程和相关的药物改良与设计具有重要的指导意义.     

A Strong Positive Allosteric Effect in the Molecular Recognition of Dicarboxylic Acids by a Cerium(IV) Bis[tetrakis(4-pyridyl)porphyrinate] Double Decker

With increasing number of bound dicarboxylic acid molecules , the binding of further molecules by the title compound becomes more favorable (a 1:4 complex is depicted schematically on the right). The association constant for binding of the first guest molecule is small, since the increase in Gibbs free energy due to binding is outweighed by the energy loss asssociated with the suppression of rotation of the porphyrin rings. Once rotation has been suppressed, further guest molecules can be more effectively bound (positive allosteric effect).     

Molecular Separation Barriers and Their Application to Catalytic Reactor Design

The use of semipermeable membranes for multicomponent separations based on molecular size has long been recognized. In certain applications, however, it is often desirable not to effect a separation of chemical constituents, but to sustain a separation which already exists. As an example, the efficient and economical design of a. chemical reactor using an enzyme as a catalyst depends on the accessibility of the reactant to the catalyst as well as on the degree to which a physical separation between the enzyme and the reactor product stream is maintained. A particularly simple and attractive means of achieving this is through the use of semipermeable asymmetric hollow fiber membranes. For example, by sequestering an enzyme solution within the annular macroporous support regions of an asymmetric hollow fiber, a physical separation between enzyme and a reactant solution flowing through the fiber lumen is achieved. In this way, small reactant molecules are free to diffuse across the ultrathin membrane skin into the opencell support structure where reaction will occur. Product molecules will diffuse back into the lumen, and a compact chemical reactor results. The operating behavior of this type of catalytic reactor will be described and its application to the hydrolysis of o-nitro-phenyl-B-d-galactopyranoside and of lactose is discussed.     

A theoretical analysis of rate constants and kinetic isotope effects corresponding to different reactant valleys in lactate dehydrogenase

In some enzymatic systems large conformational changes are coupled to the chemical step, in such a way that dispersion of rate constants can be observed in single-molecule experiments, each corresponding to the reaction from a different reactant valley. Under this perspective here we present a computational study of pyruvate to lactate transformation catalyzed by lactate dehydrogenase. The reaction consists of a hydride transfer and a proton transfer that seem to take place concertedly. The degree of asynchronicity and the energy barrier depend on the particular starting reactant valley. In order to estimate rate constants we used a free energy perturbation technique adapted to follow the intrinsic reaction coordinate for several possible reaction paths. Tunneling effects are also obtained with a slightly modified version of the ensemble-averaged variational transition state theory with multidimensional tunneling contributions. According to our results the closure of the active site by means of a flexible loop can lead to the formation of different reactant complexes displaying different features in the disposition of some key residues (such as Arg109), interactions with the substrate and number of water molecules in the active site. The chemical step of the reaction takes place with a different reaction rate from each of these complexes. Finally, primary kinetic isotope effects for replacement of the transferring hydrogen of the cofactor with a deuteride are in good agreement with experimental observations, thus validating our methodology.