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modeling a multiple ligands - fudge factor?

Petr Kuzmic pkuzmic at biokin.com
Mon Apr 30 15:25:46 EST 2001

Dominic-Luc Webb molmed wrote:

> ... I have
> therefore implemented two fudge factor equations (one for forward and
> one for reverse) in which the ratio of the fudged forward and
> reverse rates yields the correct ka for the enzyme. I did this to
> solve the numerical integration for a multiple ligand binding site
> problem of general form...
>           kx
> Lx + R <=====> LxR
>          k-x
> D(LxR)/dt = kx[Lx][R] - k-x[LxR]
> I need to enter a value for kx and k-x in each iteration and
> this is why the fudge factor equations were used.
> I have scanned a (neatly, I'd like to think) written one page
> description of what I have done, and would like to send this to
> right person for comments. I am not sure this is most intelligent
> way to model an enzyme. I would really like to hear from
> someone who knows about enzyme kinetics.

Your approach to enzyme kinetic modeling based on "fudge factors",
and especially the process of 'entering kx and k-x in each
iteration', seem quite suspicious to me.   Building a kinetic
model for multiple binding sites can be accomplished very easily
by using the software DynaFit: 

   Kuzmic, P. (1996) Anal. Biochem. 237, 260-273.
   "Program DYNAFIT for the Analysis of Enzyme Kinetic Data:
   Application to HIV Proteinase"


In DynaFit, you would type the following as part of your input

  E + L <==> EL     :   k1   k-1
  EL + L <==> EL2   :   k1   k-2
  EL2 + L <==> EL3  :   k3   k-3


Based on this input, the machine will automatically construct the
kinetic model in terms of first-order ordinary differential
equations (ODE).  Other types of biochemical problems can be
solved, for example, multiple simultaneous _equilibria_ (no
kinetic process here: just measuring the dependence of
_equilibrium_ composition on the total concentration of

Of course not all rate constants for multiple binding steps can be
extracted from all types of experimental data.  Some of the rate
constants might have to be kept constant at reasonable values,
while others would be treated as adjustable parameters.

Hope this helps,

	- Petr Kuzmic

P e t r   K u z m i c,  Ph. D.  * BioKin Ltd.
1652 S. Grand Ave. * Suite 337  * Pullman, WA 99163
509.334.4131 * 509.332.3493 fax * http://www.biokin.com

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