Graph representations are traditionally used to represent protein structures in sequence design protocols in which the protein backbone conformation is known. This infrequently extends to machine learning projects: existing graph convolution algorithms have shortcomings when representing protein environments. One reason for this is the lack of emphasis on edge attributes during massage-passing operations. Another reason is the traditionally shallow nature of graph neural network architectures. Here we introduce an improved message-passing operation that is better equipped to model local kinematics problems such as protein design. Our approach, XENet, pays special attention to both incoming and outgoing edge attributes. We compare XENet against existing graph convolutions in an attempt to decrease rotamer sample counts in Rosetta’s rotamer substitution protocol, used for protein side-chain optimization and sequence design. This use case is motivating because it both reduces the size of the search space for classical side-chain optimization algorithms, and allows larger protein design problems to be solved with quantum algorithms on near-term quantum computers with limited qubit counts. XENet outperformed competing models while also displaying a greater tolerance for deeper architectures. We found that XENet was able to decrease rotamer counts by 40% without loss in quality. This decreased the memory consumption for classical pre-computation of rotamer energies in our use case by more than a factor of 3, the qubit consumption for an existing sequence design quantum algorithm by 40%, and the size of the solution space by a factor of 165. Additionally, XENet displayed an ability to handle deeper architectures than competing convolutions.

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Protein functions result from local and collective atomic motions that span a wide range of time scales. An integrated analysis of experimental and simulation data can shed light on the detailed mechanism of these motions. Applying a high electric field to protein crystals enables conformational changes that can be captured by time-resolved X-ray crystallography. Such an experiment (referred to as EF-X) carried out on a human PDZ domain obtained a series of atomistic ''snapshots'' of ensemble averages protein dynamics at 50 to 100 ns time intervals. Here, we present a molecular dynamics (MD) study of the same system and provide a detailed picture of the protein dynamics in between the experimental ''snapshots''. We replicated the experimental conditions and system geometry in the presence and absence of an electric field. By constructing a model of the protein crystal as a 3x3x3 supercell with a total of 108 individual proteins, we achieved extensive sampling of the protein conformational ensemble at the sub-millisecond time scale. A number of techniques, including principal component analysis and strain analysis, were utilized to quantify the effects of the electric field on the protein structure and crystal symmetry. This study demonstrates how MD simulations can complement information obtained in EF-X experiments by providing the higher spatial and temporal resolution of underlying dynamical processes.