Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian

The Peterson isomorphism relates the homology of the affine Grassmannian to the quantum cohomology of any flag variety. In the case of a partial flag, Peterson’s map is only a surjection, and one needs to quotient by a suitable ideal on the affine side to map isomorphically onto the quantum cohomology. We provide a detailed exposition of this parabolic Peterson isomorphism in the case of the Grassmannian of m-planes in complex n-space, including an explicit recipe for doing quantum Schubert calculus in terms of the appropriate subset of non-commutative k-Schur functions. As an application, we recast Postnikov’s affine approach to the quantum cohomology of the Grassmannian as a consequence of parabolic Peterson by showing that the affine nilTemperley–Lieb algebra arises naturally when forming the requisite quotient of the homology of the affine Grassmannian

How Sound Are Our Ultralight Axion Approximations?

Ultralight axions (ULAs) are a promising dark-matter candidate. ULAs may have implications for small-scale challenges to the ΛCDM model and arise in string scenarios. ULAs are already constrained by cosmic microwave background (CMB) experiments and large-scale structure surveys, and will be probed with much greater sensitivity by future efforts. It is challenging to compute observables in ULA scenarios with sufficient speed and accuracy for cosmological data analysis because the ULA field oscillates rapidly. In past work, an effective fluid approximation has been used to make these computations feasible. Here this approximation is tested against an exact solution of the ULA equations, comparing the induced error of CMB observables with the sensitivity of current and future experiments. In the most constrained mass range for a ULA dark-matter component (10−27  eV≤max≤10−25  eV), the induced bias on the allowed ULA fraction of dark matter from Planck data is less than 1σ. In the cosmic-variance limit (including temperature and polarization data), the bias is ≲2σ for primary CMB anisotropies, with more severe biases (as high as ∼4σ) resulting for less reliable versions of the effective fluid approximation. If all of the standard cosmological parameters are fixed by other measurements, the expected bias rises to 4−20σ (well beyond the validity of the Fisher approximation), though the required level of degeneracy breaking will not be achieved by any planned surveys

Mutations in Viral Movement Protein Alter Systemic Infection and Identify an Intercellular Barrier to Entry into the Phloem Long-Distance Transport System

AbstractViral systemic infection of a plant host involves two processes, cell-to-cell movement and long-distance transport. Molecular determinants associated with these two processes were probed by investigating the effects that alanine scanning mutations in the movement protein (MP) of red clover necrotic mosaic virus (RCNMV) had on viral infection in the plant hostsNicotiana edwardsonii, Vigna unguiculata(cowpea), and the experimental plantNicotiana benthamiana.Plants were inoculated with RCNMV expressing wild-type and mutant forms of the MP. Immunocytochemical studies at the light and electron microscope levels were performed on these plants, using a polyclonal antibody raised against the RCNMV capsid protein to identify the cells/tissues that RCNMV could infect. These experiments demonstrated that one cellular boundary at which the RCNMV MP functions to facilitate entry into the phloem long-distance transport system is located at the interfaces between the bundle sheath and phloem parenchyma cells and the companion cell–sieve element complex. Interestingly, inNicotiana tabacum,a host that only allows a local infection, RCNMV cell-to-cell movement was found to be blocked at this same intercellular boundary. Four mutants that were able to systemically infectN. benthamianawere partially or completely defective for systemic infection ofN. edwardsoniiand cowpea, which indicated that these MP mutants exhibited host-specific defects. Thus, the roles of the RCNMV MP in cell-to-cell movement and in long-distance transport appear to be genetically distinct. These results are discussed in terms of the mechanism by which RCNMV enters the phloem to establish a systemic infection

Uncovering protein–protein interactions through a team-based undergraduate biochemistry course

How can we provide fertile ground for students to simultaneously explore a breadth of foundational knowledge, develop cross-disciplinary problem-solving skills, gain resiliency, and learn to work as a member of a team? One way is to integrate original research in the context of an undergraduate biochemistry course. In this Community Page, we discuss the development and execution of an interdisciplinary and cross-departmental undergraduate biochemistry laboratory course. We present a template for how a similar course can be replicated at other institutions and provide pedagogical and research results from a sample module in which we challenged our students to study the binding interface between 2 important biosynthetic proteins. Finally, we address the community and invite others to join us in making a larger impact on undergraduate education and the field of biochemistry by coordinating efforts to integrate research and teaching across campuses