arXiv subjects

Kim Baskerville

Publications and source records attributed to Kim Baskerville.

6 recordsLinked to original sources

arXiv2007

Node similarity within subgraphs of protein interaction networks

We propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. The twinness of a pair of nodes is the number of connected, labeled subgraphs of size n in which the two nodes possess identical neighbours. The graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art high throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than expected from a null model obtained by switching links. For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. coli from the eukaryote S. cerevisiae. Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. cerevisiae have been reported to co-cluster into the same complexes. Indeed, we find that these paralogous proteins are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data.

q-bio.MN↗

arXiv2007

Graph animals, subgraph sampling and motif search in large networks

We generalize a sampling algorithm for lattice animals (connected clusters on a regular lattice) to a Monte Carlo algorithm for `graph animals', i.e. connected subgraphs in arbitrary networks. As with the algorithm in [N. Kashtan et al., Bioinformatics 20, 1746 (2004)], it provides a weighted sample, but the computation of the weights is much faster (linear in the size of subgraphs, instead of super-exponential). This allows subgraphs with up to ten or more nodes to be sampled with very high statistics, from arbitrarily large networks. Using this together with a heuristic algorithm for rapidly classifying isomorphic graphs, we present results for two protein interaction networks obtained using the TAP high throughput method: one of Escherichia coli with 230 nodes and 695 links, and one for yeast (Saccharomyces cerevisiae) with roughly ten times more nodes and links. We find in both cases that most connected subgraphs are strong motifs (Z-scores >10) or anti-motifs (Z-scores <-10) when the null model is the ensemble of networks with fixed degree sequence. Strong differences appear between the two networks, with dominant motifs in E. coli being (nearly) bipartite graphs and having many pairs of nodes which connect to the same neighbors, while dominant motifs in yeast tend towards completeness or contain large cliques. We also explore a number of methods that do not rely on measurements of Z-scores or comparisons with null models. For instance, we discuss the influence of specific complexes like the 26S proteasome in yeast, where a small number of complexes dominate the $k$-cores with large k and have a decisive effect on the strongest motifs with 6 to 8 nodes. We also present Zipf plots of counts versus rank. They show broad distributions that are not power laws, in contrast to the case when disconnected subgraphs are included.

q-bio.MN↗

arXiv2006

Subgraph Ensembles and Motif Discovery Using a New Heuristic for Graph Isomorphism

A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for discovery of extended motifs. The network's structure is described using statistical properties of its $N$-node subgraphs for $N\leq 14$. The Zipf plots for subgraph occurrences are robust power laws that do not change when rewiring the network while fixing the degree sequence -- although the specific subgraphs may exchange ranks. However the exponent depends on $N$. The study of larger subgraphs highlights some striking patterns for various $N$. Motifs, or connected pieces that are over-abundant in the ensemble of subgraphs, have more edges, for a given number of nodes, than antimotifs and generally display a bipartite structure or tend towards a complete graph. In contrast, antimotifs, which are under-abundant connected pieces, are mostly trees or contain at most a single, small loop. The extension to directed graphs is straightforward.

q-bio.QM↗

arXiv1999

Big Bang riddles and their revelations

We describe how cosmology has converged towards a beautiful model of the Universe: the Big Bang Universe. We praise this model, but show there is a dark side to it. This dark side is usually called ``the cosmological problems'': a set of coincidences and fine tuning features required for the Big Bang Universe to be possible. After reviewing these ``riddles'' we show how they have acted as windows into the very early Universe, revealing new physics and new cosmology just as the Universe came into being. We describe inflation, pre Big Bang, and varying speed of light theories. At the end of the millennium, these proposals are seen respectively as a paradigm, a tentative idea, and outright speculation.

astro-ph↗

arXiv1998

Classification of Normal Modes for Multiskyrmions

The normal mode spectra of multiskyrmions play a key role in their quantisation. We present a general method capable of predicting all the low-lying vibrational modes of known minimal energy multiskyrmions. In particular, we explain the origin of the higher multipole breathing modes, previously observed but not understood. We show how these modes may be classified according to the symmetry group of the static solution. Our results provide strong hints that the N-skyrmion moduli space, for N>3, may have a richer structure than previously thought, incorporating 8N-4 degrees of freedom.

hep-th↗

arXiv1997

Normal Modes of the B=4 Skyrme Soliton

The Skyrme model of nuclear physics requires quantisation if it is to match observed nuclear properties. A simple technique is used to find the normal mode spectrum of the baryon number B=4 Skyrme soliton, representing the $α$ particle. We find sixteen vibrational modes and classify them under the cubic symmetry group $O_h$ of the static solution. The spectrum possesses a remarkable structure, with the lowest energy modes lying in those representations expected from an approximate correspondence between Skyrmions and BPS monopoles. The next mode up is the `breather', and above that are higher multipole breathing modes.

hep-th↗