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EN
Optimization of product in enzyme kinetics is successful by the showers of mathematical analysis with control measures. Enzymes are an important functional aspects of all biochemical processes, as they catalyze numerous reaction taking place within living organisms. With this view, optimization and quantification of product is stressed upon and in such a context, optimal control approaches have been applied in our study. In this article, we have formulated a mathematical model of enzymatic system Dynamics with control measures with a view to optimize the product as well as process conditions. Here, Pontryagin Minimum Principle is used for determination of optimal control with the help of Hamiltonian. We discuss the relevant numerical solutions for the concentration of substrate, enzyme, complex and product with respect to a specified time interval by varying control factors.
EN
It is not always clear that some equations affected by complicated factors can, actually, be interpreted as a ratio of two polynomials of first degree and so that they can be, in general, represented by rectangular hyperbolas. In this paper we present an easy procedure to rearrange those equations into Michaelis-Menten-type equations and so to make the aspects of these rectangular hyperbolas more clear, particularly for researchers familiar with general biochemistry. As an example, the method is applied to transform the classical rate equation of the Cleland's Ordered Uni Bi enzyme mechanism.
EN
Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.
EN
It is not always clear that some equations affected by complicated factors can, actually, be interpreted as a ratio of two polynomials of first degree and so that they can be, in general, represented by rectangular hyperbolas. In this paper we present an easy procedure to rearrange those equations into Michaelis-Menten-type equations and so to make the aspects of these rectangular hyperbolas more clear, particularly for researchers familiar with general biochemistry. As an example, the method is applied to transform the classical rate equation of the Cleland×s Ordered Uni Bi enzyme mechanism.
5
Content available remote A Formal Language Model of DNA Polymerase Enzymatic Activity
88%
EN
We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. We call this language operation L1-directed extension of L2 and study the closure properties of various language classes, including the classes in the Chomsky hierarchy, under directed extension. Furthermore, we answer the question under what conditions can a given language of target strings be generated from a given template language when the primer language is unknown. We use the canonic inverse of directed extension in order to obtain the optimal solution (the minimal primer language) to this question.
EN
This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.
EN
The described continuous acid phosphatase assay is based on kinetics of the release of 1-naphthol in the course of the enzyme-catalyzed hydrolysis of 1-naphthyl phosphate, measured at 320 nm in aqueous solution and at 322 nm in sodium-bis(2-ethylhexyl)sulfosuccinate isooctane-water reverse micelles in a broad pH range (1.0-8.2). The method allows precise determination of the initial rate of the reaction and therefore may be used in the steady-state and pre-steady-state studies on the phosphatase-catalyzed reaction. The kinetic parameters (Km and kcat) for human prostatic acid phosphatase in aqueous solution and in reverse micelles, at pH 3.8, 4.5 and 5.7, by the proposed 1-naphthyl phosphate assay have been determined.
EN
A combined analysis of enzyme inhibition and activation is presented, based on a rapid equilibrium model assumption in which one molecule of enzyme binds one molecule of substrate (S) and/or one molecule of a modifier X. The modifier acts as activator (essential or non-essential), as inhibitor (total or partial), or has no effect on the reaction rate (v), depending on the values of the equilibrium constants, the rate constants of the limiting velocity steps, and the concentration of substrate ([S]). Different possibilities have been analyzed from an equation written to emphasize that v = Ł([X]) is, in general and at a fixed [S], a hyperbolic function. Formulas for Su (the value of [S], different from zero, at which v is unaffected by the modifier) and vsu (v at that particular [S]) were deduced. In Lineweaver-Burk plots, the straight lines related to different [X] generally cross in a point (P) with coordinates (Su, vsu). In certain cases, point P is located in the first quadrant which implies that X acts as activator, as inhibitor, or has no effect, depending on [S]. Furthermore, we discuss: (1) the apparent Vmax and Km displayed by the enzyme in different situations; (2) the degree of effect (inhibition or activation) observed at different concentrations of substrate and modifier; (3) the concept of Ke, a parameter that depends on the concentration of substrate and helps to evaluate the effect of the modifier: it equals the value of [X] at which the increase or decrease in the reaction rate is half of that achieved at saturating [X]. Equations were deduced for the general case and for particular situations, and used to obtain computer-drawn graphs that are presented and discussed. Formulas for apparent Vmax, Km and Ke have been written in a way making it evident that these parameters can be expressed as pondered means.
9
75%
EN
Enzymes play a significant role in controlling the characteristics of various chemical and biochemical reactions. They act as catalysts that increase the rate of reaction without undergoing any change in quantity. Enzymatic reactions occur through the active sites, which combine with the substrates to form intermediate complexes, subsequently leading to products. An enzyme having two active sites can show cooperative phenomena. Against this background, an enzyme-kinetic mathematical model is formulated using fractional order derivatives. Optimal control mechanism has been incorporated into the fractional-order model system to maximize the product output. Euler-Lagrange optimality conditions are derived for the FOCP (fractional order control problem) using maximum principle. Numerical iterative schemes have been developed to solve the fractional order optimal control problem through Matlab.
EN
Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.
EN
The nonallosteric regulation mechanism of enzyme reaction velocity assumes that the substrate and enzyme interact via a metal cation and form simple and mixed, mono- and multi-nuclear complexes. A solution of equations for individual cases gives a function of initial reaction velocity at any given substrate or modifier concentration. This function can describe kinetic effects that are considered allosteric, as well as phenomena omitted by commonly-accepted models.
EN
A combined analysis of enzyme inhibition and activation is presented, based on a rapid equilibrium model assumption in which one molecule of enzyme binds one molecule of substrate (S) and/or one molecule of a modifier X. The modifier acts as activator (essential or non-essential), as inhibitor (total or partial), or has no effect on the reaction rate (v), depending on the values of the equilibrium constants, the rate constants of the limiting velocity steps, and the concentration of substrate ([S]). Different possibilities have been analyzed from an equation written to emphasize that v=([X]) is, in general and at a fixed [S], a hyperbolic function. Formulas for Su (the value of [S], different from zero, at which v is unaffected by the modifier) and vsu (v at that particular [S]) were deduced. In Lineweaver-Burk plots, the straight lines related to different [X] generally cross in a point (P) with coordinates (Su, vsu). In certain cases, point P is located in the first quadrant which implies that X acts as activator, as inhibitor, or has no effect, depending on [S]. Furthermore, we discuss: (1) the apparent Vmax and Km displayed by the enzyme in different situations; (2) the degree of effect (inhibition or activation) observed at different concentrations of substrate and modifier; (3) the concept of Ke, a parameter that depends on the concentration of substrate and helps to evaluate the effect of the modifier: it equals the value of [X] at which the increase or decrease in the reaction rate is half of that achieved at saturating [X]. Equations were deduced for the general case and for particular situations, and used to obtain computer-drawn graphs that are presented and discussed. Formulas for apparent Vmax, Km and Ke have been written in a way making it evident that these parameters can be expressed as pondered means
EN
The binding properties of the SPXK- and APXK-type peptides to the AT-rich DNA fragments of different length were studied by measuring the competition of peptides with Hoechst 33258 dye for DNA binding and by the gel shift assay analysis. In parallel to the experimental studies, molecular modeling techniques were used to analyze possible binding modes of the SPXZ and APXK motifs to the AT-rich DNA. The results of the competition measurements and gel shift assays suggest that serine at the i-1 position (i is proline) can be replaced by alanine without affecting the binding properties of the motif. Thus, the presence of the conserved serine in this motif in many DNA-binding proteins is probably not dictated by structural requirements. Based on the results of molecular modeling studies we propose that the binding mode of the SPXK- type motifs to the AT-rich DNA resembles closely that between the N-terminal arm of the homeodomain and DNA. This model confirms that serine in the SPXK motifs is not essential for the DNA binding. The model also indicates that if X in the motif is glutamic acid, this residue is probably protonated in the complex with DNA.
EN
This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.
EN
Soluble invertase from mid-milky stage grains of two wheat (Triticum aestivum L.) varieties, namely Kalyansona and PBW 343 was isolated and purified by employing ammonium sulphate precipitation, gel filtration on Sephadex G-150 and DEAE-cellulose column chromatography. Invertase from Kalyansona exhibited greater heat stability (50 °C) compared to PBW 343 (35 °C). By employing photo-oxidation and chemical modification methods, and by studying the effect of pH on Km and Vmax, the involvement of histidine, sulphydryl and α-carboxyl groups in the active site of the enzyme was indicated. The enzyme was completely inhibited by HgCl₂ and DTNB. ZnSO₄, MgSO₄, KCl, CaCl₂, EDTA and pyridoxine were strong inhibitors in PBW 343 but not in Kalyansona. The two varieties also showed differential response in respect to thermodynamic properties of the enzyme, i.e. energy of activation (Ea), enthalpy change (ΔH) and entropy change (ΔS). Overall the results suggest that genetic differences exist in soluble invertase properties of wheat grains and that the thermal adaptation of the enzyme is reflected in its altered kinetic behaviour.
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