Equations of Substrate-inhibition Kinetics Applied to Pig Kidney Diamine Oxidase (DAO,E.C. 1.4.3.6)

Pig kidney diamine oxidase (DAO) and other semicarbazide-sensitive amine oxidases (SSAO) show clear substrate-inhibition kinetics and a reaction-scheme mechanism based on two substrate binding sites. We evaluated several reaction scheme mechanisms with a non-linear regression program (NCSS), estimating R², the constants of the equations and their standard errors and we determined the deviation of experimental data from theoretical equations. The best fit was obtained with a “dead end” mechanism with two binding sites. Based on this scheme, other schemes for a two-substrate reaction and for mechanisms of inhibition were constructed. These reaction schemes, even at low substrate concentration, fitted experimental data better than Michaelis-Menten kinetics, and provided information on the mechanisms of action of inhibitors. The presence of two substrate-binding sites on pig kidney DAO was confirmed by all experimental data.     

Equations of substrate-inhibition kinetics applied to pig kidney diamine oxidase (DAO, E.C. 1.4.3.6)

Pig kidney diamine oxidase (DAO) and other semicarbazide-sensitive amine oxidases (SSAO) show clear substrate-inhibition kinetics and a reaction-scheme mechanism based on two substrate binding sites. We evaluated several reaction scheme mechanisms with a non-linear regression program (NCSS), estimating R2, the constants of the equations and their standard errors and we determined the deviation of experimental data from theoretical equations. The best fit was obtained with a "dead end" mechanism with two binding sites. Based on this scheme, other schemes for a two-substrate reaction and for mechanisms of inhibition were constructed. These reaction schemes, even at low substrate concentration, fitted experimental data better than Michaelis-Menten kinetics, and provided information on the mechanisms of action of inhibitors. The presence of two substrate-binding sites on pig kidney DAO was confirmed by all experimental data.     

Kinetics and mechanism of peptide synthesis in solution

The kinetics of the reaction of Boc-Xaa fluorophenyl esters (where Xaa = Ala, Val, Phe, Ser, Leu, Gly, Met, Pro, or Ile) with leucinamide was studied measuring changes in the fluorescence emission at 375 nm of the fluorophenyl chromophore accompanying the reaction. It was found that the experimental kinetic data couldn't be described by a simple scheme of the second order reaction. The measurements of the kinetic parameters of the reaction at various initial concentrations of reagents indicated that the reaction rate can be expressed as: v = kCNaCAEb, where k is the reaction rate constant, CN is the concentration of leucinamide, and LeuNH2, CAE is the concentration of fluorophenyl ester. The a and b reaction orders were close to 1/2 and 3/2 for Xaa = Ala, Val, Phe, Ser, or Leu, 1/2 and 1 for Gly, Met, or Pro, and 1 and 2 for Ile. The experimental equations for the reaction rate can theoretically be derived from a single scheme of chain reactions with various deactivation ways for active intermediates. The English version of the paper.     

Hidden Markov modeling for single channel kinetics with filtering and correlated noise

Hidden Markov modeling (HMM) can be applied to extract single channel kinetics at signal-to-noise ratios that are too low for conventional analysis. There are two general HMM approaches: traditional Baum's reestimation and direct optimization. The optimization approach has the advantage that it optimizes the rate constants directly. This allows setting constraints on the rate constants, fitting multiple data sets across different experimental conditions, and handling nonstationary channels where the starting probability of the channel depends on the unknown kinetics. We present here an extension of this approach that addresses the additional issues of low-pass filtering and correlated noise. The filtering is modeled using a finite impulse response (FIR) filter applied to the underlying signal, and the noise correlation is accounted for using an autoregressive (AR) process. In addition to correlated background noise, the algorithm allows for excess open channel noise that can be white or correlated. To maximize the efficiency of the algorithm, we derive the analytical derivatives of the likelihood function with respect to all unknown model parameters. The search of the likelihood space is performed using a variable metric method. Extension of the algorithm to data containing multiple channels is described. Examples are presented that demonstrate the applicability and effectiveness of the algorithm. Practical issues such as the selection of appropriate noise AR orders are also discussed through examples.     

Modelling of multi-component immunoassay kinetics — A new node-based method for simulation of complex assays

The behaviour of binding reactions in immunoassays can be predicted and studied by modelling methods. Simple antibody-analyte binding reaction kinetics can be simulated by e.g. a mechanistic assay model based on differential equations. However, the mathematical modelling becomes more complicated if multivalent-structured components are involved and the number of binding complexes increases.In this paper, a new node-based method to model complex binding reactions is introduced. The principle of this method is to construct a network of the initial components, reaction intermediates and end-products by forming a network of nodes. This network is then solved, node by node, breaking the initial problem into smaller partial problems, still obeying the laws of chemical reaction kinetics and without ignoring any parts of the problem.This method provides an easy and quick way to study complex binding reactions since simulation networks are simple to construct directly from the reaction scheme. This presented new “NODE”-method is compared with the well known mechanistic assay model.     

Systems-level Modeling with Molecular Resolution Elucidates the Rate-limiting Mechanisms of Cellulose Decomposition by Cellobiohydrolases

Interprotein and enzyme-substrate couplings in interfacial biocatalysis induce spatial correlations beyond the capabilities of classical mass-action principles in modeling reaction kinetics. To understand the impact of spatial constraints on enzyme kinetics, we developed a computational scheme to simulate the reaction network of enzymes with the structures of individual proteins and substrate molecules explicitly resolved in the three-dimensional space. This methodology was applied to elucidate the rate-limiting mechanisms of crystalline cellulose decomposition by cellobiohydrolases. We illustrate that the primary bottlenecks are slow complexation of glucan chains into the enzyme active site and excessive enzyme jamming along the crowded substrate. Jamming could be alleviated by increasing the decomplexation rate constant but at the expense of reduced processivity. We demonstrate that enhancing the apparent reaction rate required a subtle balance between accelerating the complexation driving force and simultaneously avoiding enzyme jamming. Via a spatiotemporal systems analysis, we developed a unified mechanistic framework that delineates the experimental conditions under which different sets of rate-limiting behaviors emerge. We found that optimization of the complexation-exchange kinetics is critical for overcoming the barriers imposed by interfacial confinement and accelerating the apparent rate of enzymatic cellulose decomposition.     

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization,confidence bounds,and selection of elementary modes

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Kinetic manifestations of slow conformation rearrangements of lactate dehydrogenase. An experiment and a mathematical model

Non-steady-state kinetics of lactate dehydrogenase (LDH) catalyzed reaction was investigated for a wide time interval (from 100 msec to 1-3 min) by using stopped-flow methods. A two-stage character of LDH reaction, slow changes like a lag-period on kinetic curves at pH 8.0, flexions on kinetic curves after pre-mixing LDH with NAD+ and pyruvate have been revealed. The graph theory for mathematical analysis of experimental data was applied, which has been developed for the non-steady-state kinetics. An enzyme model of the two-conformer LDH structure was used. The reaction scheme with a preferential inhibition of one of the conformers (pH 8.0) is suggested. The obtained values of kinetic constants prove that transitions between LDH conformers must be slow.     

GalaxyTBM: template-based modeling by building a reliable core and refining unreliable local regions

ABSTRACT: BACKGROUND: Protein structures can be reliably predicted by template-based modeling (TBM) when experimental structures of homologous proteins are available. However, it is challenging to obtain structures more accurate than the single best templates by either combining information from multiple templates or by modeling regions that vary among templates or are not covered by any templates. RESULTS: We introduce GalaxyTBM, a new TBM method in which the more reliable core region is modeled first from multiple templates and less reliable, variable local regions, such as loops or termini, are then detected and re-modeled by an ab initio method. This TBM method is based on "Seok-server," which was tested in CASP9 and assessed to be amongst the top TBM servers. The accuracy of the initial core modeling is enhanced by focusing on more conserved regions in the multiple-template selection and multiple sequence alignment stages. Additional improvement is achieved by ab initio modeling of up to 3 unreliable local regions in the fixed framework of the core structure. Overall, GalaxyTBM reproduced the performance of Seok-server, with GalaxyTBM and Seok-server resulting in average GDT-TS of 68.1 and 68.4, respectively, when tested on 68 single-domain CASP9 TBM targets. For application to multi-domain proteins, GalaxyTBM must be combined with domain-splitting methods. CONCLUSION: Application of GalaxyTBM to CASP9 targets demonstrates that accurate protein structure prediction is possible by use of a multiple-template-based approach, and ab initio modeling of variable regions can further enhance the model quality.     

A computer program for enzyme kinetics that combines model discrimination, parameter refinement and sequential experimental design.

A method of model discrimination and parameter estimation in enzyme kinetics is proposed. The experimental design and analysis of the model are carried out simultaneously and the stopping rule for experimentation is deduced by the experimenter when the probabilities a posteriori indicate that one model is clearly superior to the rest. A FORTRAN77 program specifically developed for joint designs is given. The method is very powerful, as indicated by its usefulness in the discrimination between models. For example, it has been successfully applied to three cases of enzyme kinetics (a single-substrate Michaelian reaction with product inhibition, a single-substrate complex reaction and a two-substrate reaction). By using this method the most probable model and the estimates of the parameters can be obtained in one experimental session. The FORTRAN77 program is deposited as Supplementary Publication SUP 50134 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5.     

Evaluation method for the drying performance of enzyme containing formulations

A method is presented for fast and cheap evaluation of the performance of enzyme containing formulations in terms of preserving the highest enzyme activity during spray drying. The method is based on modeling the kinetics of the thermal inactivation reaction which occurs during the drying process. Relevant kinetic parameters are determined from differential scanning calorimeter (DSC) experiments and the model is used to simulate the severity of the inactivation reaction for temperatures and moisture levels relevant for spray drying. After conducting experiments and subsequent simulations for a number of different formulations it may be deduced which formulation performs best. This is illustrated by a formulation design study where 4 different enzyme containing formulations are evaluated. The method is validated by comparison to pilot scale spray dryer experiments.     

Use of distraction loading to estimate subject-specific knee ligament slack lengths

Knee ligaments guide and restrain joint motion, and their properties influence joint mechanics. Inverse modeling schemes have been used to estimate specimen-specific ligament properties, where external joint forces are assumed to balance with internal ligament and contact forces. This study simplifies this assumption by adjusting experimental loads to remove internal contact forces. The purpose of this study was to use novel experimental loading in an inverse modeling scheme to estimate ligament slack lengths, perform validation using additional loading scenarios, and evaluate sensitivity to the applied loading. Joint kinematics and kinetics were experimentally measured for a set of load cases. An optimization scheme used a specimen-specific forward kinematics model to estimate ligament slack lengths by minimizing the residual between model and experimentally measured kinetics. The calibrated model was used for a form of validation by evaluating non-optimized load cases. Additionally, uncertainty analysis related kinetic errors to previously reported kinematic errors. The six DOF tibial reactions realized RMS errors less than 23 N and 0.75 Nm for optimized load cases, and 33 N and 2.25 Nm for the non-optimized load cases. The uncertainty analysis, which was performed using the optimized load cases, showed average kinetic RMS errors less than 26 N and 0.45 Nm. The model’s recruitment patterns were similar to those found in clinical and cadaveric studies. This study demonstrated that experimental distraction loading can be used in an inverse modeling scheme to estimate ligament slack lengths with a forward kinematics model.     

Kinetic cutinase-catalyzed esterification of caproic acid in organic solvent system

Practical application of any chemical reaction requires the knowledge of its kinetics; in particular if one wishes to be able to describe a chemical reactor over an extended range of reaction conditions or if one intends to optimize the reaction conditions, a suitable kinetic model must be obtained. In order to ensure that the model is applicable over a wide range of experimental conditions it should be based on a mechanistic scheme describing the fundamental steps involved in the reaction; the development of these kind of models can also be used to provide insight into the processes that are taking place.A kinetic study, using experiments carried out in a batch stirred reactor, has been made for the enzymatic esterification of caproic acid with ethyl alcohol catalyzed by Fusarium solani pisi cutinase. Different acid and alcohol concentrations (whilst also varying the acid/alcohol molar ratio) were tested and the results were used to identify the best reaction scheme to describe the results obtained over an extended range of conditions. Several different approaches were used to identify the most adequate mechanistic model, namely by resorting to the quasi stationary state and the rate-limiting hypothesis. The main kinetic characteristics observed in esterification reaction were found to follow an ordered Ping-Pong Bi–Bi mechanism but different modifications were used o ensure that the kinetic model was applicable over the entire range of experimental conditions that were covered.     

Thermodynamics-based Metabolite Sensitivity Analysis in metabolic networks

The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. Constraint based methods, such as Flux Balance Analysis (FBA) and Thermodynamics-based flux analysis (TFA), are commonly used to estimate the flow of metabolites through genome-wide metabolic networks, making it possible to identify the ranges of flux values that are consistent with the studied physiological and thermodynamic conditions. However, unless key intracellular fluxes and metabolite concentrations are known, constraint-based models lead to underdetermined problem formulations. This lack of information propagates as uncertainty in the estimation of fluxes and basic reaction properties such as the determination of reaction directionalities. Therefore, knowledge of which metabolites, if measured, would contribute the most to reducing this uncertainty can significantly improve our ability to define the internal state of the cell. In the present work we combine constraint based modeling, Design of Experiments (DoE) and Global Sensitivity Analysis (GSA) into the Thermodynamics-based Metabolite Sensitivity Analysis (TMSA) method. TMSA ranks metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. TMSA is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements.     

MLR-tagging: informative SNP selection for unphased genotypes based on multiple linear regression

The search for the association between complex diseases and single nucleotide polymorphisms (SNPs) or haplotypes has recently received great attention. For these studies, it is essential to use a small subset of informative SNPs accurately representing the rest of the SNPs. Informative SNP selection can achieve (1) considerable budget savings by genotyping only a limited number of SNPs and computationally inferring all other SNPs or (2) necessary reduction of the huge SNP sets (obtained, e.g. from Affymetrix) for further fine haplotype analysis. A novel informative SNP selection method for unphased genotype data based on multiple linear regression (MLR) is implemented in the software package MLR-tagging. This software can be used for informative SNP (tag) selection and genotype prediction. The stepwise tag selection algorithm (STSA) selects positions of the given number of informative SNPs based on a genotype sample population. The MLR SNP prediction algorithm predicts a complete genotype based on the values of its informative SNPs, their positions among all SNPs, and a sample of complete genotypes. An extensive experimental study on various datasets including 10 regions from HapMap shows that the MLR prediction combined with stepwise tag selection uses fewer tags than the state-of-the-art method of Halperin et al. (2005). AVAILABILITY: MLR-Tagging software package is publicly available at http://alla.cs.gsu.edu/~software/tagging/tagging.html