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Mathematical inverse function (equation) for enzyme kinetics

Author Affiliations

  • 1Department of Microbiology, Shardabai Pawar Mahila Mahavidyalaya, Shardanagar Tal. Baramati Dist. Pune-413115, India
  • 2Sericulture Unit, Malegaon Sheti Farm, Agricultural Development Trust Baramati, Shardanagar, (Malegaon Khurd) Post Box No-35, Baramati, Pune 413 115, Maharashtra, India
  • 3Department of Zoology, Shardabai Pawar Mahila Mahavidyalaya, Shardanagar, Tal. Baramati, Dist. Pune–413115 India

Res. J. Recent Sci., Volume 7, Issue (12), Pages 1-7, December,2 (2018)


The most significant application of Lineweaver–Burk plot lies in the determination of Constant of Michaelis in enzyme kinetics. The constant of Michaelis is well recognized as, “Km”. This constant of Michaelis is concentration of substrate [S] and it give the velocity (v) of reaction that correspond to half of it’s maximal or Vmax. The Km, the Michaelis constant, for practical purposes, is the concentration of substrate that allows the enzyme velocity to achieve half of it’s maximum Vmax (Vmax ÷ 2). Most of the readings of inverse of enzyme velocity (1 ÷ v) occupy position far to the right of the x-axis. Through the reverse the mathematical steps and get inverse of substrate concentration (1÷S) back from some output value, say inverse of respective velocity (1÷v), it is necessary to carry out the steps exactly in back sequence. That is to say, one should subtract the inverse of maximum velocity (1÷Vmax) from inverse of respective velocity (1÷v) and then multiply the result by Vmax/Km . This is going to yield the equation correspond to: 1/(S ) = (Vmax )/Km X 1/v - 1/(Km ) . The 1÷S and 1÷v for given enzyme catalyzed biochemical reaction deserve symmetry, that is to say the symmetry between a Lineweaver Burk Plot (the real function) and the inverse function for enzyme kinetics of present attempt. The co-ordinates of the point of intersection of both the equations 1/(V ) = (Km )/( Vmax) X 1/S+1/(Vmax ) and 1/(S ) = (Vmax )/Km X 1/v - 1/(Km ) correspond to: ( 1/(Vmax-Km ) , 1/(Vmax-Km ) ) .


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