Step-wandering

N. C. Bartelt, T. L. Einstein, E. D. Williams. The influence of step-step interactions on step wandering. Surf Sci Lett 240 L591, 1990. 

Usually, experimentalists quantify step fluctuations by averaging the data to find the correlation function G(t) = 0.5 < (h(x,i) - h(x,0)Y >, where h x,t) specifies the step position at time t and the average is over many sample points, x. G(f) measures how far a position on a step wanders with time. If that position were completely free to wander, it would obey a diffusive law G(t) t. However, its motion is restricted by the fact that it is connected to the other parts of the step. For that reason G(t) is sub-diffusive. The detailed law which G(f) obeys is dependent on the atomic processes which mediate step motion. For example, if the step edge is able to freely exchange... 

Reduction of the ester group in (31) requires protection of the ketone the double bond wanders during this step but returns to conjugation in (27). 

A generic problem with profile methods that iterate is the possibility of profile wander (also called matrix migration). This occurs when sequences found in early rounds of the iterative search are not found in later rounds of the search. This problem affects both PSI-BLAST and HMMER. This means that one should record all the intermediate steps so that these lost members of the family can be recovered. Profile wander only becomes a problem for large protein families, and therefore the cause of the profile wander may be related to the limits of modeling using profiles. 

One possibility is for the ion to wander about on the solution side of the interface, say, in the OHP, till it comes face to face with a hole site. Then, in one shot, the ion could get electronated, divest itself of its solvent sheath, and dive into the lattice. This would be a direct one-step deposition reaction (Fig. 7.129). 

The diagrams in Fig. 9-15 are too simple because enzymatic reactions usually occur in several intermediate steps. There will be transition states for each step with valleys in between. The valleys correspond to intermediate species, which are sometimes very unstable. The passing from reactants to products in an enzymatic reaction can be likened to wandering through a series of mountain ranges of various heights and finally reaching the other side. 

Capt. I have already told you how I wandered over the whole earth. In the course of my journeying I came to Taprobane, and was compelled to go ashore at a place, where through fear of the inhabitants I remained in a wood. When I stepped out of this I found myself on a large plain immediately under the equator. 

If the failcount value reaches the limit defined by quitreps, Ar is reduced by shrinkfac, provided the maximum number of step shrinkages has not occurred. As Kalivas [3] has noted, /3 should increase with decreasing Ar. Otherwise, the smaller changes in mean response variation between adjacent steps with reduced Ar will cause excessive wandering of the algorithm. In gsaopt, a new /3 value is calculated after each step shrinkage as follows ... 

Such a trajectory has an important property. It could converge towards a limiting scheme, it could repeat itself, or it could wander around randomly. Discount the last possibility. If it repeats itself after a fixed number of steps, then we can take that cycle of steps together as a single scheme of high arity and discover that it is essentially a stationary scheme. 

Random Walks on a One-Dimensional Lattice. We consider [249, 251] stable random walks on a one-dimensional lattice. Here the particle moves at random, and the direction is defined by the direction of the previous step. Each step is only carried out to the nearest neighbor. The mathematical definition of stability demands that at any time and position on the lattice of the wandering particle, two previous coordinates and the direction of the previous step be known. To describe the random walk process, we consider two probabilities, p,i 1 and p, where pi is the probability to be at place j at step n from place j — 1 at the previous step, is the same probability but from place j + 1. 

Figure 3.1 The process of adding one A particle to a solution is carried out in two steps. First, we insert the particle at a fixed position, then we release the particle to wander in the entire system. The corresponding free energy changes are p A and kT In pAA3, respectively.

A common view of antagonistic pleiotropy is that our genes are out of step with our lifestyle. We spent half a million years evolving as hunter-gatherers. Restless wandering was combined with an ability to subsist on a meagre diet for weeks or months at a time. Then, a few thousand years... 

Fig. 4. HnaJ steps in the cholesterol biosynthetic pathway. Alternate steps have been proposed for the conversion of zymosterol to cholesterol, which differ in the point at which the A24-reductase reaction occurs. Adapted from Waterham and Wanders [7J and Kelley and Hennekam [11].

The condition of self-avoidance of a random walk trajectory on //-dimensional lattice demands the step not to fall twice into the same cell. From the point of view of chain link distribution over cells it means that every cell cannot contain more than one chain link. Chain links are inseparable. They cannot be tom off one from another and placed to cells in random order. Consequently, the numbering of chain links corresponding to wandering steps is their significant distinction. That is why the quantity of different variants of iV distinctive chain links placement in Z identical cells under the condition that one cell cannot contain more than one chain link is equal to Z I Z-N) ... 

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