No abstract

We study quantized classically chaotic maps on a toroidal two-dimensional phase space. A discrete, topological criterion for phase-space localization is presented. To each eigenfunction is associated an integer, analogous to a quantized Hall conductivity, which when nonzero reflects phase-space derealization. A model system is studied, and a correspondence between delocalization and chaotic classical dynamics is discussed.

Bacteria are the simplest living organisms. In particular, Escherichia coli has been extensively studied and it has become one of the standard model systems in microbiology. However, optical microscopy studies of single E. coli have been limited by its small size, approximately 1 x 3 microm, not much larger than the optical resolution, approximately 0.25 microm. As a result, not enough quantitative dynamical information on the life cycle of single E. coli is presently available. We suggest that, by careful analysis of images from phase contrast and fluorescence time-lapse microscopy, this limitation can be bypassed. For example, we show that applying this approach to monitoring morphogenesis in individual E. coli leads to a simple, quantitative description of this process. First, we find the time when the formation of the septum starts, tau(c). It occurs much earlier than the time when the constriction can be directly observed by phase contrast. Second, we find that the growth law of single cells is more likely bilinear/trilinear than exponential. This is further supported by the relations that hold between the corresponding growth rates. These methods could be further extended to study the dynamics of cell components, e.g., the nucleoid and the Z-ring.

The polymerization of RecA on individual double-stranded DNA molecules is studied. A linear DNA ( DNA, 48.5 Kb), anchored at one end to a cover glass and at the other end to an optically trapped 3-m diameter polystyrene bead, serves as a template. The elongation caused by RecA assembly is measured in the presence of ATP and ATP [␥S]. By using force extension and hydrodynamic recoil, a value of the persistence length of the RecA-DNA complex is obtained. In the presence of ATP, the polymer length is unstable, first growing to saturation and then decreasing. This suggests a transient dynamics of association and dissociation for RecA on a double-stranded DNA, the process being controlled by ATP hydrolysis. Part of this dynamics is suppressed in the presence of ATP[␥S], leading to a stabilized RecA-DNA complex. A one-dimensional nucleation and growth model is presented that may account for the protein assembly.RecA protein plays an essential role in bacterial recombination and DNA repair and is ubiquitous in nature (1-14, 29). RecA or a homolog of RecA is found in all biological cells so far examined. RecA is an example of a protein having a strong structural effect on DNA. During genetic processes, the structural modification of DNA is a key step in sequence recognition and specificity. From early electron microscopy studies, RecA is found to cooperatively bind to DNA; the resulting complex is observed to be stretched by a factor of 1.5 with respect to the naked form and has a twist of 20°per bp instead of 35°in double-stranded DNA (dsDNA) (4-8). An important function of the protein is the DNA strand exchange reaction, whereby a single-stranded DNA (ssDNA) replaces the homologous strand on a dsDNA. Biochemical and electron microscopy studies have suggested that, during strand exchange reactions, RecA polymerizes both on ssDNA and dsDNA in the presence of ATP. In in vitro experiments, RecA monomers are also found to polymerize in the absence of DNA, and its self assembly is reminiscent of the assembly of actin into F-actin and tubulin into microtubules. The depolymerization of RecA is thought to occur via the hydrolysis of ATP (1-3, 9-14, 29). The wide range of roles played by the small RecA protein (molecular mass 37.8 kDa) makes its study interesting. Although an extensive documentation exists, a complete understanding of the molecular mechanisms of its function remains elusive.In this paper, one directly measures the kinetics of polymerization of RecA on a single dsDNA molecule and the resulting changes in the entropic elasticity of DNA. Single molecule measurements of the role of ATP hydrolysis in RecA polymerization are performed. The physical parameters of the experiment are T ϭ 37°C, pH 6.8 Ϯ 0.2. For this study, -phage DNA is used. Single DNA molecules are attached at one end to a glass cover slide and at the other to a bead of 3-m diameter. By using an optical tweezer to trap the bead, one can extend the length of DNA away from its equilibrium configuration (15-18). To measure the ensuing tension in ...