Patch clamp data driven stochastic modeling and simulation of hTREK1 potassium ion channel gating

Chemical reactions involving small number of molecules are noisy and are simulated using stochastic simulation algorithms, which are valid when the reaction environments are well mixed. However, biological media are crowded reaction environments where alternative simulation methods have to be used. Single molecule experiments have revealed non-markovian nature of biological reactions due to a phenomenon called dynamic disorder which makes the rate constants random. This happens when there are additional slow scale conformational transitions, giving the molecule a memory of its previous states. Traditionally, ion channel gating is modeled as Markovian transitions between fixed states. hTREK1 channel, a two pore domain potassium channel, has been shown to have long term memory in its kinetics under the influence of trichloroethanol, an anaesthetic. Here we show that lactate, a metabolite that increases in concentration during ischemia, is also able to induce memory in the channel. We have provided a simple diffusion model for its gating that assumes ion channel diffusion through a continuum of states on its potential energy landscape, derived from the steady state probability distribution of ionic current recorded from patch clamp experiments. A stochastic differential equation (SDE) driven by Gaussian white noise is proposed to model this motion in an asymmetric double well potential which can reproduce the amplitude histogram very well. Such cases where ligands like lactate are added, the SDE is modified by introducing an auxiliary variable to run on coloured noise such that increasing the noise correlation with ligand concentration improves the fits to experimental data. These methods unlike the Markovian models are true to the physical picture of gating and are able to efficiently reproduce the whole raw data trace over a few seconds' interval.