Principles of Brownian and Molecular Motors

Molecular motors convert chemical energy (typically from ATP hydrolysis) to directed motion and mechanical work. Biomolecular motors are proteins able of converting chemical energy into mechanical motion and force. Because of their dimension, the many small parts that make up molecular motors must operate at energies only a few times greater than those of the thermal baths. The description of molecular motors must be stochastic in nature. Their actions are often described in terms of Brownian Ratchets mechanisms. In order to describe the principles used in their movement, we need to use the tools that theoretical physics give us. In this book we centralize on the some physical mechanisms of molecular motors.

Auteur
Prof. Dr. José Antonio Fornés studied Physics at La Plata University, Argentina, where he received his doctoral degree in Physics in 1972. In 1973 he worked as a postdoctoral fellow in Quantum Chemistry at Uppsala University, Sweden. In 1974 he was a postdoctoral fellow at Middlesex Hospital Medical School of London University, in experimental biophysics. He was visiting Professor at the University of California at Irvine, Department of Physiology and Biophysics, during 1989-1991. Also, he was visiting Professor at the Department of Physics of São Paulo University, Brazil, during 1998-2001. He was visiting professor at the Department of Applied Physics of the Complutense University in Madrid, Spain, during 2005-2006. He has been full Professor of Physics at the Department of Physics of the Federal University of Goiás during 1981-1998, and retired after that. His research interests comprise electrical fluctuations in molecular systems, molecular biophysics, hydrodynamic fluctuations as well as molecular motors

Contenu
1Brownian Ratchets and Molecular Motors3 1.1The force-generation 3 1.1.1Maximum Driving Force 3 1.1.2Stall Force 5 1.2Smoluchowski-Feynman's ratchet as a heat engine 6 1.2.1Parrondo Criticism 7 1.3Ratchet Efficiency 7 1.4Ratchet Coherency 9 1.5First Passage Time 9 1.6Power Stroke 102The Fokker-Planck equation17 2.1The Methods 17 2.2The Fokker-Planck Equation 18 2.3Discretization of the Fokker-Planck equation 19 2.3.1Forward Time Central Space (FTCS) Method 19 2.3.2Crank-Nicholson Method 20 2.3.3Stability Analysis 21 2.4Program 2.1, F-P Equation, Matlab code 253Biased Brownian Motion27 3.0.1Parametrization of the Langevin Equation 27 3.0.2Numerical Simulations 28 3.0.3Building the Fokker-Plank's matrices 30 3.0.4Dichotomous Markov noise 33 3.0.5Fluctuating Potential, or Flashing Ratchet 36 3.0.6Fluctuating Force, or Rocking Ratchet 41 3.1Programs 46 3.1.1Program 3.1, Euler Equation, Matlab code 46 3.1.2Program 3.2, F-P Equation, Matlab code 46 3.1.3Program 3.3, Dichotomous Noise, Matlab code 48 3.1.4Program 3.4, Flashing Ratchet, Matlab code
3.1.5Program 3.5, Rocking Ratchet, Matlab code 4 The Smoluchowski model49 4.1Diffusion 52
4.2Chemical kinetics 54 4.2.1Absolute Reaction Rate Theory 55 4.3A mechanochemical model 58 4.3.1Numerical computation of mechanochemical coupling 59 4.4Program 4.1, Matlab code 625Rotation of a dipole.67 5.1Introduction 67 5.2Langevin Equation for the rotor 68 5.3Dipole in a Ratchet Electrical Potential 70 5.4Program 5.1, Matlab code 806Ratchet dimer Brownian motor with Hydrodynamic interactions84 6.1Introduction 84 6.2The Model 85 6.3Hydrodynamic interactions 88 6.4Brownian dynamics with hydrodynamic interactions 90 6.4.1Efficiency 91 6.5Program 6.1, Fortran code 1007Fluctuations of the proton electromotive force across inner mitochondrial membrane115 7.1Introduction 115 7.2Theory 116 7.3Fluctuations of th Proton-Electromotive 116 7.4Parameter Definitions 118 7.5Calculation of Buffer Equivalent Electrical Capacitance 118 7.6Calculation of IMM Electrical Resistance Rm 119 7.7Relaxation Times of the Electrical and Buffer Reservoirs 119 7.8Program 7.1, Fluctuations of the PMF, Matlab code 1268Quantum Ratchets128 8.1The Quantum Langevin Equation 128 8.1.1The Correlation Quantum Function 131 8.1.2The Quantum Overdamped Langevin Equation with colored noise 132 8.1.3The Quantum Underdamped Langevin Equation 136 8.1.4The Ranges 1388.2Programs
8.2.1Program 8.1a, Moderate Damping, Matlab code 8.2.2Program 8.1b, Complete Langevin Equation, Matlab code Appendices145
A01 155 A.1Master Equation 155 A.1.1Transition Rate 155 A.1.2Prob...