Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation functions that although being formally down by powers of $N$ (the population size) nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher-order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.Comment: Revtex, 15 pages, + 4 embedded PS figure

Photochemistry of Furyl- and Thienyldiazomethanes: Spectroscopic Characterization of Triplet 3-Thienylcarbene

Photolysis (λ \u3e 543 nm) of 3-thienyldiazomethane (1), matrix isolated in Ar or N2 at 10 K, yields triplet 3-thienylcarbene (13) and α-thial-methylenecyclopropene (9). Carbene 13 was characterized by IR, UV/vis, and EPR spectroscopy. The conformational isomers of 3-thienylcarbene (s-E and s-Z) exhibit an unusually large difference in zero-field splitting parameters in the triplet EPR spectrum (|D/hc| = 0.508 cm–1, |E/hc| = 0.0554 cm–1; |D/hc| = 0.579 cm–1, |E/hc| = 0.0315 cm–1). Natural Bond Orbital (NBO) calculations reveal substantially differing spin densities in the 3-thienyl ring at the positions adjacent to the carbene center, which is one factor contributing to the large difference in D values. NBO calculations also reveal a stabilizing interaction between the sp orbital of the carbene carbon in the s-Z rotamer of 13 and the antibonding σ orbital between sulfur and the neighboring carbon—an interaction that is not observed in the s-E rotamer of 13. In contrast to the EPR spectra, the electronic absorption spectra of the rotamers of triplet 3-thienylcarbene (13) are indistinguishable under our experimental conditions. The carbene exhibits a weak electronic absorption in the visible spectrum (λmax = 467 nm) that is characteristic of triplet arylcarbenes. Although studies of 2-thienyldiazomethane (2), 3-furyldiazomethane (3), or 2-furyldiazomethane (4) provided further insight into the photochemical interconversions among C5H4S or C5H4O isomers, these studies did not lead to the spectroscopic detection of the corresponding triplet carbenes (2-thienylcarbene (11), 3-furylcarbene (23), or 2-furylcarbene (22), respectively)

Time Scales for transitions between free energy minima of a hard sphere system

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E, March 1996 or s

Phase Diagram Of A Hard-sphere System In A Quenched Random Potential: A Numerical Study

We report numerical results for the phase diagram in the density-disorder plane of a hard sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.Comment: 14 pages, 10 postscript figures (included), submitted to Phys. Rev.

DNA methylation in the promoter region of the p16 (CDKN2/MTS-1/INK4A) gene in human breast tumours

The p16 (CDKN2/MTS-1/INK4A) gene is one of several tumour-suppressor genes that have been shown to be inactivated by DNA methylation in various human cancers including breast tumours. We have used bisulphite genomic sequencing to examine the detailed sequence specificity of DNA methylation in the CpG island promoter/exon 1 region in the p16 gene in DNA from a series of human breast cancer specimens and normal human breast tissue (from reductive mammaplasty). The p16 region examined was unmethylated in the four normal human breast specimens and in four out of nine breast tumours. In the other five independent breast tumour specimens, a uniform pattern of DNA methylation was observed. Of the nine major sites of DNA methylation in the amplified region from these tumour DNAs, four were in non-CG sequences. This unusual concentration of non-CG methylation sites was not a general phenomenon present throughout the genome of these tumour cells because the methylated CpG island regions of interspersed L1 repeats had a pattern of (almost exclusively) CG methylation similar to that found in normal breast tissue DNA and in DNA from tumours with unmethylated p16 genes. These data suggest that DNA methylation of the p16 gene in some breast tumours could be the result of an active process that generates a discrete methylation pattern and, hence, could ultimately be amenable to theraputic manipulation. © 1999 Cancer Research Campaig

Relationship between Structure, Entropy and Diffusivity in Water and Water-like Liquids

Anomalous behaviour of the excess entropy ($S_e$) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO$_2$ and BeF$_2$) and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behaviour, the density range of the excess entropy anomaly is shown to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities ($D^*$) conform to the excess entropy scaling relation, $D^* =A\exp (\alpha S_e)$ for all the systems (Y. Rosenfeld, Phys. Rev. A {\bf 1977}, {\it 15}, 2545), the exponential scaling parameter, $\alpha$, shows a small isochore-dependence in the case of water. Replacing $S_e$ by pair correlation-based approximants accentuates the isochore-dependence of the diffusivity scaling. Isochores with similar diffusivity scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.Comment: 24 pages, 4 figures, to be published in Journal of Physical Chemistry

Development of a GPU-based Monte Carlo dose calculation code for coupled electron-photon transport

Monte Carlo simulation is the most accurate method for absorbed dose calculations in radiotherapy. Its efficiency still requires improvement for routine clinical applications, especially for online adaptive radiotherapy. In this paper, we report our recent development on a GPU-based Monte Carlo dose calculation code for coupled electron-photon transport. We have implemented the Dose Planning Method (DPM) Monte Carlo dose calculation package (Sempau et al, Phys. Med. Biol., 45(2000)2263-2291) on GPU architecture under CUDA platform. The implementation has been tested with respect to the original sequential DPM code on CPU in phantoms with water-lung-water or water-bone-water slab geometry. A 20 MeV mono-energetic electron point source or a 6 MV photon point source is used in our validation. The results demonstrate adequate accuracy of our GPU implementation for both electron and photon beams in radiotherapy energy range. Speed up factors of about 5.0 ~ 6.6 times have been observed, using an NVIDIA Tesla C1060 GPU card against a 2.27GHz Intel Xeon CPU processor.Comment: 13 pages, 3 figures, and 1 table. Paper revised. Figures update

Chromatin: a tunable spring at work inside chromosomes

This paper focuses on mechanical aspects of chromatin biological functioning. Within a basic geometric modeling of the chromatin assembly, we give for the first time the complete set of elastic constants (twist and bend persistence lengths, stretch modulus and twist-stretch coupling constant) of the so-called 30-nm chromatin fiber, in terms of DNA elastic properties and geometric properties of the fiber assembly. The computation naturally embeds the fiber within a current analytical model known as the ``extensible worm-like rope'', allowing a straightforward prediction of the force-extension curves. We show that these elastic constants are strongly sensitive to the linker length, up to 1 bp, or equivalently to its twist, and might locally reach very low values, yielding a highly flexible and extensible domain in the fiber. In particular, the twist-stretch coupling constant, reflecting the chirality of the chromatin fiber, exhibits steep variations and sign changes when the linker length is varied. We argue that this tunable elasticity might be a key feature for chromatin function, for instance in the initiation and regulation of transcription.Comment: 38 pages 15 figure

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt