Ratchet potential

To provide a caricature of a forward-moving process, Figure 6.6 is a sketch of the ratchet potential model. It shows how a combination of thermal motion and weak binding can generate a forward motion. The coordinate is the position of... 

Besides the remarkable directionality of the motion, the images also demonstrate a periodic variation of the cluster from an elongated to a circular shape (Fig. 39). The diagrams in Fig. 39 depict the time dependence of the displacement and the cluster size. Until the cluster was finally trapped, the speed remained fairly constant as can be seen from the constant slope in Fig. 39 a. The oscillatory variation of the cluster shape is shown in Fig. 39b. Although a coarse model for the motion has been presented in Fig. 39, the actual cause of the motion remains unknown. The ratchet model proposed by J. Frost requires a non-equiUb-rium variation in the energetic potential to bias the Brownian motion of a molecule or particle under anisotropic boundary conditions [177]. Such local perturbations of the molecular structure are believed to be caused by the mechanical contact with the scaiming tip. A detailed and systematic study of this question is still in progress. 

Now we can substitute the renormalized potential U = U + W for U in Eq. (2). The Fourier component W2kF is different for the opposite voltage signs. Hence, we obtain the asymmetric part of the I — V characteristics /r eU3 eV i9 2/(hEp). The ratchet effect is strongest for g —> 0 when the ratchet current grows as the voltage decreases. 

If all ak = 0 then the ratchet current is zero. Indeed, at ak = 0 the action (3) is invariant under the transformation —> — —V while the current operator (4) changes its sign. As discussed above, for an asymmetric potential we expect a2 0. Then a ratchet current Ir emerges in the order U2k r. Before the calculation of Ir let us determine its voltage... 

In conclusion, we have found the ratchet current for strong and weak asymmetric potentials. It exhibits a set of universal power dependencies on the voltage and can grow as the voltage decreases. In Ref. [25] our analysis was extended to include the electron spin. This leads to a complicated phase diagram with several qualitatively different transport regimes for different interaction strengths. 

As a search technique, using mutation and selection alone has several limitations. Evolution via asexual reproduction tends to build up deleterious mutations, ultimately limiting the potential of the experiment, an effect known as Muller s ratchet (Muller, 1964). This effect is exacerbated by high mutagenesis rates, as slightly deleterious amino acid substitutions can hitchhike with positive mutations. Recombination can act to remove neutral and deleterious mutations while allowing the accumulation of... 

In a landmark paper, Muller (1964) demonstrated that clonal lineages may be subject to reduce fitness due to a relentless increase in the load of deleterious mutations, and that sexual recombination would tend to reduce that load. The progressive increase in deleterious mutations has become known as Muller s ratchet, and there is evidence for the ratchet in nonrecombining genomes present in eukaryotic cells, namely, mitochondrial DNA (Lynch, 1997 Moran, 1996), sex chromosomes, and Drosophila chromosomes that are prevented from recombining (Rice, 1994). A potential consequence of the ratchet is extinction of clonal lineages (Lynch et al., 1993). Some models indicate that clonal species... 

Bidochka MJ, De Koning J. Are teleomorphs really necessary modeling the potential effects of Muller s ratchet on deuteromycetous entomopathogenic fungi. Mycol Res 105 1014-1019, 2001. 

Fig. 9 Two shift ratchets with different mechanical potentials t/i(x) and U2 x). Appearance suggests that the ratchet in (a) is designed to move to the right and that in (b) is designed to move to the left when > 0. However, when rate constants consistent with microscopic reversibility are used in the description of the chemical transitions, this is seen not to be the case, and that the direction is controlled by the chemical specificity...

Fig. 10 Plots of the 2-D potential calculated by taking piece-wise linear functions for the shift ratchet shown in Fig. 9b with amplitude of 13 along the mechanical coordinate, and transition state saddlepoint) energies of (9i) = = 8.5 and S (d2) = = 0. Two periods in each...

The value of the integral in (28) is path independent and depends only on the start and end points. The values of each of the terms identified as torque and chemistry, however, depend on path. Further, had we chosen the ratchet in Fig. 9a rather than that in Fig. 9b on which to base the 2-D potential landscape, the term describing torque in the integral over the least energy forward path 3 would be positive and that for the chemistry would be less than Afi. It is therefore... 

The concept of Brownian ratchets has been applied to construct asymmetric obstacle courses that provide a spatially asymmetric steric potential for biomolecule separation [20, 21], The basic idea is to use such asymmetric obstacles to rectify the Browiuan motion laterally and thereby to deflect diffusing biomolecules based on their sizes. So far, the Brownian ratchet systems have been successfully demonstrated for long DNA and phospholipids [15, 16], even though the separation resolution reported so far was not ideal. 

Traditionally, efficiency of molecular motors has been studied within ratchet models where the motor undergoes a continuous motion in a periodic potential that depends on the current chemical. Dissipation then involves both the continuous degree of freedom and the discrete switching of the potential. 

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