Optimization and improvement of hodgkin-huxley model under the influence of ion channel noise in neurons - Khudhur, Ahmed Mahmood (2018)
In recent years, it has been argued and shown experimentally that ion channel noise in neurons can cause fundamental effects on the neuron’s dynamical behavior. Most profoundly, ion channel noise was seen to be able to cause spontaneous firing and stochastic resonance. However, Hodgkin-Huxley model affected when inserting some colored noise terms inside the conductance’s, where those effects captured by colored noise due to the gate multiplicity. Regarding the position of the trans-membrane voltage fluctuations, and the element of open-channel fluctuations is attributed to gate multiplicity. Furthermore, the phenomenon was found to significantly enhance the spike coherence. In this thesis, the proposed model directly determines a set of maximal functions of voltage parameters to fit the model neuron from the Hodgkin-Huxley equations. The statistic will be obtained using different membrane size and different input current values. Firstly, introduced the effect of (without, with) colored noise on the proposed model and the comparison of ion channel based on HH, Fox- Lu, and Linaro models. Additionally, in order to overcome the limitations of other parameter estimation methods, the proposed method fully constraints their models and obtains all models capabilities of reproducing the data. The colored stochastic Hodgkin-Huxley equations were studied when the input current to the neuron is (noise-free input currents and noisy currents). The spiking rates and the spike coherence were examined, and the coefficient of variation to be extracted from the colored noise model will be explained through a sequence of experiments by comparing the proposed model with the microscopic simulations. In particular, the role played by the presence of the colored noise terms in the conductances was focused on in the examination. Finally, statistics of spike generation, spike coherence, firing efficiency, latency, and jitter from the articulated set of equations are found to be highly accurate in comparison with the corresponding statistics from the exact microscopic Markov simulations. The simulation results revealed that above a critical value of the input frequency and also below a certain amplitude value, the colored terms play a very prominent role in the firing statistics. In addition, the spiking rate generated from the proposed model is very close to microscopic simulations and does not affect the membrane size. On the other hand, Particle Swarm Optimization (PSO) methods are commonly used to optimize compartment model parameters, by using an objective function that includes both voltage (V) and current (I) with ion channel gate variables dynamics (n for potassium channel and m h for sodium channel) based on Hodgkin–Huxley formalism in the squid giant axon, for a point-neuron model. Meanwhile, the development of regression equations was used for the estimation gating variables in the membrane current. The simulation results revealed that the larger action potentials, whose size is controlled by the difference between the voltage and current with choosing optimal gating variables for activation and inactivation membrane channels can be affected more rapidly, travel at a faster speed than smaller ones.