A growing string method for determining transition states: comparison to the nudged elastic band and string methods

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.     

Adapting the nudged elastic band method for determining minimum-energy paths of chemical reactions in enzymes

Optimization of reaction paths for enzymatic systems is a challenging problem because such systems have a very large number of degrees of freedom and many of these degrees are flexible. To meet this challenge, an efficient, robust and general approach is presented based on the well-known nudged elastic band reaction path optimization method with the following extensions: (1) soft spectator degrees of freedom are excluded from path definitions by using only inter-atomic distances corresponding to forming/breaking bonds in a reaction; (2) a general transformation of the distances is defined to treat multistep reactions without knowing the partitioning of steps in advance; (3) a multistage strategy, in which path optimizations are carried out for reference systems with gradually decreasing rigidity, is developed to maximize the opportunity of obtaining continuously changing environments along the path. We demonstrate the applicability of the approach using the acylation reaction of type A beta-lactamase as an example. The reaction mechanism investigated involves four elementary reaction steps, eight forming/breaking bonds. We obtained a continuous minimum energy path without any assumption on reaction coordinates, or on the possible sequence or the concertedness of chemical events. We expect our approach to have general applicability in the modeling of enzymatic reactions with quantum mechanical/molecular mechanical models.     

A doubly nudged elastic band method for finding transition states

A modification of the nudged elastic band (NEB) method is presented that enables stable optimizations to be run using both the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton and slow-response quenched velocity Verlet minimizers. The performance of this new "doubly nudged" DNEB method is analyzed in conjunction with both minimizers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to 2 orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.     

A comment to the nudged elastic band method

The minimum energy path (MEP) is an important reaction path concept of theoretical chemistry, and the nudged elastic band (NEB) method with its many facets is a central method to determine the MEP. We demonstrate in this comment that the NEB does not have to lead to a steepest descent pathway (as always assumed). In contrast, as long as it is used without spring forces, it can lead to a gradient extremal. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A simple apparatus for rapidly initiating spectrophotometrically monitored enzymatic reactions

A relatively simple and inexpensive apparatus is described for rapidly initiating spectrophotometrically monitored reactions by adding a reagent to the cuvette without opening the sample chamber of the spectrophotometer. The apparatus allows the recording of initial reaction rate data within 2 sec after initiating the reaction.     

Reflectometry in kinetic studies of immunological and enzymatic reactions on solid surfaces

An optical method is described, by means of which immunological and enzymatic reactions can be followed at a primary level on a solid surface, without labelling procedures. When plane-polarized light is reflected at a solid surface, there is a minimum in reflectance at a certain angle of incidence, the pseudo-Brewster angle. For example, a layer of protein adsorbed on a silicon surface increases the reflectance with increasing amount of adsorbed material. High sensitivity is obtained because of the large difference in refractive index between silicon and organic material; about 0.1 μg cm^?2 adsorbed protein can be detected. In a model system of human IgG and anti-human IgG, the primary adsorption of IgG on a hydrophobic surface is first measured, and on this IgG-coated surface the binding kinetics of anti-IgG could be measured. The kinetics of proteolytic degradation of IgG-coated surfaces by trypsin was also investigated.     

Model for solvent viscosity effect on enzymatic reactions

The solvent viscosity dependence for enzymatic reactions is discussed. We suggest the interpretation of the phenomenon that requires neither a modification of the Kramers’ theory nor that of the Stokes law. We assume that an enzyme solution is an ensemble of samples with different values of the viscosity for the movement of the system along the reaction coordinate. We quantify the extent of this difference by some parameter, introduce heterogeneity in our system with the help of a distribution over this parameter and find the solution of the integral equation for the function of the distribution. All parameters of the model are related to experimentally observable values. The meaning of fractional exponents appears to be the characteristic for the behavior of the distribution. Our approach yields the existence of the limit value for the fractional power exponent with the decrease of cosolvent molecular weight in agreement with known experimental data.     

Query generation to search for inhibitors of enzymatic reactions

A method for the generation of intermediates of enzyme-catalyzed reactions is presented. These intermediates can be used as three-dimensional structural queries for searching for inhibitors of enzymatic reactions. The intermediates can be considered as being structurally quite close to transition-state analogues. For this application, a database containing detailed chemical information on metabolic reactions is used. The likely three-dimensional structure of the intermediates of enzyme-catalyzed reactions can be generated from the information in the database. For three reactions catalyzed by the enzymes AMP deaminase (EC code 3.5.4.6), triose phosphate isomerase (EC code 5.3.1.1), and arginase II (EC code 3.5.3.1), we show how a 3D model of these intermediates can be superimposed onto known inhibitors of these enzymes by a program that uses a genetic algorithm. For this, we test different methods for the superimposition using information on the enzymatic binding site, using information on physicochemical properties calculated from the molecular structure, or without having any information in the superimposition process. We show that these inhibitors are most similar to the corresponding intermediates regarding the 3D structure.     

Computational modeling of enzymatic keto-enol isomerization reactions

Catalysis of proton abstraction from nonacidic carbon atoms adjacent to a carbonyl or carboxylate group is a fundamental reaction in enzymology that has been extensively studied during the last few decades. Enzymes catalyzing these reactions, which normally involve labile enolic intermediates, need to overcome large pK _a differences between the reacting groups as well as high intrinsic free-energy barriers. Here, we present an overview of results from recent computer simulation studies of keto-enol isomerization reactions catalyzed by the enzymes glyoxalase I, triosephopsphate isomerase and ketosteroid isomerase. For all three enzymes it is found that electrostatic stabilization of the transient enolate intermediates, either by charge–charge interactions or by hydrogen bonding, accounts for the main part of the activation free-energy barrier reduction. Another catalytic effect observed in all cases is the reduction of the reorganization energy by the enzyme active site. Some other factors that have been proposed to be important for these reactions are also discussed and evaluated. Received: 3 January 2002 / Accepted: 13 May 2002 / Published online: 29 July 2002     

Statistical modeling of effective elastic modulus for multiphased hybrid composites

We explored the effective elastic moduli of hybrid composites by using different statistical models to understand and analyze the effect of fiber length distribution (FLD) on the mechanical properties. Micro-CT was used to investigate the internal structure of the hybrid composites, and FLD was calculated via image-processing for the composite samples. The interaction between inclusions and matrix was considered using a perturbed stress-strain theory. Statistical modeling with the Weibull, Log-normal and Generalized Extreme Value (GEV) functions was carried out to understand the role of skewness. The results show that different skewness and FLD have significant impacts on the effective elastic moduli of the hybrid composites, which demonstrates the practical importance of statistical modeling when evaluating and analyzing the their mechanical properties.     

Construction of coacervate-in-coacervate multi-compartment protocells for spatial organization of enzymatic reactions

Coacervate microdroplets, formed via liquid–liquid phase separation, have been extensively explored as a compartment model for the construction of artificial cells or organelles. In this study, coacervate-in-coacervate multi-compartment protocells were constructed using four polyelectrolytes, in which carboxymethyl-dextran and diethylaminoethyl-dextran were deposited on the surface of as-prepared polydiallyldimethyl ammonium/deoxyribonucleic acid coacervate microdroplets through layer-by-layer assembly. The resulting multi-compartment protocells were composed from two immiscible coacervate phases with distinct physical and chemical properties. Molecule transport experiments indicated that small molecules could diffuse between two coacervate phases and that macromolecular enzymes could be retained. Furthermore, a competitive cascade enzymatic reaction of glucose oxidase/horseradish peroxidase–catalase was performed in the multi-compartment protocells. The different enzyme organization and productions of H₂O₂ led to a distinct polymerization of dopamine. The spatial organization of different enzymes in immiscible coacervate phases, the distinct reaction fluxes between coacervate phases, and the enzymatic cascade network led to distinguishable signal generation and product outputs. The development of this multi-compartment structure could pave the way toward the spatial organization of multi-enzyme cascades and provide new ideas for the design of organelle-containing artificial cells.

A coacervate-in-coacervate micro-architecture is constructed as a multi-compartment protocell model, in which a multi-enzyme cascade is spatially organized for competitive enzymatic reactions.     

Facilitating enzymatic reactions by using ionic liquids: A mini review

1. Download : Download high-res image (297KB)
2. Download : Download full-size image

     

Determination of kinetic parameters for interfacial enzymatic reactions on self-assembled monolayers

This paper reports a method to characterize the kinetic constants for the action of enzymes on immobilized substrates. This example uses cutinase, a serine esterase that hydrolyzes 4-hydroxyphenyl valerate moieties that are immobilized on a self-assembled monolayer of alkanethiolates on gold. The product of the enzyme reaction is a hydroquinone, which is redox active and therefore permits the use of cyclic voltammetry to monitor the extent of reaction in situ. A kinetic model based on the Michaelis-Menten formalism is used to analyze the dependence of initial rates of reaction on both the substrate density and the enzyme concentration. The resulting value of k(cat)/K(M) for the interfacial reaction is comparable to that for a homogeneous phase reaction with a substrate of similar structure. This strategy of using monolayers presenting substrates for the enzyme and cyclic voltammetry to measure reaction rates provides quantitative and real-time information on reaction rates and permits a level of analysis of interfacial enzyme reactions that to date has been difficult to realize.