Molecular dynamics data analysis

Sparks CJ Jr (1980) X-ray fluorescence microprobe for chemical analysis. In Winick H, Doniach S (eds) Synchrotron Radiation Research, Plenum Press, New York, p 459-512 Spngberg D, Hermansson K, Lindqvist-Reis P, Jalilehvand F, Sandstroem M, Persson I (2000) Model extended X-ray absorption fine structure (EXAFS) spectra from molecular dynamics data for Ca2+ and Al3+ aqueous solutions. J Phys Chem 104 10467-10472 Sposito G. (1986) Distinguishing adsorption from surface precipitation. In Geochemical Processes at Mineral Surfaces, Davis JA, Hayes KF (eds) ACS Symposium Series 323, The American Chemical Society, Washington, DC, p 217-228... 

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

In numerous cases an atomically detailed picture is required to understand function of biological molecules. The wealth of atomic information that is provided by the Molecular Dynamics (MD) method is the prime reason for its popularity and numerous successes. The MD method offers (a) qualitative understanding of atomic processes by detailed analysis of individual trajectories, and (b) comparison of computations to experimental data by averaging over a representative set of sampled trajectories. 

How can we apply molecular dynamics simulations practically. This section gives a brief outline of a typical MD scenario. Imagine that you are interested in the response of a protein to changes in the amino add sequence, i.e., to point mutations. In this case, it is appropriate to divide the analysis into a static and a dynamic part. What we need first is a reference system, because it is advisable to base the interpretation of the calculated data on changes compared with other simulations. By taking this relative point of view, one hopes that possible errors introduced due to the assumptions and simplifications within the potential energy function may cancel out. All kinds of simulations, analyses, etc., should always be carried out for the reference and the model systems, applying the same simulation protocols. 

TJ Oldfield. SQUID A program for the analysis and display of data from crystallography and molecular dynamics. J Mol Graphics 10 247-252, 1992. 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

If all nuclei are assigned and the spectral parameters for the conformational analysis are extracted, a conformation is calculated - usually by distance geometry (DG) or restrained molecular dynamics calculations (rMD). A test for the quality of the conformation, obtained using the experimental restraints, is its stability in a free MD run, i.e. an MD without experimental restraints. In this case, explicit solvents have to be used in the MD calculation. An indication of more than one conformation in fast equilibrium can be found if only parts of the final structure are in agreement with experimental data [3]. Relaxation data and heteronuclear NOEs can also be used to elucidate internal dynamics, but this is beyond the scope of this article. 

Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness fluctuations derived from molecular dynamics simulations can serve such a purpose. A possible difficulty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the fluctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. 

Current (3) Intensity MDA (2) Molecular dynamics Multivariate data analysis... 

For the first time, the primary nitrone (formaldonitrone) generation and the comparative quantum chemical analysis of its relative stability by comparison with isomers (formaldoxime, nitrosomethane and oxaziridine) has been described (357). Both, experimental and theoretical data clearly show that the formal-donitrones, formed in the course of collision by electronic transfer, can hardly be molecularly isomerized into other [C,H3,N,0] molecules. Methods of quantum chemistry and molecular dynamics have made it possible to study the reactions of nitrone rearrangement into amides through the formation of oxaziridines (358). 

The size of the atoms and the rigidity of the bonds, bond angles, torsions, etc. are determined empirically, that is, they are chosen to reproduce experimental data. Electrons are not part of the MM description, and as a result, several key chemical phenomena cannot be reproduced by this method. Nevertheless, MM methods are orders of magnitude cheaper from a computational point of view than quantum mechanical (QM) methods, and because of this, they have found a preferential position in a number of areas of computational chemistry, like conformational analysis of organic compounds or molecular dynamics. 

Equations (1-3) are widely used for protein dynamics analysis from relaxation measurements. The primary goals here are (A) to measure the spectral densities J(co) and, most important, (B) to translate them into an adequate picture of protein dynamics. The latter goal requires adequate theoretical models of motion that could be obtained from comparison with molecular dynamics simulations (see for example Ref. [23]). However, accurate analysis of experimental data is an essential prerequisite for such a comparison. 

There are many types of data in chemistry that are not specifically covered in this book. For example, we do not discuss NMR data. NMR spectra of solutions that do not include fast equilibria (fast on the NMR time scale) can be treated essentially in the same way as absorption spectra. If fast equilibria are involved, e.g. protonation equilibria, other methods need to be applied. We do not discuss the highly specialised data analysis problems arising from single crystal X-ray diffraction measurements. Further, we do not investigate any kind of molecular modelling or molecular dynamics methods. While these methods use a lot of computing time and power, they are more concerned with data generation than with data analysis. 

Of great interest to the molecular biologist is the relationship of protein form to function. Recent years have shown that although structural information is necessary, some appreciation of the molecular flexibility and dynamics is essential. Classically this information has been derived from the crystallographic atomic thermal parameters and more recently from molecular dynamics simulations (see for example McCammon 1984) which yield independent atomic trajectories. A diaracteristic feature of protein crystals, however, is that their diffraction patterns extend to quite limited resolution even employing SR. This lack of resolution is especially apparent in medium to large proteins where diffraction data may extend to only 2 A or worse, thus limiting any analysis of the protein conformational flexibility from refined atomic thermal parameters. It is precisely these crystals where flexibility is likely to be important in the protein function. 

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