An algorithm for series expansions based on hierarchical rate equations

We propose a computational method to obtain series expansions in powers of time for general dynamical systems described by a set of hierarchical rate equations. The method is generally applicable to problems in both equilibrium and nonequilibrium statistical mechanics such as random sequential adsorption, diffusion-reaction dynamics, and Ising dynamics. New result of random sequential adsorption of dimers on a square lattice is presented.Comment: LaTeX, 9 pages including 1 figur

Partly melted DNA conformations obtained with a probability peak finding method

Peaks in the probabilities of loops or bubbles, helical segments, and unzipping ends in melting DNA are found in this article using a peak finding method that maps the hierarchical structure of certain energy landscapes. The peaks indicate the alternative conformations that coexist in equilibrium and the range of their fluctuations. This yields a representation of the conformational ensemble at a given temperature, which is illustrated in a single diagram called a stitch profile. This article describes the methodology and discusses stitch profiles vs. the ordinary probability profiles using the phage lambda genome as an example.Comment: 11 pages, 9 figures; v3: major changes; v4: applications sectio

Current status of plague and plague control in the United States

During the first quarter of the 20th century, massive rat-borne plague epidemics occurred in port cities of the United States in conjunction with the last world-wide pandemic which originated in China in 1893. By 1950, plague was found to be firmly established in wild rodent populations in states west of the 100th meridian. Presumably because of improved sanitation coupled with retreat of the world-wide pandemic, there have been no human cases in this country associated with urban rats since 1924. However, sporadic cases, fewer than 10 per year, are reported as due to contact with wild rodents, lagomorphs, rural rats, and/or their fleas. Recent observations suggest that: a) in the current decade there has been an increase in human plague cases; b) there continues to be a serious potential of a single undiagnosed and untreated case, which possibility is intensified by the very paucity of human cases decreasing the likelihood of a correct diagnosis and by changing patterns of life exhibited by members of our society (e.g., hippie communes and a generally increased mobility); and c) the apparent distribution of plague only in the area west of the 100th meridian might be found to represent an unrealistic generalization if adequate surveillance were carried out. At the present time human plague cases from wild animal sources tend to be isolated events both spatially and temporally and often cannot be attributed to confined and definable epizootic sources amenable to effective control programs. Improved means for epizootic control and long-term management of enzootic plague sources must be sought aggressively. These measures should include development of: a) a surveillance network to detect plague activity in rodent and lagomorph populations throughout the western United States; b) effective, yet ecologically sound, means of ectoparasite control, including suitable materials and methods of application; c) methods for management of plague-susceptible wild animal populations, particularly where they exist in contact with high use recreation and residential areas; and d) more extensive knowledge of enzootic plague and the factors that bring about epizootic plague and potential human contact

Looking into DNA breathing dynamics via quantum physics

We study generic aspects of bubble dynamics in DNA under time dependent perturbations, for example temperature change, by mapping the associated Fokker-Planck equation to a quantum time-dependent Schroedinger equation with imaginary time. In the static case we show that the eigenequation is exactly the same as that of the $\beta$-deformed nuclear liquid drop model, without the issue of non-integer angular momentum. A universal breathing dynamics is demonstrated by using an approximate method in quantum mechanics. The calculated bubble autocorrelation function qualitatively agrees with experimental data. Under time dependent modulations, utilizing the adiabatic approximation, bubble properties reveal memory effects.Comment: 5 pages, 1 figur

Effects of mechanical strain on thermal denaturation of DNA

As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the undenatured sections can, in principle, alter the nature of the thermal denaturation process. Assuming that the strains associated with this overwinding are not relieved, we find that a simple model of strain-altered melting leads to a suppression of the melting transition when the unaltered transition is continuous. When the melting transition is first order in the absence of strain associated with overwinding, the modification is to a third order phase transition.Comment: 4 pages, 5 figures, RevTe

Conformal Field Theories in Fractional Dimensions

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.Comment: 11 pages, 4 figures - references updated - one affiliation modifie

Unfolding and unzipping of single-stranded DNA by stretching

We present a theoretical study of single-stranded DNA under stretching. Within the proposed framework, the effects of basepairing on the mechanical response of the molecule can be studied in combination with an arbitrary underlying model of chain elasticity. In a generic case, we show that the stretching curve of ssDNA exhibits two distinct features: the second-order "unfolding" phase transition, and a sharp crossover, reminiscent of the first-order "unzipping" transition in dsDNA. We apply the theory to the particular cases of Worm-like Chain (WLC) and Freely-Joint Chain (FJC) models, and discuss the universal and model--dependent features of the mechanical response of ssDNA. In particular, we show that variation of the width of the unzipping crossover with interaction strength is very sensitive to the energetics of hairpin loops. This opens a new way of testing the elastic properties of ssDNA.Comment: 7 pages, 4 figures, substantially revised versio

Exactly Solvable Model for Helix-Coil-Sheet Transitions in Protein Systems

In view of the important role helix-sheet transitions play in protein aggregation, we introduce a simple model to study secondary structural transitions of helix-coil-sheet systems using a Potts model starting with an effective Hamiltonian. This energy function depends on four parameters that approximately describe entropic and enthalpic contributions to the stability of a polypeptide in helical and sheet conformations. The sheet structures involve long-range interactions between residues which are far in sequence, but are in contact in real space. Such contacts are included in the Hamiltonian. Using standard statistical mechanical techniques, the partition function is solved exactly using transfer matrices. Based on this model, we study thermodynamic properties of polypeptides, including phase transitions between helix, sheet, and coil structures.Comment: Updated version with correction