where p(ψ i )/p(ψ eq ) is the ratio of peptide bonds with ψangles angles, ψ i and ψ eq , respectively. The angle, ψ eq , is the "equilibrium" or minimum energy ψ-angle angle for reach polymorph, while R is the molar gas constant, T is the temperature, and ∆G(ψ i ) = G(ψ i ) -G(ψ eq ) is the apparent Gibbs free energy difference between ψ i and ψ eq . From eq. 1, ∆G(ψ i ), can be determined: Eq. 2 can be used to determine an apparent free energy landscape for the fibril peptide bonds along the ψ-angle structure coordinate. As shown in Figure , the apparent energy landscapes behave harmonically around ψ eq and can be modeled in terms of a simple torsional spring using Hooke's Law: