WebLogo generates sequence logos, graphical representations of the patterns within a multiple sequence alignment. Sequence logos provide a richer and more precise description of sequence similarity than consensus sequences and can rapidly reveal significant features of the alignment otherwise difficult to perceive. Each logo consists of stacks of letters, one stack for each position in the sequence. The overall height of each stack indicates the sequence conservation at that position (measured in bits), whereas the height of symbols within the stack reflects the relative frequency of the corresponding amino or nucleic acid at that position. WebLogo has been enhanced recently with additional features and options, to provide a convenient and highly configurable sequence logo generator. A command line interface and the complete, open WebLogo source code are available for local installation and customization.Sequence logos were invented by Tom Schneider and Mike Stephens (Schneider and Stephens 1990;Shaner et al. 1993) to display patterns in sequence conservation, and to assist in discovering and analyzing those patterns. As an example, the accompanying figure (Fig. 1) shows how WebLogo can help interpret the sequence-specific binding of the protein CAP to its DNA recognition site (Schultz et al. 1991). Homodimeric DNA-binding proteins typically display a symmetric double hump in the DNA binding-site logo (Schneider and Stephens 1990), as shown in the figure. Deviations from this basic pattern can indicate additional features; a highly conserved residue in the center of such a pattern may indicate DNA distortion or base flipping (Schneider 2001); an unexpectedly high-sequence conservation may be due to overlapping binding sites (Schneider et al. 1986). Protein logos can illuminate patterns of amino acid conservation that are often of structural or functional importance (Galperin et al. 2001;Rigden et al. 2003). Sequence logos have also been used to display patterns in the BLOCKS protein sequence database (Henikoff et al. 1995), and in DNA-binding site motifs (Robison et al. 1998;Nelson et al. 2002), to analyze splice sites (Stephens and Schneider 1992;Emmert et al. 2001), and in a variety of other contexts. Additional examples, and the raw data for the example presented here, can be found on the WebLogo examples page (http://weblogo.berkeley.edu/examples.html).The logo generation form (http://weblogo.berkeley.edu/ logo.cgi) can process RNA, DNA, or protein multiple sequence alignments provided in either FASTA (Pearson and Lipman 1988) or CLUSTAL (Higgins and Sharp 1988) formats. If the user does not explicitly specify the sequence type, then WebLogo will make a determination on the basis of the symbols found within the sequences. A logo represents each column of the alignment by a stack of letters, with the height of each letter proportional to the observed frequency of the corresponding amino acid or nucleotide, and the overall height of each stack proportional to the sequence conservation, measured in bits, at tha...

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.

The Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external perturbation. In contrast to linear response theory, these expressions are exact no matter the strength of the perturbation, or how far the system has been driven away from equilibrium. In this paper I show that these three relations (and several other closely related results) can all be considered special cases of a single theorem. This expression is explicitly derived for discrete time and space Markovian dynamics, with the additional assumptions that the single time step dynamics preserve the appropriate equilibrium ensemble, and that the energy of the system remains finite.

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A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out-of-equilibrium. In this paper, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length.

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the conditionspecific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions. single-cell dynamics | cell-to-cell variability | exponential growth | Hinshelwood cycle | Arrhenius law

Photoactivated localization microscopy analysis of chemotaxis receptors in bacteria suggests that the non-random organization of these proteins results from random self-assembly of clusters without direct cytoskeletal involvement or active transport.