By Hugo O. Villar (Eds.)
The second one quantity in a sequence which goals to target advances in computational biology. This quantity discusses such themes as: statistical research of protein sequences; growth in large-scale series research; and the structure of loops in proteins
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Above this value of F^, the transition is of first order. The data on which these conclusions are based are presented in Figure 4 which shows that the free energy as a function of area per lipid chain exhibits two minima separated by an energy barrier. The height of this barrier, AiF(L), changes with system size very differently for different values of F^. F(L) is shown as a function of system size for the three values of F^ corresponding to Figures 4(a-c). Figure 5 shows that Air(L) decreases with increasing L for F^ = 3 x 10~^^erg/A, implying the absence of a transition, and increases with increasing L for F^ = 5 x 10~^^erg/A, implying the occurrence of a first-order phase transition.
F(TmiL)), in the free energy functional at the transition for mismatch values (from bottom to top) TA = 3 (no transition), 4 (critical point), and 5 (first-order transition) as a function of linear lattice size, L TA is in units of x10"^^ erg/A. 6 Ji ]| X ? 4 n n _ 311 ^ 313 ; ^ ^>-— 1 1 315 317 T (K) 1 1 1 310 Figure 6. Mismatch model of the main phase transition in DPPC lipid bilayers; cf. Eq. (3). (a) Temperature dependence of the specific heat, C(7), for /. = 8, 12,16, 20, 24, 32 and TA = 5 x 10"^^ erg/A.
F(x^^, r, L) - /(jci, r, L) = Y(^, T)L^' + OiL^'^), (16) where d is the spatial dimension of the system (d = 2m the present case). Y(|Li, T) is the interfacial free-energy density or interfacial tension. Therefore Ajr(|X, T, L) increases monotonically with L at afirst-ordertransition (or at phase coexistence) corresponding to afiniteinterfacial tension. The detection of such an increase is an unambiguous sign of afirst-ordertransition and two-phase coexistence. In contrast, Air(|X, r, L) approaches a constant at a critical point, corresponding to vanishing interfacial tension in the thermodynamic limit.
Advances in Computational Biology by Hugo O. Villar (Eds.)