Biomolecular motors are tiny engines that transport materials at the microscopic level within biological cells. In recent years, Elston and Peskin et al have investigated the effect of the elastic properties of the te...Biomolecular motors are tiny engines that transport materials at the microscopic level within biological cells. In recent years, Elston and Peskin et al have investigated the effect of the elastic properties of the tether that connects the motor to its cargo at the speed of the motor. In this paper we extend their work and present a tether in the form of symmetric linear potential. Our results show that when the driving mechanism is an imperfect Brownian ratchet, the average speed decreases as the stiffness of the tether increases in the limit of large motor diffusion coefficient, which is similar to the results of Elston and Peskin. However, a threshold for the stiffness of the tether connecting the motor to its cargo is found in our model. Only when the tether is stiffer than the threshold can the motor and its cargo function co-operatively, otherwise, the motor and its cargo depart from each other. This result is more realistic than that of the spring model of Elston and Peskin.展开更多
T7 RNA polymerase can transcribe DNA to RNA by translocating along the DNA. Structural studies suggest that the pivoting rotation of the O helix in the fingers domain may drive the movement of the O helix C-terminal T...T7 RNA polymerase can transcribe DNA to RNA by translocating along the DNA. Structural studies suggest that the pivoting rotation of the O helix in the fingers domain may drive the movement of the O helix C-terminal Tyr639 from pre- to post-translocation positions. In a series of all-atom molecular dynamics simulations, we show that the movement of Tyr639 is not tightly coupled to the rotation of the O helix, and that the two processes are only weakly dependent on each other. We also show that the internal potential of the enzyme itself generates a small difference in free energy （△E） between the post- and pre-translocation positions of Tyr639. The calculated value of △E is consistent with that obtained from single-molecule experimental data. These findings lend support to a model in which the translocation takes place via a Brownian ratchet mechanism, with the small free energy bias △E arising from the conformational change of the enzyme itself.展开更多
The ratchet motion of a Brownian particle in a symmetric periodic potential under a rocking force thatbreaks the temporal symmetry is studied. As long as the relaxation time in the thermal background is much shorter t...The ratchet motion of a Brownian particle in a symmetric periodic potential under a rocking force thatbreaks the temporal symmetry is studied. As long as the relaxation time in the thermal background is much shorter thanthe forcing period, the unidirectional transport can be analytically treated. By solving the Fokker-Planck equations, weget an analytical expression of the current. This result indicates that with an appropriate match between the potentialfield, the asymmetric ac force and the thermal noise, a net current can be achieved. The current versus thermal noiseexhibits a stochastic-resonance-like behavior.展开更多
We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic...We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency.展开更多
We study the Brownian ratchet conditions starting with Feynman’s proposal. We show that this proposal is incomplete, and is in fact non-workable. We give the correct model for this ratchet.
Molecular motors are proteins or protein complexes which function as transporting engines in biological cells. This paper models the tether between motor and its cargo as a symmetric linear potential. Different from E...Molecular motors are proteins or protein complexes which function as transporting engines in biological cells. This paper models the tether between motor and its cargo as a symmetric linear potential. Different from Elston and Peskin＇s work for which performance of the system was discussed only in some limiting cases, this study produces analytic solutions of the problem for general cases by simplifying the transport system into two physical states, which makes it possible to discuss the dynamics of the motor--cargo system in detail. It turns out that the tether strength between motor and cargo should be greater than a threshold or the motor will fail to transport the cargo, which was not discussed by former researchers yet. Value of the threshold depends on the diffusion coefficients of cargo and motor and also on the strength of the Brownian ratchets dragging the system. The threshold approaches a finite constant when the strength of the ratchet tends to infinity.展开更多
On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal tile dynamical mechanism of cooperat...On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal tile dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional trans- port of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asym- metric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Di- rected transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.展开更多
In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two...In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied, reverse motion can be achieved by modulating the coupling free length and the phase shift of tile pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be maniplflated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.展开更多
A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. Extensive Langevin simulations of the model are performed. We disc...A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. Extensive Langevin simulations of the model are performed. We discuss the dependences of motion and efficiency on the model parameters, including the external force and the temperature. A good qualitative agreement with the expected behavior is observed.展开更多
We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usua...We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation(linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein–Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.展开更多
The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel w...The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears.展开更多
We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of...We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of which is periodic.For this particular case,the least period of the potential function is a common period amongst all of its component functions.An approximation of the MST for the potential function is derived,and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions.Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription.We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes.Two examples using truncated Fourier series are presented and analyzed.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 39970217）.
文摘Biomolecular motors are tiny engines that transport materials at the microscopic level within biological cells. In recent years, Elston and Peskin et al have investigated the effect of the elastic properties of the tether that connects the motor to its cargo at the speed of the motor. In this paper we extend their work and present a tether in the form of symmetric linear potential. Our results show that when the driving mechanism is an imperfect Brownian ratchet, the average speed decreases as the stiffness of the tether increases in the limit of large motor diffusion coefficient, which is similar to the results of Elston and Peskin. However, a threshold for the stiffness of the tether connecting the motor to its cargo is found in our model. Only when the tether is stiffer than the threshold can the motor and its cargo function co-operatively, otherwise, the motor and its cargo depart from each other. This result is more realistic than that of the spring model of Elston and Peskin.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374352 and 11274374)the National Key Research and Development Program of China(Grant No.2016YFA0301500)
文摘T7 RNA polymerase can transcribe DNA to RNA by translocating along the DNA. Structural studies suggest that the pivoting rotation of the O helix in the fingers domain may drive the movement of the O helix C-terminal Tyr639 from pre- to post-translocation positions. In a series of all-atom molecular dynamics simulations, we show that the movement of Tyr639 is not tightly coupled to the rotation of the O helix, and that the two processes are only weakly dependent on each other. We also show that the internal potential of the enzyme itself generates a small difference in free energy （△E） between the post- and pre-translocation positions of Tyr639. The calculated value of △E is consistent with that obtained from single-molecule experimental data. These findings lend support to a model in which the translocation takes place via a Brownian ratchet mechanism, with the small free energy bias △E arising from the conformational change of the enzyme itself.
文摘The ratchet motion of a Brownian particle in a symmetric periodic potential under a rocking force thatbreaks the temporal symmetry is studied. As long as the relaxation time in the thermal background is much shorter thanthe forcing period, the unidirectional transport can be analytically treated. By solving the Fokker-Planck equations, weget an analytical expression of the current. This result indicates that with an appropriate match between the potentialfield, the asymmetric ac force and the thermal noise, a net current can be achieved. The current versus thermal noiseexhibits a stochastic-resonance-like behavior.
文摘We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency.
文摘We study the Brownian ratchet conditions starting with Feynman’s proposal. We show that this proposal is incomplete, and is in fact non-workable. We give the correct model for this ratchet.
基金supported by the National Natural Science Foundation of China (Grant No. 30600121)Doctoral Foundation of Shandong Province of China (Grant No. 2007BS09002)
文摘Molecular motors are proteins or protein complexes which function as transporting engines in biological cells. This paper models the tether between motor and its cargo as a symmetric linear potential. Different from Elston and Peskin＇s work for which performance of the system was discussed only in some limiting cases, this study produces analytic solutions of the problem for general cases by simplifying the transport system into two physical states, which makes it possible to discuss the dynamics of the motor--cargo system in detail. It turns out that the tether strength between motor and cargo should be greater than a threshold or the motor will fail to transport the cargo, which was not discussed by former researchers yet. Value of the threshold depends on the diffusion coefficients of cargo and motor and also on the strength of the Brownian ratchets dragging the system. The threshold approaches a finite constant when the strength of the ratchet tends to infinity.
基金This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11075016 and 11475022）, the Scientific Research project of Zhangjiakou city （Grant No. 1611064B）, and the Scientific Re- search Funds of Huaqiao University.
文摘On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal tile dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional trans- port of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asym- metric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Di- rected transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.
基金This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11075016 and 11475022） and the Scientific Research Funds of Huaqiao University.
文摘In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied, reverse motion can be achieved by modulating the coupling free length and the phase shift of tile pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be maniplflated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.
基金Project supported by the Educational Commission of Henan Province,China (Grant No. 2006140015)the Science and Technology Planning Project of Henan Province,China (Grant No. 092300410142)
文摘A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. Extensive Langevin simulations of the model are performed. We discuss the dependences of motion and efficiency on the model parameters, including the external force and the temperature. A good qualitative agreement with the expected behavior is observed.
基金supported by the "Granular-Chaos" projectfunded by the Italian MIUR under the FIRB-IDEAS grant number RBID08Z9JE
文摘We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation(linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein–Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.
基金Supported by National Natural Science Foundation of China under Grant No.11175067
文摘The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears.
文摘We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of which is periodic.For this particular case,the least period of the potential function is a common period amongst all of its component functions.An approximation of the MST for the potential function is derived,and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions.Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription.We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes.Two examples using truncated Fourier series are presented and analyzed.
