Conformational order parameter

Figure 8 shows a plot of a fluid-like DPPC bilayer, in which a small fraction of the lipids are replaced by a pyrene-containing PyrPC probe, see Fig. 1 (26). The study has demonstrated that the perturbations in the vicinity of the probe are substantial, as the conformational order parameter (Scd) of lipid hydrocarbon chains close to the probe may change as much as about 100%. However, what is also found is the short range of perturbations, because the perturbations are negligible beyond a distance of about 1.5 nm. In practice, this finding implies that about 20-30 lipids around the probe are affected by the marker, but the global properties averaged across the membrane are affected only little.

SO that the anisotropy in % depends on the mixed second rank orientational-conformational order parameters and the pure second rank orientational ordering tensor it is independent of the pure conformational order parameters. The variation of the magnetic anisotropy with the mixed order parameters appears somewhat involved. The extent of this complexity is detomined by the numb of terms needed in the Fourier expansion of the tenstnr K ( limiting case when ( (pj ) is indepaKlent of the molecular crmformation, that is when the only contribution to ( q>j ) originates from the rigid sub-unit used to define the molecular fl me. Then... 

With all-atom simulations the locations of the hydrogen atoms are known and so the order parameters can be calculated directly. Another structural property of interest is the ratio of trans conformations to gauche conformations for the CH2—CH2 bonds in the hydrocarbon tail. The trans gauche ratio can be estimated using a variety of experimental techniques such as Raman, infrared and NMR spectroscopy. 

Fig. 1 Solid-state NMR structure analysis relies on the 19F-labelled peptides being uniformly embedded in a macroscopically oriented membrane sample, (a) The angle (0) of the 19F-labelled group (e.g. a CF3-moiety) on the peptide backbone (shown here as a cylinder) relative to the static magnetic field is directly reflected in the NMR parameter measured (e.g. DD, see Fig. 2c). (b) The value of the experimental NMR parameter varies along the peptide sequence with a periodicity that is characteristic for distinct peptide conformations, (c) From such wave plot the alignment of the peptide with respect to the lipid bilayer normal (n) can then be evaluated in terms of its tilt angle (x) and azimuthal rotation (p). Whole-body wobbling can be described by an order parameter, S rtlo. (d) The combined data from several individual 19F-labelled peptide analogues thus yields a 3D structural model of the peptide and how it is oriented in the lipid bilayer...

From these overall profiles, it is not easy to extract conformational properties, other than that it will be clear that the lipid molecules are strongly anisotropically oriented in the bilayer. For this, other characteristics are much more appropriate. It is possible to define an order parameter which indicates how much the lipid tails are oriented normal to the membrane ... 

Many conformations were sampled by the usual MC procedure. The result is of course that there is no preferred orientation of the molecule. Each conformation can, however, be characterised by an instantaneous main axis this is the average direction of the chain. Then this axis is defined as a director . This director is used to subsequently determine the orientational order parameter along the chain. The order is obviously low at the chain ends, and relatively high in the middle of the chain. It was found that the order profile going from the centre of the molecules towards the tails fell off very similarly to corresponding chains (with half the chain length) in the bilayer membrane. As an example, we reproduce here the results for saturated acyl chains, in Figure 10. The conclusion is that the order of the chains found for acyl tails in the bilayer is dominated by intramolecular interactions. The intermolecular interactions due to the presence of other chains that are densely packed around such a chain,... 

From the density profiles one cannot really judge the effect of the double bonds the density profiles for membranes of saturated lipids are very similar to those of unsaturated ones. Therefore it is necessary to consider some of the conformational characteristics of the tails. It is possible to compute the order parameter profile for both the saturated and the unsaturated chains. The order parameter profile for the saturated chain closely follows the results presented in Figure 17 for DMPC membranes for both the SCF and the MD predictions. The order parameter profiles for the unsaturated chain closely follows the MC predictions, as discussed in Figure 9. A pronounced dip is found near the cis double bond. For this reason, we choose here to present complementary data about the conformational properties of the acyl chains. 

The above spectral densities can be modified for the occurence of chain flexibility, and for the director being oriented at dLD w.r.t. the external BQ field in the L frame. For CD bonds located in the flexible chain, the effect of DF is reduced due to an additional averaging of the time dependent factor (/f g) by conformational transitions in the chain. Consequently, the spectral densities given in Eqs. (60)-(62) are modified by replacing Soc%0(Pm,q) by the segmental order parameter YCD of the C-D bond at a particular carbon site on the chain.146,147 As observed experimentally,148,149 the spectral densities in a flexible chain show a SqD dependence when DF dominate the relaxation rates. The general expression of Jm(co 0LD) due to DF in uniaxial nematic phases is given by... 

Hilvert s group used the same hapten [26] with a different spacer to generate an antibody catalyst which has very different thermodynamic parameters. It has a high entropy of activation but an enthalpy lower than that of the wild-type enzyme (Table 1, Antibody 1F7, Appendix entry 13.2a) (Hilvert et al., 1988 Hilvert and Nared, 1988). Wilson has determined an X-ray crystal structure for the Fab fragment of this antibody in a binary complex with its TSA (Haynes et al., 1994) which shows that amino acid residues in the active site of the antibody catalyst faithfully complement the components of the conformationally ordered transition state analogue (Fig. 11) while a trapped water molecule is probably responsible for the adverse entropy of activation. Thus it appears that antibodies have emulated enzymes in finding contrasting solutions to the same catalytic problem. 

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