Order parameter molecular

TUt angle of the peptide symmetry axis with respect to the membrane normal Azimuthal rotation angle of the peptide Molecular order parameter of the peptide... 

Because nematic liquid-crystalline polymers by definition are both anisotropic and polymeric, they show elastic effects of at least two different kinds. They have director gradient elasticity because they are nematic, and they have molecular elasticity because they are polymeric. As discussed in Section 10.2.2, Frank gradient elastic forces are produced when flow creates inhomogeneities or gradients in the continuum director field. Molecular elasticity, on the other hand, is generated when the flow is strong enough to shift the molecular order parameter S = S2 from its equilibrium value 5 . (Microcrystallites, if present, can produce a third type of elasticity see Section 11.3.6.)... 

Figure 4 Angles involved in the calculation of molecular order parameters. The molecular order parameters are calculated using p, the angle between the bilayer normal (C/BfJ and the normal to the plane spanned by the two C—H veaors. C, j, Cy, and Cy+j are atoms contained in the alkyl chain of the lipid molecule and NMR order parameters are calculated using the angle 0 between the bilayer normal (CfBfJ and the C—H vectors.

Figure 5 Example of an experimental molecular order parameter profile. O, di-palmitoylphosphatidylcholine (DPPC) A, palmitoleicphosphatidylcholine (POPC) , dipalmitoylphosphatidylserine (DPPS) based bilayers X, bilayers derived from Acholeplasma laidlawii. All measurements were taken at the same reduced temperature 0 = (T - Tc)/T = 0.0605 (where = phase transition temperature).

Figure 7 Computed molecular order parameter profile for a bilayer based on dilau-roylphosphatidylethanolamine (DLPE).

The molecular order parameter profile obtained from the MD trajectory is shown in Figure 7. Because there is not an experimental order parameter profile for DLPE itself, the order parameter profile of dipalmitoylphos-phatidylcholine (DPPC) from the NMR work of Seelig and Seelig was used. The order parameter profiles of different lipids can be compared using the concept of a reduced temperature = (T - where is the gel-to-... 

Figure 2. Molecular order parameter (Smoi- Sco) averaged between the chains...

Using these definitions, components of the molecular order parameter tensor can be determined (for example, Sjj is determined by measuring the angle between the molecular z axis and the bilayer normal). The experimental order parameter can be related to the molecular order parameter using the equation ... 

Structural changes in the lipid bilayer upon insertion of the transmembrane domain of the membrane-bound protein phospholamban (PLB) were studied using P and solid state NMR. Phospholamban is a 52-amino acid integral membrane protein that regulates the flow of Ca " ions in cardiac muscle cells. Solid state NMR experiments were carried out to study the behavior of lipid bilayers in the presence of the hydrophobic PLB at different temperatures. P NMR was used to study the different phases formed by phospholipid membranes. Simulations of the P NMR spectra were carried out to reveal the formation of different vesicle sizes upon PLB insertion. Molecular order parameters were calculated by performing solid state NMR studies on deuterated phospholipid bilayers. 

As the shear rate increases, large viscous stresses cause refinement of the texture until eventually individual molecules experience significant viscous torques, and the molecular order parameter can be distorted from its equilibrium value. This occurs when the Deborah number approaches or exceeds unity. 

The overall order parameter, (Pa), for an oriented nematic solution may be expressed in terms of the order parameter of the director field of the domains. Pa, and of the molecular order parameter, (Pa), characterizing the degree of order... 

FIGURE 7.20 Photocontrol surface relief of crosslinked PLCPs by light-induced molecular order parameters. Reproduced with permission from Reference 44. Copyright 2012 John Wiley Sons, Inc. 

To proceed we need to know how the functional A[f(fi-, 22 Ri 2)] varies when the equilibrium state of the liquid crystal is elastically distorted. A macroscopic strain will not influence Mi 2 or g, p. since these are dependent only on molecular parameters of the model the free energy changes because the single particle distribution functions change. We assume that for the small distortions described by the Frank elastic constants, the single particle orientational distribution function, defined with respect to a local director axis, is also independent of strain i. e. elastic torques do not change the molecular order parameters. The product of distribution functions /(i2j, R ) f, Q2i R2) will change with strain because the director orientations at R1 and R2 will differ, and the evaluation of the strain dependence of the... 

Figure 6 The measured deuterium order parameters, pfor the sn-1 (saturated) and sn-2 (unsaturated, C9=C10) bilayers of phospholipids specifically deuterated In their acyl chains, showing the consequence of the presence of double bonds causing the staggered conformation of the chains thus affecting the quadrupolar averaging (B), even though the molecular order parameter, S oi, remains for each chain (A). Reproduced with permission from Seelig J and Seelig A (1977) Effect of single cis double bond on the structure of a phospholipid bilayer. Biochemistry 45-50.

AVj is the quadrupolar splitting (peak for the 90 orientation of the director with respect to Bq) of the i th deuteron, is the angle between the i th C-D bond and the rotation axis, and the last term describes the anisotropic motion of the rotation axis. The last term involves only the motion of the molecule as a whole, and is therefore the molecular order parameter, It... 

The angles d, y and 0 may be distinct or fluctuating (partly or all), describing a microcrystalline uT trastructure (MCU) and a liquid crystalline ultrastructure (LCU), respectively. Sy is referred to as the molecular order parameter... 

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