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The spike protein of SARS-CoV-2 is a highly flexible membrane receptor that triggers the translocation of the virus into cells by attaching to the human receptors. Like other type I membrane receptors, this protein has several extracellular domains connected by flexible hinges. The presence of these hinges results in high flexibility, which consequently results in challenges in defining the conformation of the protein. Here, We developed a new method to define the conformational space based on a few variables inspired by the robotic field’s methods to determine a robotic arm’s forward kinematics. Using newly performed atomistic molecular dynamics (MD) simulations and publicly available data, we found that the Denavit-Hartenberg (DH) parameters can reliably show the changes in the local conformation. Furthermore, the rotational and translational components of the homogenous transformation matrix constructed based on the DH parameters can identify the changes in the global conformation of the spike and also differentiate between the conformation with a similar position of the spike head, which other types of parameters, such as spherical coordinates, fail to distinguish between such conformations. Finally, the new method will be beneficial for looking at the conformational heterogeneity in all other type I membrane receptors.
We prove that the projectivized strata of differentials are not contained in pointed Brill-Noether divisors, with only a few exceptions. For a generic element in a stratum of differentials, we show that many of the associated pointed Brill-Noether loci are of expected dimension. We use our results to study the Auel-Haburcak Conjecture: We obtain new non-containments between maximal Brill-Noether loci in Mg. Our results regarding quadratic differentials imply that the quadratic strata in genus 6 are uniruled.