Simulation And Analysis Of Microtubule Transport In Crop Cells Based On Exclusion Process With Intersected Channels

Transport phenomenon widely exists in all fields of nature and human society.It is the transmission and transfer of material and information in space and time.To study this phenomenon,scientists have put forward many related models to study transport behavior.The asymmetric simple exclusion process(ASEP)model is a very classic transport model,because of its simple rules,ease of calculation,and ease of expansion,it has attracted the interest of scholars and has been widely used in traffic flow research,biological transport,and cell biology.In the microtubule network of motor protein movement in plants,there are two microtubule intersection structures.Microtubules are an important part of plant cells.Plant responses to abiotic stress are closely related to the dynamic changes of microtubules,so it is necessary to study such structures.In this thesis,the Monte Carlo simulation method and Mean Field Theory analytical method are used to study four intersecting channels ASEP models.The main contents and conclusions are as follows:(1)In the study of the intersecting ASEP model of downstream particle motion probability changes,the random update rule was used to find that when the particle motion probability p changes,the system has three symmetric phases.The simple mean field and 5-cluster mean field methods are used to analyze the model.In the simple mean field analysis,the correlation between lattice is ignored,the intersection model is split into four single channel ASEP models,and the existing conditions of each phase in the system are calculated by the conclusion of the known single channel model.In the 5-cluster mean field analysis,considering the correlation among the five lattices including intersections,the transfer equations of 48 states in the system and the density and flow conditions of the upstream and downstream are listed,and through the relaxation iteration by solving the linear equations,the phase boundary of the system is obtained.The analysis results show that the 5-cluster mean field analysis considering the lattice correlation performs better and is more consistent with the Monte Carlo simulation results.In addition,it is also verified that no asymmetric phase in the system.(2)In the study of the intersecting channel ASEP model with changing upstream particle motion probability,the random update rule is used,and the results of the study show that when the upstream particle motion probability p is taken as 0.8 and 0.9,three symmetric phases of the system exist: symmetric LD phase,symmetric HD phase and symmetric HD/LD phase;when p is taken as 0.7,0.6,0.5,0.4,0.3,0.3 0.2,0.1,the symmetric LD phase and symmetric HD phase still exist,but the symmetric HD/LD phase disappears and a new phase appears in the system: the symmetric MC phase.The mean field theory is used to analyze the steady state phase and its existing conditions in the system.The results show that the mean-field theory analysis results are consistent with the Monte Carlo simulation results.(3)An extended study of the intersecting channel ASEP model with varying global particle motion probabilities is carried out,using random update rules.By using Monte Carlo simulation method to simulate the model,there are three symmetric phases,namely symmetric LD phase,symmetric HD phase,and symmetric HD/LD phase.Using a simple mean-field analysis method to split the model into four single channel ASEP models for analysis,the conditions for the existence of the phases were obtained,and the analysis results were in good agreement with the Monte Carlo simulation results.When p = 1,the phase boundary of the mean-field analysis is,and as p varies,the phase-boundary also varies and the analysis results in p.(4)The intersecting channel ASEP model with a global parallel update rule is investigated,with the probability of motion of particles in the system p = 1.The case of conflicting particle motions in the model is treated specially.The Monte Carlo simulation results show that there are three phases in the system,namely symmetric LD phase,symmetric HD phase and special MC phase,and the simulated phase-boundary is 0.334.The conditions for the existence of each phase are resolved using simple mean-field theory,and the results obtained are in good agreement with the Monte Carlo simulation results,which are resolved at 0.309.In this thesis,four kinds of intersecting channel ASEP models with different updating rules are constructed,and the density distribution and phase diagram of the models are studied by Monte Carlo simulation and mean field theory analysis,and the relationship between particle jump probability and system density is analyzed.It can provide some theoretical support for the research of traffic flow theory,microbiology,and other fields.