Biophysical Fitness Landscapes for Transcription Factor Binding Sites

Evolutionary trajectories and phenotypic states available to cell populations are ultimately dictated by intermolecular interactions between DNA, RNA, proteins, and other molecular species. Here we study how evolution of gene regulation in a single-cell eukaryote S. cerevisiae is affected by the interactions between transcription factors (TFs) and their cognate genomic sites. Our study is informed by high-throughput in vitro measurements of TF-DNA binding interactions and by a comprehensive collection of genomic binding sites. Using an evolutionary model for monomorphic populations evolving on a fitness landscape, we infer fitness as a function of TF-DNA binding energy for a collection of 12 yeast TFs, and show that the shape of the predicted fitness functions is in broad agreement with a simple thermodynamic model of two-state TF-DNA binding. However, the effective temperature of the model is not always equal to the physical temperature, indicating selection pressures in addition to biophysical constraints caused by TF-DNA interactions. We find little statistical support for the fitness landscape in which each position in the binding site evolves independently, showing that epistasis is common in evolution of gene regulation. Finally, by correlating TF-DNA binding energies with biological properties of the sites or the genes they regulate, we are able to rule out several scenarios of site-specific selection, under which binding sites of the same TF would experience a spectrum of selection pressures depending on their position in the genome. These findings argue for the existence of universal fitness landscapes which shape evolution of all sites for a given TF, and whose properties are determined in part by the physics of protein-DNA interactions

Spinons in Conformal Field Theory

We study the $su(2)$ conformal field theory in its spinon description, adapted to the Yangian invariance. By evaluating the action of the Yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with $su(2)$ spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible Yangian multiplet, and also to exhibit operators creating the $N$-spinon highest weight vectors.Comment: 18 page

Dynamical correlation functions in the Calogero-Sutherland model

We compute the dynamical Green function and density-density correlation in the Calogero-Sutherland model for all integer values of the coupling constant. An interpretation of the intermediate states in terms of quasi-particles is found.Comment: 20pgs, (1 reference added

Yang-Baxter equation in spin chains with long range interactions

We consider the $su(n)$ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.Comment: Saclay-t93/00

Integrals of motion of the Haldane Shastry Model

In this letter we develop a method to construct all the integrals of motion of the $SU(p)$ Haldane-Shastry model of spins, equally spaced around a circle, interacting through a $1/r^2$ exchange interaction. These integrals of motion respect the Yangian symmetry algebra of the Hamiltonian.Comment: 13 pages, REVTEX v3.

The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions

We discuss the effect of Fermi surface curvature on long-distance/time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge field-like propagator. By comparing the predictions based on the idea of multi-dimensional bosonization with those of the strong- coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.Comment: Latex, 4+ pages. Phys. Rev. Lett., to appea

Quantum Chemistry, Anomalous Dimensions, and the Breakdown of Fermi Liquid Theory in Strongly Correlated Systems

We formulate a local picture of strongly correlated systems as a Feynman sum over atomic configurations. The hopping amplitudes between these atomic configurations are identified as the renormalization group charges, which describe the local physics at different energy scales. For a metallic system away from half-filling, the fixed point local Hamiltonian is a generalized Anderson impurity model in the mixed valence regime. There are three types of fixed points: a coherent Fermi liquid (FL) and two classes of self-similar (scale invariant) phases which we denote incoherent metallic states (IMS). When the transitions between the atomic configurations proceed coherently at low energies, the system is a Fermi liquid. Incoherent transitions between the low energy atomic configurations characterize the incoherent metallic states. The initial conditions for the renormalization group flow are determined by the physics at rather high energy scales. This is the domain of local quantum chemistry. We use simple quantum chemistry estimates to specify the basin of attraction of the IMS fixed points.Comment: 12 pages, REVTE

Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics

We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.Comment: 10pp, REVTE

Spin nematics in the bilinear-biquadratic S=1 spin chain

We report the existence of an extended critical, nondimerized region in the phase diagram of the bilinear-biquadratic spin-one chain. The dominant power law correlations are ferroquadrupolar, i.e. spin nematic in character. Another known critical region is also characterized by dominant quadrupolar correlations, although with a different wave vector. Our results show that spin nematic correlations play an important role in quantum magnets with spin S >= 1 in regions between antiferromagnetic and ferromagnetic phases.Comment: 4 pages, 7 figure

Single particle Green's function in the Calogero-Sutherland model for rational couplings β=p/q\beta=p/q

We derive an exact expression for the single particle Green function in the Calogero-Sutherland model for all rational values of the coupling $\beta$. The calculation is based on Jack polynomial techniques and the results are given in the thermodynamical limit. Two type of intermediate states contribute. The firts one consists of a particle propagating out of the Fermi sea and the second one consists of a particle propagating in one direction, q particles in the opposite direction and p holes.Comment: 9 pages, RevTeX, epsf.tex, 4 figures, files uuencode