Molecular modelling ensembles

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

The molecular modelling of systems consisting of many molecules is the field of statistical mechanics, sometimes called statistical thermodynamics [28,29], Basically, the idea is to go from a molecular model to partition functions, and then, from these, to predict thermodynamic observables and dynamic and structural quantities. As in classical thermodynamics, in statistical mechanics it is essential to define which state variables are fixed and which quantities are allowed to fluctuate, i.e. it is essential to specify the macroscopic boundary conditions. In the present context, there are a few types of molecular systems of interest, which are linked to so-called ensembles. 

MR is an ensemble of techniques that aims to place and orientate an approximate molecular model in the unit cell of the crystal being studied. This will provide the starting phases needed to calculate the initial electron density map from which the protein model can be built, either manually by iterative use of reconstruction with molecular graphics packages (Jones et al., 1991) followed by refinement (Murshudov et al., 1997), or automatically if diffraction data up to 2.3 Angstroms or better are available (ARP/wARP (Perrakis et al., 2001), Solve/Resolve (Terwilliger, 2003)). 

At first glance, the averaged model would appear to serve most researchers who are looking for a molecular model to help them explain the function of the molecule and rationalize other chemical, spectroscopic, thermodynamic, and kinetic data. On the other hand, you might think that the ensemble and distance-restraint files are of most use to those working to improve structure determination techniques. There are good reasons however, for all researchers to look carefully at the ensemble, as discussed in the next section. 

A series of articles were published by Ennari et al. on MD simulation of transport processes in Poly(Ethylene Oxide) and sulfonic acid-based polymer electrolyte.136,137 The work was started by the determination of the parameters for the ions missing from the PCFF forcefield made by MSI (Molecular Simulations Inc.), to create a new forcefield, NJPCFF. In the models, the proton is represented as a hard ball with a positive charge. Zhou et al. used the similar approach to model Nation.138 The repeating unit of Nafion (Fig. 17) was optimized using ab initio VAMP scheme. The protons were modeled with hydronium ions. Three unit cell or molecular models were used for the MD simulation. The unit cell contains 5000 atoms 20 pendent side chains, and branched Nafion backbone created with the repeating unit. Their water uptakes or water contents were 3, 13, or 22 IEO/SO3, which correspond to the room temperature water uptakes at 50% relative humidity (RH), at 100% RH, and in liquid water respectively.18 The temperature was initially set at a value between 298.15 and 423.15 K under NVE ensemble with constant particle number, constant volume (1 bar), and constant energy. 

Figure 2. Forms of the potential wells described in the chapter and the features pertinent to the corresponding molecular models, if and 2% denote, respectively, ensembles of librating and rotating dipoles p denotes a dipole moment VIB refers to the charges 8 of a nonrigid dipole vibrating along the H-bond p(t) denotes a given harmonically changing component of a dipole moment.

The most detailed modelling approach summarized in Figure 1 is found at the mechanistic level. These models are explicit accounts of the chemistry of elementary steps. Thus the hierarchy of the levels, i.e., reaction models in Figure 1, now becomes quite clear. Mechanistic models, which provide the temporal and many times spatial variation of the composition of each component and reaction intermediate, are based at the lowest modelling level. Their output, however, is typically phrased in terms of ensembles of stable molecular constituents which is more characteristic of the intermediate level molecular models. The molecular models, in turn, require subsequent organization in order to connect to the global reaction models and relevant product fractions at the top or global level. 

The statistical mechanics formalism is probably the most effrcient way to connect molecular models with experimental data. We present here a brief summary of the most important equations used for numerical simulations. Of all the statistical ensembles that can be employed, the canonical and grand canonical... 

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