I am trying to find the inhibition constant Ki using time dependent inhibition equation given in the paper (Yu-Ting Lee, Hang Thu Ta, Ronald G. Duggleby, Cyclopropane-1,1-dicarboxylate is a slow-, tight-binding inhibitor of rice ketol-acid reductoisomerase, Plant Science, Volume 168, Issue 4, April 2005, Pages 1035-1040). In order to find Ki i have to find Koff and that is where the prblem starts. the Kon value is fine but the error for koff value is higher than actual koff value. I am using MATLAB to produce graphs and calculate the values.
Is there any other way to find the koff value where the error is not higher than actual value. I am using only one assay to find all the values.
I am new to enzyme kinetics so might need detailed information for an answer :)
Thank you !
For a truly irreversible inhibitor, koff is zero. However, some covalent inhibitors are not irreversible.
One method for measuring koff that has been applied to beta-lactamase inhibitors, for example, is the "jump-dilution" experiment. The inhibitor and the enzyme are co-incubated. The inhibitor concentration should be in excess over the enzyme, and the incubation time should be long enough, so that 100% inhibition is achieved during the incubation. The complex is then diluted into the substrate to start the reaction. The dilution factor should preferably be high enough that the inhibitor is essentially fully dissociated at equilibrium so that the enzyme activity could eventually recover fully, although this is not essential. The progress of the reaction is followed over time. The reaction rate will be seen to increase with time as the inhibitor dissociates. The resulting reaction progress curve is fit to an equation containing an exponential function (see below). The exponential coefficient is koff.
[P]=Vst + (Vi -Vs)[1-exp(-kofft)]/koff
[P] is product concentration, Vi is initial rate, Vs is steady-state rate, t is time
The mathematical treatment is the same as for onset of slow-binding inhibition, except the reaction rate speeds up instead of slowing down. The treatment of slow-binding inhibition can be found on p.141 of Copeland's Evaluation of Enzyme Inhibitors in Drug Discovery. I have just replaced kobs with koff.
The method to measure Ki from the onset of inhibition progress curves is given in section 6.3 of the same book. It can be difficult to implement, however, if the affinity of the inhibitor's equilibrium binding (Ki) is low relative to its covalent reactivity (kon). Under those conditions, the kobs vs [I] plot is linear, so that no estimate of Ki is obtained.
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