Coordinate systems to represent compositional space for ternary phase diagrams. A) The Gibbs' triangle represents mixtures of the three lipid components, brain-sphingomyelin (SPM or S), dioleoylphosphatidylcholine (DOPC or D), and Cholesterol (C), with coordinates in mole fractions. Every point within the triangle represents a ternary mixture of all three lipids. A point on an edge represents a binary mixture of either SPM/DOPC (bottom edge), DOPC/Cholesterol (left edge), or SPM/Cholesterol (right edge). The left vertex of the triangle is pure DOPC, the top vertex is pure Cholesterol, and the right vertex is pure SPM. B) The linear transformation of the Gibbs' triangle from the three-dimensional mole fraction space to the plane of the ψ-coordinate system, ψS = ξS + ξC * cos(π/3) and ψC = ξC * sin(π/3). The eS and eC are the basis vectors that span the Gibbs' triangle.