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Triangular Form of Lineweaver-Burk Plot for Enzyme Kinetics and Euler’s Line

Vitthalrao Bhimasha Khyade


In enzyme biochemistry, the double-reciprocal plot (Lineweaver-Burk plot) is well established concept. It is graphical presentation of numerical data on reciprocal of velocity of enzyme reaction (1÷v) and reciprocal of substrate concentration [1÷S]. This is useful for analysis of role of enzyme in the presence of inhibitors, competitive, non-competitive, or a mixture of the two. The present attempt deals with establishment of Euler’s line through the use of Triangular form of Lineweaver-Burk plot. Lineweaver-Burk plot (double reciprocal plot) is with positive value of (Km÷Vmax) as a slope. The slope for Euler Line for Enzyme Kinetics is same, but with minus sign. The intercept on y-axis for Lineweaver-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 +1) ÷ 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) ÷ 2Vmax]. 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.


Enzyme kinetics, centroid, orthocenter, circumcenter, Euler’s line, Lineweaver-Burk plot

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Michaelis, L.; Menten, M.L.(1913). Die Kinetik der Invertin-Wirkung. Biochem. Z. 49: 333–369

Lineweaver, H. and Burk, D., 1934. The determination of enzyme dissociation constants. Journal of the American chemical society, 56(3), pp.658–666.

Hayakawa, K., Guo, L., Terentyeva, E.A., Li, X.K., Kimura, H., Hirano, M., Yoshikawa, K., Nagamine, T., Katsumata, N., Ogata, T. and Tanaka, T., 2006. Determination of specific activities and kinetic constants of biotinidase and lipoamidase in LEW rat and Lactobacillus casei (Shirota). Journal of Chromatography B, 844(2), pp.240–250.

Greco, W.R. and Hakala, M.T., 1979. Evaluation of methods for estimating the dissociation constant of tight binding enzyme inhibitors. Journal of Biological Chemistry, 254(23), pp.12104–12109.

Dowd, John E.; Riggs, Douglas S. (1965). A comparison of estimates of Michaelis–Menten kinetic constants from various linear transformations (pdf). Journal of Biological Chemistry, 240 (2), pp. 863–869.

Altshiller-Court, Nathan (1925), College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2nd ed.), pp. 334, Dover Publications, New York: Barnes & Noble,

Johnson, R. A., Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle(1929)., pp. 173–176, Houghton Mifflin Company Boston, MA.

Wells, D. Curious and Interesting Geometry., The Penguin Dictionary of penguin Science(1991), p. 150, Penguin Books, London.

Mitchell, D.W., 2005. 89.80 A Heron-type formula for the reciprocal area of a triangle. The Mathematical Gazette, 89(516), pp.494–494.

Andrica D, Marinescu DS. New Interpolation Inequalities to Euler’s R≥ 2г. InForum Geometricorum (2017), 17, pp. 149–156.

Leversha, G. and Smith, G.C., 2007. Euler and triangle geometry. The Mathematical Gazette, 91(522), pp.436–452..

Richinick, Jennifer (2008). The upside-down Pythagorean Theorem, Mathematical Gazette, 92(584),


Euler, Leonhard (1767). Solutio facilis problematum quorundam geometricorum difficillimorum [Easy solution of some difficult geometric problems]. Novi Commentarii Academiae Scientarum Imperialis Petropolitanae.ser. I, vol. XXVI, pp. 139–157, Societas Scientiarum Naturalium Helveticae, Lausanne.

Sandifer, C. Edward (2007). The Early Mathematics of Leonhard Euler. Pp. 416 Mathematical Association of America.

Clark Kimberling's Encyclopedia of Triangle Centers Archived copy. Archived from the original on 2012–04–19. Retrieved 2012–04–19.

Kimberling, Clark (1998). Triangle centers and central triangles. Congressus Numerantium. 129: i–xxv, 1–295

Vitthalrao Bhimasha Khyade, Avram Hershko and Seema Karna Dongare (2019). Euler’s Line for Enzyme Kinetics. International Journal of Recent Academic Research,1(9),pp.


Robert Welkos (October 11, 1988). Dean Burk, Supporter of Laetrile, Dies. Los Angeles Times. Los Angeles Times.

Nicolás, J.M.L. and Carmona, F.G., 2015. Los cuatro mosqueteros de la cinética enzimática. Eubacteria, (34), p.5.

Bennett, T. P., and Frieden, E.: Modern Topics in Biochemistry, p. 43–45, Macmillan, London (1969).

Henri, Victor (1902). Theorie generale de l'action de quelques diastases. Compt. Rend. Acad. Sci. Paris, 135, pp. 916–919.

WILUNSON, G., 1961. Statistical estimations in enzyme kinetics. Biochem J, 80(2), pp.324–332..

Haldane, J.B.S.; Stern, K.G. (1932). Allgemeine Chemie der Enzyme, 38(12), pp. 968–969.

Haldane, J.B.S., 1957. Graphical methodsN in enzyme chemistry. ature, 179(4564), pp.832–832..

Di Domenico, A.S., 2003. 87.46 A property of triangles involving area. The Mathematical Gazette, 87(509), pp.323–324.

Posamentier, Alfred S., and Salkind, Charles T.( 1996). Challenging Problems in Geometry, 2nd edition, 272 pages, Dover Publications, New York.

Beauregard, Raymond A.; Suryanarayan, E. R. (2000), Parametric representation of primitive Pythagorean triples, in Nelsen, Roger B. (ed.), Proofs Without Words: More Exercises in Visual Thinking, II, Mathematical Association of America, p. 120.

Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, New York, pp. 788.

Charles William Hackley (1853). A treatise on trigonometry, plane and spherical: with its application to navigation and surveying, nautical and practical astronomy and geodesy, with logarithmic, trigonometrical, and nautical tables. Ann Arbor, Michigan: University of Michigan Library, New York, G. P. Putnam, pp.282.

Seema Karna Dongare, Manali Rameshrao Shinde, Vitthalrao Bhimasha Khyade (2018). Mathematical Inverse Function (Equation) For Enzyme Kinetics. International Journal of Scientific Research in Chemistry (IJSRCH), 3(4), pp: 35–42.

Vitthalrao Bhimasha Khyade, Seema Karna Dongare, Manali Rameshrao Shinde (2019). The Indian Square for Enzyme Kinetics through the Regular Form of Lineweaver-Burk Plot (Double Reciprocal Plot); its Inverse Form and Other Additional Form of Plots (Equations). International Journal of Scientific Research in Chemistry, 4 ( 1 ), pp. 40–42

Michaelis, Leonor (1913). Die Kinetik der Invertinwirkung [The kinetics of invertin action]. Biochemische Zeitschrift. 49 (17): 335–369.


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