For canonical lipid raft mixtures of cholesterol (chol), N-palmitoylsphingomyelin (PSM), and 1-palmitoyl-2-oleoylphosphatidylcholine (POPC), electron paramagnetic resonance (EPR) of spin-labeled phospholipids--which is insensitive to domain size--is used to determine the ternary phase diagram at 23°C. No phase boundaries are found for binary POPC/chol mixtures, nor for ternary mixtures with PSM content <24 mol %. EPR lineshapes indicate that conversion from the liquid-disordered (L(α)) to liquid-ordered (L(o)) phase occurs continuously in this region. Two-component EPR spectra and several tie lines attributable to coexistence of gel (L(β)) and fluid phases are found for ternary mixtures with low cholesterol or low POPC content. For PSM/POPC alone, coexistence of L(α) and L(β) phases occurs over the range 50-95.5 mol % PSM. A further tie line is found at 3 mol % chol with endpoints at 50 and ≥77 mol % PSM. For PSM/chol, L(β)-L(o) coexistence occurs over the range 10-38 mol % chol and further tie lines are found at 4.5 and 7 mol % POPC. Two-component EPR spectra indicative of fluid-fluid (L(α)-L(o)) phase separation are found for lipid compositions: 25%POPC>10%, and confirmed by nonlinear EPR. Tie lines are identified in the L(α)-L(o) coexistence region, indicating that the fluid domains are of sufficient size to obey the phase rule. The three-phase triangle is bounded approximately by the compositions 40 and 75 mol % PSM with 10 mol % chol, and 60 mol % PSM with 25 mol % chol. These studies define the compositions of raft-like L(o) phases for a minimal realistic biological lipid mixture.
A new method is proposed for locating saddle points on potential energy surfaces. The method involves walking on the ridge separating reactants' and products' valleys toward its minimum, which is a saddle point in coordinate space. Of particular advantage for ab inirio calculations, the ridge method does not require evaluation of second derivatives of the potential energy. Another important feature of the method is that no assumptions about the transition state geometry are needed, and it is easy to impose linear constraints on the molecular structure. The ridge method is supplemented by a heuristic detour algorithm, which enables one to deal with unfortunate choices of reactants' and products' coordinates. Both algorithms are illustrated by several examples where the complexity of the potential energy surface ranges from a simple analytical formula to a numerical manybody ab inirio potential.
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