Abstract
BackgroundModellers using the MWC allosteric framework have often found it difficult to validate their models. Indeed many experiments are not conducted with the notion of alternative conformations in mind and therefore do not (or cannot) measure relevant microscopic constant and parameters. Instead, experimentalists widely use the Adair-Klotz approach in order to describe their experimental data.ResultsWe propose a way of computing apparent Adair-Klotz constants from microscopic association constants and allosteric parameters of a generalised concerted model with two different states (R and T), with an arbitrary number of non-equivalent ligand binding sites. We apply this framework to compute Adair-Klotz constants from existing models of calmodulin and hemoglobin, two extreme cases of the general framework.ConclusionThe validation of computational models requires methods to relate model parameters to experimentally observable quantities. We provide such a method for comparing generalised MWC allosteric models to experimentally determined Adair-Klotz constants.
Highlights
Modellers using the MWC allosteric framework have often found it difficult to validate their models
We develop a set of equations that uses the parameters of such a generalised MWC model to compute apparent association constants according to the Adair-Klotz model. We show how these can be used in order to compare model results with experimental data using two examples which constitute extreme cases of the general framework, calmodulin and hemoglobin
The generalised MWC model proposed here opens up new ways of applying the allosteric framework: to multimers consisting of identical subunits with one ligand binding site on each, and to proteins with several binding sites of different affinities for the same ligand, be Yonetani et al [16]
Summary
The MWC model can be adapted to describe a protein (whether oligomeric or monomeric) with several ligand binding sites possessing different affinities. Obtaining the ith Adair-Klotz constants from microscopic association constants for a protein with n non-equivalent binding sites In general, for a protein with n ligand binding sites, we can express the apparent association constant for the ith binding event by computing the ratio between the concentrations of end products and initial reactants. The equation for the ith apparent association constant reads as follows: As above, both [Pi-1] and [Pi] are sums of protein populations in two different states and with ligand molecules bound to combinations of different binding sites. This comparison shows that all four AdairKlotz constants computed from the general MWC model. Both methods yield essentially the same results, slight differences are presumably due to rounding errors and/or to limitations of the data fitting algorithms used, as well as possible over-fitting in the case of the Adair-Klotz framework
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