Heteroscedastic Nonlinear Regression Models with Random Effects and Their Application to Enzyme Kinetic Data

We present a new modification of nonlinear regression models for repeated measures data with heteroscedastic error structures by combining the transform-both-sides and weighting model from Caroll and Ruppert (1988) with the nonlinear random effects model from Lindstrom and Bates (1990). The proposed parameter estimators are a combination of pseudo maximum likelihood estimators for the transform-both-sides and weighting model and maximum likelihood (ML) or restricted maximum likelihood (REML) estimators for linear mixed effects models. The new method is investigated by analyzing simulated enzyme kinetic data published by Jones (1993).     

From Enzyme Kinetics to Metabolic Network Modeling – Visualization Tool for Enhanced Kinetic Analysis of Biochemical Network Models

Model‐based analysis of enzyme kinetics allows the determination of optimal conditions for their use in biocatalysis. For biotransformations or fermentative approaches the modeling of metabolic pathways or complex metabolic networks is necessary to obtain model‐based predictions of steps which limit product formation within the network. To set up adequate kinetic models, relevant mechanistic information about enzyme properties is required and can be taken from in vitro studies with isolated enzymes or from in vivo investigations using stimulus‐response experiments which provide a lot of kinetic information about the metabolic network. But with increasing number of reaction steps and regulatory interdependencies in the network structure the amount of simulation data dramatically increases and the simulation results from the dynamic models become difficult to analyze and interpret. Demonstrated for an Escherichia coli model of the central carbon metabolism, methods for visualization and animation of simulation data were applied and extended to facilitate model analysis and biological interpretation. The dynamic metabolite pool and metabolic flux changes were visualized simultaneously by a software tool. In addition, a new quantification method for enzyme activation/inhibition was proposed, and this information was implemented in the metabolic visualization.     

Kinetic and Functional Analysis of l-Threonine Kinase, the PduX Enzyme of Salmonella enterica

The PduX enzyme of Salmonella enterica is an l-threonine kinase used for the de novo synthesis of coenzyme B₁₂ and the assimilation of cobyric acid. PduX with an N-terminal histidine tag (His₈-PduX) was produced in Esch e richia coli and purified. The recombinant enzyme was soluble and active. Kinetic analysis indicated a steady-state Ordered Bi Bi complex mechanism in which ATP is the first substrate to bind. Based on a multiple sequence alignment of PduX homologues and other GHMP (galactokinase, homoserine kinase, mevalonate kinase, and phosphomevalonate kinase) family members, 14 PduX variants having changes at 10 conserved serine/threonine and aspartate/glutamate sites were constructed by site-directed mutagenesis. Each variant was produced in E. coli and purified. Comparison of the circular dichroism spectra and kinetic properties of the PduX variants with those of the wild-type enzyme indicated that Glu-24 and Asp-135 are needed for proper folding, Ser-99 and Glu-132 are used for ATP binding, and Ser-253 and Ser-255 are critical to l-threonine binding whereas Ser-100 is essential to catalysis, but its precise role is uncertain. The studies reported here are the first to investigate the kinetic and catalytic mechanisms of l-threonine kinase from any organism.The B₁₂ coenzymes (adenosylcobalamin (AdoCbl)² and methylcobalamin) are the largest cofactors known in biology. They are essential for human health and have important metabolic roles in many microbes (1, 2). The B₁₂ coenzymes are synthesized de novo only by certain prokaryotes and from corrinoid precursors by a broader range of organisms (1, 2). De novo synthesis by prokaryotes is the ultimate source of B₁₂, and this process has been extensively studied because of its importance to diverse biological forms and to the commercial production of B₁₂ as a dietary supplement (1). Salmonella enterica is an important model organism for studies of B₁₂ synthesis (3, 4). This organism carries out de novo synthesis under anaerobic conditions and assimilates corrinoids such as cobinamide and cobyric acid (Cby) under both aerobic and anaerobic conditions (3, 5). We recently showed that the PduX enzyme of S. enterica is an l-threonine (l-Thr) kinase, which is required for the de novo synthesis of AdoCbl and methylcobalamin and the assimilation of Cby (6). PduX catalyzes the conversion of l-Thr and ATP to ADP and l-threonine-O-3-phosphate (l-Thr-P), a required building block for the de novo synthesis of B₁₂ (Fig. 1) (6). By sequence similarity, the PduX enzyme of S. enterica belongs to the galactokinase, homoserine kinase, mevalonate kinase, and phosphomevalonate kinase (GHMP) family (7), which is a novel family of kinases found in metabolic pathways of small molecules. Although there have been no three-dimensional structures of PduX or other l-Thr kinases reported to date, the crystal structures of several GHMP kinases have been solved (8–22). These structures reveal a unique kinase fold and a novel nucleotide-binding mode that are conserved among members of the GHMP kinase family. Members also contain three common sequence motifs consisting of about 10–15 contiguous amino acids (9, 23). Motif I is at the N-terminal region, and its function is uncertain. Motif II is the most conserved with a typical sequence of Pro-X-X-X-Gly-Leu-X-Ser-Ser-Ala. This region is involved in nucleotide binding and distinguishes the GHMP family from other protein kinase families. Motif III is near the C terminus and contains a small glycine-rich loop that appears well positioned to interact with substrate that is phosphorylated by ATP (24). However, there are highly divergent sequences outside these three motifs, and modes of oligomerization, substrate binding, and catalytic mechanism vary among different GHMP family members (14).Open in a separate windowFIGURE 1.Roles of PduX in B₁₂ synthesis in S. enterica. PduX is required for both the de novo synthesis of AdoCbl and methylcobalamin (MeCbl) and the assimilation of cobyric acid. AdoCbl is required for growth of S. enterica on 1,2-PD and ethanolamine as well for the activity of the MetH methionine synthase that converts homocysteine to methionine. Btu, B₁₂ uptake system; Cbi, cobinamide; AdoCbi, adenosylcobinamide; AdoCby, adenosylcobyric acid; AdoCbi-P, adenosylcobinamide phosphate; AP-P, (R)-1-amino-2-propanol-O-2-phosphate.Based on structural and biochemical data, members of the GHMP family are subdivided into two groups depending on their catalytic mechanisms. In the first group, which includes rat mevalonate kinase, the crystal structure shows an aspartate residue in the active site positioned to act as a catalytic base that abstracts a proton from the substrate hydroxyl group. In addition, there is a lysine residue that is thought to reduce the pK_a of the substrate hydroxyl group and to stabilize the pentacoordinated γ-phosphoryl group of ATP (18). In the second group, such as Escherichia coli homoserine kinase, there appears to be no suitable residue positioned to act as a catalytic base. Consequently it has been hypothesized that homoserine kinase achieves catalysis through transition state stabilization alone (14).In the present study we investigated the catalytic mechanism of PduX by a series of kinetic studies and mutational analyses of 10 invariant serine/threonine and aspartate/glutamate residues. Results indicate a steady-state Ordered Bi Bi mechanism in which ATP binds first. We also identified several amino acids critical to substrate binding and catalysis. To our knowledge, these are the first reported studies on the catalytic mechanism of l-Thr kinase from any organism.     

α-Chymotrypsin Immobilized on Chitin. Relationships Between the Enzyme Kinetic Constant and Support Structure

-Chymotrypsin was immobilized on chitin from squills, lobsters and prawns by means of glutaraldehyde. Hydrolase and peptide synthetase activities were determined in aqueous and homogeneous aqueous-organic media, respectively.

The results show -chymotrypsin immobilized on chitin from prawn to be the most active immobilized derivative based on its synthetase activity (90% yield of Bz-Tyr-Leu-NH₂ in carbonate buffer, p^H 9 containing 70% 1,4- butanediol).

The relationship between the kinetic constant of hydrolysis and chitin structure was also studied. -Chymotrypsin immobilized on prawn chitin was found to be the best derivative in kinetic terms.

The stability of the three derivatives was studied at 37C.     

A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions

As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis–Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis–Menten equations. Moreover, we show that when the indicator reaction is fast, the quasi-steady-state dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis–Menten equations, are derived. The theory can be extended to deal with more complex sequences of enzyme-catalyzed reactions.     

基于序列和结构分析的酶热稳定性改造策略*

功能酶被广泛应用于食品、化工、医药等领域,但却容易受高温环境限制,导致催化效率降低。以分子改造为目的的蛋白质工程技术是解决这一问题的关键环节,其能够对酶结构和功能进行改造,获得热稳定性好的工业酶。传统的定向进化方法只能依靠随机突变进行人工筛选,具有效率低、针对性差等缺点;理性设计作为酶热稳定性改造的主要方法,可借助各种计算机程序和软件预测潜在突变位点,但其要求对酶的催化机制、热稳定性机制有深入了解。对于大多数天然酶而言,酶的序列和晶体结构是最容易获取的信息,也是预测功能的重要基础。从酶的序列和晶体结构入手,重点介绍了共识突变、基于序列偏好性的突变、截短柔性区域、优化分子内相互作用力、刚化催化活性区域及计算机辅助筛选柔性位点等常用策略,这些策略具有筛选效率高、改造准确性高、实用性强等优点。结合多种酶的热稳定性改造案例进行分析,旨在为不同酶的改造策略选择提供有效参考,同时也为工业酶的耐热性研究提供理论支持。     

度量误差模型及其应用

本文介绍度量误差模型的基本概念和参数估计的基本结果以及与通常回归之间的关系．并讨论了这个模型在生物学中应用的可能性．     

Impact of the Enzyme Flexibility on the Enzyme Enantio-selectivity in Organic Media Towards Specific and Non-specific Substrates

A rationale is presented as to why the enantioselectivity of enzymes in dry organic media towards specific substrates is increased when the enzyme flexibility is increased. This is outlined for serine proteases towards N -acetyl-amino acid esters. The reasons why this relationship does not hold in the case of non-specific substrates are discussed.     

Impact of the Enzyme Flexibility on the Enzyme Enantio-selectivity in Organic Media Towards Specific and Non-specific Substrates

A rationale is presented as to why the enantioselectivity of enzymes in dry organic media towards specific substrates is increased when the enzyme flexibility is increased. This is outlined for serine proteases towards N -acetyl-amino acid esters. The reasons why this relationship does not hold in the case of non-specific substrates are discussed.     

酶、多肽电荷数的理论计算及误差研究

对酶的电荷数随ｐＨ变化的定量关系进行了理论推导,将推导出的酶的电荷数与ｐＨ的关系式应用于多肽等电点的计算,理论计算结果与文献实验结果完全一致,并推导出酸性氨基酸、碱性氨基酸及中性氨基酸等电点的计算式,与现有计算式完全一致．应用荧光光谱和荧光偏振对肌酸激酶带电性随ｐＨ值的变化关系的研究表明,理论计算符合实验结果,表明：此文理论关系式是可靠的．     

苯甘氨酸氨基转移酶基因hpgt的原核优化表达与酶动力学特性研究

苯甘氨酸氨基转移酶(4-Hydroxyphenylglycine aminotransferase)是假单胞菌所产生的一种能够合成D-苯甘氨酸的重要转氨酶。利用密码子优化技术,合成苯甘氨酸转移酶基因。构建原核重组质粒pCDF-hpgt,转入感受态细胞E.coli BL21(DE3),优化表达His-HpgT蛋白。利用Ni-NTA柱纯化技术获得高纯度的His-HpgT融合蛋白。分别测定融合蛋白在正反向反应中的酶活力单位及最佳的反应温度、pH值及其他动力学参数,并对该酶特性作相关的机理分析。测定结果表明,正向反应和反向反应的酶比活力分别为749mU/mg、2 257mU/mg,此酶分解苯甘氨酸的能力要强于合成苯甘氨酸;正向反应的最适温度与pH分别是35℃和8.0;由米氏方程得出该酶对苯甘氨酸的亲和力远大于谷氨酸;较低浓度的苯乙醛酸即可抑制反应的进行。     

Usefulness of Kinetic Enzyme Parameters in Biotechnological Practice

The k_cat /K_M ratio, where k_cat is the catalytic constant for the conversion of substrate into product, and K_M is the Michaelis constant, has been widely used as a measure of enzyme performance, but recent analyses have underscored the inadequacy of this ratio to describe the efficiency of a biocatalyst, particularly when employed as a criterion for selecting between enzyme variants for industrial purposes. The main problem with this kinetic relationship is that it neglects the contribution of important factors operating in actual bioprocess conditions, such as substrate concentrations and product inhibition, leading to unreal expectations on enzyme performance and erroneous selection of the most adequate biocatalyst. Two complementary formalisms, the efficiency function and the catalytic effectiveness, have been introduced to incorporate important features of any bio-industrial system. We review herein the rationales underlying each derivation, and the strengths and fields of application of both strategies. Examples of different situations, including continuous and batch-type reactors, as well as reversible and irreversible processes, are provided, together with recommendations on the use of both approaches.     

Solvent Structure and Enzyme Activity

Abstract

Enzymes are fluctuating particles in thermal equilibrium with their solvent environment. A variety of models of enzyme action have postulated selective excitation of enzyme vibrational modes or triggering of correlated motion of catalytic groups through collisions with solvent particles as the basis of catalytic activity. Solvent composition and structure are expected to influence such interactions. Solutes such as p-dioxane, t-butanol, and tetraalkylammonium chlorides are known to be strong perturbants of the structure of water. However, when the kinetic parameters of two enzymes, carboxypeptidase A and α-chymotrypsin, were examined carefully in aqueous mixtures containing these solutes, no significant influence of solvent structure or mass composition on the catalytic rate constant was found. The results indicate, furthermore, that, within the low viscosity limit, fluctuations in enzyme structure that are responsible for activated processes in the catalytically rate limiting step appear not to be significantly influenced by dynamic processes in the bulk solvent.     

Kinetic and Structural Properties of NADP-Malic Enzyme from Sugarcane Leaves

Oligomeric structure and kinetic properties of NADP-malic enzyme, purified from sugarcane (Saccharam officinarum L.) leaves, were determined at either pH 7.0 and 8.0. Size exclusion chromatography showed the existence of an equilibrium between the dimeric and the tetrameric forms. At pH 7.0 the enzyme was found preferentially as a 125 kilodalton homodimer, whereas the tetramer was the major form found at pH 8.0. Although free forms of l-malate, NADP⁺, and Mg²⁺ were determined as the true substrates and cofactors for the enzyme at the two conditions, the kinetic properties of the malic enzyme were quite different depending on pH. Higher affinity for l-malate (K_m = 58 micromolar), but also inhibition by high substrate (K_i = 4.95 millimolar) were observed at pH 7.0. l-Malate saturation isotherms at pH 8.0 followed hyperbolic kinetics (K_m = 120 micromolar). At both pH conditions, activity response to NADP⁺ exhibited Michaelis-Menten behavior with K_m values of 7.1 and 4.6 micromolar at pH 7.0 and 8.0, respectively. Negative cooperativity detected in the binding of Mg²⁺ suggested the presence of at least two Mg²⁺ - binding sites with different affinity. The K_a values for Mg²⁺ obtained at pH 7.0 (9 and 750 micromolar) were significantly higher than those calculated at pH 8.0 (1 and 84 micromolar). The results suggest that changes in pH and Mg²⁺ levels could be important for the physiological regulation of NADP-malic enzyme.     

Refolding and Enzyme Kinetic Studies on the Ferrochelatase of the Cyanobacterium Synechocystis sp. PCC 6803

Heme is a cofactor for proteins participating in many important cellular processes, including respiration, oxygen metabolism and oxygen binding. The key enzyme in the heme biosynthesis pathway is ferrochelatase (protohaem ferrolyase, EC 4.99.1.1), which catalyzes the insertion of ferrous iron into protoporphyrin IX. In higher plants, the ferrochelatase enzyme is localized not only in mitochondria, but also in chloroplasts. The plastidic type II ferrochelatase contains a C-terminal chlorophyll a/b (CAB) motif, a conserved hydrophobic stretch homologous to the CAB domain of plant light harvesting proteins and light-harvesting like proteins. This type II ferrochelatase, found in all photosynthetic organisms, is presumed to have evolved from the cyanobacterial ferrochelatase. Here we describe a detailed enzymological study on recombinant, refolded and functionally active type II ferrochelatase (FeCh) from the cyanobacterium Synechocystis sp. PCC 6803. A protocol was developed for the functional refolding and purification of the recombinant enzyme from inclusion bodies, without truncation products or soluble aggregates. The refolded FeCh is active in its monomeric form, however, addition of an N-terminal His₆-tag has significant effects on its enzyme kinetics. Strikingly, removal of the C-terminal CAB-domain led to a greatly increased turnover number, k_cat, compared to the full length protein. While pigments isolated from photosynthetic membranes decrease the activity of FeCh, direct pigment binding to the CAB domain of FeCh was not evident.     

Enzyme peptide synthesis and semisynthesis: Kinetic and thermodynamic aspects

The hydrolysis/synthesis equilibrium of the peptide bond is governed by the relative magnitudes of the corresponding Gibbs' energies of hydrolysis to non-ionized products and of their ionization. The positive energy change in peptide hydrolysis to non-ionized products is the thermodynamic basis for the acyl and leaving group specificity of proteinases. With a proteinase of suitable specificity, some peptide bonds can be synthesized by a thermodynamically controlled enzyme aminolysis of specific acylamino or peptide acids; any peptide bond can be formed by a kinetically controlled enzyme aminolysis of the corresponding acylamino or peptide esters.