Propagating structure of Alzheimer’s β-amyloid(10–35) is parallel β-sheet with residues in exact register

The pathognomonic plaques of Alzheimer’s disease are composed primarily of the 39- to 43-aa β-amyloid (Aβ) peptide. Crosslinking of Aβ peptides by tissue transglutaminase (tTg) indicates that Gln15 of one peptide is proximate to Lys16 of another in aggregated Aβ. Here we report how the fibril structure is resolved by mapping interstrand distances in this core region of the Aβ peptide chain with solid-state NMR. Isotopic substitution provides the source points for measuring distances in aggregated Aβ. Peptides containing a single carbonyl 13C label at Gln15, Lys16, Leu17, or Val18 were synthesized and evaluated by NMR dipolar recoupling methods for the measurement of interpeptide distances to a resolution of 0.2 Å. Analysis of these data establish that this central core of Aβ consists of a parallel β-sheet structure in which identical residues on adjacent chains are aligned directly, i.e., in register. Our data, in conjunction with existing structural data, establish that the Aβ fibril is a hydrogen-bonded, parallel β-sheet defining the long axis of the Aβ fibril propagation.

Computation, prediction, and experimental tests of fitness for bacteriophage T7 mutants with permuted genomes

We created a simulation based on experimental data from bacteriophage T7 that computes the developmental cycle of the wild-type phage and also of mutants that have an altered genome order. We used the simulation to compute the fitness of more than 105 mutants. We tested these computations by constructing and experimentally characterizing T7 mutants in which we repositioned gene 1, coding for T7 RNA polymerase. Computed protein synthesis rates for ectopic gene 1 strains were in moderate agreement with observed rates. Computed phage-doubling rates were close to observations for two of four strains, but significantly overestimated those of the other two. Computations indicate that the genome organization of wild-type T7 is nearly optimal for growth: only 2.8% of random genome permutations were computed to grow faster, the highest 31% faster, than wild type. Specific discrepancies between computations and observations suggest that a better understanding of the translation efficiency of individual mRNAs and the functions of qualitatively “nonessential” genes will be needed to improve the T7 simulation. In silico representations of biological systems can serve to assess and advance our understanding of the underlying biology. Iteration between computation, prediction, and observation should increase the rate at which biological hypotheses are formulated and tested.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Molecular computation: RNA solutions to chess problems

We have expanded the field of “DNA computers” to RNA and present a general approach for the solution of satisfiability problems. As an example, we consider a variant of the “Knight problem,” which asks generally what configurations of knights can one place on an n × n chess board such that no knight is attacking any other knight on the board. Using specific ribonuclease digestion to manipulate strands of a 10-bit binary RNA library, we developed a molecular algorithm and applied it to a 3 × 3 chessboard as a 9-bit instance of this problem. Here, the nine spaces on the board correspond to nine “bits” or placeholders in a combinatorial RNA library. We recovered a set of “winning” molecules that describe solutions to this problem.

ParAlign: a parallel sequence alignment algorithm for rapid and sensitive database searches

There is a need for faster and more sensitive algorithms for sequence similarity searching in view of the rapidly increasing amounts of genomic sequence data available. Parallel processing capabilities in the form of the single instruction, multiple data (SIMD) technology are now available in common microprocessors and enable a single microprocessor to perform many operations in parallel. The ParAlign algorithm has been specifically designed to take advantage of this technology. The new algorithm initially exploits parallelism to perform a very rapid computation of the exact optimal ungapped alignment score for all diagonals in the alignment matrix. Then, a novel heuristic is employed to compute an approximate score of a gapped alignment by combining the scores of several diagonals. This approximate score is used to select the most interesting database sequences for a subsequent Smith–Waterman alignment, which is also parallelised. The resulting method represents a substantial improvement compared to existing heuristics. The sensitivity and specificity of ParAlign was found to be as good as Smith–Waterman implementations when the same method for computing the statistical significance of the matches was used. In terms of speed, only the significantly less sensitive NCBI BLAST 2 program was found to outperform the new approach. Online searches are available at http://dna.uio.no/search/

Computation of Surface Electrical Potentials of Plant Cell Membranes : Correspondence to Published Zeta Potentials from Diverse Plant Sources

A Gouy-Chapman-Stern model has been developed for the computation of surface electrical potential (ψ0) of plant cell membranes in response to ionic solutes. The present model is a modification of an earlier version developed to compute the sorption of ions by wheat (Triticum aestivum L. cv Scout 66) root plasma membranes. A single set of model parameters generates values for ψ0 that correlate highly with published ζ potentials of protoplasts and plasma membrane vesicles from diverse plant sources. The model assumes ion binding to a negatively charged site (R− = 0.3074 μmol m−2) and to a neutral site (P0 = 2.4 μmol m−2) according to the reactions R− + IΖ ⇌ RIΖ−1 and P0 + IΖ ⇌ PIΖ, where IΖ represents an ion of charge Ζ. Binding constants for the negative site are 21,500 m−1 for H+, 20,000 m−1 for Al3+, 2,200 m−1 for La3+, 30 m−1 for Ca2+ and Mg2+, and 1 m−1 for Na+ and K+. Binding constants for the neutral site are 1/180 the value for binding to the negative site. Ion activities at the membrane surface, computed on the basis of ψ0, appear to determine many aspects of plant-mineral interactions, including mineral nutrition and the induction and alleviation of mineral toxicities, according to previous and ongoing studies. A computer program with instructions for the computation of ψ0, ion binding, ion concentrations, and ion activities at membrane surfaces may be requested from the authors.

The evolution of emergent computation.

A simple evolutionary process can discover sophisticated methods for emergent information processing in decentralized spatially extended systems. The mechanisms underlying the resulting emergent computation are explicated by a technique for analyzing particle-based logic embedded in pattern-forming systems. Understanding how globally coordinated computation can emerge in evolution is relevant both for the scientific understanding of natural information processing and for engineering new forms of parallel computing systems.

Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons.

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that a variety of model systems exhibit the same short-time behavior and rapidly converge to (approximately) periodic firing patterns with locally synchronized action potentials. The dynamics of one model can be described by a downhill motion on an abstract energy landscape. Since an energy landscape makes it possible to understand and program computation done by an attractor network, the results will extend our understanding of collective computation from models based on a firing-rate description to biologically more realistic systems with integrate-and-fire neurons.