Loop models, Marginally Rough Interfaces, and the Coulomb Gas

We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville theory with imaginary couplings. This field theory is {\it completely specified} by geometry and conformal invariance {\it alone}, and it leads to exact results for the critical exponents and the conformal charge of loop models. A physical interpretation of the Dotsenko-Fateev screening charge is found.Comment: LaTex, 7 pages, 1 PostScript figure; uses epsf.sty. To appear in the proceedings of the symposium''Exactly soluable models in Statistical Mechanics'', March 1996, Northeastern University, Bosto

Critical Dynamics of Dimers: Implications for the Glass Transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy vanishing phase transition, and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments and numerical diagonalizations of the master equation, we find non-exponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point, and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics

Membrane mechanics as a probe of ion-channel gating mechanisms

The details of conformational changes undergone by transmembrane ion channels in response to stimuli, such as electric fields and membrane tension, remain controversial. We approach this problem by considering how the conformational changes impose deformations in the lipid bilayer. We focus on the role of bilayer deformations in the context of voltage-gated channels because we hypothesize that such deformations are relevant in this case as well as for channels that are explicitly mechanosensitive. As a result of protein conformational changes, we predict that the lipid bilayer suffers deformations with a characteristic free-energy scale of 10kBT. This free energy is comparable to the voltage-dependent part of the total gating energy, and we argue that these deformations could play an important role in the overall free-energy budget of gating. As a result, channel activity will depend upon mechanical membrane parameters such as tension and leaflet thickness. We further argue that the membrane deformation around any channel can be divided into three generic classes of deformation that exhibit different mechanosensitive properties. Finally, we provide the theoretical framework that relates conformational changes during gating to tension and leaflet thickness dependence in the critical gating voltage. This line of investigation suggests experiments that could discern the dominant deformation imposed upon the membrane as a result of channel gating, thus providing clues as to the channel deformation induced by the stimulus

Deciphering transcriptional dynamics in vivo by counting nascent RNA molecules

Transcription of genes is the focus of most forms of regulation of gene expression. Even though careful biochemical experimentation has revealed the molecular mechanisms of transcription initiation for a number of different promoters in vitro, the dynamics of this process in cells is still poorly understood. One approach has been to measure the transcriptional output (fluorescently labeled messenger RNAs or proteins) from single cells in a genetically identical population, which could then be compared to predictions from models that incorporate different molecular mechanisms of transcription initiation. However, this approach suffers from the problem, that processes downstream from transcription can affect the measured output and therefore mask the signature of stochastic transcription initiation on the cell-to-cell variability of the transcriptional outputs. Here we show theoretically that measurements of the cell-to-cell variability in the number of nascent RNAs provide a more direct test of the mechanism of transcription initiation. We derive exact expressions for the first two moments of the distribution of nascent RNA molecules and apply our theory to published data for a collection of constitutively expressed yeast genes. We find that the measured nascent RNA distributions are inconsistent with transcription initiation proceeding via one rate-limiting step, which has been generally inferred from measurements of cytoplasmic messenger RNA. Instead, we propose a two-step mechanism of initiation, which is consistent with the available data. These findings for the yeast promoters highlight the utility of our theory for deciphering transcriptional dynamics in vivo from experiments that count nascent RNA molecules in single cells.Comment: 28 pages including S

Antenna mechanism of length control of actin cables

Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This antenna mechanism involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. We compute the probability distribution of cable lengths as a function of several experimentally tuneable parameters such as the formin-binding affinity of Smy1 and the concentration of myosin motors delivering Smy1. These results provide testable predictions of the antenna mechanism of actin-cable length control

Operator Sequence Alters Gene Expression Independently of Transcription Factor Occupancy in Bacteria

A canonical quantitative view of transcriptional regulation holds that the only role of operator sequence is to set the probability of transcription factor binding, with operator occupancy determining the level of gene expression. In this work, we test this idea by characterizing repression in vivo and the binding of RNA polymerase in vitro in experiments where operators of various sequences were placed either upstream or downstream from the promoter in Escherichia coli. Surprisingly, we find that operators with a weaker binding affinity can yield higher repression levels than stronger operators. Repressor bound to upstream operators modulates promoter escape, and the magnitude of this modulation is not correlated with the repressor-operator binding affinity. This suggests that operator sequences may modulate transcription by altering the nature of the interaction of the bound transcription factor with the transcriptional machinery, implying a new layer of sequence dependence that must be confronted in the quantitative understanding of gene expression