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Using a well known result that every FP equation has an antecedent Langevinequation LE Fox and Lu proposed such a description for ion channels in 1994.Their contraction followed the works of van Kampen and of T. Kurtz. Thecontraction produces a diffusion term with a state dependent diffusion matrix,D, that arises from the coupling matrix, S, in the LE. This S connected thenoise terms to the channel subunit variables in the LE. Fox and Lu and manyothers later on observed that SS = D. Since D was determined by the contractionof the MC equations into the FP equation, this left the problem of determiningthe square root matrix, S, for every time step of the simulation. Since this istime consuming, Fox and Lu introduced simplified models not requiring thesquare root of a matrix. Subsequently, numerous studies were published thatshowed the several shortcomings of these simplified models. In 2011, Goldwyn etal. [6] rediscovered the overlooked original matrix dependent approach in theFox-Lu 1994 paper. They showed that it produced results in very good agreementwith the MC results. In 1991, Fox and Keizer [7] wrote a paper on an unrelatedtopic that utilized the work of van Kampen and of Kurtz. In that work theconnection between D and S is SST = D. ST is the adjoint (transpose) of S. Dremains a positive definite symmetric matrix but S need not be. Fox hasreproduced the 2012 results of Orio and Soudry for potassium channels and hasalso found in closed form the solution for the more complicated sodiumchannels. The square root problem generally must be done numerically, but theCholesky is always doable in closed form. Thereby the S matrix for sodium isgiven explicitly for the first time in this paper

Critique of the Fox-Lu model for Hodgkin-Huxley fluctuations in neuron ion channels