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Thermodynamics of amyloid formation and the role of intersheet interactions

The self-assembly of proteins into $β$-sheet-rich amyloid fibrils has been observed to occur with sigmoidal kinetics, indicating that the system initially is trapped in a metastable state. Here, we use a minimal lattice-based model to explore the thermodynamic forces driving amyloid formation in a finite canonical ($NVT$) system. By means of generalized-ensemble Monte Carlo techniques and a semi-analytical method, the thermodynamic properties of this model are investigated for different sets of intersheet interaction parameters. When the interactions support lateral growth into multi-layered fibrillar structures, an evaporation/condensation transition is observed, between a supersaturated solution state and a thermodynamically distinct state where small and large fibril-like species exist in equilibrium. Intermediate-size aggregates are statistically suppressed. These properties do not hold if aggregate growth is one-dimensional.