The Theoretical Study On Chemical Kinetics Of Molecular Motors

Molecular motors are nanomachines in a cell that convert the chemical energy of ATP hydrolyses into the mechanical energy.Studying the structure and working principle of molecular motors is one of the most important frontier topics in life sciences,biotechnology and even new materials and new energy technologies.The mechanical properties of molecular motors are closely related to the concentration of various chemical components in the solution.Therefore,it is an effective way to reveal their working principle by understanding the mechanochemical cycle mechanism of molecular motors.In this paper,the chemical dynamics mechanism was studied in view of Spontaneous Oscillatory Contraction?SPOC?of cardiac myofibrils,the growth process of tumors under the action of chemotherapeutic drugs,and the velocity of processive movement of molecular motors.SPOC of myocardial fibers is a third state other than myocardial contraction and relaxation.Studying the underlying causes of SPOC helps to understand the molecular biological mechanisms of cardiac work.Although the previous theoretical models can explain most of the phenomena of muscle contraction,but it has the following shortcomings:?1?It is difficult to explain the reason why the period of ADP-SPOC is about ten times longer than that of Ca-SPOC?2?Failure to establish a quantitative relationship between the two mechanisms of forward regulation(excitation-contraction coupling under Ca²⁺modulation)and backward regulation?feedback of force generating form cardiac deformation?and the rate of chemical reaction in the ATP hydrolysis cycle.Theoretical and experimental studies in recent years have pointed out that the no-force-generating state of myosin plays an important role in the mechano-chemical cycle,and the role of this state in the ATP hydrolysis cycle was only qualitatively analyzed,never been quantitatively analyzed the SPOC of myocardial fibers.In this paper,the no-force-generating state of myosin is introduced into the traditional ATP hydrolysis cycle as an independent state.The binding competitive mechanism to myosin between ADP and ATP binding to myosin is fully considered,and the chemical kinetic model of ADP-SPOC is established.Considering the passive detachment of myosin from actin filament during the process of SPOC,and the following step of myosin rebinding to actin filament under Ca²⁺,the mechanochemical model of Ca-SPOC is also established.Numerical simulations show that the proportion of various states of myosin changes with time,which is the chemical dynamic mechanism for SPOC of myocardial fibers.The results confirm that the binding rate of myosin to actin filaments is directly proportional to the value of pCa,and the combination of ADP to no-force-generating myosin greatly reduced the rate of ATP binding to myosin,which is the main reason why the period of ADP-SPOC is much longer than that of Ca-SPOC.Based on the effect of kinesin inhibitors on Eg5 enzyme activity,this paper proposes a growth model of tumor cells under the action of chemotherapy drugs.The amount of tumor growth is closely related to the natural growth rate,kill rate and drug resistance rate of cancer cells.Previous mathematical models of tumor growth focused on describing tumor growth mechanisms,or to compare the degree of drug resistance in different treatment strategies,failing to make comprehensive and in-depth studies on the relationship between the concentration of chemotherapeutic drugs and the number of tumor growth.On the base of the linear negative correlation between chemotherapeutic drug concentration and Eg5 enzyme activity,this paper proposes the model of tumor growth,in which a quantitative relationship between drug concentration and natural growth rate,kill rate and drug resistance rate of cancer cells is formed.The numerical results show that the theoretical calculations are in agreement with the experimental data at lower drug concentrations,and there is a certain deviation at higher concentrations.In order to further validate and promote the tumor growth model proposed in this paper,we compare the experimental data of tumor growth under cytotoxic drug chemotherapy with the theoretical calculation results,and find that if the tumor kill rate and drug concentration are assumed to satisfy the Mie equation,the experimental data is in good agreement with the theoretical curve.The above research results confirm that the tumor growth model proposed in this paper is simple and effective.The previous theoretical studies have proved that the move speed of molecular motors and the concentration of ATP satisfy the Mie equation under the condition that ADP does not exist.But for the case of ATP,ADP and Pi coexistence,most theoretical studies only give a fitting equation based on the experimental curve,lacking strict mathematical reasoning.Based on the four-state actomyosin ATPase cycle,considering the effects of nucleotides?ATP,ADP?and inorganic phosphate?Pi?on the motion characteristics of molecular motors,the mathematical equations for the velocity of molecular motors are given.It is proved that even if ADP and Pi are present in the solution,the velocity and the concentration of ATP are still in Mie relationship.In addition,the paper also proves that the relationship between the binding rate of ATP to motors and the concentration of ATP also meets the Mie equation,rather than the linear relationship generally considered.This conclusion needs to be further confirmed by experiments.