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We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether ``breather'' solitons could play a role in the facilitated location of promoters by RNA polymerase. In an effective potential formalism, we find excellent correlation between potential minima and {\em Escherichia coli} promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while ``flat'' regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein ``particle'' about a bent DNA axis., Comment: Latex file 20 pages, 5 figures. Manuscript of paper to appear in J. Biol. Phys., accepted 02/09/05

We present a base-pairing model of oligonuleotide duplex formation and show in detail its equivalence to the Nearest-Neighbour dimer methods from fits to free energy of duplex formation data for short DNA-DNA and DNA-RNA hybrids containing only Watson Crick pairs. In this approach the connection between rank-deficient polymer and rank-determinant oligonucleotide parameter, sets for DNA duplexes is transparent. The method is generalised to include RNA/DNA hybrids where the rank-deficient model with 11 dimer parameters in fact provides marginally improved predictions relative to the standard method with 16 independent dimer parameters ($\Delta G$ mean errors of 4.5 and 5.4 % respectively)., Comment: Latex file, 13 pages, no figures. Refereed draft of manuscript submitted to Biopolymers

A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantised, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of nonequilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The `free' theory (without branching) is solved, and the correct trilinear `interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with 2 or 3 leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrisation covariance., Comment: 25 pages LaTeX, uses pstricks. Appendix added deriving Feynman rules, appropriate text and title changes, figure for Feynman rules added

An analysis of the Kimura 3ST model of DNA sequence evolution is given on the basis of its continuous Lie symmetries. The rate matrix commutes with a U(1)xU(1)xU(1) phase subgroup of the group GL(4) of 4x4x4 invertible complex matrices acting on a linear space spanned by the 4 nucleic acid base letters. The diagonal `branching operator' representing speciation is defined, and shown to intertwine the U(1)xU(1)xU(1) action. Using the intertwining property, a general formula for the probability density on the leaves of a binary tree under the Kimura model is derived, which is shown to be equivalent to established phylogenetic spectral transform methods., Comment: 9 pages, LaTeX, uses amsmath

We investigate a proposal to address several outstanding shortcomings of the perturbative Standard Model (SM) of particle physics. The appeal of this proposal is that these features are a manifestation of the non-perturbative sector of the SM, requiring no assumptions about new physics beyond presently attainable experimental limits. In this thesis we apply non-perturbative techniques to two complementary models: a toy 4-fermion model containing explicit chiral symmetry-breaking terms and the quenched hypercharge gauge interaction. Understanding of how fermion mass, generations and CP-violation might arise is first investigated in the toy 4-fermion model. It is shown that different scale-invariant 4-fermion operators are present for the three subspaces of the full theory, enabling self-consistent introduction of three fermion generations. The second part of the thesis is concerned with dynamical fermion mass generation in the quenched hypercharge interaction. In particular we follow the successful procedure developed for QED, developing a 1-loop renormalisable vertex {\it ansatz} for solution of the fermion self-energy Dyson-Schwinger equation. We find two mass "gaps", possibly corresponding to two types of scalar 4-fermion pairing. These "gaps" cannot, however, be interpreted as physical fermion mass. An alternative possibility, that of a rearrangement of fermionic degrees of freedom analogous to spin-charge separation in condensed matter physics, is also briefly outlined., Comment: PhD thesis, accepted 24/09/03. 108 pages, 11 figures (ps and eps)

Higlighting certain similarities between the two-dimensional Luttinger liquid model and the effective fermionic theory obtained from the hypercharge Lagrangian, we argue the case for a new type of Standard Model extension., Comment: 7 pages, 1 postscript figure

A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching events. The spatial dimension L is the number of leaves of the evolutionary tree under consideration. Momentum conservation modulo ${\mathbb Z}_{2}^{times L}$ in $L \leftarrow 1$ scattering corresponds to tree edge labelling using binary L-vectors. The bilocal quadratic term allows for momentum-dependent rate constants - only the tree(s) compatible with selected nonzero edge rates contribute to the branching probability distribution. Applications to models of evolutionary branching processes are discussed., Comment: LaTex file, 6 pages, 1 postscript figure. Typographical errors corrected, minor changes added. Submitted to J.Phys.Lett.A

The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, data can be fitted as low-order polynomials of the 6 coordinates in the 64-dimensional codon weight space. The work confirms and extends recent studies by Siemion of amino acid conformational parameters. The connections between the present work, and recent studies of the genetic code structure using dynamical symmetry algebras, are pointed out., Comment: 26 pages Latex, 10 figures (4 ps, 6 Tex). Refereed version, small changes to discussion (conclusion unaltered). Minor alterations to format of figures and tables. To appear in BioSystems

Important aspects of the process of information storage and retrieval in DNA and RNA, and its evolution, are the role of the anticodons and associated $t$RNA's, and correlations between anticodons and amino acids; the degeneracy of the genetic code, and the periodicity of many amino acid physico-chemical properties. Such factors are analysed in the context of a $sl(6/1)$ supersymmetric model of the genetic code., Comment: 4 pages LaTex, uses icmp.sty, 2 figures, Contribution to proceedings of oXXII International Colloquium on Group Theoretical Methods in Physics (Group22) Hobart, 13-17 July 1998, to be published by International Press