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1
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0000073949
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P.G. Bergmann and J.L. Lebowitz, Phys. Rev. 99, 578 (1955). The paper sets up the foundation for using stochastic dynamics to study nonequilibrium processes in both closed and open systems. Its Sec. IV provided a mathematical justification for the existence of NESS in open systems.
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Phys. Rev.
, vol.99
, pp. 578
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Bergmann, P.G.1
Lebowitz, J.L.2
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2
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0035305311
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Section III of Ref. 1 also showed that in a closed system Helmholtz potential decreases monotonically in the course of time and is at its minimum when equilibrium canonical distribution is reached. This result has been rediscovered independently in the mesoscopic theory of single macromolecules: H. Qian, Phys. Rev. E 63, 042103 (2001);
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(2001)
Phys. Rev. E
, vol.63
, pp. 42103
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Qian, H.1
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3
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85036133596
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Phys. Rev. EH. Qian65, 016102 (2002).
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(2002)
, vol.65
, pp. 16102
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Qian, H.1
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9
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84926605024
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G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1977)
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R. Graham, Springer Tracts Mod. Phys. 66, 1 (1973);G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1977).
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Springer Tracts Mod. Phys.
, vol.66
, pp. 1
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Graham, R.1
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0033991808
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Biophys. Chem.H. Qian83, 35 (2000).
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(2000)
, vol.83
, pp. 35
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Qian, H.1
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0034111877
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D. Keller and C. Bustamante, Biophys. J. 78, 541 (2000). The important difference between this class of models and that of rectified Brownian motion 9 and fluctuating potential models 10 is that the driving force is introduced into the x direction a priori. Hence, the energy transduction is built into the model explicitly rather than being an emerging property.
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(2000)
Biophys. J.
, vol.78
, pp. 541
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Keller, D.1
Bustamante, C.2
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22
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0035333535
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Phys. Rev. ER.F. Fox and M.H. Choi, 63, 051901 (2001).
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(2001)
, vol.63
, pp. 51901
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Fox, R.F.1
Choi, M.H.2
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85036201554
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H. Qiane-print cond-mat/0106302.
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Qian, H.1
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85036200357
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If in the exchange process the lifetime of the motor protein without nucleotide is significantly long, and the dynamics of the unligated motor protein is complex, a second molecular dynamic simulation should be introduced for the bare protein. This further complicates the model but introduces no conceptual difficulties. Hence we assume that the exchange process is fast and simple in the present work
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If in the exchange process the lifetime of the motor protein without nucleotide is significantly long, and the dynamics of the unligated motor protein is complex, a second molecular dynamic simulation should be introduced for the bare protein. This further complicates the model but introduces no conceptual difficulties. Hence we assume that the exchange process is fast and simple in the present work.
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30
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85036305485
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(Formula presented) ’s are the macroscopic rate constants for the ADP-ATP exchange and (Formula presented) characterizes the location of the transition state of the reaction. See Eq. (6) for more discussions
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(Formula presented) ’s are the macroscopic rate constants for the ADP-ATP exchange and (Formula presented) characterizes the location of the transition state of the reaction. See Eq. (6) for more discussions.
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33
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85036332646
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With the presence of (Formula presented) the boundary conditions are (Formula presented) and (Formula presented)
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With the presence of (Formula presented) the boundary conditions are (Formula presented) and (Formula presented)
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34
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0033180722
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A. Parmeggiani, F. Jülicher, A. Ajdari, and J. Prost, Phys. Rev. E 60, 2127 (1999).
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(1999)
Phys. Rev. E
, vol.60
, pp. 2127
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Parmeggiani, A.1
Jülicher, F.2
Ajdari, A.3
Prost, J.4
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37
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85036179990
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The frictional coefficient of motor protein is (Formula presented) So when a frictional object with (Formula presented) is attached, assuming the force generated by the motor is F, then the velocity of the complex is (Formula presented) where f is the tension between the motor and the object. Hence, the total heat dissipation rate (Formula presented) and the (Formula presented) associated with dragging the object is (Formula presented) Hence (Formula presented)
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The frictional coefficient of motor protein is (Formula presented) So when a frictional object with (Formula presented) is attached, assuming the force generated by the motor is F, then the velocity of the complex is (Formula presented) where f is the tension between the motor and the object. Hence, the total heat dissipation rate (Formula presented) and the (Formula presented) associated with dragging the object is (Formula presented) Hence (Formula presented)
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38
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85036146280
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The phase space of our model is called cylinder in dynamical systems theory. Stochasticity aside, there are two classes of periodic solutions to a dynamical system on a cylinder: zero and nonzero rotation numbers. The former is a futile cycle in our theory. The tight coupling is related to periodic solution with rotation number 1. Higher rotation numbers correspond to multiple steps with single hydrolysis
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The phase space of our model is called cylinder in dynamical systems theory. Stochasticity aside, there are two classes of periodic solutions to a dynamical system on a cylinder: zero and nonzero rotation numbers. The former is a futile cycle in our theory. The tight coupling is related to periodic solution with rotation number 1. Higher rotation numbers correspond to multiple steps with single hydrolysis.
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41
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85036421743
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Computing the potential of mean force (Formula presented) which involves chemical bond breaking requires a hybrid quantum mechanics/molecular mechanics computation 11. After that, the standard state chemical potentials of the discrete states can be computed as follows: (Formula presented)and similarly for (Formula presented)
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Computing the potential of mean force (Formula presented) which involves chemical bond breaking requires a hybrid quantum mechanics/molecular mechanics computation 11. After that, the standard state chemical potentials of the discrete states can be computed as follows: (Formula presented)and similarly for (Formula presented)
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