scholarly journals Stokes Efficiency of Molecular Motor-Cargo Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Hongyun Wang ◽  
Hong Zhou
Keyword(s):  
Free Energy ◽  
Molecular Motor ◽  
Planck Equation ◽  
Viscous Friction ◽  
Thermal Fluctuations ◽  
Viscous Drag ◽  
Langevin Equations ◽  
Stochastic Motion ◽  
Chemical Free Energy ◽  
Surrounding Fluid

A molecular motor utilizes chemical free energy to generate a unidirectional motion through the viscous fluid. In many experimental settings and biological settings, a molecular motor is elastically linked to a cargo. The stochastic motion of a molecular motor-cargo system is governed by a set of Langevin equations, each corresponding to an individual chemical occupancy state. The change of chemical occupancy state is modeled by a continuous time discrete space Markov process. The probability density of a motor-cargo system is governed by a two-dimensional Fokker-Planck equation. The operation of a molecular motor is dominated by high viscous friction and large thermal fluctuations from surrounding fluid. The instantaneous velocity of a molecular motor is highly stochastic: the past velocity is quickly damped by the viscous friction and the new velocity is quickly excited by bombardments of surrounding fluid molecules. Thus, the theory for macroscopic motors should not be applied directly to molecular motors without close examination. In particular, a molecular motor behaves differently working against a viscous drag than working against a conservative force. The Stokes efficiency was introduced to measure how efficiently a motor uses chemical free energy to drive against viscous drag. For a motor without cargo, it was proved that the Stokes efficiency is bounded by 100% [H. Wang and G. Oster, (2002)]. Here, we present a proof for the general motor-cargo system.

scholarly journals An Asymmetric Mechanism in a Symmetric Molecular Machine

2020 ◽  
Author(s):  
Florian Blanc ◽  
Marco Cecchini
Keyword(s):  
Free Energy ◽  
Large Scale ◽  
Technological Development ◽  
Thermal Fluctuations ◽  
Free Energy Calculations ◽  
Molecular Machine ◽  
Free Energy Surface ◽  
Promising Area ◽  
Sequential Mechanism ◽  
External Stimuli

The design of molecular architectures exhibiting functional motions is a promising area for disruptive technological development. Towards this goal, rotaxanes and catenanes, which undergo relative motions of their sub-units in response to external stimuli, are prime candidates. Here, we report on the computational analysis of the contraction/extension of a bistable [c2]-daisy chain rotaxane. Using free energy calculations and transition path optimizations, we explore the free energy landscape governing the functional motions of a prototypical molecular machine with atomic resolution.<br>The calculations reveal a sequential mechanism for contraction/extension in which the asynchronous gliding of each ring is preferred over the concerted movement suggested by chemical intuition. Analysis of the underlying free energy surface indicates that dissymmetric gliding is favored because it entails crossings of much smaller barriers.<br>Our findings illustrate an important design principle for molecular machines, namely that efficient exploitation of thermal fluctuations may be realized by breaking down the large-scale functional motions into smaller steps.

Modelling biomacromolecular assemblies with continuum mechanics

2015 ◽  
Vol 43 (2) ◽  
pp. 186-192 ◽  
Author(s):  
Benjamin Hanson ◽  
Robin Richardson ◽  
Robin Oliver ◽  
Daniel J. Read ◽  
Oliver Harlen ◽  
...  
Keyword(s):  
Finite Element ◽  
Molecular Motor ◽  
Md Simulations ◽  
Thermal Fluctuations ◽  
Theoretical Background ◽  
Thermal Agitation ◽  
Element Analysis ◽  
Biomolecular Dynamics ◽  
Modelling Methods ◽  
Element Algorithm

We have developed a continuum mechanical description of proteins using a finite element algorithm which has been generalized to include thermal fluctuations and which is therefore known as fluctuating finite element analysis (FFEA). Whereas conventional molecular dynamics (MD) simulations provide a trajectory in which each individual atomic position fluctuates, a FFEA trajectory shows how the overall shape of the protein changes due to thermal agitation. We describe the theoretical background to FFEA, its relationship to more established biomolecular modelling methods and provide examples of its application to the mesoscale biomolecular dynamics of the molecular motor dynein.

scholarly journals Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

2015 ◽  
Vol 308 (5) ◽  
pp. H510-H523 ◽  
Author(s):  
Xiao Wang ◽  
Seth H. Weinberg ◽  
Yan Hao ◽  
Eric A. Sobie ◽  
Gregory D. Smith
Keyword(s):  
Calcium Release ◽  
Ventricular Myocytes ◽  
Cell Model ◽  
Ryanodine Receptors ◽  
Planck Equation ◽  
Linear Increase ◽  
Langevin Equations ◽  
Cell Models ◽  
Whole Cell ◽  
Alternative Approach

Population density approaches to modeling local control of Ca2+-induced Ca2+ release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca2+ signals. Unfortunately, the computational complexity of such “local/global” whole cell models scales with the number of Ca2+ release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca2+ concentration ([Ca2+]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca2+ homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca2+] promotes elevated network sarcoplasmic reticulum (SR) [Ca2+] via SR Ca2+-ATPase-mediated Ca2+ uptake. However, elevated myoplasmic [Ca2+] may also activate RyRs and promote stochastic SR Ca2+ release, which can in turn decrease SR [Ca2+]. Increasing myoplasmic [Ca2+] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca2+] depending on whether myoplasmic [Ca2+] is low or high. In the later case, spontaneous release decreases SR [Ca2+] in a manner that maintains robust Ca2+ sparks.

scholarly journals Computational design of faster rotating second-generation light-driven molecular motors by control of steric effects

2015 ◽  
Vol 17 (33) ◽  
pp. 21740-21751 ◽  
Author(s):  
Baswanth Oruganti ◽  
Changfeng Fang ◽  
Bo Durbeej
Keyword(s):  
Free Energy ◽  
Molecular Motors ◽  
Energy Barrier ◽  
Second Generation ◽  
Molecular Motor ◽  
Computational Design ◽  
Steric Effects ◽  
Free Energy Barrier

By tuning the steric bulkiness of the stereogenic substituent, the rate-determining thermal free-energy barrier of an already MHz-capable rotary molecular motor can be reduced by a further 15–17 kJ mol−1.

Estimation of the System Free Energy of the Lath Martensite Phase in High Cr Ferritic Steels

2006 ◽  
Vol 15-17 ◽  
pp. 690-695 ◽  
Author(s):  
Tomonori Kunieda ◽  
Kensuke Akada ◽  
Yoshinori Murata ◽  
Toshiyuki Koyama ◽  
Masahiko Morinaga
Keyword(s):  
Free Energy ◽  
Ternary Alloy ◽  
Elastic Strain ◽  
Lath Martensite ◽  
Elastic Strain Energy ◽  
Martensite Phase ◽  
Interfacial Energies ◽  
Martensite Packet ◽  
Chemical Free Energy ◽  
Martensite Microstructure

The system free energy was estimated for the martensite phase of an Fe-Cr-C ternary alloy, 12Cr2W and 12Cr2W0.5Re steels. The system free energy of the martensite phase is defined as, Gsys = G0 + Estr + Esurf , where G0 is the chemical free energy, Esurf is the interfacial energy for the boundaries in the martensite microstructure, and Estr is the elastic strain energy due to the dislocations in the martensite phase. From the experimental results on SEM/EBSD, the total interfacial energies were estimated to be 0.83J/mol for the ternary alloy and 4.8J/mol for both 12Cr2W and 12Cr2W0.5Re steels in the as-quenched state. Also, the elastic strain energies were estimated to be 7.1J/mol for the ternary alloy, 9.6J/mol for 12Cr2W steel and 9.8J/mol for 12Cr2W0.5Re steel in the as-quenched state. So, the system free energy was about 7.9J/mol for ternary alloy. On the other hand, the system free energy was about 14.4J/mol for 12Cr2W steel and 14.6J/mol for 12Cr2W0.5Re steel. So, these microstructural energies operate as a driving force for the microstructure evolution, e.g., recovery of dislocations and the coarsening of the sub-structures such as martensite-packet, -block and -lath.

Two-Phase Microstructures Formed by Phase-Separation of Coherent Precipitates in Elastically Constrained Alloy Systems

2010 ◽  
Vol 638-642 ◽  
pp. 2215-2220 ◽  
Author(s):  
Minoru Doi
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Surface Energy ◽  
Phase Region ◽  
Precipitate Phase ◽  
Two Phase ◽  
Phase Separations ◽  
Chemical Free Energy ◽  
Elastic Constraint ◽  
Alloy Systems

Coherent two-phase microstructures consisting of ordered precipitate and disordered matrix phases sometimes exhibit a phase-separation, which brings the split and/or the decelerated coarsening of precipitates. When the coherent two-phase microstructure of A1+L12 (+’) in Ni-base alloys are aged inside the two-phase region of A1+L12 , the L12 precipitate sometimes exhibit a phase-separation and A1 phase newly appears and grows in each L12 precipitate. Phase-separations of the same type to the above also take place due to ageing of coherent two-phase microstructures of A2+D03 and A2+B2 in Fe-base alloys: D03 and B2 precipitates sometimes exhibit phase-separations and A2 phase newly appears and grows in both precipitates. These types of phase-separation take place under the influence of chemical free energy. In the course of further ageing, the new disordered phases of A1 and A2 change their morphology in various ways depending on the elastic constraint: i.e. the morphology of new A1 or A2 phase is influenced by the elastic energies and the surface energy.

The role of chemical free energy and elastic strain in the nucleation of zirconium hydride

2013 ◽  
Vol 441 (1-3) ◽  
pp. 395-401 ◽  
Author(s):  
A.T.W. Barrow ◽  
C. Toffolon-Masclet ◽  
J. Almer ◽  
M.R. Daymond
Keyword(s):  
Free Energy ◽  
Elastic Strain ◽  
Zirconium Hydride ◽  
Chemical Free Energy

scholarly journals Measurements of to Temperatures of Supersaturated Si-As Alloys

1990 ◽  
Vol 205 ◽  
Author(s):  
Kwang-Ryeol Lee ◽  
Jeffrey A. West ◽  
Patrick M. Smith ◽  
M. J. Aziz ◽  
J. A. Knapp
Keyword(s):  
Free Energy ◽  
Pulsed Laser ◽  
Congruent Melting ◽  
Laser Melting ◽  
Concentration Region ◽  
Energy Functions ◽  
Congruent Melting Point ◽  
Liquid Phases ◽  
Chemical Free Energy ◽  
Beam Technique

AbstractThe congruent melting point, or To curve, of crystalline Si-As alloys has been measured in the range of 1.6 to 18.1 at. % arsenic by line source electron beam annealing. Alloys were created by ion implantation of As into 0.1mm Si-on-sapphire and crystallized by pulsed laser melting. To temperatures decrease from 1673±10K at 2.0 at.% As to 1516±30K at 18.1 at.% As. The results of these measurements are significantly higher than the previous results of studies using pulsed laser melting techniques. Advantages of the e-beam technique over previous techniques are discussed. Chemical free energy functions of the solid and liquid phases were calculated from existing thermodynamic data. The calculated To curve agrees with the measured values only in low concentration region (less than 8 at.%).

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