This is confusing and limits compari sons across profiles. A recently proposed method is the partition index. This selects a reference kinase, and calculates the fraction of inhibitor molecules that would bind this kinase, research use only in an imaginary pool of all panel kinases. The partition index is a Kd based score with a thermodynamical underpinning, and performs well when test panels are smaller. However, this score is still not ideal, since it doesnt characterize the complete inhibitor distribu tion in the imaginary kinase mixture, but just the frac tion bound to the reference enzyme. Consider two inhibitors A binds to 11 kinases, one with a Kd of 1 nM and ten others at 10 nM. Inhibitor B binds to 2 kinases, seen as containing more information about which active site to bind than a promiscuous inhibitor.
The selectivity difference between the inhibitors can therefore be quan tified by information entropy. The distribution of a compound across energy states is given by the Boltzmann formula both with Kds of 1 nM. The partition index would score both inhibitors as equally specific, whereas the second is intuitively more specific. Another down side is the necessary choice of a reference kinase. If an inhibitor is relevant in two projects, it can have two dif ferent Pmax values. Moreover, because the score is rela tive to a particular kinase, the error on the Kd of this reference kinase dominates the error in the partition index. Ideally, in panel profiling, the errors on all Kds are equally weighted. Here we propose a novel selectivity metric without these disadvantages.
Our method is based on the princi ple that, when confronted with multiple kinases, inhibi tor molecules will assume a Boltzmann distribution over the various targets. The broadness of this distribution can be assessed through a theoretical entropy calculation. We show the advantages of this method and some applications. Because it can be used with any activity profiling dataset, it is a universal parameter for expressing selectivity. Results and discussion Theory Imagine a theoretical mixture of all protein targets on which selectivity was assessed. No competing factors are present such as ATP. To this mixture we add a small amount of inhibitor, in such a way that approximately all inhibitor molecules are bound by targets, and no par ticular binding site gets saturated.
A selective inhibitor Where j1 is the fraction of molecules occupying GSK-3 state 1, and G1 is the free energy of occupying state 1 when the inhibitor comes from solution. In order to arrive at a fraction, the denominator in equation contains the summation of occupancies of all states, which are labelled i, with free energies Gi. In general, entropy can be calculated from fractions of all l states using the Gibbs formula Ssel is shorthand for selectivity entropy. Compared to the original Gibbs formulation, equation contains a minus sign on the right hand to ensure that Ssel is a positive value.