Letter, to Bill Kauffman and Warren Corman, from W.E. Keating, October 25, 1977

Letter discussing the 1977 Session of the Legislature and Senate Bill No. 130, Chapter 284 discussing historical preservation and Rarick Hall.https://scholars.fhsu.edu/rarick/1039/thumbnail.jp

Locating Herpesvirus Bcl-2 Homologs in the Specificity Landscape of Anti-Apoptotic Bcl-2 Proteins

Viral homologs of the anti-apoptotic Bcl-2 proteins are highly diverged from their mammalian counterparts, yet they perform overlapping functions by binding and inhibiting BH3 (Bcl-2 homology 3)-motif-containing proteins. We investigated the BH3 binding properties of the herpesvirus Bcl-2 homologs KSBcl-2, BHRF1, and M11, as they relate to those of the human Bcl-2 homologs Mcl-1, Bfl-1, Bcl-w, Bcl-xL, and Bcl-2. Analysis of the sequence and structure of the BH3 binding grooves showed that, despite low sequence identity, M11 has structural similarities to Bcl-xL, Bcl-2, and Bcl-w. BHRF1 and KSBcl-2 are more structurally similar to Mcl-1 than to the other human proteins. Binding to human BH3-like peptides showed that KSBcl-2 has similar specificity to Mcl-1, and BHRF1 has a restricted binding profile; M11 binding preferences are distinct from those of Bcl-xL, Bcl-2, and Bcl-w. Because KSBcl-2 and BHRF1 are from human herpesviruses associated with malignancies, we screened computationally designed BH3 peptide libraries using bacterial surface display to identify selective binders of KSBcl-2 or BHRF1. The resulting peptides bound to KSBcl-2 and BHRF1 in preference to Bfl-1, Bcl-w, Bcl-xL, and Bcl-2 but showed only modest specificity over Mcl-1. Rational mutagenesis increased specificity against Mcl-1, resulting in a peptide with a dissociation constant of 2.9 nM for binding to KSBcl-2 and > 1000-fold specificity over other Bcl-2 proteins, as well as a peptide with > 70-fold specificity for BHRF1. In addition to providing new insights into viral Bcl-2 binding specificity, this study will inform future work analyzing the interaction properties of homologous binding domains and designing specific protein interaction partners.National Institute of General Medical Sciences (U.S.) (R01GM110048)National Science Foundation (U.S.) (0821391

Design of Peptide Inhibitors That Bind the bZIP Domain of Epstein–Barr Virus Protein BZLF1

Designing proteins or peptides that bind native protein targets can aid the development of novel reagents and/or therapeutics. Rational design also tests our understanding of the principles underlying protein recognition. This article describes several strategies used to design peptides that bind to the basic region leucine zipper (bZIP) domain of the viral transcription factor BZLF1, which is encoded by the Epstein–Barr virus. BZLF1 regulates the transition of the Epstein–Barr virus from a latent state to a lytic state. It shares some properties in common with the more studied human bZIP transcription factors, but also includes novel structural elements that pose interesting challenges to inhibitor design. In designing peptides that bind to BZLF1 by forming a coiled-coil structure, we considered both affinity for BZLF1 and undesired self-association, which can weaken the effectiveness of an inhibitor. Several designed peptides exhibited different degrees of target-binding affinity and self-association. Rationally engineered molecules were more potent inhibitors of DNA binding than a control peptide corresponding to the native BZLF1 dimerization region itself. The most potent inhibitors included both positive and negative design elements and exploited interaction with the coiled-coil and basic DNA-binding regions of BZLF1.David H. Koch Institute for Integrative Cancer Research at MIT (Graduate Fellowship)National Institutes of Health (U.S.) (Award GM067681)National Science Foundation (U.S.) (Award 0821391

Some recursive formulas for Selberg-type integrals

A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur integrals whenever the Kostka numbers relating Schur functions and the corresponding monomial polynomials are explicitly known. We illustrate the usefulness of our results discussing some interesting examples.Comment: 11 pages. To appear in Jour. Phys.

A self‐consistent model of helium in the thermosphere

We have found that consideration of neutral helium as a major species leads to a more complete physics‐based modeling description of the Earth's upper thermosphere. An augmented version of the composition equation employed by the Thermosphere‐Ionosphere‐Electrodynamic General Circulation Model (TIE‐GCM) is presented, enabling the inclusion of helium as the fourth major neutral constituent. Exospheric transport acting above the upper boundary of the model is considered, further improving the local time and latitudinal distributions of helium. The new model successfully simulates a previously observed phenomenon known as the “winter helium bulge,” yielding behavior very similar to that of an empirical model based on mass spectrometer observations. This inclusion has direct consequence on the study of atmospheric drag for low‐Earth‐orbiting satellites, as well as potential implications on exospheric and topside ionospheric research.Key PointsTIE‐GCM has been modified to account for neutral heliumSeasonal behavior is successfully capturedNeutral densities from the new model agree well with previous observationsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113723/1/jgra51979.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/113723/2/jgra51979_am.pd

Random matrix theory, the exceptional Lie groups, and L-functions

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are here extended to non-classical groups. We focus on an explicit example: the exceptional Lie group G_2. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G_2, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the 7-dimensional representation of G_2. The random matrix calculations extend to all exceptional Lie groupsComment: 14 page

Applications and generalizations of Fisher-Hartwig asymptotics

Fisher-Hartwig asymptotics refers to the large $n$ form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher-Hartwig formula to the asymptotic decay of the Ising correlations above $T_c$, while the study of the Bose gas density matrix leads us to generalize the Fisher-Hartwig formula to the asymptotic form of random matrix averages over the classical groups and the Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our generalizations is that they extend to Hankel determinants the Fisher-Hartwig asymptotic form known for Toeplitz determinants.Comment: 25 page

Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

We determine the asymptotics of the two-point correlation function for quantum systems with half-integer spin which show chaotic behaviour in the classical limit using a method introduced by Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472-1475]. For time-reversal invariant systems we obtain the leading terms of the two-point correlation function of the Gaussian symplectic ensemble. Special attention has to be paid to the role of Kramers' degeneracy.Comment: 7 pages, no figure

Rate of convergence of linear functions on the unitary group

We study the rate of convergence to a normal random variable of the real and imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a deterministic complex matrix. We show that the rate of convergence is O(N^{-2 + b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the singular values of A; for example, if the singular values are non-degenerate, different from zero and O(1) as N -> infinity, then b=0. The proof uses a Berry-Esse'en inequality for linear combinations of eigenvalues of random unitary, matrices, and so appropriate for strongly dependent random variables.Comment: 34 pages, 1 figure; corrected typos, added remark 3.3, added 3 reference

Classical, semiclassical, and quantum investigations of the 4-sphere scattering system

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional 3-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the 4-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The 4-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.