Some explicit values for ratios of theta-functions

In his notebooks [9], Ramanujan recorded several values of thetafunctions.B. C. Berndt and L-C. Zhang [6], Berndt and H. H. Chan[5] have proved all these evaluations. The main purpose of this paperis to establish several new explicit evaluations of ratios of thetafunctions. We also explicitly determine a(−2√2π),a(−2√2/9π),a(−√2π)and a(e−√2/9π), where a(q) is the Borweins cubic thetafunction. 2000 Mathematical Subject Classification: 33D15 , 33D20

Some explicit values for ratios of theta-functions.

In his notebooks [9], Ramanujan recorded several values of thetafunctions.B. C. Berndt and L-C. Zhang [6], Berndt and H. H. Chan[5] have proved all these evaluations. The main purpose of this paper is to establish several new explicit evaluations of ratios of thetafunctions. We also explicitly determine a(e−2√2π), a(e−2√2/9π), a(e −√2π)and a(e−√2/9π), where a(q) is the Borweins cubic theta-function

Protein complex compositions predicted by structural similarity

Proteins function through interactions with other molecules. Thus, the network of physical interactions among proteins is of great interest to both experimental and computational biologists. Here we present structure-based predictions of 3387 binary and 1234 higher order protein complexes in Saccharomyces cerevisiae involving 924 and 195 proteins, respectively. To generate candidate complexes, comparative models of individual proteins were built and combined together using complexes of known structure as templates. These candidate complexes were then assessed using a statistical potential, derived from binary domain interfaces in PIBASE (). The statistical potential discriminated a benchmark set of 100 interface structures from a set of sequence-randomized negative examples with a false positive rate of 3% and a true positive rate of 97%. Moreover, the predicted complexes were also filtered using functional annotation and sub-cellular localization data. The ability of the method to select the correct binding mode among alternates is demonstrated for three camelid VHH domain—porcine α–amylase interactions. We also highlight the prediction of co-complexed domain superfamilies that are not present in template complexes. Through integration with MODBASE, the application of the method to proteomes that are less well characterized than that of S.cerevisiae will contribute to expansion of the structural and functional coverage of protein interaction space. The predicted complexes are deposited in MODBASE ()

The Need for Laboratory Measurements and Ab Initio Studies to Aid Understanding of Exoplanetary Atmospheres

Laboratory astrophysics and astrochemistr

DEMM: A meta-algorithm to predict the pka of ionizable amino acids in proteins

10.1007/978-3-319-11776-8_84IFMBE Proceedings46343-34

Alignment of protein sequences by their profiles

The accuracy of an alignment between two protein sequences can be improved by including other detectably related sequences in the comparison. We optimize and benchmark such an approach that relies on aligning two multiple sequence alignments, each one including one of the two protein sequences. Thirteen different protocols for creating and comparing profiles corresponding to the multiple sequence alignments are implemented in the SALIGN command of MODELLER. A test set of 200 pairwise, structure-based alignments with sequence identities below 40% is used to benchmark the 13 protocols as well as a number of previously described sequence alignment methods, including heuristic pairwise sequence alignment by BLAST, pairwise sequence alignment by global dynamic programming with an affine gap penalty function by the ALIGN command of MODELLER, sequence-profile alignment by PSI-BLAST, Hidden Markov Model methods implemented in SAM and LOBSTER, pairwise sequence alignment relying on predicted local structure by SEA, and multiple sequence alignment by CLUSTALW and COMPASS. The alignment accuracies of the best new protocols were significantly better than those of the other tested methods. For example, the fraction of the correctly aligned residues relative to the structure-based alignment by the best protocol is 56%, which can be compared with the accuracies of 26%, 42%, 43%, 48%, 50%, 49%, 43%, and 43% for the other methods, respectively. The new method is currently applied to large-scale comparative protein structure modeling of all known sequences