Simulated annealing molecular dynamics simulation

P. Auffinger and G. Wipff, J. Comput. Chem., 11, 19 (1990). High Temperature Annealed Molecular Dynamics Simulations as a Tool for Conformational Sampling. Application to the Bicydic 222 Cryptand. 

Figure 4. Nuclear trajectories generated by the simulated annealing molecular dynamics defined by the Lagrangian in Equation(4) using masses for all parameters equal to either 0.1 or 0.01 times the proton mass. For comparison, the exact nuclear trajectory on the Born-Oppenheimer surface is shown.

Selloni et al. [48] were the first to simulate adiabatic ground state quantum dynamics of a solvated electron. The system consisted of the electron, 32 K+ ions, and 31 Cl ions, with electron-ion interactions given by a pseudopotential. These simulations were unusual in that what has become the standard simulating annealing molecular dynamics scheme, described in the previous section, was not used. Rather, the wave function of the solvated electron was propagated forward in time with the time-dependent Schrodinger equation,... 

Most of the current implementation of DFT within simulated annealing molecular dynamics calculations follows the basic outlines given in Section 1.2. Ample details particular to DFT have been given in other reviews of Car-Parrinello techniques [44-47,99]... 

Simulated annealing molecular dynamics has been used in conjunction with tight-binding Hamiltonians to model the properties of silicon [188-191], potassium [190] and carbon [190] clusters. 

Certain Schrodinger equation based methods, such as coupled cluster theory, are not based on a variational principle. They fall outside schemes that use the energy expectation value as a optimization function for simulated annealing, although these methods could be implemented within a simulated annealing molecular dynamics scheme with alternative optimization function. 

Restraints can also be incorporated into an annealed molecular dynamics protocol, performing simulations at decreasing temperatures. This approach has been used to generate protein structures consistent with NMR constraints and has recently attracted much attention for its use in solving crystal structures. In this latter application, information from the diffraction data (e.g., structure factors and phases) is incorporated as appropriate pseudo-eneigy terms in the potential energy function. 

Auffinger, P. and Wipfif, G. (1990) High temperature annealed molecular dynamics simulation as a tool for conformational sampling. J. Comput. Chem. 11 19-31. 

Niv et al. [89] have developed a method to model activated states of GPCRs using the structure-related information for fhe active state of rhodopsin and ofher GPCRs (http //physiology.med.cornell.edu/GPCRactivation/gpcrindex.html) as structural constrains for a Simulated Annealing Molecular Dynamics protocol. 

D. D. Humphreys, R. A. Friesner, and B. J. Berne. Simulated annealing of a protein in a continuum solvent by multiple-time-step molecular dynamics. J. Phys. Chem., 99 10674-10685, 1995. 

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

Quenched dynamics is a combination of high temperature molecular dynamics and energy minimization. This process determines the energy distribution of con formational families produced during molecular dynamics trajectories. To provide a better estimate of conformations, you should combine quenched dynamics with simulated annealing. 

Humphreys D D, R A Friesner and B ] Berne 1995. Simulated Annealing of a Protein in a Continuu Solvent by Multiple Time-step Molecular Dynamics. Journal of Physical Chemistry 99 10674-1068... 

Solving Protein Structures Using Restrained Molecular Dynamics and Simulated Annealing... 

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... 

A key feature of the Car-Parrinello proposal was the use of molecular dynamics a simulated annealing to search for the values of the basis set coefficients that minimise I electronic energy. In this sense, their approach provides an alternative to the traditioi matrix diagonalisation methods. In the Car-Parrinello scheme, equations of motion ... 

Model optimization is a further refinement of the secondary and tertiary structure. At a minimum, a molecular mechanics energy minimization is done. Often, molecular dynamics or simulated annealing are used. These are frequently chosen to search the region of conformational space relatively close to the starting structure. For marginal cases, this step is very important and larger simulations should be run. 

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. 

Quenched dynamics can trap structures in local minima. To prevent this problem, you can cool the system slowly to room temperature or some appropriate lower temperature. Then run room temperature molecular dynamics simulations to search for conformations that have lower energies, closer to the starting structure. Cooling a structure slowly is called simulated annealing. 

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