A Theoretical Approach To The Walking Dynamics Of The Microtubule-kinesin Transport System

In a series of life activities such as vesicle transport and cell division,kinesin converts chemical energy into mechanical energy through configuration transformation,and generates relative motion with microtubule orbits.Incorrect mechanical regulation between microtubules and kinesins can cause detachment of kinesins and collapse of microtubules,and even cause cell proliferation failure,canceration or death.A large number of experimental observations on kinesin transport behavior and microtubule buckling and vibration studies have shown that the microtubule-kinesin transport system has a complex molecular structure and a fine movement mechanism.Studying the walking dynamics of the microtubule-kinesin transport system will help to clarify the mechanical mechanism of the interaction between microtubules and kinesin,to deeply understand the movement mechanism of the molecular transport system,and further promote the design and synthesis of biomimetic nanomachines.Most of the current theoretical researches focus on the static solution of the system,or use the minimal model to solve the dynamics,failing to consider the difference in mechanical properties of different domains of the kinesin and the spiral chirality of the microtubule structure,it is difficult to solve the kinesin walking State changes and dynamic response of the system to external disturbances.In view of the above-mentioned shortcomings,this paper proposes a new walking dynamics model of the microtubule-kinesin transport system,and constructs a theoretical calculation method for the transient response of the transport system.The impact of learning behavior.The specific research contents and conclusions are as follows:(1)A moving load-non-local Timoshenko beam model(FNTB)for calculating the quasistatic solution of the system is proposed.Taking into account the bending and shear deformation of microtubules under the action of kinesin,the basic equations of the microtubule Timoshenko beam model are derived based on non-local theory.The deflection equation of the microtubules under the action of a moving load and itself under a uniform load Combined with the deformation equations,a quasi-static analytical solution of microtubule deformation during kinesin walking is successfully obtained.(2)A fluid-free-environment protein spring-microtubule network model(SNB)and a viscous-fluid-environment protein beam-microtubule network model(BNB)are proposed to calculate the transient dynamics of the system.When there is no influence of the fluid environment,the kinesin is simplified as a spring;in a viscous fluid environment,the kinematics of the neck chain of the kinesin is considered to be bent and sheared,and it is simplified to a space beam structure.The vibration characteristics of the kinesin stem and neck chains,the switching between single-head and double-heads states,and the scale effect of the microtubule anisotropic nano-network are comprehensively considered.Based on the Lagrange equation,the overall transport system during the kinesin walking is derived Kinetic equations.The model parameters are obtained based on molecular potential energy and structural strain energy equivalently,so that the SNB and BNB models can accurately reflect the interaction between kinesin and microtubules and the dynamic characteristics of the transport system.(3)The transient dynamic response of a single kinesin walking on a microtubule in a fluid-free environment is studied.In a fluid-free environment,the kinesin tail is only affected by the load of the cargo.Considering the repeated switching of the combined state of the protein head and the microtubules during the transport process,the deformation field and inertial field of the SNB model are discretized by finite elements.The system dynamic response is calculated.The comparison between the dynamic response of the microtubule fibrils of the SNB model and the quasi-static solution of the FNTB model proves the accuracy of the SNB model.At the same time,it proves that SNB can accurately predict the large local deformation of the microtubules,reflecting the scale effect caused by the long-range forces of the microtubules.(4)The transient dynamic response of a single kinesin walking on a microtubule in a viscous fluid environment is studied.The kinesin beam model is established to enable the new model of the transport system(BNB)to analyze and analyze the bending,shear deformation and stress propagation of microtubule fibrils and kinesin neck chains simultaneously.The comparison between the theoretical response and the quasi-static solution of the FNTB model verifies the accuracy of the BNB model.Meanwhile,the deformation and stress propagation laws of the neck chain and microtubule fibrils are summarized.It is found that the deformation of the transport system is approximately linearly related to the viscous resistance and vertical load.(5)The dynamic response of the dual-kinesins transport system is studied.The vibration response of the microtubules during co-transportation is calculated by changing the spatial distribution density of kinesin.The influence of the protein spacing change and the load distribution of the tail of the double driving proteins on the vibration response and internal force propagation of the microtubules is analyzed.