Study On The Motor-Assisted Transport Of Intracellular Particles

Molecular motor is a kind of protein that can convert chemical energy to mechanical energy directly and efficiently,and produce directional motion to work.It participates in all the life of cells,such as muscle contraction,DNA replication,organelle transportation.Besides passive transport by diffusion,active transport by molecular motors along the cytoskeleton is crucial for the survival of cells.There are three kinds of common molecular motors:kinesin family and dynein family that move toward the plus-end and minus-end of microtubules,respectively,and myosin family that move along the microfila-ment.The transportation involves three kinds of particles:the free cargo,the free motor and the cargo combined with the motor.They achieve reciprocal transformation by attaching and separating between motor and microtubules.Similar to highway traffic,motor-assisted transport may be crowded.Molec-ular motors participate in a variety of biological activities in vivo.The jam of the transport often results in many neurodegenerative diseases,such as Amy-otrophic Lateral Sclerosis,Parkinson’s disease,Huntington disease,Heredi-tary Sensory Neuropath.Therefore,it is worth to study the jam of motor-assisted transport of intracellular particles,which is one of the hot spots in the biomedicine field.In this paper,which is divided into five chapters,mathematical models are used to study the motor-assisted transport.Chapter one is about the research background.Firstly,three different kinds of molecular motors and their transport mechanisms are introduced.Secondly,the research status quo is summarized,and the merits and drawbacks of the main references are analyzed in detail.Thirdly,mathematical methods referred to in this paper are presented briefly.Finally,the primary jobs and innovation points are summarized.In chapter two,which selects plus-end transport as the research object,the unidirectional transport of molecular motors is analyzed.Based on Smith-Simmons model,the relation between the flux and concentration is modified.Then perturbation theory is utilized to obtain the approximate solution of the model and the applicability of the zero order approximate solution is also proved.At last,the particle concentration is analyzed by graphs on factors such as binding rate k,diffusivity D.Chapter three is about the jam of the unidirectional transport.The situ-ation where the model exists steady-state solution is defined as normal trans-port,and the other opposite situation is defined as jam.On the basis of the second chapter,the mathematical expression of the jam critical state is ob-tained and the formation of the jam is explained.Last but not least,the influences of the boundary and internal disturbance on the transportation are respectively studied,and the thresholds of the disturbance under normal trans-port are presented.In chapter four,the mathematical model studying the bidirectional trans-port is built,which is similar to the model in the second chapter.Then the zero order approximate solution is obtained and the mathematical expression of the critical state is also proved.Next the formation of jam is explained,which is compared with the third chapter.Finally,graphs are utilized to ana-lyze the effect of plus-end binding rate k+ and the minus-end binding rate k_on the bidirectional transport.Coupling effect is also studied emphatically.The last chapter is the summary of this paper.The research significance is presented.The deficiencies and pending problems of this paper are pointed out.