A thermodynamically consistent constitutive equation for the elastic force-length relation of soft biological materials

Starting from the laws of thermodynamics of reversible processes, a temperature-dependent constitutive equation is derived for the elastic force-length relation of soft biological tissues. These tissues are composed of a network of fibres (mainly collagen). The equation is based on a model which uses a simplified two-dimensional representation of the alpha-helix of collagen.     

酶反应速率方程的普适形式

酶反应速率方程的普适形式是应用于相互关联的大规模代谢途径动力学建模的重要方法.把酶反应速率方程写成Michaelis-Menten-King-Altman方程形式可以使得动力学参数(或函数)容易与数据库中的实验数据相接轨,并可以处理任意数量的底物和产物,有利于大规模的计算.普适形式可以同时描述正、负反应方向,并能精确地用于准稳态条件.展示了在三类生物体系中广泛存在的酶反应机制中普适方程的严格推导过程,并讨论了普适方程的特点,针对不可逆反应酶反应产生的产物抑制效应可以自然消除,总结了在普适速率方程中体现调节剂的作用和协同作用.     

A note on the kinetics of enzyme action: A decomposition that highlights thermodynamic effects

Michaelis and Menten’s mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis–Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis.     

Inactivation of chymotrypsin and human skin chymase: kinetics of time-dependent inhibition in the presence of substrate

The reaction of chymase, a chymotryptic proteinase from human skin, and bovine pancreatic chymotrypsin with a number of time-dependent inhibitors has been studied. An integrated equation, relating product formation with time, has been derived for the reaction of enzymes with time-dependent inhibitors in the presence of substrate. This is based on a two-step model in which a rapidly reversible, non-covalent complex (EI) is formed prior to a tighter, less readily reversible complex (EI)*). The equation depends on the simplifying assumption [I] much greater than [E], but is applicable to reversible and irreversible slow-binding and tight-binding inhibitors whether or not they show saturation kinetics. The method has been applied to the reaction of chymase and chymotrypsin with the tetrapeptide aldehyde, chymostatin, basic pancreatic trypsin inhibitor and Ala-Ala-Phe-chloromethylketone (AAPCK). The irreversible inhibitor, AAPCK, showed the expected saturation kinetics for both enzymes and the apparent first-order rate constants (k2) and dissociation constants (Ki) for the non-covalent complexes were determined. Chymostatin was a much more potent inhibitor which failed to show a saturation effect. The second-order rate constant of inactivation (k2/Ki), the first-order reactivation rate constant (k-2), and the dissociation constant of the covalent complex (Ki*) were determined. Basic pancreatic trypsin inhibitor, a potent inhibitor of chymotrypsin, had similar kinetics to chymostatin but failed to inhibit chymase. The applicability of the two-step model and the integrated equation to slow- and tight-binding inhibitors is discussed in relation to a number of examples from the literature.     

THE PHOTOCHEMICAL NATURE OF THE PHOTOSENSORY PROCESS

On page 243, Vol. ii, No. 3, January 20, 1920, line 12 (counting each equation as a line) for a photochemical reaction read a reversible photochemical reaction.     

Evaluation of the effectiveness factor along immobilized enzyme fixed-bed reactors: Design of a reactor with naringinase covalently immobilized into glycophase-coated porous glass

A design equation is presented for packed-bed reactors containing immobilized enzymes in spherical porous particles with internal diffusion effects and obeying reversible one-intermediate Michaelis-Menten kinetics. The equation is also able to explain irreversible and competitive product inhibition kinetics. It allows the axial substrate profiles to be calculated and the dependence of the effectiveness factor along the reactor length to be continuously evaluated. The design equation was applied to explain the behavior of naringinase immobilized in Glycophase-coated porous glass operating in a packed-bed reactor and hydrolyzing both p-nitrophenyl-alpha-L-rhamnoside and naringin. The theoretically predicted results were found to fit well with experimentally measured values.     

Evaluation of reversible and irreversible models for the determination of the enantiomerization energy barrier for N-(p-methoxybenzyl)-1,3,2-benzodithiazol-1-oxide by supercritical fluid chromatography

It has been found that the interconversion of enantiomers on a chromatographic column during the separation process can be studied by the first-order kinetic equations derived both for reversible and irreversible reactions in a stationary system if the extent of interconversion is not too high. The equation derived for irreversible reactions gives, however, results also for higher degrees of enantiomerization while that derived for reversible interconversion failed. The irreversible equation was used to determine the enantiomerization barrier of N-(p-methoxybenzyl)-l,3,2-benzodithiazol-l-oxide enantiomers by supercritical fluid chromatography. The racemate of N-(p-methoxybenzyl)-l,3,2-benzodithiazol-l-oxide was separated by supercritical fluid chromatography on the (R,R)-Whelk-Ol column with supercritical carbon dioxide containing 20% methanol as a mobile phase. Peak areas of enantiomers prior to and after the separation used for the calculation of the enantiomerization barrier were determined by computer-assisted peak deconvolution of peak clusters registered on chromatograms using commercial software.     

Dynamics of matrix synthesis in molecular biophysics]

The paper deals with connections of structural-functional and dynamic approaches in the problems of molecular biophysics with reversible problems of the dynamics of matrix synthesis of biopolymers. Operator equation of dynamics describing such connections is obtained.     

Intramolecular esterification by lipase powder in microaqueous benzene: effect of moisture content

In view of the biochemical reaction catalyzed by enzyme powder suspended in a water-insoluble organic solvent, an equation was derived to estimate the amount of water bound to the enzyme powder. With this equation, an apparent adsorption isotherm between free water (water freely dissolved in benzene) and bound water (water bound to crude lipase powder of Pseudomonas fluorescens) was obtained. A direct lactonization reaction (synthesis of cyclopentadenolide from 15-hydroxypen-tadecanoic acid) catalyzed by crude lipase powder of Pseudomonas fluorescens was carried out batchwise in microaqueous benzene at 40oC. A kinetic model of the enzymatic reversible lactonization reaction was derived, from which the effect of moisture content on the initial reaction rate with a fully hydrated enzyme was mathematically expressed. The observed initial reaction rate first increased, then decreased with increasing moisture content, giving rise to the maximum rate at a certain level of the moisture content. The drop in the reaction rate at lower moisture content was due to a lesser hydration of the enzyme molecule (hydration-limited) and the decrease in the reaction rate at higher moisture content was attributed to the dependence of the true initial rate of the reversible reaction on the moisture content (true reversible reaction limited), and could be simulated by the kinetic model. The equilibrium yield approached 100% at a lower moisture content.     

Lipase adsorption as a factor of lipolysis regulation

Sorption isotherms of pancreatic lipase on solid supports were studied. It was shown that the enzyme adsorption can be described by Langmuir equation for hydrophobic surface and by the equation which takes into account reversible dimerization of the protein in the absorption layer for hydrophilic surface. The catalytic properties of adsorbed lipase depend on the nature of solid support. The significant role of the structure of adsorption layer in heterogeneous activation of the enzyme on hydrophobic surface was suggested.     

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.     

Thermal stabilization of human albumin by medium- and short-chain n-alkyl fatty acid anions

A comprehensive study of the thermal stabilization of defatted human albumin monomer by n-alkyl fatty acid anions (FAAs), formate through n-decanoate, was carried out by differential scanning calorimetry (DSC). The concentration of each ligand affording maximum thermal stabilization was determined; n-nonanoate provides the greatest stabilization but is only marginally better than n-octanoate and n-decanoate. The use of reversible thermodynamics and a two-state denaturation model for albumin has been validated. Standard free energies of binding, calculated from increases in free energy of denaturation, for n-butanoate and longer FAAs, are linear with n-alkyl chain length whereas those for formate, acetate, and n-propionate deviate from linearity; those for acetate and n-propionate are even greater than that of n-butanoate, thereby suggesting, in addition to the common class of sites available to all such ligands, the presence of an additional class of lower affinity binding sites available only to these shortest ligands. Competition experiments involving acetate and n-octanoate and involving n-pentanoate and n-octanoate confirmed the binding of acetate to lower affinity sites unavailable to n-octanoate and n-pentanoate. Furthermore, an equation is provided, allowing computation of the transition temperature as a function of the free energy for any reversible process causing a change in thermal stability of a protein undergoing reversible, two-state denaturation. With this equation, modeling the competition experiments by using the binding parameters determined by DSC provides additional support for the class of lower affinity sites, which play a significant role in thermal stabilization of albumin at higher concentrations of these shortest FAAs.     

一类平面可积二次非Hamilton系统的Poincare’分支

文章研究了一类可逆情况下，可积非Hamilton系统在二次多项式扰动下的Poincar6分支问题，此类问题归于弱化的Hilbert第16问题，等价于研究Abel积分的零点个数．首先采用适当的坐标变换，借助于数学软件Matlab的符号计算功能，将Abel积分写成三个线性无关的函数形式；再利用Picard—Fuchs方程和Riccati方程法，得出此系统的Poincar6分支可以扰动出极限环的个数为2≤n≤3．     

Optimization of glucose isomerase reactor: optimum operating temperature mode

The optimum temperature operation mode required to achieve high fructose productivity is studied for immobilized glucose isomerase (GI) packed bed reactor. In this study, the reactor design equation based on reversible Michaelis-Menten kinetics assumes both thermal enzyme deactivation and substrate protection. The optimization problem is formulated as a discretized constrained nonlinear programming problem (NLP). The formulation is expressed in terms of maximization of fructose productivity as the objective function subject to reactor design equation, kinetic parameter equations, substrate protection factor equation and feasibility constraints. The constraints are discretized along the reactor operating period by employing piecewise polynomial approximations. Approximately 7% improvement in terms of fructose productivity is achieved when running the reactor at the optimum decreasing temperature operation mode as compared to the constant optimum isothermal operation.     

Glucose isomerase immobolized on porous glass

Partially purified glucose isomerase from a Streptomyces species was immobilized on porous glass particles and studied for various characteristics concerning its use as an industrial catalyst. The activities were investigated in relation to the reaction parameters and the enzyme deactivation was studied systematically under various reaction conditions. The half-life of the immobilized enzyme was found to exceed 200 days at 50°C. The rate equation of the reversible glucose ? fructose reaction was derived and the kinetic constants were determined. The rate equation was found to be in good agreement with experimental data for both forward and reverse reactions. The degree of diffusional effects was experimentally measured and theoretically analyzed.     

Kinetic properties of derepressible acid phosphatase from the yeast from of Yarrowia lipolytica

(1) An acid phosphatase from depressed cells of the yeast form of Yarrowia lipolytica has been characterized kinetically by studies on specificity, inhibition, rate equation forms and modelling of the enzyme mechanisms. (2) The study on specificity revealed that the acid phosphatase is a rather unspecific phosphohydrolase that has similar activity on several different phosphate esters. A very weak transphosphorylating activity was also detected. (3) Among the reversible inhibitors, phosphate and vanadate were outstanding, whereas EDTA behaved as an activator. (4) v vs. [S] studies with o-carboxyphenyl phosphate as substrate show that the acid phosphatase of Y. lipolytica exhibits non-Michaelian behaviour, a minimum degree of 2:2 being detected for the rate equation in [S]. (5) The inhibition by phosphate and vanadate seems to have the same pattern of partial inhibition with a certain non-competitive nature, 1:1 being the minimum degree of the rate equation detected in (I).     

The development of a high-order Taylor expansion solution to the chemical rate equation for the simulation of complex biochemical systems

A numerical method for evaluating chemical rate equations ispresented. This method was developed by expressing the systemof coupled, first-degree, ordinary differential chemical rateequations as a single tensor equation. The tensorial rate equationis invariant in form for all reversible and irreversible reactionschemes that can be expressed as first- and second-order reactionsteps, and can accommodate any number of reactive components.The tensor rate equation was manipulated to obtain a simpleformula (in terms of rate constants and initial concentrations)for the power coefficients of the Taylor expansion of the chemicalrate equation. The Taylor expansion formula was used to developa FORTRAN algorithm for analysing the time development of chemicalsystems. A computational experiment was performed with a Michaelis-Mentenscheme in which step size and expansion order (to the 100thterm) were varied; the inclusion of high-order terms of theTaylor expansion was shown to reduce truncation and round-offerrors associated with Runge-Kutta methods and lead to increasedcomputational efficiency. Received on July 14, 1989; accepted on February 28, 1990     

A new graphical method for determining parameters in Michaelis-Menten-type kinetics for enzymatic lactose hydrolysis

A new graphical method was developed to determine the kinetic parameters in the Michaelis-Menten-type equation. This method was then applied to studying the kinetics of lactose hydrolysis by Aspergillus niger beta-galactosidase. In this study, the reaction temperature ranged between 8 and 60 degrees C, and the initial lactose concentration ranged between 2.5 and 20%. A kinetic model similar to the conventional Michaelis-Menten equation with competitive product inhibition by galactose was tested using this graphical method as well as a nonlinear computer regression method. The experimental data and the model fit together fairly well at 50 degrees C. However, a relative large disparity was found for reactions at 30 degrees C. A three-parameter integrated model derived from the reversible reaction mechanism simulates the experimental data very well at all temperatures studied. However, this reversible reaction model does not follow the Arrhenius temperature dependence. Nevertheless, reaction rate constants for the proposed model involving the enzyme-galactose complex (in addition to the Michaelis complex) as an intermediate in lactose hydrolysis follow the Arrhenius temperature dependence fairly well, suggesting that this model can be best used for describing the enzymatic lactose hydrolysis. The lack of fit between the model predictions and data may be largely attributed to the effects of galactose mutarotation and oligosaccharide formation during lactose hydrolysis.     

Fluorescence nanoscopy: Breaking the diffraction barrier by the RESOLFT concept

A general concept is described for breaking the diffraction barrier in far-field microscopy through reversible saturable optical transitions. This concept is based on the huge optical nonlinearities required for the saturation that are realized at relatively low light intensities. Thus, subdiffraction resolution in the nanometer scale is feasible under realistic physical conditions. The subdiffraction resolution achievable is expressed in a simple equation as a function of the saturation level of the involved transitions, and experimental examples of fluorescence microscopy techniques with resolution of a few nanometers are given.