Volume 11, Number 02, February 2021

Cell Switches Model Applying Markov Chain Stochastic Model Check on Between Two Population with Regards to MRNA and Proteins and Neurons both Classically and Quantum Computationally

  Authors

Qin He, Rubin Wang and Xiaochuan Pan, East China University of Science and Technology, China

  Abstract

Arc, one virus-like gene, crucial for learning and memory, was dis-covered by researchers in neurological disorders fields, Arc mRNA’s single directed path and allowing protein binding regional restric-tively is a potential investigation on helping shuttle toxic proteins responsible for some diseases related to memory deficiency. Mean time to switching (MTS) is calculated explicitly quantifying the switching process in statistical methods combining Hamiltonian Markov Chain(HMC). The model derived from predator and prey with typeII functional response studies the mechanism of normals with intrin-sic rate of increase and the persisters with the instantaneous discovery rate and converting coefficients. During solving the results, since the numeric method is applied for the 2D approximation of Hamiltonion with intrinsic noise induced switching combining geometric minimum action method. In the application of Hamiltonian Markov Chain, the behavior of the convertion (between mRNA and proteins through 6 states from off to on ) is described with probabilistic conditional logic formula and the final concentration is computed with both Continuous and Discret Time Markov Chain(CTMC/DTMC) through Embedding and Switching Diffusion. The MTS, trajectories and Hamiltonian dynamics demonstrate the practical and robust advantages of our model on interpreting the switching process of genes (IGFs, Hax Arcs and etc.) with respects to memory deficiency in aging process which can be useful in further drug efficiency test and disease curing. Coincidentally, the Hamiltonian is also well used in describing quantum mechanics and convenient for computation with time and position information using quantum bits while in the second model we construct, switching between excitatory and inhibitory neurons, similarity of qubit and neuron is an interesting object as well. Especially with the interactions operated with phase gates, the excitation from the ground state to excitation state is a well analogue to the neuron excitation. Not only on theoretical aspect, the experimental methods in neuron switching model is also inspiring to quantum computing. Most basic one is as stimulate hippocampus can be identical to spontaneous neural excitation(|g>|e>), pi-pulse is utilized to drive the ground state to the higher state. There thus exists prosperous potential to study the transfer between states with our switch models both classical and quantum computationally.

  Keywords

switching model, mean time to switching, Hamiltonian Markov Chain, geometric minimum action method, firing rate, neuron models, Hopfield network, excitation and inhibition, quantum computation, fast gates, phase estimation, sweep entanglement.