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The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to mathematically formulate. Data-driven approaches for approximating anisotropic pair potentials have gained significant interest due to their flexibility and generality but often require large sets of training data, potentially limiting their feasibility when training data is computationally demanding to collect. Here, we investigate the use of multivariate polynomial interpolation to approximate anisotropic pair potentials from a limited set of prescribed particle configurations. We consider both standard Chebyshev polynomial interpolation as well as mixed-basis polynomial interpolation that uses trigonometric polynomials for coordinates along which the pair potential is known to be periodic. We exploit mathematical reasoning and physical knowledge to refine the interpolation domain and to design our interpolants. We test our approach on two-dimensional and three-dimensional model anisotropic nanoparticles, finding satisfactory approximations can be constructed in all cases. 

Poxviruses are dangerous pathogens, which can cause fatal infection in unvaccinated individuals. The causative agent of smallpox in humans, variola virus , is closely related to the bovine vaccinia virus , yet the molecular basis of their selectivity is currently incompletely understood. Here, we examine the role of the electrostatics in the selectivity of the smallpox protein SPICE and vaccinia protein VCP toward the human and bovine complement protein C3b, a key component of the complement immune response. Electrostatic calculations, in-silico alanine-scan and electrostatic hotspot analysis, as introduced by Kieslich and Morikis ( PLoS Comput. Biol . 2012), are used to assess the electrostatic complementarity and to identify sites resistant to local perturbation where the electrostatic potential is likely to be evolutionary conserved. The calculations suggest that the bovine C3b is electrostatically prone to selectively bind its VCP ligand. On the other hand, the human isoform of C3b exhibits a lower electrostatic complementarity toward its SPICE ligand. Yet, the human C3b displays a highly preserved electrostatic core, which suggests that this isoform could be less selective in binding different ligands like SPICE and the human Factor H. This is supported by experimental cofactor activity assays revealing that the human C3b is prone to bind both SPICE and Factor H, which exhibit diverse electrostatic properties. Additional investigations considering mutants of SPICE and VCP that revert their selectivity reveal an “electrostatic switch” into the central modules of the ligands, supporting the critical role of the electrostatics in the selectivity. Taken together, these evidences provide insights into the selectivity mechanism of the complement regulator proteins encoded by the variola and vaccinia viruses to circumvent the complement immunity and exert their pathogenic action. These fundamental aspects are valuable for the development of novel vaccines and therapeutic strategies.