Calculation of Conformational Free Energies with the Focused Confinement Method

Exploring Free Energies of Specific Protein Conformations Using the Martini Force Field

Coarse-grained (CG) level molecular dynamics simulations are routinely used to study various biomolecular processes. The Martini force field is currently the most widely adopted parameter set for such simulations. The functional form of this and several other CG force fields enforces secondary protein structure support by employing a variety of harmonic potentials or restraints that favor the protein's native conformation. We propose a straightforward method to calculate the energetic consequences of transitions between predefined conformational states in systems in which multiple factors can affect protein conformational equilibria. This method is designed for use within the Martini force field and involves imposing conformational transitions by linking a Martini-inherent elastic network to the coupling parameter λ. We demonstrate the applicability of our method using the example of five biomolecular systems that undergo experimentally characterized conformational transitions between well-defined structures (Staphylococcal nuclease, C-terminal segment of surfactant protein B, LAH4 peptide, and β2-adrenergic receptor) as well as between folded and unfolded states (GCN4 leucine zipper protein). The results show that the relative free energy changes associated with protein conformational transitions, which are affected by various factors, such as pH, mutations, solvent, and lipid membrane composition, are correctly reproduced. The proposed method may be a valuable tool for understanding how different conditions and modifications affect conformational equilibria in proteins.

Learned mappings for targeted free energy perturbation between peptide conformations

Targeted free energy perturbation uses an invertible mapping to promote configuration space overlap and the convergence of free energy estimates. However, developing suitable mappings can be challenging. Wirnsberger et al. [J. Chem. Phys. 153, 144112 (2020)] demonstrated the use of machine learning to train deep neural networks that map between Boltzmann distributions for different thermodynamic states. Here, we adapt their approach to the free energy differences of a flexible bonded molecule, deca-alanine, with harmonic biases and different spring centers. When the neural network is trained until "early stopping"-when the loss value of the test set increases-we calculate accurate free energy differences between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å. For more distant thermodynamic states, the mapping does not produce structures representative of the target state, and the method does not reproduce reference calculations.