MD simulations

This is connnonly used to measure the temperature in a MD simulation. Less well known is the hypervirial relation... 

Equilibration of the interface, and the establislnnent of equilibrium between the two phases, may be very slow. Holcomb et al [183] found that the density profile p(z) equilibrated much more quickly than tire profiles of nonnal and transverse pressure, f yy(z) and f jfz), respectively. The surface tension is proportional to the z-integral of Pj z)-Pj z). The bulk liquid in the slab may continue to contribute to this integral, indicatmg lack of equilibrium, for very long times if the initial liquid density is chosen a little too high or too low. A recent example of this kind of study, is the MD simulation of the liquid-vapour surface of water at temperatures between 316 and 573 K by Alejandre et al [184]. 

The method of molecular dynamics (MD), described earlier in this book, is a powerful approach for simulating the dynamics and predicting the rates of chemical reactions. In the MD approach most commonly used, the potential of interaction is specified between atoms participating in the reaction, and the time evolution of their positions is obtained by solving Hamilton s equations for the classical motions of the nuclei. Because MD simulations of etching reactions must include a significant number of atoms from the substrate as well as the gaseous etchant species, the calculations become computationally intensive, and the time scale of the simulation is limited to the... 

Equation (C3.5.3) shows tire VER lifetime can be detennined if tire quantum mechanical force-correlation Emotion is computed. However, it is at present impossible to compute tliis Emotion accurately for complex systems. It is straightforward to compute tire classical force-correlation Emotion using classical molecular dynamics (MD) simulations. Witli tire classical force-correlation function, a quantum correction factor Q is needed 5,... 

Knowledge of the underlying nuclear dynamics is essential for the classification and description of photochemical processes. For the study of complicated systems, molecular dynamics (MD) simulations are an essential tool, providing information on the channels open for decay or relaxation, the relative populations of these channels, and the timescales of system evolution. Simulations are particularly important in cases where the Bom-Oppenheimer (BO) approximation breaks down, and a system is able to evolve non-adiabatically, that is, in more than one electronic state. 

Fig, 4. (a) Eigenvalues and distributions for the ct-carbon atoms in the 56-residue B l-domain of streptococcal protein G, from a 1 ns MD simulation in water (courtesy of Bort de Groot, Groningen). 

We assume that the unbinding reaction takes place on a time scale long ( ompared to the relaxation times of all other degrees of freedom of the system, so that the friction coefficient can be considered independent of time. This condition is difficult to satisfy on the time scales achievable in MD simulations. It is, however, the most favorable case for the reconstruction of energy landscapes without the assumption of thermodynamic reversibility, which is central in the majority of established methods for calculating free energies from simulations (McCammon and Harvey, 1987 Elber, 1996) (for applications and discussion of free energy calculation methods see also the chapters by Helms and McCammon, Hermans et al., and Mark et al. in this volume). 

Grubmiiller described a method to induce conformational transitions in proteins and derived rate constants for these ([Grubmiiller 1994]). The method employs subsequent modifications of the original potential function based on a principal component analysis of a short MD simulation. It is discussed in more detail in the chapter of Eichinger et al. in this volume. 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

This completes the outline of FAMUSAMM. The algorithm has been implemented in the MD simulation program EGO VIII [48] in a sequential and a parallelized version the latter has been implemented and tested on a number of distributed memory parallel computers, e.g., IBM SP2, Cray T3E, Parsytec CC and ethernet-linked workstation clusters running PVM or MPI. 

The previous application — in accord with most MD studies — illustrates the urgent need to further push the limits of MD simulations set by todays computer technology in order to bridge time scale gaps between theory and either experiments or biochemical processes. The latter often involve conformational motions of proteins, which typically occur at the microsecond to millisecond range. Prominent examples for functionally relevant conformatiotial motions... 

Fig. 9. Two-dimensional sketch of the 3N-dimensional configuration space of a protein. Shown are two Cartesian coordinates, xi and X2, as well as two conformational coordinates (ci and C2), which have been derived by principle component analysis of an ensemble ( cloud of dots) generated by a conventional MD simulation, which approximates the configurational space density p in this region of configurational space. The width of the two Gaussians describe the size of the fluctuations along the configurational coordinates and are given by the eigenvalues Ai.

Step 1 A short conventional MD simulation (typically extending over a few lOOps) is performed to generate an ensemble of protein structures x 6 71 (each described by N atomic positions), which characterizes the initial conformational substate. The 2-dimensional sketch in Fig. 9 shows such an ensemble as a cloud of dots, each dot x representing one snapshot of the protein. 

Fig. 10. Conformational flooding accelerates conformational transitions and makes them accessible for MD simulations. Top left snapshots of the protein backbone of BPTI during a 500 ps-MD simulation. Bottom left a projection of the conformational coordinates contributing most to the atomic motions shows that, on that MD time scale, the system remains in its initial configuration (CS 1). Top right Conformational flooding forces the system into new conformations after crossing high energy barriers (CS 2, CS 3,. . . ). Bottom right The projection visualizes the new conformations they remain stable, even when the applied flooding potentials (dashed contour lines) is switched off.

MD simulations are valuable tools if one wants to gain detailed insight into fast dynamical processes of proteins and other biological macromolecules at atomic resolution. But since conventional MD simulations are confined to the study of very fast processes, conformational flooding represents a complementary and powerful tool to predict and understand also slow conformational motions. Another obvious application is an enhanced refinement of Xray- or NMR-structures. 

Fig. 3. MD simulation of a polymer chain of 100 CH2 groups due to [10], The dynamics of the distance between two CHj-groups ( 12 and 36). The series of plots illustrates the oscillations of the distance at time scales increasing by a zoom factor of 10 at each level.

In molecular mechanics and molecular dynamics studies of proteins, assig-ment of standard, non-dynamical ionization states of protein titratable groups is a common practice. This assumption seems to be well justified because proton exchange times between protein and solution usually far exceed the time range of the MD simulations. We investigated to what extent the assumed protonation state of a protein influences its molecular dynamics trajectory, and how often our titration algorithm predicted ionization states identical to those imposed on the groups, when applied to a set of structures derived from a molecular dynamics trajectory [34]. As a model we took the bovine... 

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