A probabilistic framework for the exploration of enzymatic capabilities based on feasible kinetics and control analysis

BackgroundAnalysis of limiting steps within enzyme-catalyzed reactions is fundamental to understand their behavior and regulation. Methods capable of unravelling control properties and exploring kinetic capabilities of enzymatic reactions would be particularly useful for protein and metabolic engineering. While single-enzyme control analysis formalism has previously been applied to well-studied enzymatic mechanisms, broader application of this formalism is limited in practice by the limited amount of kinetic data and the difficulty of describing complex allosteric mechanisms.MethodsTo overcome these limitations, we present here a probabilistic framework enabling control analysis of previously unexplored mechanisms under uncertainty. By combining a thermodynamically consistent parameterization with an efficient Sequential Monte Carlo sampler embedded in a Bayesian setting, this framework yields insights into the capabilities of enzyme-catalyzed reactions with modest kinetic information, provided that the catalytic mechanism and a thermodynamic reference point are defined.ResultsThe framework was used to unravel the impact of thermodynamic affinity, substrate saturation levels and effector concentrations on the flux control and response coefficients of a diverse set of enzymatic reactions.ConclusionsOur results highlight the importance of the metabolic context in the control analysis of isolated enzymes as well as the use of statistically sound methods for their interpretation.General SignificanceThis framework significantly expands our current capabilities for unravelling the control properties of general reaction kinetics with limited amount of information. This framework will be useful for both theoreticians and experimentalists in the field.     

A simple method to determine the enantiomeric ratio in enantioselective biocatalysis

The enantiomeric ratio (E) is commonly used to characterize the enantioselectivity in enzyme-catalyzed kinetic resolution. In this paper this parameter is directly derived from the enantiomeric excess of substrate and product. This is formally more correct than using Chen's equation after calculating the degree of conversion from both ee values using the relation of Sih and Wu. New expressions and useful graphs have been generated for reversible and irreversible uni-uni reactions. The theoretical predictions have been verified experimentally for various reactions. Values for E and the thermodynamic equilibrium constant,K_EQ, were obtained for a ( -dehalogenase-catalyzed dehalogenation, a hydrolysis reaction by porcine pancreatic lipase, and for C. Cylindracea lipase-catalyzed esterification and transesterification. In view of the current developments in the field of chiral analysis, this method is an easily available tool in the quantitative treatment of enzyme-catalyzed resolution of enantiomers.     

Monitoring enzyme catalysis with mass spectrometry

Mass spectrometry is a rapid, sensitive, and accurate quantitative approach for the direct monitoring of enzyme-catalyzed reactions that does not require a chromophore or radiolabeling and thus provides a viable alternative to existing analytical techniques. In this study the proteolysis of intact viral capsid proteins, the alpha-glucosidase-catalyzed hydrolysis of p-nitrophenyl-alpha-glucopyranoside and the lipoprotein lipase-catalyzed ester hydrolysis of resorufin were examined. Matrix-assisted laser desorption/ionization and electrospray ionization mass spectrometry were used to examine the proteolysis of viral protein capsids, providing information about capsid dynamics and the stabilizing force of viral protein/RNA interactions. In addition, k(cat) and K(m) values of enzyme-catalyzed hydrolysis were obtained (without the use of a chromophore). These results also demonstrate the effect an unnatural substrate can have on enzyme activity. Overall, mass spectrometry provides for efficient and quantitative analysis of enzyme-catalyzed reactions, as well as the direct observation of reaction dynamics.     

Thermodynamics of the reactions of carbamoyl phosphate

Two measurements of equilibrium constants by Marshall and Cohen make it possible to calculate standard Gibbs energies of formation of the species of carbamate and carbamoyl phosphate. Carbamate formation from carbon dioxide and ammonia does not require an enzyme, and the equilibrium concentrations of carbamate in ammonium bicarbonate are calculated. Knowing the values of standard Gibbs energies of formation of species of carbamate and carbamoyl phosphate make it possible to calculate the dependencies of the standard transformed Gibbs energies of formation of these reactants on pH and ionic strength and to calculate apparent equilibrium constants for several enzyme-catalyzed reactions and several chemical reactions. These calculations are sufficiently complicated that computer programs in Mathematica are used to make tables and plots. The dependences of apparent equilibrium constants on pH are consequences of the production or consumption of hydrogen ions, which are shown in plots. As usual the increase in the number of enzyme-catalyzed reactions for which apparent equilibrium constants can be calculated is larger than the number of reactions required to obtain the thermodynamic properties of the species involved.     

Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry

BackgroundIsothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data.Scope of reviewThis article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions.Major conclusionsA complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error.General significanceMethods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Standard apparent reduction potentials of biochemical half reactions and thermodynamic data on the species involved

Standard apparent reduction potentials E' degrees of half reactions of enzyme-catalyzed reactions are useful because they provide a global view of the apparent equilibrium constants of redox reactions. A table of E' degrees at a specified pH shows at a glance whether a given half reaction will drive another half reaction or be driven by it. This table can be used to calculate apparent equilibrium constants. Standard Gibbs energies of formation of species in a half reaction can be used to calculate E' degrees values at pHs in the range 5-9 and ionic strengths in the range of 0-0.35 M. My previously published values of E' degrees values for 42 half reactions has been extended by 22 new E' degrees values in this paper. When DeltafG degrees and DeltafH degrees are both known for all the species in an enzyme-catalyzed reaction at 298.15 K, it is possible to calculate all the standard transformed thermodynamic properties of the reaction over a range of pHs, ionic strengths, and temperatures.     

Simultaneous determination of thermodynamic and kinetic data by isothermal titration calorimetry

BackgroundThermodynamic and binding kinetic data increasingly support and guide the drug optimization process.MethodsBecause ITC thermograms contain binding thermodynamic and kinetic information, an efficient protocol for the simultaneous extraction of thermodynamic and kinetic data for 1:1 protein ligand reactions from AFFINImeter kinITC in one single experiment are presented.ResultsThe effort to apply this protocol requires the same time as for the standard protocol but increases the precision of both thermodynamic and kinetic data.ConclusionsThe protocol enables reliable extraction of both thermodynamic and kinetic data for 1:1 protein-ligand binding reactions with improved precision compared to the ‘standard protocol’.General significanceThermodynamic and kinetic data are recorded under exactly the same conditions in solution without any labeling or immobilization from a protein sample that is not 100% active and would otherwise render the extraction of kinetic parameters impossible.     

Use of a windows program for simulation of the progress curves of reactants and intermediates involved in enzyme-catalyzed reactions

A program that performs simulation of the kinetics of enzyme-catalyzed reactions with up to 32 species is described. The program is written in C++ for MS Windows 95/98/NT and uses a simple text file to define the kinetic model. The use of the program is illustrated with some examples. WES is available free of charge on request from the authors (e-mail: fgarcia@iele-ab.uclm.es).     

PathMiner: predicting metabolic pathways by heuristic search

MOTIVATION: Automated methods for biochemical pathway inference are becoming increasingly important for understanding biological processes in living and synthetic systems. With the availability of data on complete genomes and increasing information about enzyme-catalyzed biochemistry it is becoming feasible to approach this problem computationally. In this paper we present PathMiner, a system for automatic metabolic pathway inference. PathMiner predicts metabolic routes by reasoning over transformations using chemical and biological information. RESULTS: We build a biochemical state-space using data from known enzyme-catalyzed transformations in Ligand, including, 2917 unique transformations between 3890 different compounds. To predict metabolic pathways we explore this state-space by developing an informed search algorithm. For this purpose we develop a chemically motivated heuristic to guide the search. Since the algorithm does not depend on predefined pathways, it can efficiently identify plausible routes using known biochemical transformations.     

Standard transformed Gibbs energies of coenzyme A derivatives as functions of pH and ionic strength

The best way to store data on apparent equilibrium constants for enzyme-catalyzed reactions is to calculate the standard Gibbs energies of formation of the species involved at 298.15 K and zero ionic strength so that equilibrium constants can be calculated at the desired pH and ionic strength. These calculations are described for CoA, acetyl-CoA, oxalyl-CoA, succinyl-CoA, methylmalonyl-CoA, malyl-CoA and CoA-glutathione. The species properties are then used to calculate standard transformed Gibbs energies of formation for these reactants as functions of pH at ionic strength 0.25 M. The species data also make it possible to calculate apparent equilibrium constants of 23 enzyme-catalyzed reactions as a function of pH, including some that cannot be determined directly because they are so large.     

赤小豆抑制剂对胰蛋白酶不可逆抑制作用的动力学探讨

本文从中药赤小豆(Phaseolus Calcaratus,Roxb)中分离出一种胰蛋白酶抑制剂。通过一系列酶促反应动力学的研究表明,赤小豆抑制剂对胰蛋白酶有较强的不可逆竞争性抑制作用。其Km和ki值分别为1.43×10~(-3)mmol/L和2.4×10~(-6)mmol/L。     

Thermodynamically based solvent design for enzymatic saccharide acylation with hydroxycinnamic acids in non-conventional media

Enzyme-catalyzed synthesis has been widely studied with lipases (EC 3.1.1.3), but feruloyl esterases (FAEs; EC 3.1.1.73) may provide advantages such as higher substrate affinity and regioselectivity in the synthesis of hydroxycinnamate saccharide esters. These compounds are interesting because of their amphiphilicity and antioxidative potential. Synthetic reactions using mono- or disaccharides as one of the substrates may moreover direct new routes for biomass upgrading in the biorefinery. The paper reviews the available data for enzymatic hydroxycinnamate saccharide ester synthesis in organic solvent systems as well as other enzymatic hydroxycinnamate acylations in ionic liquid systems. The choice of solvent system is highly decisive for enzyme stability, selectivity, and reaction yields in these synthesis reactions. To increase the understanding of the reaction environment and to facilitate solvent screening as a crucial part of the reaction design, the review explores the use of activity coefficient models for describing these systems and - more importantly - the use of group contribution model UNIFAC and quantum chemistry based COSMO-RS for thermodynamic predictions and preliminary solvent screening. Surfactant-free microemulsions of a hydrocarbon, a polar alcohol, and water are interesting solvent systems because they accommodate different substrate and product solubilities and maintain enzyme stability. Ionic liquids may provide advantages as solvents in terms of increased substrate and product solubility, higher reactivity and selectivity, as well as tunable physicochemical properties, but their design should be carefully considered in relation to enzyme stability. The treatise shows that thermodynamic modeling tools for solvent design provide a new toolbox to design enzyme-catalyzed synthetic reactions from biomass sources.     

Towards the development of a minimal cell model by generalization of a model of Escherichia coli: use of dimensionless rate parameters.

A model of a minimal cell would be a valuable tool in identifying the organizing principles that relate the static sequence information of the genome to the dynamic functioning of the living cell. Our approach for developing a minimal cell model is to first generalize an existing model of Escherichia coli by expressing reaction rates as ratios to a set of reference parameters. This generalized model is a prototype minimal cell model that will be developed by adding detail to explicitly include each chemical species. We tested the concept of a generalized model by testing the effect of scaling all enzyme-catalyzed reactions in the E. coli model. The scaling has little effect on cellular function for a wide range of kinetic ratios, where the kinetic ratio is defined as the rate of all enzyme-catalyzed reactions in a given model relative to those in the E. coli model.     

Cysteinyl-tRNA synthetase from Escherichia coli does not need an editing mechanism to reject serine and alanine. High binding energy of small groups in specific molecular interactions.

The cysteinyl-tRNA synthetase from Escherichia coli only very slowly activates serine, alanine, and alpha-aminobutyrate, the possible competitors of cysteine. The upper limits on the values of kcat/KM for the amino acid dependent ATP/pyrophosphate exchange reactions, relative to that of cysteine, are less than 10(-8), 2 x 10(-7), and 3 x 10(-6), respectively. It is calculated from these data and the concentrations of the amino acids in vivo that the error rates for the misincorporation of serine and alanine for cysteine are less than 10(-9) and 5 x 10(-8), respectively. There is no need for an error correcting mechanism and no evidence has been found to implicate one: there is no detectable ATP/pyrophosp hatase activity of the enzyme in the presence of tRNACys and alanine; Ala-tRNACys has been synthesized by the reductive desulfurization of Cys-tRNACys and has been found to be relatively resistant to the enzyme-catalyzed deacylation. Part of the high selectivity of the enzyme for the -SH group of cysteine (approximately 5 kcal/mol) appears to be caused by dispersion forces: simple calculations suggest that the dispersion energy between sulfur and a methylene group is about 2.5 times greater than that between two methylene groups. This high "hydrophobicity" of sulfur is consistent with the relative binding energies of substrates of the methionyl-tRNA synthetase. The rest of the high binding energy of the-SH group may come from hydrogen bonding.     

On the validity of using semilogarithmic plots to determine initial velocities of enzyme-catalyzed reactions

It has been proposed (Johnston & Diven, 1969a) that it is valid to use semilogarithmic (first-order) plots of the extent of reaction versus time for graphic determination of initial velocities of enzyme-catalyzed reactions. This proposition suggests the assumption that the initial velocity error expected to be introduced by the proposed procedure is smaller than or comparable to the error introduced by the customary graphic procedure. The latter is based on the assumption that the progress curves of enzyme-catalyzed reactions have an initial linear segment of sufficient duration to permit accurate determination of slope. The validity of the procedure proposed by Johnston and Diven is examined in this report. It is concluded that the procedure is applicable to a very small class of enzyme-catalyzed reactions and only under certain experimental conditions.     

Synergy within structural biology of single crystal optical spectroscopy and X-ray crystallography

Advances in the adaptation of optical spectroscopy to monitor photo-induced or enzyme-catalyzed reactions in the crystalline state have enabled X-ray crystal structures to be accurately linked with spectroscopically defined intermediates. This, in turn, has led to a deeper understanding of the role protein structural changes play in function. The integration of optical spectroscopy with X-ray crystallography is growing and now extends beyond linking crystal structure to reaction intermediate. Recent examples of this synergy include applications in protein crystallization, X-ray data acquisition, radiation damage, and acquisition of phase information important for structure determination.     

ProTherm, version 2.0: thermodynamic database for proteins and mutants

ProTherm 2.0 is the second release of the Thermo-dynamic Database for Proteins and Mutants that includes numerical data for several thermodynamic parameters, structural information, experimental methods and conditions, functional and literature information. The present release contains >5500 entries, an approximately 67% increase over the previous version. In addition, we have included information about reversibility of data, details about buffer and ion concentrations and the surrounding residues in space for all mutants. A WWW interface enables users to search data based on various conditions with different sorting options for outputs. Further, ProTherm has links with other structural and literature databases, and the mutation sites and surrounding residues are automatically mapped on the structures and can be directly viewed through 3DinSight developed in our laboratory. The ProTherm database is freely available through the WWW at http://www.rtc.riken.go.jp/protherm.html     

Nonequilibrium linear behavior of biological systems. Existence of enzyme-mediated multidimensional inflection points.

The linear phenomenological equations of nonequilibrium thermodynamics are limited theoretically to near equilibrium although a number of biological systems have been shown to exhibit a "linear" relationship between steady-state flows and conjugate thermodynamic forces outside the range of equilibrium. We have found a multidimensional inflection point which can exist well outside the range of equilibrium around with enzyme-catalyzed reactions exhibit "linear" behavior between the logarithm of reactant concentrations and enzyme catalyzed flows. A set of sufficient conditions has been derived which can be applied to any enzyme mechanism to determine whether a multidimensional inflection point exists. The conditions do not appear overly restrictive and may be satisfied by a large variety of coupled enzyme reactions. It is thus possible that the linearity observed in some biological systems may be explained in terms of enzyme operating near this multidimensional point.     

Calculation of immobilized enzyme reaction progress curves from nested ordered-sequential rate expressions

A method for estimating immobilized enzyme reaction progress curves, using simultaneous non-linear regression analysis of 2–3 substrate concentrations with time, is presented. These facile procedures involve using nested Gauss–Newton curve fitting algorithms on a Microsoft EXCEL spreadsheet. We refer to our technique as "nested" because the analysis consists of two or three mutually parameter-dependent sets of computations associated with bi- or termolecular enzyme-catalyzed reactions, respectively. We have applied the method to immobilized glucose oxidase-catalyzed reactions ([ -glucose] and [O₂] with time) and found that the kinetic parameters from initial velocity data were similar to those determined by the nested curve fitting method discussed herein.