Annealing protocol

A finite difference formula is used to estimate the second derivatives of the coordinate vector with respect to time and S is now a function of all the intermediate coordinate sets. An optimal value of S can be found by a direct minimization, by multi-grid techniques, or by an annealing protocol [7]. We employed in the optimization analytical derivatives of S with respect to all the Xj-s. 

Incorporation of Dipolar Couplings into Simulated Annealing Protocols 1159... 

In a typical free NOESY experiment of a molecule in the absence of any interacting protein, cross-peak volumes are interpreted in terms of a set of interproton distances r that can be used as distance restraints in structure determination procedures, like restrained simulated annealing protocols [44], In a tr-NOESY, i.e. a NOESY measured under exchange-transferred conditions in the presence of a protein - i.e., an excess of soluble ligand is in fast exchange equilibrium with a smaller amount of protein-bound ligand -, these r reflect the interproton distances of the ligand in the bound... 

When low energy structures are required, a simulated annealing protocol can be used in which the system is heated to high temperature to surmount energy barriers and then cooled down. This procedure can be performed repeatedly to generate an ensemble of low energy structures. [78, 81, 66]... 

The parameters of the annealing protocol are largely determined empirically and are characteristic of the general topology of the particular solution space. But, in theory, there is a lower bound on the value of Ic- The expected distance... 

F ure 2. A flow di am illustrating the particular implementation of the simulated annealing protocol for the real-space search problem of crystallography. All variable and parameter names are as described in the text. The inputs to the program include initial values for the various parameters (e.g. g, To, II, I2), the coordinates of the search model and a suitably large search map. Reprinted from S. Subbiah and S.C. Harrison, Acta. Cryst., 1989, A45, p337-42. 

The particular implementation of the simulated annealing protocol for the real space search problem is outlined in detail in the accompanying flow diagram (Figure 2). The one obvious difference is that the quantity. 

The particular implementation of the general annealing protocol described earlier involves some modification in the parameter Ic. At each value of T at most... 

Table 1 presents the results of five consecutive trials of the annealing protocol starting from five different random positions. The parameters used were = 0.0, Oj. = 7.5, g = 0.98, To= 2o, I2 = 10 000, Ii= 212. The cumulative success of obtaining the pool of good solutions, as ascertained by the exhaustive search above, is indicated in fractional form. Each trial took approximately 3 c.p.u. minutes on a 10 mip machine. Within two trials, the top log peaks were attained. After five trials, approximately 75% of aU the top 67 2og peaks were obtained. Therefore, in this case, the top lOg solutions were generated with some 80-fold reduction in computer time. Similarly, all top 2o peaks were formd in 25-fold less time. 

The scheduling of the annealing protocol, including the notion of cooling and freezing cycles, was as before. The previous ratio of Ii to l2 of 2 and the optimal values of g 0.98-0.99 were found to be adequate. The value of Tq was a little lower at 20j.. 

C. A. Laughton, A Study of Simulated Annealing Protocols for Use with Molecular Dynamics in Protein Structure Prediction, Prot. Eng., 7 (1994) 235. 

Our trajectories are sampled with the help of a simulated annealing protocol. But how can we test that the sampling is appropriate One measure that can help us to assess the quality of the simulation is the distribution of the orientation of the initial momentum vector. If we sample effectively the space of initial conditions (by sampling complete trajectories), then the momentum vectors should cover all of the orientation space. Alternatively, the vectors of the initial direction of the momentum behave as random vectors (with norm of one). In... 

Initial structures were refined against both the experimental restraints and the CHARMM energy using a novel simulated annealing protocol to define the torsion angle solutions to within an error of about 5°. Forty refined structures were used to obtain an average structure which was then further refined. A dielectric constant of 1 was used in the calculations. 

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