Internal correlations

Ikebe, N., Takayanagi, Y, Chiji, M. and Chinzei, K. (1972) Neogene biostratigraphy and radiometric time scale of Japan — an attempt at international correlation. Pacific Geology, 4, 39-78. 

In case of special conditions, viz. internal correlations, interactions can be estimated in addition to the main effects by means of a 2m 1 design. 

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

Figure 4.4. Relative internal correlation function /2(r)//2(0). The ratio is calculated using Eqs. (4.29) with the values eo = 70.5, te = tt= lOOps, and < = <<5 2>sin2e0=0.0149, which corresponds to an rms angular libra-tion of 7° in both the polar and 0 12 3 4 5 azimuthal directions. The dashed line...

Most FPA studies to date on DNA have lacked sufficient time resolution to observe directly the relaxation of the internal correlation functions. Instead, the initial anisotropy r0 is taken as an adjustable parameter. Equations (4.30) show that such a procedure is completely valid for anisotropic diffusors (i.e., (A ft)2 = (dx(t)2)), provided the rapid internal motion of the transition dipole is isotropic. It has not yet been ascertained whether the internal motion actually is isotropic, so this must be assumed.(83) A recent claim(86) that large amplitudes of polar wobble are required to fit both the small amplitude of initial FPA relaxation 87 and the linear dichroism88 has been refuted. 83j... 

The strength of PCA is the ability to take more than the optimal number of descriptors (that appear to be uncorrelated) and construct latent variables that are internally correlated yet uncorrelated to each other. The best feature of PCA is the ease of determining which of the original descriptors are most important. 

Objects can be internally correlated in time or space. For mixed objects such as tanks (and the products that have been subjected to storage for longer or shorter times), rivers, lakes, gases and environmental air this correlation can be rendered by auto-correlagrams and modelled by a simple negative exponential function of the correlation distance. 

These results immediately yield all the internal correlations among chain segments. The spatial distribution function for the pair of segments k-i < k2 is defined as... 

The predictive powers of the two models are almost identical although, at first glance, deviation from experimental values is smaller making use of the classical pharmacophore-CoMFA approach [e.g. AAG° = 0.39 (PA) vs 0.70 kcal mol-1 (PrA)]. On closer inspection, one has to take into account that the pseudoreceptor-derived model shows a stronger internal correlation (higher r2 and r v values) and therefore the differences in the prediction are statistically not relevant. 

McKitrick R. (2002). Trends in data on air temperature obtained with internal correlations taken into account. Proc. Russ. Geogr. Soc., 134(3), 16-24 [in Russian]. 

Objects which are internally correlated for example volumes sampled from rivers, soils, or ambient air, can be treated by autocorrelation analysis or semivariogram analysis. The range up to a critical level of error probability is an expression of the critical spatial or temporal distance between sampling points. 

If the purpose of sampling is the detailed description of the composition of an object, the character of the internal correlation has to be investigated. The methods of autocorrelation and/or semivariogram analysis, as described in Sections 6.6 and 4.4.2, may be useful for clarification of the internal spatial and/or temporal relationships existing within the parent population to be sampled. Geostatistical methods, e.g. kriging, enable undistorted estimation of the composition of unsampled locations in the area of investigation. 

The whole sampling process may be subdivided into two practical steps primary and secondary sampling. This division is described by FLATMAN et al. [1988] for the application of geostatistical methods in particular. These authors differentiate between primary sampling to obtain the internal correlation of the sampling locations in space and the secondary step for map-making. 

Wynder and Shigematsu (15) were the first to suggest that nutritional factors in general and specifically differences in fat intake may be responsible for the international variation in colon cancer incidence. Subsequent descriptive epidemiologic studies have found a strong positive association between colon cancer mortality or incidence in different countries and per capita availability in national diets of total fat (4,16) and of animal fat, estimated from food balance sheets. Such international correlations may be supportive of a hypothesis, but they should be interpreted with caution because the dietary data were based not on actual intake information but on food disappearance data. 

The main conclusion drawn from the MD simulations is that the proteins are highly flexible. The parts of the proteins that have high B-factors in the crystal structure also show great flexibility in the dynamics. The same regions are flexible in both runs, but the internal correlations of movements differ. This is reflected in the CPCA score plot the snapshots of each of the two CYP2C9 runs and the X-ray structures showed up in a different quadrant and did not overlap at any time point of the simulation. Thus, the molecular dynamics simulations cover a different CPCA space from the crystal structures with and without substrate bound, independent of the different starting structures. 

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