(515c) Improved Theories of Cooperative Folding of Oligomers and Demonstrations in Coarse-Grained Models

Non-specific coarse-grained models are valuable tools for understanding the basic principles of molecular folding and efficient testing of hypotheses. A greater understanding of how the physical features of molecular models give rise to cooperative transitions is still needed to achieve the level of control over secondary and tertiary structure required in many potential foldamer applications, ranging from protein-like catalysts to stable drug delivery vesicles and nanostructured materials.

We describe how folding systems, thermal cooperativity can be captured solely by the entropy difference between the states of interest at the melting point. This same relationship arises from multiple different definitions of cooperativity that have been introduced in the literature. The entropy change-cooperativity relationship can be directly compared in systems with different topologies and force field parameters in the event that the potential energy difference between folded and unfolded states and the melting point are the same across all models.

We explore these theories both with analytical models and with homo-oligomer helix foldamer systems differing in residue side chain topology, including number of side chain beads, torsion potentials, and rotational degrees of freedom. Guided by a helix geometrical modeling tool, we designed side chain motifs leading to optimal packing in the folded state, and extended high-entropy configurations in the unfolded state. Energetic parameters are tuned to meet the equal potential energy change criteria in a series of REMD simulations and subsequent configurational resampling using MBAR. We then compare trends in the entropy of folding with alternative measures of cooperativity, including the characteristic width of the transition region in the native contact fraction versus temperature curve, and the full-width half-maximum of the heat capacity curve, and show how they relate.

These analyses are done within a Python framework cg_openmm which facilitates the setup and thermodynamic analysis of coarse-grained temperature replica exchange molecular dynamics (REMD) simulations. In particular, the multistate Bennett acceptance ratio (MBAR) method is applied to replica trajectories and energies to generate nearly smooth curves of heat capacity, configurational state populations, and entropy, enthalpy, and free energy of folding as functions of temperature. This framework allows for efficient exploration of broad force field parameter spaces and in-depth investigation into thermodynamics of folding transitions.