Network rigidity at finite temperature: Relationships between thermodynamic stability, the non-additivity of entropy and cooperativity in molecular systems

摘要

A statistical mechanical distance constraint model (DCM) is presented thatexplicitly accounts for network rigidity among constraints present within asystem. Constraints are characterized by local microscopic free energyfunctions. Topological re-arrangements of thermally fluctuating constraints arepermitted. The partition function is obtained by combining microscopic freeenergies of individual constraints using network rigidity as an underlyinglong-range mechanical interaction -- giving a quantitative explanation for thenon-additivity in component entropies exhibited in molecular systems. Twoexactly solved 2-dimensional toy models representing flexible molecules thatcan undergo conformational change are presented to elucidate concepts, and tooutline a DCM calculation scheme applicable to many types of physical systems.It is proposed that network rigidity plays a central role in balancing theenergetic and entropic contributions to the free energy of bio-polymers, suchas proteins. As a demonstration, the distance constraint model is solvedexactly for the alpha-helix to coil transition in homogeneous peptides.Temperature and size independent model parameters are fitted to Monte Carlosimulation data, which includes peptides of length 10 for gas phase, andlengths 10, 15, 20 and 30 in water. The DCM is compared to the Lifson-Roigmodel. It is found that network rigidity provides a mechanism for cooperativityin molecular structures including their ability to spontaneously self-organize.In particular, the formation of a characteristic topological arrangement ofconstraints is associated with the most probable microstates changing underdifferent thermodynamic conditions.