Dynamic structures, comparison

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Fig. 21. Comparison of the dynamic structure factors from long PTHF chains in a matrix of long chains (x) with that in a matrix of short chains ( ). The Q-value of the experiment was Q = 0.09 A-1, the temperature T = 418 K (Reprinted with permission from [57]. Copyright 1985 Royal Society of Chemistry, Cambridge, UK)...

Figure 7. (a) Stereo view of comparison of the main chain of the X-ray structure of the HIV-1 protease complex with compound 2 (red) with the main chains of the minimized complex (yellow) and a 20ps average dynamical structure of the same complex of HIV-1 protease (green), (b) Stereoview of the active-site geometry of the crystal structure (in half-bond color) of the HIV-1 protease complexed with the compound 2 (with the indole and phenyl groups shown in red) as revealed by X-ray crystallography. 

In order to learn more about the Rouse model and its limits a detailed quantitative comparison was recently performed of molecular dynamics (MD) computer simulations on a 100 C-atom PE chain with NSE experiments on PE chains of similar molecular weight [52]. Both the experiment and the simulation were carried out at T=509 K. Simulations were imdertaken,both for an explicit (EA) as well as for an united (l/A) atom model. In the latter the H-atoms are not explicitly taken into account but reinserted when calculating the dynamic structure factor. The potential parameters for the MD-simulation were either based on quantum chemical calculations or taken from literature. No adjusting... 

We now address the dynamic structure factor which incorporates all time-dependent correlations of segments along the chain. While the early MD-sim-ulations of Kremer and Grest did very well with the msd, the dynamic structure factor was only poorly described. Figure 3.25b displays a comparison with NSE results on PEP and PE, where the simulation results were mapped to the experiment in terms of time units measured by (F= f/r ) and length scales measured by the tube diameter d(Q = Qld) [50]. 

Fig. 3.25 Comparison of the experimental dynamic single chain structure factors for PEP at Q=0.135 Qd=6A) and PE at Q=0.128 A (Qd=5.5) with the dynamic structure factors from the computer polymer. The various/w// lines represent MD results for different Qd=3.1 (a), 3.9 (b), 4.6 (c), 6.2 (d), and 7.7 (e). In the upper part the computer results are the structure factors from a fully labelled chain, while in the lower part only the centre 35 monomers are labelled. (Reprinted with permission from [49]. Copyright 1992 American Chemical Society)...

From this comparison it follows that the observation of the structural relaxation by standard relaxation techniques in general might be hampered by contributions of other dynamic processes. It is also noteworthy that the structural relaxation time at a given temperature is slower than the characteristic time determined for the a-relaxation by spectroscopic techniques [105]. An isolation of the structural relaxation and its direct microscopic study is only possible through investigation of the dynamic structure factor at the interchain peak - and NSE is essential for this purpose. 

Fig. 5.15 Momentum transfer dependence of the amplitude of the KWW functions describing the dynamic structure factor. For 390 K all the values obtained are shown (filled triangle)y while the dashed and solid lines represent the smoothed behaviour for 335 K and 365 K, respectively. The static structure factor is shown in arbitrary units for comparison (cross). (Reprinted with permission from [147]. Copyright 2002 The American Physical Society)...

Fig. 6.5 Comparison between NSE spectra at Q=0.1 A and T=473 K of both binary blends (filled circle and filled triangle), and those of the isotopic PDMS blends filled square). The solid lines result from a fit t with the dynamic structure factor for the Rouse model filled square) and of a spatially limited Rouse dynamics, as derived in [256] filled square and filled triangle). (Reprinted with permission from [255]. Copyright 2003)...

The electron diffraction study was complemented by an all-electron theoretical calculation of Lu, Wei, and Zunger (LWZ) (1992), using the local density approximation for the exchange and correlation terms in the Hamiltonian. They find agreement within x0.6% between the calculated and dynamic structure factor values for the lowest three reflections, (100), (110), and (111). But for (200), with sin 0/A = 0.3464 A-1, the discrepancy is as large as 1.7%. The discrepancy is attributed to insufficiently accurate knowledge of the temperature factors in this diatomic crystal, which affect the derivation of the X-ray structure factor from the electron diffraction measurement, as well as the calculation of the dynamic theoretical structure factors needed for the comparison with experiment. For the monoatomic Si crystal for which the B values are well known, the agreement is... 

Figure 18. (a) Response versus the dynamical structure factor for the binary mixture Lennard-Jones particles system in a quench from the initial temperature Ti = 0.8 to a final temperature T( = 0.25 and two waiting times t = 1024 (square) and = 16384 (circle). Dashed lines have slope l/Tf while thick hues have slope l/T (t ). (From Ref. 182.) (b) Integrated response function as a function of IS correlation, that is the correlation between different IS configurations for the ROM. The dashed fine has slope Tf = 5.0, where Tf is the final quench temperature, whereas the full lines are the prediction from Eq. (205) andF = F (T ) Teff(2") 0.694, Teff(2 ) 0.634, and 7 eff(2 ) 0.608. The dot-dash line is for t , = 2" drawn for comparison. (From Ref. 178.)... 

Having developed and parameterized potential models, the final stage before their use in a simulation study should be their evaluation. Nonempirically derived potentials should be evaluated by reference to their ability to predict empirical crystal properties. For empirical potentials, it is clearly necessary to use data outside the range employed in the parameterization. We have already referred to the use of lattice dynamical data. Comparison with the results of high-pressure studies, in particular the variation of structural and elastic properties with pressure, is also of great value and... 

DNA is not the perfect double helix of traditional textbooks. Slight, but significant structiu e variations have been demonstrated from comparison of crystal structures of oligonucleotides. It has also become evident that these structure variations are not entirely determined by the individual base-steps (AA, AT, GC, etc), but are influenced by sequence contexts (1,2). The emerging picture of the DNA duplex, in fact, suggests a dynamic structure that is continuously contorted in a sequence-dependent manner. 

Figure 1. Outer dynamics in comparison with model of Mohler et al. [4] virus yield vs. time post infection for different MOI (circles experimental results, solid line unstructured model, dashed line structured model, tshift = 4.5 h)...

In order to test the quality and validity of the theoretical models we need to compare with experiments. Nowadays it is possible to calculate the position and vibrations of atoms in solids and molecules, the comparison with experiment, however, is usually limited to only the description of the atomic positions, structure. Comparisons with the dynamical data are not routinely made and when made it is most generally restricted to infrared and Raman data, which are limited to information at the gamma point and it also presents difficulties on the theoretical calculation of spectral intensities. 

A. Pasquarello, J. Samthein R. Car (1998). Phys. Rev. B, 57, 14133-14140. Dynamic structure factor of vitreous silica from first principles Comparison to neutron-inelastic-scattering experiments. 

Taylor W. R., Protein structure comparison using iterated double dynamic programming. Protein Sci, 1999. 8(3) p. 654-65. 

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