The Vestibulo-Ocular Reflex (VOR) produces compensatory eye movements in response to head and body rotations movements, over a wide range of frequencies and in a variety of dimensions. The individual components of the VOR are separated into parallel pathways, each dealing with rotations or movements in individual planes or axes. The Horizontal VOR (hVOR) compensates for eye movements in the Horizontal plane, and comprises a linear and non-linear pathway. The linear pathway of the hVOR provides fast and accurate compensation for rotations, the response being produced through 3-neuron arc, producing a direct translation of detected head velocity to compensatory eye velocity. However, single neurons involved in the middle stage of this 3-neuron arc cannot account for the wide frequency over which the reflex compensates, and the response is produced through the population response of the Medial Vestibular Nucleus (MVN) neurons involved. Population Heterogeneity likely plays a role in the production of high fidelity population response, especially for high frequency rotations. Here we present evidence that, in populations of bio-physical compartmental models of the MVN neurons involved, Heterogeneity across the population, in the form of diverse spontaneous firing rates, improves the response fidelity of the population over Homogeneous populations. Further, we show that the specific intrinsic membrane properties that give rise to this Heterogeneity may be the diversity of certain slow voltage activated Potassium conductances of the neurons. We show that Heterogeneous populations perform significantly better than Homogeneous populations, for a wide range of input amplitudes and frequencies, producing a much higher fidelity response. We propose that variance of Potassium conductances provides a plausible biological means by which Heterogeneity arises, and that the Heterogeneity plays an important functional role in MVN neuron population responses. We discuss our findings in relation to the specific mechanism of Desynchronisation through which the benfits of Heterogeneity may arise, and place those findings in the context of previous work on Heterogeneity both in general neural processing, and the VOR in particular. Interesting findings regarding the emergence of phase leads are also discussed, as well as suggestions for future work, looking further at Heterogeneity of MVN neuron populations.

Chemical reactions involving small number of reacting molecules are noisy processes. They are simulated using stochastic simulation algorithms like the Gillespie SSA, which are valid when the reaction environment is well-mixed. This is not the case in reactions occuring on biological media like cell membranes, where alternative simulation methods have to be used to account for the crowded nature of the reacting environment. Ion channels, which are membrane proteins controlling the flow of ions into and out of the cell, offer excellent single molecule conditions to test stochastic simulation schemes in crowded biological media. Single molecule reactions are of great importance in determining the functions of biological molecules. Access to their experimental data have increased the scope of com-putational modeling of biological processes. Recently, single molecule experiments have revealed the non-Markovian nature of chemical reactions, due to a phenomenon called `dynamic disorder', which makes the rate constants a deterministic function of time or a random process. This happens when there are additional slow scale conformational transitions, giving the molecule a memory of its previous states. In a previous work, the hTREK1 two pore domain potassium channel was revealed to have long term memory in its kinetics, prompting alternate non-Markovian schemes to analyze its gating. Traditionally, ion channel gating is modeled as Markovian transitions between fixed states. In this work, we have used single channel data from hTREK1 ion channel and have provided a simple diffusion model for its gating. The main assumption of this model is that the ion channel diffuses through a continuum of states on its potential energy landscape, which is 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. The method is computationally very simple and efficient and reproduces the amplitude histogram very well. For the case when ligands are added, leading to incorporation of long term memory in the kinetics, the SDE is modified to run on coloured noise. This has been done by introducing an auxiliary variable into the equation. It has been shown that increasing the noise correlation with ligand concentration improves the fits to the experimental data. This has been validated for several datasets. These methods are more advantageous for simulation than the Markovian models as they are true to the physical picture of gating and also computationally very efficient. Reproducing the whole raw data trace takes no more than a few seconds with our scheme, with the only input being the amplitude histogram and four parameters. Finally a quantitative model based on a modified version of the Chemical Langevin equation is given, which works on random rate parameters. This model is computationally simple to implement and reproduces the catalytic activity of the channel as a function of time. From the computational analysis undertaken in this work, we can infer that ion channel activity can be modeled using the framework of non-Markovian processes, lending credence to the recent understanding that single molecule reactions are basically processes with long-term memory. Since the ion channel is basically a protein, we can also hypothesize that the some of the properties that make proteins so vital to living organ-isms could be attributed to long-term memory in their folding kinetics, giving them the ability to sample specific regions of their conformation space, which are of interest to biological functions.