Chain unconstrained

Havel, T. F. The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide-chains a smdy of 1830 independently computed conformations. Biopolymers 1990, 29,1565-1585. 

Alkyl chain heterogeneities cause cell membrane bilayers to remain in the fluid state over a broad temperature range. This permits rapid lateral diffusion of membrane lipids and proteins within the plane of the bilayer. The lateral diffusion rate for an unconstrained phospholipid in a bilayer is of the order of 1 mm2 s 1 an integral membrane protein such as rhodopsin would diffuse 40nm2 s 1. 

Fig. 9 Left Simulation results for the rescaled averaged polymer paths which end at a certain distance from the wall for = 0.02, 0.06, 0.17 (from top to bottom)y corresponding to stretching values of y = 1.3, 1.8, 2.7. The thick solid line shows the unconstrained mean path obtained hy averaging over all end-point positions. Right Endpoint distributions. AH data are obtained for simulations with 50 chains consisting of N = 50 monomers each...

We conclude that a) all degrees of freedom should be unconstrained (including those related to the shape of the sugar rings)/ b) the packing forces can significantly influence the conformation even of a polymer main chain and c) a suitable potential set (with all atoms), used in total energy minimization, can account for these effects. With these considerations in mind, we attempted to model the crystal structures of DeS and an isolated chain of Hep. 

Adam s results for three of the higher normal aldoximes are reproduced in the curve. The line AB, common to all three, closely resembles the usual line giving the compressibility of the hydrocarbon chains, though the somewhat greater value for the area, 21 8 A., at which it cuts the axis of area, may be due to some other form of packing. The lower part of the line has different though parallel courses for the compound with 16 carbon atoms and for those with 14 or 15 the lines BO and FD represent the more open type of packing which is determined by the area of the head, or soluble end, of the molecule. The area of the head when unconstrained is thus 25-4 A. for the lower and 1-... 

The hydrocarbon chains of the surfactant molecules are constrained to remain with the polar headgroups in contact with water and therefore have a conformational free energy relative to the unconstrained chains. The conformational free energy per chain can be calculated using the following expressions22 41... 

T. F. Havel, Biopolymers, 29, 1565 (1990). The Sampling Properties of Some Distance Geometry Algorithms Applied to Unconstrained Polypeptide Chains A Study of 1830 Independently Computed Conformations. 

In strong bases such as the one provided by sodium hydride and dimethyl sulfoxide (DMSO)—namely, dimsyl sodium—one should expect the formation of carbanions at sites of acidic protons. Ketones are attractive as potential sources of carbanions. However, ketone I features two blocked a carbons, without protons. Conversely, the tosyl group is ill suited for carbanion stabilization. The last functionality one may appeal to is the phenyl sulfone substituent at the end of the jec-pentyl chain. Recent investigations have revealed their potential as carbanion precursors, adding an important feature to their considerable usefulness in organic synthesis That is, sulfones can be removed under such mild conditions that carbonyl groups are not affected, and unconstrained a-sulfonyl carbanions have the unusual quality of retaining the asymmetry of their precursors in a wide variety of experimental conditions. ... 

One may visualize a tube as the continuum limit of a discrete chain of tethered disks or coins [21] of fixed radius separated from one another by a distance a in the limit of a -> 0. The inherent anisotropy associated with a coin (the heads-to-tails direction being different from the other two) reflects the fact that a special local direction at each position is defined by the locations of the adjacent objects along the chain. An alternative description of a discrete chain molecule is a string-and-beads model in which the tethered objects are spheres. The key difference between these two descriptions is the different symmetry of the tethered objects. On compaction, spheres tend to surround themselves isotropically with other spheres, unlike the tube situation in which nearby tube segments need to be placed parallel to one another. Even for unconstrained particles, deviations from spherical symmetry (replacing a system of hard spheres with one of hard rods, for example) lead to rich new liquid crystal phases [22, 23]. Likewise, the tube and a chain of tethered spheres exhibit quite distinct behaviors. 

Nature has used several classes of chain molecule - DNA, RNA, and proteins -to create living matter. (Small, unconstrained molecules are not very useful for this because one cannot associate a natural context for them.) The DNA molecule carries information and is able to replicate itself, albeit with occasional mistakes. Importantly, these mistakes, which form the basis of molecular evolution, are also replicated in future generations. The RNA molecule plays a key role in translating the information contained in the DNA for making proteins. Proteins, the workhorse... 

Ideas on the three-dimensional structure of proteins were no less preliminary. It was agreed that they were big molecules - macromolecules - probably composed of linear chains of amino acids of up to 100 or more. But just how their primary sequences were determined, how they were synthesized, and how they arrived at their native three-dimensional conformations was a complete mystery (Hunter, 2000, ch. 11). It is a testimony to how little was known about protein function that a majority of biochemists considered that it was proteins, rather then nucleic acids, that played the primary role in heredity and formed the basic aperiodic molecule that made up the material structure of the gene (McCarty, 2003j. The question of whether proteins represented a potentially infinite set of Lego -like assemblages, largely unconstrained by physical law and determined by natural selection, or whether they represented a finite set of natural forms determined mainly by natural law and therefore were antecedent to life and evolution (like a set of atoms or crystals), was simply impossible to answer. 

The harmonic dynamical treatment of a model of the -alkanes as a zigzag chain of point mass beads with unconstrained ends and an infinitely strong stretching force constant (so that only CCC bending occurs) has been presented [13]. The analytic result for the infinite chain for which the frequencies of the LAMs are ... 

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