Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl

One-parameter scaling theory for DNA extension in a nanochannel

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.Comment: Revised version. 5 pages, 4 figures, revised version, supplementary informatio

Hairpins in the conformations of a confined polymer

If a semiflexible polymer confined to a narrow channel bends around by 180 degrees, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.Comment: Revised version. 22 pages, 7 figures, 2 tables, supplementary materia

Photosynthetic reaction center as a quantum heat engine

Two seemingly unrelated effects attributed to quantum coherence have been reported recently in natural and artificial light-harvesting systems. First, an enhanced solar cell efficiency was predicted and second, population oscillations were measured in photosynthetic antennae excited by sequences of coherent ultrashort laser pulses. Because both systems operate as quantum heat engines (QHEs) that convert the solar photon energy to useful work (electric currents or chemical energy, respectively), the question arises whether coherence could also enhance the photosynthetic yield. Here, we show that both effects arise from the same population–coherence coupling term which is induced by noise, does not require coherent light, and will therefore work for incoherent excitation under natural conditions of solar excitation. Charge separation in light-harvesting complexes occurs in a pair of tightly coupled chlorophylls (the special pair) at the heart of photosynthetic reaction centers of both plants and bacteria. We show the analogy between the energy level schemes of the special pair and of the laser/photocell QHEs, and that both population oscillations and enhanced yield have a common origin and are expected to coexist for typical parameters. We predict an enhanced yield of 27% in a QHE motivated by the reaction center. This suggests nature-mimicking architectures for artificial solar energy devices

Time-, Frequency-, and Wavevector-Resolved X-Ray Diffraction from Single Molecules

Using a quantum electrodynamic framework, we calculate the off-resonant scattering of a broad-band X-ray pulse from a sample initially prepared in an arbitrary superposition of electronic states. The signal consists of single-particle (incoherent) and two-particle (coherent) contributions that carry different particle form factors that involve different material transitions. Single-molecule experiments involving incoherent scattering are more influenced by inelastic processes compared to bulk measurements. The conditions under which the technique directly measures charge densities (and can be considered as diffraction) as opposed to correlation functions of the charge-density are specified. The results are illustrated with time- and wavevector-resolved signals from a single amino acid molecule (cysteine) following an impulsive excitation by a stimulated X-ray Raman process resonant with the sulfur K-edge. Our theory and simulations can guide future experimental studies on the structures of nano-particles and proteins

Bulgac-Kusnezov-Nos\'e-Hoover thermostats

In this paper we formulate Bulgac-Kusnezov constant temperature dynamics in phase space by means of non-Hamiltonian brackets. Two generalized versions of the dynamics are similarly defined: one where the Bulgac-Kusnezov demons are globally controlled by means of a single additional Nos\'e variable, and another where each demon is coupled to an independent Nos\'e-Hoover thermostat. Numerically stable and efficient measure-preserving time-reversible algorithms are derived in a systematic way for each case. The chaotic properties of the different phase space flows are numerically illustrated through the paradigmatic example of the one-dimensional harmonic oscillator. It is found that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic, both of the Nos\'e-Hoover controlled dynamics sample the canonical distribution correctly

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.Comment: 48 pages, 3 ps fig

Clustering of matter in waves and currents

The growth rate of small-scale density inhomogeneities (the entropy production rate) is given by the sum of the Lyapunov exponents in a random flow. We derive an analytic formula for the rate in a flow of weakly interacting waves and show that in most cases it is zero up to the fourth order in the wave amplitude. We then derive an analytic formula for the rate in a flow of potential waves and solenoidal currents. Estimates of the rate and the fractal dimension of the density distribution show that the interplay between waves and currents is a realistic mechanism for providing patchiness of pollutant distribution on the ocean surface.Comment: 4 pages, 1 figur

Lyapunov Exponents from Kinetic Theory for a Dilute, Field-driven Lorentz Gas

Positive and negative Lyapunov exponents for a dilute, random, two-dimensional Lorentz gas in an applied field, $\vec{E}$, in a steady state at constant energy are computed to order $E^{2}$. The results are: $\lambda_{\pm}=\lambda_{\pm}^{0}-a_{\pm}(qE/mv)^{2}t_{0}$ where $\lambda_{\pm}^{0}$ are the exponents for the field-free Lorentz gas, $a_{+}=11/48, a_{-}=7/48$, $t_{0}$ is the mean free time between collisions, $q$ is the charge, $m$ the mass and $v$ is the speed of the particle. The calculation is based on an extended Boltzmann equation in which a radius of curvature, characterizing the separation of two nearby trajectories, is one of the variables in the distribution function. The analytical results are in excellent agreement with computer simulations. These simulations provide additional evidence for logarithmic terms in the density expansion of the diffusion coefficient.Comment: 7 pages, revtex, 3 postscript figure