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F1-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the central γ-subunit rotates inside the α3 β3cylinder. A stochastic four-state mechanochemical coupling model of F1-ATPase is studied with the aid of the master equation. In this model, the ATP hydrolysis and synthesis are dependent on ATP, ADP, and Pi concentrations. The effects of ATP concentration, ADP concentration, and the external torque on the occupation probability of binding-state, the rotation rate and the diffusion coefficient of F1-ATPase are investigated. Moreover, the results from this model are compared with experiments. The mechanochemical mechanism F1-ATPase is qualitatively explained by the model.

It is well known that the strong coupling can synchronize a network of nonlinear oscillators. Synchronization provides the basis of the remarkable computational performance of the brain. In this paper the FitzHugh–Nagumo neuron network is constructed. The dependence of the synchronization on the coupling strength, the noise intensity and the size of the neuron network has been discussed. The results indicate that the coupling among neurons works to improve the synchronization, and noise increases the neuron random dynamics and the local fluctuations; the larger the size of network, the worse the synchronization. The dependence of the synchronization on the strength of the electric synapse coupling and chemical synapse coupling has also been discussed, which proves that electric synapse coupling can enhance the synchronization of the neuron network largely.

We study force generation and motion of molecular motors using a simple two-state model in the paper. Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that are periodic and polar. The current and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the current is also calculated. It is shown that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states.

It is well known that potassium ion channels have higher permeability than K ions, and the permeable rate of a single K ion channel is about 108 ions per second. We develop a hierarchical model of potassium ion channel permeation involving ab initio quantum calculations and Brownian dynamics simulations, which can consistently explain a range of channel dynamics. The results show that the average velocity of K ions, the mean permeable time of K ions and the permeable rate of single channel are about 0.92 nm/ns, 4.35 ns and 2.30×108 ions/s, respectively.

Oligochitosan (OC) can regulate plant defense responses in many aspects, but the basic signal transduction pathway is still unclear. In this study, we used transgenic (TG) tobacco (Nicotiana Tabacum var. Samsun NN) as plant material whose oligochitosan induced protein kinase (OIPK) gene was inhibited by antisense transformation, to study the role of OIPK in tobacco defense reactions. The results showed that OIPK could increase tobacco resistance against tobacco mosaic virus (TMV), in that wild-type (WT) tobacco showed longer lesion appearance time, higher lesion inhibition ratio, smaller average final lesion diameter and lower average final lesion area percent to whole leaf area. It led us to analyze some pathogenesis related (PR) enzymes' activities and mRNA level, which played roles in tobacco resistance against TMV. We found that phenylalanine ammonia-lyase (PAL) and peroxidase (POD) activities were positively related to OIPK, but not polyphenol oxidase (PPO). It was also demonstrated that OIPK mRNA could be induced by OC, wound and TMV infection. In addition, OIPK could up-regulated three PR genes, PAL, chitinase (CHI) and beta-1, 3-glucanase (GLU) mRNA level to different extent. Taken together, these results implied that OIPK could function in tobacco resistance against both biotic and abiotic stress, possibly via various PR proteins.

Oligochitosan (OC) could regulate plant defense responses in many aspects, but the basis signal transduction pathway is still unclear. In this study, we use transgenic (TG) tobacco as plant material whose OIPK gene was inhibited by antisense transformation, to identify the role oligochitosan induced protein kinase (OIPK) played in OC treated tobacco plants. Pathogen-related (PR) proteins enzymes activity assays and reverse transcriptional polymerase (RT-PCR) were conducted to compare the differences between TG and the corresponding wild type (WT) tobacco plants. Firstly, it was validated that OIPK could induce Phenylalanine ammonialyase (PAL, E.C. 4.3.1.5) and peroxidase (POD, E.C. 1.11.1.7 ) activities in respect to both activation time and activation fold after OC treatment, while OIPK had no influences on polyphenol oxidase (PPO, E.C.I.14.18.1) activity. Secondly, it was found that in TG tobacco, there was nearly just basis pal transcriptional expression after OC treatment, which showed that OIPK could determine pal gene expression in some sense. Thirdly, OIPK could enhance defense related gene transcription chi and glu activation intension and rapidity.

Master equation is used in the paper under the condition of dissociation rate to study the directed motion of molecular motor. The drift velocity, the diffusion constant, the dwell time and the mean length of the motor are calculated. We found the dissociation rate affects the directed motion of the molecular motor.

� Abstract—Force generation and directed motion of molecular motors using a simple two-state model are studied in the paper. Here we consider the asymmetric and periodic potential in the model. The symmetric and periodic potential is adopted to describe the interactions between motor proteins and filaments that are periodic and polar. The flux and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the flux is also calculated. It is concluded that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states. Moreover, we compare the theoretical relationship of load force and velocity with the experimental data. It is shown that they are consistent. I. INTRODUCTION

In this paper, a Brownian dynamics model of cell membrane calcium ion channels exposure to ELF magnetic fields has been proposed for the first time. Based on the model, the permeation of calcium channels activation by applied magnetic fields is given here. The number of opened calcium channel is increase with magnetic fields. The currents of calcium ions in the channel in controls and exposure to ELF magnetic fields are almost the same. These results are consistent with experiments. Thus it can be seen that the current of single calcium channel was nearly unaffected by applied magnetic fields, the increased number of opened calcium channel may be the reason of increased intracellular calcium concentration.

In this paper, a new approach is proposed to model permeation of calcium channels activation by applied magnetic fields. The curves of average velocity and displacement of calcium ions in the channels exposed to ELF magnetic fields are obtained, and they are higher than the controls. The relative numbers of calcium ions in ELF magnetic field stimulated channels is no different from that of controls. The increased number of opened calcium channel may be the reason of increased intracellular calcium concentration.

We propose a dynamical model to study the dynamical mechanism of the negative feedback loop composed of p53 and Mdm2 proteins regulated by p14/19ARF. The different oscillatory behaviors for the activities of p53 and Mdm2 proteins regulated by p14/19ARF in individual of cells are described in our dynamical model. The results help us build a basal network about oscillatory behaviors between p53, Mdm2 and P14/19ARF. The dynamical model on p53-Mdm2 feedback loop regulated by p14/19ARF and its numerical results will help us understand the oscillatory behavior of p53, Mdm2 and P14/19ARF more deeply and rationally. It is also give a good model to study the relations among the network of different protein within cell.

Under the effect of external driving force and noise, a directed transport model for coupled particles in a two-dimensional potential is established. Here, a one-dimensional potential is taken as the periodic piecewise ratchet potential, and the other one is taken as the periodic symmetric non-ratchet potential to which the external periodic driving force and noise are applied. According to the nonequilibrium statistical theory and the nonlinear dynamics, the transport characters of the coupled system in the overdamped case are researched and discussed. Numerical results show that an obvious directed transport can appear both in the ratchet potential and in the non-ratchet potential case. But, the average velocities of the coupled system in the two potentials have completely different dependence on the system parameters. In the case of ratchet potential, the average velocity is strongly dependent on the coupling intensity, noise intensity, the driving strength, and the particle population; the average velocity can reach the maximum at appropriate coupling intensity, noise intensity, the driving strength or the particle population. Otherwise, in the case of non-ratchet potential, the average velocity is strongly dependent on the barrier height for the non-ratchet potential, but fluctuates as the coupling intensity, the driving strength, the driving initial phase difference or the particle population varies. This shows that the average velocity of the coupled system in the non-ratchet potential has weak dependence on system parameters, including the coupling intensity, the driving strength, the driving initial phase difference and the particle population.

Because of the special structure and intracellular functions of myosin Ⅵ molecular motor, its dynamic principle has become a research focus. Starting from its structure and experimental phenomenon, the elastic-diffusion model of myosin Ⅵ in a periodic potential field is established, and the stochastic dynamics of the molecular motors, which conform to the Langevin equation, is analyzed by Monte Carlo simulations. By means of the environmental noise, myosin Ⅵ molecular motors could take stable stepping motion and effective transport according to its elastic potential energy and periodic potential of track, and a load can weaken the transportation power of the molecular motor system. For a given elastic coefficient, the longer the elastic chain of myosin Ⅵ, the lower the average velocity of it. By selecting a reasonable size of elasticity coefficient, the average velocity can be the maximum for a given elastic chain. In addition, the load can increase exponentially the mean dwelling time of myosin Ⅵ at the connection site.

The dynamic principle of molecular motor transport in overdamped solution remains unclear. Starting from the transport characteristics and phenomenon of the molecular motor system, the single-direction energy transition model is established, which conforms to the Langevin equation, and the stochastic dynamics of molecular motors is analyzed by Monte Carlo simulations. Results show that with the right transition energy, molecular motors could take a stable stepping motion and effective transport by means of the environment noise, and the load force can weaken material transportation of the molecular motor system. The potential field between a molecular motor and its orbit can affect the magnitude of the velocity of motor, but cannot change the direction of the velocity, the direction of motion of the molecular motor therefore is adjusted by the transition energy of the motor. In addition, although the average velocity is not zero for different noise intensities, the efficient transport of a molecular motor system indicates that the system is selective for the noise intensity.