X patterns

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It is generally considered a good idea to tighten the nuts in an X pattern as illustrated in Figure 54.13. Always tighten the nuts in the sequence in which the positions are numbered (1,2, 3 and 4). 

These correlations are of generally poorer precision than those for reactivity and F-nmr shift data, and in the case of the ortho data set they required rejection of data for the substituents CHjCO, NO2, and CO2R (which give large deviations if included). Ihe latter deviations may be associated with ortho chelation effects. In any case, the Kj and X patterns, as noted above, appear essentially as expected. 

I-Solenoid repeats usually have several x or x x sequence patterns that correspond to the /1-strands (here, denotes an apolar residue, and x is mostly polar but can be any residue except pro line). The middle -position in x x usually has a bulky apolar residue, while -residues in positions close to turns are often alanine, glycine, serine, or threonine. These positions are also occupied by asparagine residues that stack to form H-bonded ladders inside the /1-solenoid. The strand-associated x and x x patterns are interrupted by regions enriched in polar residues and glycine (Hennetin et al., 2006). These are regions of turns and loops. The long loops frequently contain proline residues. In several /1-solenoids, the alternation of apolar and polar residues that is typical for /1-strands is not well observed and outside positions are occupied by apolar residues. 

A) Positive ions. In Fig. 9 it is seen that extraction with warm water introduced a series of relatively high mass positive ion fragments from mlz = 310 to 650. Most of the fragments extend the w and x patterns for the... 

Figure 9.2 shows some simple helices and their transforms. The transform of the helix in Fig. 9.2a exhibits an X pattern that is always present in transforms of helices. I will explain the mathematical basis of the X pattern later. Although each layer line looks like a row of reflections, it is actually continuous intensity. This would be apparent if the pattern were plotted at higher overall intensity. The layer lines are numbered with integers from the equator (/ = 0). Because of symmetry, the first lines above and below the equator are labeled 1=1, and so forth. 

Helix (d) has the same pitch and radius as helix (a), but is a helix of discrete objects or "repeats," like a polymeric chain of repeating subunits. The transform appears at first to be far more complex, but it is actually only slightly more so. It is merely a series of X patterns distributed along the meridian of the transform. To picture how multiple X patterns arise from a helix of discrete objects, imagine that the helix beginning with arbitrarily chosen object number I produces the X at the center of the transform. Then imagine... 

Figure 9.2 Helices and their Fourier transforms, (a) Simple, continuous helix. The first intensity peaks from the centers of each row form a distinctive X pattern, (b) Helix with longer pitch than (a)gives smaller spacing between layer lines. (c)Hclix with larger radius than (a) gives narrower X pattern, (d) Helix of same dimensions as (a)but composed of discrete objects gives X patterns repeated along the meridian.

Now let s look briefly at just enough of the mathematics of fiber diffraction to explain the origin of the X patterns. Whereas each reflection in the diffraction pattern of a crystal is described by a Fourier series of sine and cosine waves, each layer line in the diffraction pattern of a noncrystalline fiber is described by one or more Bessel functions, graphs that look like sine or cosine waves that damp out as they travel away from the origin (Fig. 9.3). Bessel functions appear when you apply the Fourier transform to helical objects. A Bessel function is of the form... 

Francis Crick showed in his doctoral dissertation that in the transform of a continuous helix, the intensity along a layer line is described by the square of the Bessel function whose order a equals the number I of the layer line, as shown in Fig. 9.3 b, which is an enlargement of three layer lines from the diffraction pattern of Fig. 9.2 a. Thus, the intensity of the central layer line, layer-line zero, varies according to [(/0(x)]2, which is the square of Eq. 9.1 with a = 0. The intensity of the first line above (or below) center varies according to [(7,(a )]2, and so forth. This means that, for a helix, the first and largest peak of intensity lies farther out from the meridian on each successive layer line. The first peaks in a series of layer lines thus form the X pattern described earlier. The distance to the first peak in each layer line decreases as the helix radius increases, so thinner helices give wider X patterns. 

The frequency variation occurring on going from one molecule to another or to the molecular complex depends on force constants in noncomplexed molecules and reflects, in the final analysis, the ionic nature of the bonds. When no spectra can be obtained in solution or in the gas phase, the inter-molecular contributions should be taken into account, especially in interpreting the Sn—X patterns. It should also be remembered that Sn—X frequencies are markedly dependent on the mass of the halogen involved and increase with atomic number. Nevertheless, the frequencies, which are a function of the nature and the number of halogens and vary over a wide range, are a good reflection of the bond ionicities and of the coordination number. 

This sequence closely resembles that of collagen. In particular, the repeating (Gly-Pro-X) pattern and the occurrence of hydroxy proline are characteristic of collagen. It is possible, then, that the peptide was derived from a protein resembling collagen. 

The X pattern (having 12 theoretical lines) consists here of a doublet having high intensity, superimposed on a quartet. From the doublet, by direct measurement, Jax = c7a x- = 8.6 c.p.s. it is assumed that Jxx — J AX — J A X = 0. 

How many PQS might one expect if these sequences had no physical reality In order to address this question, it is necessary to develop models for the DNA in these locations. One control that can be used in these models is to consider patterns analogous to the G-rich PQS. Labelling such base-rich sequences as X-patterns, where X is the frequent base, we have G-patterns, which correspond to sequences that form PQS in the strand being considered, and C-patterns, which correspond to sequences that form PQS in the complementary strand. 

Table 3 Relative frequency of X-patterns in exonic regions...

Directionally reinforced molding compound (XMC) continuous fibers crossed in an X pattern. 

Directionally reinforced molding compound (XMC) contains continuous reinforcements (up to 70 wt%) arranged in an X pattern with some chopped fibers and the final product has strong directional properties in the continuous fiber direction. XMC can be made on almost any filament winding machine as shown in Fig. 3.11. 

The spectrum of (f/ -C3H5)Mn(CO)4 conforms to the A B X pattern. Some allyl complexes show this pattern at low temperatures, but as the temperature is raised the resonances broaden, finally coalescing to an A X spectrum in which the syn and anti protons show an averaged signal. Such observations indicate that dynamic processes are proceeding at a rate comparable with the lifetime of the nuclear spin states. 

Fig. 4.32 FESEM of a Celgard microporous membrane shows (A) that the pores are filling in due to contamination, (B) fibrils are joining together and one pore region is filled, and (C) two fibrils are formed into an X pattern due to time in the electron beam. (From M. Jamieson, unpublished [341].)...

For 77% CaCOg in the raw meal the above-mentioned "X" pattern for computation gives ... 

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