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PDF Open Access International Journal of Recent Academic Research (ISSN: 2582-158X) Vol. 01, Issue 09, pp.532-542, December, 2019 Available online at http://www.journalijrar.com RESEARCH ARTICLE EULER’S LINE FOR ENZYME KINETICS 1, *Vitthalrao Bhimasha Khyade, 2Avram Hershko and 3Seema Karna Dongare 1Department of Zoology, Shardabai Pawar Mahila Mahavidyalaya, Shardanagar Tal., Baramati Dist., Pune – 413115, India 2Unit of Biochemistry, The B. Rappaport Faculty of Medicine, and the Rappaport Institute for Research in the Medical Sciences, Technion-Israel Institute of Technology, Haifa 31096, Israel 3P.G. Student, Department of Microbiology, Maharashtra Education Society's, Abasaheb Garware College, Karve Road, Pune – 411004, India ARTICLE INFO ABSTRACT Article History: A graph of the double-reciprocal equation is also called a Line weaver-Burk, reciprocal of velocity of enzyme Received 10th September 2019, reaction (1÷v) against reciprocal of substrate concentration [1÷S]. Lineweaver-Burk graphs are particularly useful Received in revised form for analyzing the changes in enzyme kinetics in the presence of inhibitors, competitive, non-competitive, or a 28th October 2019, mixture of the two. One more attempt is carried out for establishment of Euler’s line through the use of Line Accepted 04th November 2019, weaver-Burk plot. Line weaver-Burk plot (double reciprocal plot) is with positive value of (Km÷Vmax) as a Published online th slope. Euler Line for Enzyme Kinetics is with negative value of (Km÷Vmax) as a slope. The intercept on y-axis 30 December 2019. for Line weaver-Burk plot (double reciprocal plot) for Enzyme Kinetics correspond to: (1 ÷ Vmax). The intercept on y-axis for Euler Line for Enzyme Kinetics correspond to: [(Km +2) ÷ Vmax)]. Lineweaver-Burk plot (double reciprocal plot) and Euler Line for Enzyme Kinetics are intersecting at the point, x – co-ordinate of which correspond to: (1÷2) and y- co-ordinate of which correspond to: [(Km+2) ÷ Vmax]. The centroid for enzyme kinetics is always located between the orthocenter and the circumcenter of enzyme kinetics. The distance from the centroid to the orthocenter is always twice the distance from the centroid to the circumcenter of enzyme kinetics. Attempt may open a new avenue for three dimensional enzyme structure of and mechanism of enzyme involved reactions. *Corresponding Author: Vitthalrao Bhimasha Khyade Key Words: Centroid, Orthocenter, Circumcenter, Euler’s line. Copyright © 2019, Vitthalrao Bhimasha Khyade. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The rate of the forward reaction from E + S to ES may be INTRODUCTION termed k1, and the reverse reaction as k-1. Likewise, for the reaction from the ES complex to E and P, the forward reaction Enzymes are protein molecules that manipulate other rate is k2, and the reverse is k-2. Therefore, the ES complex molecules the enzymes' substrates. These target molecules may dissolve back into the enzyme and substrate, or move bind to an enzyme's active site and are transformed into forward to form product. At initial reaction time, when t ≈ 0, products through a series of steps known as the enzymatic little product formation occurs, therefore the backward reaction mechanism. Enzyme kinetics is the study of the chemical rate of k-2 may be neglected. The new reaction becomes: reactions that are catalyzed by enzymes. In enzyme kinetics, the reaction rate is measured and the effects of varying the E + S ↔ ES → E + P conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic Assuming steady state, the following rate equations may be mechanism of this enzyme, its role in metabolism, how its written as: activity is controlled, and how a drug or an agonist might inhibit the enzyme (Kraut, Carroll and Herschlag (2003). The Rate of formation of ES = k1[E][S] Michaelis-Menten equation arises from the general equation Rate of breakdown of ES = (k-1 + k2) [ES] and set equal to for an enzymatic reaction: each other (Note that the brackets represent concentrations). E + S ↔ ES ↔ E + P, Therefore: k1[E][S] = (k-1 + k2) [ES] Where E is the enzyme, Rearranging terms, S is the substrate, [E][S]/[ES] = (k-1 + k2)/k1 ES is the enzyme-substrate complex, and P is the product. The fraction [E][S]/[ES] has been coined Km, or the Michaelis constant. According to Michaelis-Menten's kinetics equations, Thus, the enzyme combines with the substrate in order to form at low concentrations of substrate, [S], the concentration is the ES complex, which in turn converts to product while almost negligible in the denominator as KM >> [S], so the preserving the enzyme. equation is essentially 533 International Journal of Recent Academic Research, Vol. 01, Issue 09, pp.532-542, December, 2019 V0 = Vmax [S]/KM A graph of the double-reciprocal equation is also called a Lineweaver-Burk, 1/Vo vs 1/[S]. The y-intercept is 1/Vmax; Which resembles a first order reaction. the x-intercept is -1/KM; and the slope is KM/Vmax. Lineweaver-Burk graphs are particularly useful for analyzing At High substrate concentrations, [S] >> KM, and thus the term how enzyme kinematics change in the presence of inhibitors, [S]/([S] + KM) becomes essentially one and the initial velocity competitive, non-competitive, or a mixture of the two. There approached Vmax, which resembles zero order reaction. are four reversible inhibitors: competitive, uncompetitive, non- competitive and mixed inhibitors. They can be plotted on The Michaelis-Menten equation is: double reciprocal plot. Competitive inhibitors are molecules that look like substrates and they bind to active site and slow down the reactions. Therefore, competitive inhibitors increase Km value (decrease affinity, less chance the substrates can go to active site), and Vmax stays the same. On double reciprocal plot, competitive inhibitor shifts the x-axis (1/[s]) to the right Michaelis-Menten Equation towards zero compared to the slope with no inhibitor present. Uncompetitive inhibitors can bind close to the active site but In this equation: don't occupy the active site. As a result, uncompetitive inhibitors lower Km (increase affinity) and lower Vmax. On V is the initial velocity of the reaction. 0 double reciprocal plot, x-axis (1/[s]) is shifted to the left and up V is the maximal rate of the reaction. max on the y-axis (1/V) compared to the slope with no inhibitor. [Substrate] is the concentration of the substrate. Non-competitive inhibitors are not bind to the active site but somewhere on that enzyme which changes its activity. It has K is the Michaelis-Menten constant which shows the m the same Km but lower Vmax to those with no inhibitors. On concentration of the substrate when the reaction velocity is the double reciprocal plot, the slope goes higher on y-axis equal to one half of the maximal velocity for the reaction. It (1/V) than the one with no inhibitor. Km value is numerically can also be thought of as a measure of how well a substrate equal to the substrate concentration at which the half of the complexes with a given enzyme, otherwise known as its enzyme molecules are associated with substrate. km value is an binding affinity. An equation with a low K value indicates a m index of the affinity of enzyme for its particular substrate. large binding affinity, as the reaction will approach V more max The velocity (v) of biochemical reaction catalyzed by the rapidly. An equation with a high K indicates that the enzyme m enzyme vary according to the status of factors like: does not bind as efficiently with the substrate, and V will max concentration of the substrate [S]; hydrogen ion concentration; only be reached if the substrate concentration is high enough to temperature; concentration of the respective enzyme; activators saturate the enzyme. As the concentration of substrates and inhibitors. There is no linear response of velocity (v) of increases at constant enzyme concentration, the active sites on biocatalyzed reaction to the concentration of the substrate [s]. the protein will be occupied as the reaction is proceeding. This may be due to saturable nature of enzyme catalyzed When all the active sites have been occupied, the reaction is biochemical reactions. If the initial velocity (v) or rate of the complete, which means that the enzyme is at its maximum enzyme catalyzed biochemical reaction is expressed in terms capacity and increasing the concentration of substrate will not of substrate-concentration of [S], it appears to increase. That is increase the rate of turnover. Here is an analogy which helps to to say, initial velocity (v) of the enzyme catalyzed biochemical understand this concept easier. reaction get increase according to the increase in the concentration of substrate [S]. This tendency of increase in Vmax is equal to the product of the catalyst rate constant (kcat) initial velocity (v) of the enzyme catalyzed biochemical and the concentration of the enzyme. The Michaelis-Menten reaction according to the increase in the concentration of equation can then be rewritten as V= Kcat [Enzyme] [S] / (Km substrate [S] is observed up to certain level of the + [S]). Kcat is equal to K2, and it measures the number of concentration of substrate [S]. At this substrate concentration substrate molecules "turned over" by enzyme per second. The [S], the enzyme exhibit saturation and exert the initial velocity unit of Kcat is in 1/sec. The reciprocal of Kcat is then the time (v) of the biocatalyzed reaction to achieve maximum velocity required by an enzyme to "turn over" a substrate molecule. The (V ).
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