In this article we give an existence theorem for localized travelling wave solutions on one-dimensional lattices with Hamiltonian where V( -) is the potential energy due to nearest-neighbour interactions. Until now, apart from rare integrable lattices like the Toda lattice V(φ) -ab~l(e~b^ + bφ -1), the only evidence for existence of such solutions has been numerical. Our result in particular recovers existence of solitary waves in the Toda lattice, establishes for the first time existence of solitary waves in the (nonintegrable) cubic and quartic lattices V(φ) = ^ φ 2 + | α 3 , V(φ) ~\Φ L ^\ bφ 4 , thereby confirming the numerical findings in [1] and shedding new light on the recurrence phenomena in these systems observed first by Fermi, Pasta and Ulam [2], and shows that contrary to widespread belief, the presence of exact solitary waves is not a peculiarity of integrable systems, but "generic" in this class of nonlinear lattices. The approach presented here is new and quite general, and should also be applicable to other forms of lattice equations: the travelling waves are sought as minimisers of a naturally associated variational problem (obtained via Hamilton's principle), and existence of minimisers is then established using modern methods in the calculus of variations (the concentration-compactness principle of P.-L. Lions [3]).

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We aimed to identify novel molecular mechanisms for muscle growth during administration of anabolic agents. Growing pigs (Duroc/(Landrace/Large-White)) were administered Ractopamine (a beta-adrenergic agonist; BA; 20 ppm in feed) or Reporcin (recombinant growth hormone; GH; 10 mg/48 hours injected) and compared to a control cohort (feed only; no injections) over a 27-day time course (1, 3, 7, 13 or 27-days). Longissimus Dorsi muscle gene expression was analyzed using Agilent porcine transcriptome microarrays and clusters of genes displaying similar expression profiles were identified using a modified maSigPro clustering algorithm. Anabolic agents increased carcass (p = 0.002) and muscle weights (Vastus Lateralis: p < 0.001; Semitendinosus: p = 0.075). Skeletal muscle mRNA expression of serine/one-carbon/glycine biosynthesis pathway genes (Phgdh, Psat1 and Psph) and the gluconeogenic enzyme, phosphoenolpyruvate carboxykinase-M (Pck2/PEPCK-M), increased during treatment with BA, and to a lesser extent GH (p < 0.001, treatment x time interaction). Treatment with BA, but not GH, caused a 2-fold increase in phosphoglycerate dehydrogenase (PHGDH) protein expression at days 3 (p < 0.05) and 7 (p < 0.01), and a 2-fold increase in PEPCK-M protein expression at day 7 (p < 0.01). BA treated pigs exhibit a profound increase in expression of PHGDH and PEPCK-M in skeletal muscle, implicating a role for biosynthetic metabolic pathways in muscle growth.

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left-and righthanded types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to 'poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable.The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomer and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steadystate solutions described above.