Interpreting protein structural dynamics from NMR chemical shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged (1)H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail.     

Auslander-Regular Algebras and Maximal Orders

Let R be an Auslander-regular, Cohen-Macaulay, Noetherian ringthat is stably free. Then, we prove that R is a domain and amaximal order in its division ring of fractions. In particular,this applies to the Sklyanin algebra S and shows that, whenS satisfies a polynomial identity, it is actually a finite moduleover its centre.     

Noncommutative graded domains with quadratic growth

Letk be an algebraically closed field, and letR be a finitely generated, connected gradedk-algebra, which is a domain of Gelfand-Kirillov dimension two. Write the graded quotient ringQ(R) ofR asD[z,z^–1; ], for some automorphism of the division ringD. We prove thatD is a finitely generated field extension ofk of transcendence degree one. Moreover, we describeR in terms of geometric data. IfR is generated in degree one then up to a finite dimensional vector space,R is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curveY. This implies, in particular, thatR is Noetherian, thatR is primitive when ||= and thatR is a finite module over its centre when ||<. IfR is not generated in degree one, thenR will still be Noetherian and primitive if has infinite order, butR need not be Noetherian when has finite order.Dedicated to the memory of Shimshon AmitsurOblatum 5-XI-1994 & 28-III-1995This research was supported in part by NSF grants     

HNC calculations of the partial structure factors of molten AgI

We have calculated the pair distribution functions and partial structure factors of molten AgI within the hypernetted chain (HNC) approximation. We have assumed that the effective interionic pair potentials are the same in the liquid and solid states, and have used the potentials constructed by Parrinello et al., which they used to describe both -AgI and the phase transition in AgI. The structure of molten AgI exhibits features similar to those of molten CuCl. Both of these salts melts from a superionic phase.     

On the Development of a Mixed-Integer Linear Programming Model for the Flowshop Sequencing Problem

This paper describes the development of a mixed-integer linear programming (MILP) model for the standard N-job, M-machine flowshop sequencing problem. Based on an earlier all-integer model developed by Wagner, this MILP model has been used to solve optimally problems with as many as 25 jobs and as many as 10 machines. Variants of the standard flowshop model, including a variety of performance measures, are also presented. Computational experience involving the successful solution of over 175 flowshop problems is discussed, and suggestions for future research projects are offered.     

Groups of Permutation Polynomials over Finite Fields

LetFbe a finite field. We apply a result of Thierry Berger (1996,Designs Codes Cryptography,7, 215–221) to determine the structure of all groups of permutations onFgenerated by the permutations induced by the linear polynomials and any power map which induces a permutation onF. This generalizes a result of Leonard Carlitz (1953,Proc. Amer. Math. Soc.,4, 538).