Michaelis-Menten UDL Library

TableCurve 2D furnishes the user-defined function library MICHMENT.UDL. The Michaelis-Menten equation, often used in enzyme kinetics, is based upon a hyperbolic rate equation: dC/dt=A1*C/(A2+C). The solution, C(t), involves an implicit form: Y=A0+A2*LN(A0)-A1*X-A2*LN(Y). Y is concentration, X is time, A0 is the concentration at time 0, and A1 and A2 are the parameters of the underlying rate equation.

The first UDF solves this model implicitly:

F1=IF((Y.EQ.DATAERR).OR.(Y.LE.0),0,A0+A2*LN(A0)-A1*X-A2*LN(Y)-Y)

Y=IMPLICIT(F1,YMIN,YMAX,1E-8)

The second UDF offers an explicit solution via Lambert's W function:

Y=OMEGA((1/A2)*EXP(-(-A0-A2*LN(A0)+X*A1)*(1/A2)))*A2

The UDFs use the following formula for initial estimates:

A0=YMAX

A1=YMAX*(LN(3)-LN(2))/(2*X50*LN(3)+2*XWTR*LN(2))

A2=-YMAX*(X50+XWTR)/(2*X50*LN(3)+2*XWTR*LN(2))

where,

YMAX=maximum Y, should be value at time X=0 where data begins

X50 = X at 50% of Y range

XWTR

= X at 75% Y range - X at 25% Y range

The initial estimates will be accurately determined, provided sufficient data exists for TableCurve 2D to accurately map a transition center and width.

Since all active UDFs are automatically fitted in all processing options, the Curve Fit Kinetics Equations can be used to fit this model and the standard kinetics models in a single step.