Fitting Michaelis-Menten directly to substrate concentration data

A GenStat procedureProcedure MICHAELISM.C. Hannah (May, 2011)1. PurposeFits Michaelis-Menten curve to substrate concentration vs time data2. DescriptionThe Michaelis-Menten non-linear curve, for biochemical reaction rate versus substrateconcentration,dS(t)VmaxS(t)v( t)= =dt K + ,mS(t)can be fitted in GenStat using FITCURVE [CURVE=ldl]. However, in practice, data areavailable only for substrate concentration, S, at time t, and not for the reaction rate, v. Thefunction S(t), that is the solution to this differential equation, has no closed form expression.The procedure MICHAELIS fits the curve S (t)versus t, obtaining parameter estimates forV max , K m and, if required, S 0 (the initial substrate) and, also if required, an additive constantK 1 representing the quantity of non-reactive substrate. This generalized Michaelis-Mentencurve is thus,dS(t)Vmax[ S(t)− K1]= .dt K + S(t)− Km1