Simulated annealing method

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

The tests in the two previous paragraphs are often used because they are easy to perform. They are, however, limited due to their neglect of intermolecular interactions. Testing the effect of intennolecular interactions requires much more intensive simulations. These would be simulations of the bulk materials, which include many polymer strands and often periodic boundary conditions. Such a bulk system can then be simulated with molecular dynamics, Monte Carlo, or simulated annealing methods to examine the tendency to form crystalline phases. 

Roitberg, A. Elber, R., Modeling side chains in peptides and proteins application of the locally enhanced sampling technique and the simulated annealing methods to find minimum energy conformations, J. Chem. Phys. 1991, 95, 9277-9287... 

In kinetic analysis of complex reactions, 210, 382 fluorescence decay rate distributions, 210, 357 implementation in Laplace de-convolution noniterative method, 210, 293 in multiexponential decays, 210, 296 partial global analysis by simulated annealing methods, 210, 365 spectral resolution, 210, 299. 

The semiquinone biradical produced in the photocycle of bacterial photosynthetic reaction centres was trapped at 77 K and examined at 9.6, 35, and 94 GHz.16 Simulations of spectra at the multiple resonant frequencies using the simulated annealing method revealed the spatial and electronic structure of the biradical. The value of r was found to be 17.2 + 0.2 A, which is in good agreement with the value of 17.4 0.2 A obtained in an X-ray crystal structure. This study shows the power of high-frequency EPR combined with data obtained at lower frequencies. 

Given the mere handful of reports in the published literature (6,38,39,52), there are many avenues open in the development of systematic approaches to optimization in SFC. In addition to the opportunities mentioned in the sections on the simplex method and window diagram approach, others include the exploration of other sequential or simultaneous optimization strategies such as optiplex, simulated annealing, method of steepest ascent, etc. that are potentially useful in SFC. 

Conformational Analysis of Flexible Molecules Location of the Global Minimum Energy Conformation by the Simulated Annealing Method. 

H. Kawai, T. Kikuchi, and Y. Okamoto, Protein Engin., 3, 85 (1989). A Prediction of Tertiary Structures of Peptide by the Monte Carlo Simulated Annealing Method. 

Simulated annealing calculations were performed to acquire the mechanisms of thermolysis of thiirane and thiiranium cation <2002JMT71>. The AMPAC 6.55 package along with AIMl and SAMI methods were used to estimate structures, which were then used as starting points for further ab initio calculations. Critical points were confirmed by calculation of the vibrational frequencies. The primary reactions thiirane 19 —> S-f ethene, thiirane—> vinyl thiol 20, and thiirane ethanethial (thioacetaldehyde) 21 were examined for thermolysis of thiirane Scheme 1. Many secondary reactions were also examined. The simulated annealing method was predicted to be very useful in the future for the study of competing chemical reactions. 

In the approach of Chin et al., the simulated annealing method was employed on molecules that tend to form hydrogen-bonded tapes (Schwiebert et al. 1995), thus providing a well-defined (but necessarily limited) starting model for the subsequent trial structures. 

For zeolites, the simulated annealing method has been used to solve the structures of some new materials [35], including the product that results from a framework reconstruction on dehydration of Na6(ZnAs04)6.8H20 with the sodalite structure at 190°C [43] and the novel aluminosilicate UiO-7 [44], Analogously to the impact of simiilated annealing in structure solution sind hypothetic framework structure development, simulation will also be an exciting medium for new approaches to structure completion and refinement. 

The simulated annealing method can generate large numbers of hypothetical structures in a short time frame. A non-exhaustive series of simulations based on the unit celL sizes and symmetries of 64 known zeolite structures produced over 5000 hypothetical structures [36]. Many of these structures are not 3-dimensional frameworks, instead forming discrete cages, chains or layers. However, for each different set of input data, each derived structure has a unique set of coordination sequences for the inequivalent T-atoms and therefore has a distinct topology. 

The molecular model of GIF was constructed using QUANTA/XFIT (MSI). The refinement of structure was executed with the simulated annealing method using X-PLOR (11). Water molecules were located using the program... 

Therefore, novel techniques potentially applicable to solving crystal structures are under continuous testing and development. A recent collective monograph on the structure determination from powder diffraction data provides an excellent discussion of the problem and introduces different approaches that may be used in its solution. In this chapter, unconventional structure solution methods are only briefly reviewed most of them are still controversial and do not always work well with different kinds of compounds and data, although solutions of several complex structures have been demonstrated. Summarized below are the genetic algorithm, maximum entropy, maximum likelihood, and simulated annealing methods. 

In this introductory chapter we discuss in Sec.2 the formulation of the simulated annealing approach to optimization, computations with the algorithm and their termination and we illustrate the method with an example. In Sec. 3 we present attempts to model and to analyze the performance of the algorithm, in particular, the dependence of the computational effort on the dimensionality of the problem and the termination criterion. We combine the results presented in this section with observations of the results of many applications and discuss in Sec. 4 some of the characteristics of the simulated annealing method. Results of calculations that minimize the total energy of molecular conformation for several compounds and a summary conclude the chapter. 

Optimization with the simulated annealing method requires ... 

The computational approach described here, based on the combination of the Kalman filter algorithm and iterative optimization by the simulated annealing method, was able to find the optimal alignment of the pure component peaks with respect to the shifted components in the overlapped spectra, and hence, to correctly estimate the contributions of each component in the mixture. The simulated annealing demonstrated superior ability over the other optimization methods, simplex and steepest descent, in yielding more reliable convergences at the expense of not much more computer time, at least for resolving ternary shifted overlapped spectra. 

The effective use of temperature as a control factor in the Metropolis Monte Carlo process is the most important factor for the success of simulated annealing method. This has inspired an attempt to exploit temperature in a new way. Von Freyberg [21] has proposed a Simulated Shocking protocol for the efficient search for conformations of polypeptides. In this protocol, the temperature jumps between a very low (T = 5 K) and very high temperature... 

In the simulated annealing method, minimization of c) is mapped onto a statistical mechanical problem by considering (c) to be the potential energy governing a fictitious thermal system. If this fictitious thermal system can be brought to thermal equilibrium at sufficiently low temperature, then the variables c will be brought to the minimum of (c), i.e. to the Born-Oppenheimer surface. 

C. P. Chang, Y.H. Lee, S.Y. Wu, Optimization of a thin-film multilayer design by use of the generalized simulated-annealing method, Optics Letters, 15 (1990) 595. 

H. Raittinen, K. Kaski, Image deconvolution with simulated annealing method. Physica Scripta, 33 (1990) 126. 

T. Satoh, K. Nara, Maintenance scheduling by using simulated annealing method, IEEE Transactions on Power Systems, 6 (1991) 850. 

S.H. Nilar, Applications of the simulated annealing method to intermolecular interactions. Journal of Computational Chemistry, 12 (1991) 1008. 

J. Higo, V. Collura, J. Gamier, Development of an extended simulated annealing method application to the modeling of complementary determining regions of immunoglobulins. Biopolymers, 32 (1992) 33. 

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