en>Brirush at 12:59, 24 August 2014

2014-08-24T12:59:13Z

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	~~In [[polymer science]], the ''~~'~~Lifson–Roig model''' is a [[helix-coil transition model]] applied to the [[alpha helix]]-[[random coil]] transition of [[polypeptide]]~~s;<ref name="Lifson">{{cite journal \|author=Lifson S, Roig A \|year=1961 \|title=On the theory of helix-coil transition in polypeptides \|journal=J Chem Phys \|volume=34 \|pages=1963–1974 \|doi=10.1063/1.1731802 \|issue=6}}</ref> it is a refinement of the [[Zimm-Bragg model]] that recognizes that a polypeptide [[alpha helix]] is only stabilized by a [[hydrogen bond]] only once three consecutive residues have adopted the helical conformation. To consider three consecutive residues each with two states (helix and coil), the Lifson–Roig model uses a 4x4 transfer matrix instead of the 2x2 transfer matrix of the Zimm-Bragg model, which considers only two consecutive residues. However, the simple nature of the coil state allows this to be reduced to a 3x3 matrix for most applications.		They contact me Emilia. Minnesota is where he's been residing for years. Managing people is what I do and the wage has been really fulfilling. Playing baseball is the hobby he will by no means quit doing.<br><br>Feel free to visit my web site: std testing at home ([http://www.teenvalley.net/user/RLay please click the following webpage])

	~~The Zimm-Bragg and Lifson–Roig models are but the first two in a series of analogous transfer-matrix methods in polymer science that have also~~ been ~~applied to [[nucleic acid]]s and branched polymers. The transfer-matrix approach is especially elegant~~ for ~~homopolymers, since the statistical mechanics may be solved exactly using a simple [[eigenanalysis]]~~.

	~~==Parameterization==~~
	~~The Lifson–Roig model~~ is ~~characterized by three parameters: the [[statistical weight]] for [[nucleation\|nucleating]] a helix, the weight for propagating a helix~~ and the ~~weight for forming a hydrogen bond, which is granted only if three consecutive residues are in a helical state~~. ~~Weights are assigned at each position in a polymer as a function of the conformation of the residue in that position and as a function of its two neighbors. A statistical weight of 1~~ is ~~assigned to~~ the ~~"reference state" of a coil unit whose neighbors are both coils, and a "nucleation" unit is defined (somewhat arbitrarily) as two consecutive helical units neighbored~~ by ~~a coil. A major modification of the original Lifson–Roig model introduces "capping" parameters for the helical termini, in which the N- and C-terminal capping weights may vary independently~~.<~~ref name="Doig"~~>{{cite journal \|doi=10.1002/pro.5560040708 \|author=Doig AJ, Baldwin RL \|year=1995 \|title=N- and C-capping preferences for all 20 amino acids in alpha-helical peptides \|journal=Protein Sci \|volume=4 \|issue=7 \|pages=1325–1336 \|pmid=7670375 \|pmc=2143170}}<~~/ref~~> ~~The correlation matrix for this modification can be represented as a matrix M, reflecting the statistical weights of the helix state ''h'' and coil state ''c''.~~
	~~{\| class="wikitable" style="text-align~~:~~center" align="right"~~
	\|-
	~~! ''M'' !! hh !! hc !! ch !! cc~~
	\|-
	~~! hh~~
	~~\| w \|\| v \|\| 0 \|\| 0~~
	\|-
	~~! hc~~
	~~\| 0 \|\| 0 \|\| <math>\sqrt{nc}</math> \|\| c~~
	\|-
	~~! ch~~
	~~\| v \|\| v \|\| 0 \|\| 0~~
	\|-
	~~! cc~~
	~~\| 0 \|\| 0 \|\| n \|\| 1~~
	\|}

	~~The Lifson–Roig model may be solved by the [[transfer-matrix method]] using the transfer matrix '''M''' shown~~ at ~~the right, where ''w'' is the [[statistical weight]] for helix propagation, ''v'' for initiation, ''n'' for N-terminal capping, and ''c'' for C-terminal capping.~~ (~~In the traditional model ''n'' and ''c'' are equal to 1.) The~~ [~~[partition function (statistical mechanics)\|partition function]] for the helix-coil transition equilibrium is~~
	:~~<math>~~
	~~Z = V \left(\prod_{i=0}^{N+1} M(i)\right)\tilde{V}~~
	</~~math>~~

	~~where ''V'' is the end [[coordinate vector\|vector]] <math>V=[0 0 0 1]<~~/~~math>, arranged to ensure the coil state of the first and last residues in the polymer~~.

	This strategy for parameterizing helix-coil transitions was originally developed for [[alpha helix\|alpha helices]], whose [[hydrogen bond]]s occur between residues ''i'' and ''i+4''; however, it is straightforward to extend the model to [[310 helix\|3<sub>10</sub> helices]] and [[pi helix\|pi helices]], with ''i+3'' and ''i+5'' hydrogen bonding patterns respectively. ~~The complete alpha/3<sub>10</sub>~~/~~pi transfer matrix includes weights for transitions between helix types as well as between helix and coil states. However, because 3<sub>10<~~/~~sub> helices are much more common in~~ the ~~[[tertiary structure~~]]s of proteins than pi helices, extension of the Lifson–Roig model to accommodate 3<sub>10</sub> helices - resulting in a 9x9 transfer matrix when capping is included - has found a greater range of application.<ref name="Rohl">{{cite journal \|author=Rohl CA, Doig AJ \|year=1996 \|title=Models for the 3(10)-helix/coil, pi-helix/coil, and alpha-helix/3(10)-helix/coil transitions in isolated peptides \|journal=Protein Sci \|pmid=8844857 \|volume=5 \|issue=8 \|pmc=2143481 \|pages=1687–1696 \|doi=10.1002/pro.5560050822}}</ref> Analogous extensions of the Zimm-Bragg model have been put forth but have not accommodated mixed helical conformations.<ref name="Sheinerman">{{cite journal \|doi=10.1021/ja00145a022 \|author=Sheinerman FB, Brooks CL \|year=1995 \|title=310 helices in peptides and proteins as studied by modified Zimm-Bragg theory \|journal=J Am Chem Soc \|volume=117 \|issue=40 \|pages=10098–10103}}</ref>

	~~==References==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Lifson-Roig model}}~~
	~~[[Category:Polymer physics]]~~
	~~[[Category:Protein structure]]~~
	~~[[Category:Statistical mechanics]]~~

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