522 research outputs found
Multiple Crossover Phenomena and Scale Hopping in Two Dimensions
We study the renormalization group for nearly marginal perturbations of a
minimal conformal field theory M_p with p >> 1. To leading order in
perturbation theory, we find a unique one-parameter family of ``hopping
trajectories'' that is characterized by a staircase-like renormalization group
flow of the C-function and the anomalous dimensions and that is related to a
recently solved factorizable scattering theory. We argue that this system is
described by interactions of the form t phi_{(1,3)} - t' \phi_{(3,1)} . As a
function of the relevant parameter t, it undergoes a phase transition with new
critical exponents simultaneously governed by all fixed points M_p, M_{p-1},
..., M_3. Integrable lattice models represent different phases of the same
integrable system that are distinguished by the sign of the irrelevant
parameter t'.Comment: 20 pages, 5 figure
The Freezing of Random RNA
We study secondary structures of random RNA molecules by means of a
renormalized field theory based on an expansion in the sequence disorder. We
show that there is a continuous phase transition from a molten phase at higher
temperatures to a low-temperature glass phase. The primary freezing occurs
above the critical temperature, with local islands of stable folds forming
within the molten phase. The size of these islands defines the correlation
length of the transition. Our results include critical exponents at the
transition and in the glass phase.Comment: 4 pages, 8 figures. v2: presentation improve
Adaptive evolution of transcription factor binding sites
The regulation of a gene depends on the binding of transcription factors to
specific sites located in the regulatory region of the gene. The generation of
these binding sites and of cooperativity between them are essential building
blocks in the evolution of complex regulatory networks. We study a theoretical
model for the sequence evolution of binding sites by point mutations. The
approach is based on biophysical models for the binding of transcription
factors to DNA. Hence we derive empirically grounded fitness landscapes, which
enter a population genetics model including mutations, genetic drift, and
selection. We show that the selection for factor binding generically leads to
specific correlations between nucleotide frequencies at different positions of
a binding site. We demonstrate the possibility of rapid adaptive evolution
generating a new binding site for a given transcription factor by point
mutations. The evolutionary time required is estimated in terms of the neutral
(background) mutation rate, the selection coefficient, and the effective
population size. The efficiency of binding site formation is seen to depend on
two joint conditions: the binding site motif must be short enough and the
promoter region must be long enough. These constraints on promoter architecture
are indeed seen in eukaryotic systems. Furthermore, we analyse the adaptive
evolution of genetic switches and of signal integration through binding
cooperativity between different sites. Experimental tests of this picture
involving the statistics of polymorphisms and phylogenies of sites are
discussed.Comment: published versio
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