Molecular motor linear

In nonequilibrium steady states, the mean currents crossing the system depend on the nonequilibrium constraints given by the affinities or thermodynamic forces which vanish at equihbrium. Accordingly, the mean currents can be expanded in powers of the affinities around the equilibrium state. Many nonequilibrium processes are in the linear regime studied since Onsager classical work [7]. However, chemical reactions are known to involve the nonlinear regime. This is also the case for nanosystems such as the molecular motors as recently shown [66]. In the nonlinear regime, the mean currents depend on powers of the affinities so that it is necessary to consider the full Taylor expansion of the currents on the affinities ... 

The external forces may be optical tweezers, microneedles, or the viscous load of the substance that is carried. These generalized forces create motion, characterized by an average velocity v, and average rate of ATP consumption JT. Molecular motors mostly operate far from equilibrium, and the velocity and rate of ATP consumptions are not linear functions of the forces. However, in the vicinity of the linear region, where A kBT, linear relations hold... 

Dynamic Covalent Changes that Make Linear Molecular Motors Work. 

Dynamic Covalent Changes that Make Linear Molecular Motors Work. Controlling the Sense of Displacement (Walking)... 

Barrell, Campana, von Delius, Geertsema, and Leigh [50] combined the features of the above type of linear molecular motor with light induced E —> Z and Z —> E alkene isomerization. They synthesized and studied a walker-on-track-like light-driven molecular motor, where positions 2 and 3 of the track are connected through a CH = CH unit (Fig. 12). It can operate in either direction, depending on the order in which the stimuli are applied to it. 

Fig. la-e. Biological examples of molecular motors. Motors shown in a and b are rotary motors and c-e are linear motors. Motion takes place in the direction indicated by the arrows, and diagrams are not drawn to scale (reproduced with permission from [15])... 

Molecular motors or machines are inspired by biological molecules such as myosin which uses the chemical energy from hydrolysis of adenosine triphosphate to drive the linear push-pull motion of muscle. The different coordination demands of Cu and Cu are the basis of electro-chemically induced molecular motion in a pseudorotaxane complex of copper. As shown in Scheme 2, Cu 4, the stable, four-coordinate form is oxidized to unstable Cu°4, which rearranges to the stable five-coordinate form by sliding along the ligand. Reduction of the stable Cir s... 

Equation (a) identifies the independent fluxes and forces. These forces cause motion and ATP consumption characterized by fluxes (currents) that are average velocity v(/ext,AM) and average rate of ATP hydrolysis J(/ext> A/r)- Molecular motors mostly operate far from equilibrium (Am lOi uT) and the fluxes are not linearly dependent on the forces. Within the linear regime (Am << pT), however, a linear flux—force relationships hold... 

A molecular motor functions on a cycle of transformations between different mechanical and chemical states corresponding to different conformations of the protein complex. For rotary motors these states form a cycle of periodicity L with the revolution by 360°, for linear motors the states undergo the reinitialization. The transitions between the states a are caused by the chemical reactions of the binding a substrate S and releasing the products P ... 

The chemical affinity generates fluctuating flows, which can be the rate of chemical reaction, or the velocity of a linear molecular motor, or the rotation rate of a rotary motor. According to the fluctuation theorem, the probability of backward substeps (s) is given by P(—s) = P(,s) exp [—sA/(6feB7)] where the affinity A is... 

Natural molecular motors (motor proteins) are intriguing, both as efficient products of evolution and as power sonrces for nanotechnology (7). Some representative rotary and linear motor proteins are subjects of this chapter. Not discussed here are a wide range of additional proteins in which linear motion is coupled with enzyme activity, or which perform physical work. Examples are RNA polymerase and DNA topoisomerase, respectively. 

Figure 12.18 Schematic representation of a linear motor powered by light Adapted from V. Balzani, A. Credi and M. Venturi, Light-powered molecular-scale machines , Pure and Applied Chemistry Volume 75, No. 5,541-547 International Union of Pure and Applied Chemistry IUPAC 2003...

Interestingly, the dumbbell component of a molecular shuttle exerts on the ring motion the same type of directional restriction as imposed by the protein track for linear biomolecular motors (an actin filament for myosin and a microtubule for kinesin and dynein).4 It should also be noted that interlocked molecular architectures are largely present in natural systems—for instance, DNA catenanes and rotaxanes... 

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