A flexible approach for understanding protein stability.

A distance constraint model (DCM) is presented that identifies flexible regions within protein structure consistent with specified thermodynamic condition. The DCM is based on a rigorous free energy decomposition scheme representing structure as fluctuating constraint topologies. Entropy non-additivity is problematic for naive decompositions, limiting the success of heat capacity predictions. The DCM resolves non-additivity by summing over independent entropic components determined by an efficient network-rigidity algorithm. A minimal 3-parameter DCM is demonstrated to accurately reproduce experimental heat capacity curves. Free energy landscapes and quantitative stability-flexibility relationships are obtained in terms of global flexibility. Several connections to experiment are made.

Network rigidity at finite temperature: relationships between thermodynamic stability, the nonadditivity of entropy, and cooperativity in molecular systems.

A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free-energy functions. Topological rearrangements of thermally fluctuating constraints are permitted. The partition function is obtained by combining microscopic free energies of individual constraints using network rigidity as an underlying long-range mechanical interaction, giving a quantitative explanation for the nonadditivity in component entropies exhibited in molecular systems. Two exactly solved two-dimensional toy models representing flexible molecules that can undergo conformational change are presented to elucidate concepts, and to outline a DCM calculation scheme applicable to many types of physical systems. It is proposed that network rigidity plays a central role in balancing the energetic and entropic contributions to the free energy of biopolymers, such as proteins. As a demonstration, the distance constraint model is solved exactly for the alpha-helix to coil transition in homogeneous peptides. Temperature and size independent model parameters are fitted to Monte Carlo simulation data, which includes peptides of length 10 for gas phase, and lengths 10, 15, 20, and 30 in water. The DCM is compared to the Lifson-Roig model. It is found that network rigidity provides a mechanism for cooperativity in molecular structures including their ability to spontaneously self-organize. In particular, the formation of a characteristic topological arrangement of constraints is associated with the most probable microstates changing under different thermodynamic conditions.