The melting curves of short heterogeneous DNA chains in solution are calculated on the basis of statistical thermodynamics, and compared to experiments. The computation of the partition function is based on the Peyrard-Bishop Hamiltonian, which has already been adopted in a theoretical description of the melting of long DNA chains. In the case of short chains it is necessary to consider not only the breaking of the hydrogen bonds between single base pairs, but also the complete dissociation of the two strands forming the double helix
The Hamiltonian mean-field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasistationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate in the recent past. We introduce a numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasistationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasistationary states are present not only below, but also above the critical temperature of the second-order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures.
The framework of percolation theory is used to analyze the hydration dependence of the capacitance measured for protein samples of pH 3-10, at frequencies from 10 kHz to 4 MHz. For all samples there is a critical value of the hydration at which the capacitance sharply increases with increase in hydration level. The threshold hc = 0.15 g of water per g of protein is independent of pH below pH 9 and shows no solvent deuterium isotope effect. The fractional coverage of the surface at h, is in close agreement with the prediction of theory for surface percolation. We view the protonic conduction process described 'here for low hydration and previously for high hydration as percolative proton transfer along threads of hydrogen-bonded water molecules. A principal element of the percolation picture, which explains the invariance of hc to change in pH and solvent, is the sudden appearance of long-range connectivity and infinite clusters at the threshold ho. The relationship of the protonic conduction threshold to other features of protein hydration is described. The importance of percolative processes for enzyme catalysis and membrane transport is discussed.In a previous paper we have described the protonic conductivity induced by hydration below monolayer coverage for single molecules of the protein lysozyme (1). Under these conditions, the hydration water is severely disordered (2). Thus, it seems appropriate to consider the protonic conductivity in the framework of the percolation model (3, 4). This model has been shown applicable to a broad range of chemical and physical phenomena where spatially random processes and topological disorder are of vital importance, such as polymer gelation and the electrical conductivity of a network of conducting and nonconducting elements. One of the most appealing aspects ofthe percolation model is the presence ofa percolation transition, where a long-range connectivity among the elements of the system suddenly appears. In this paper we focus on a transition of this kind, a sharp change in dielectric properties in the low hydration region for the protein lysozyme. This analysis extends that reported for the high hydration region (1).MATERIALS AND METHODS A previous paper (1) described the preparation of protein samples of pH 3-10 and the measurement of their dielectric properties at frequencies from 10 kHz to 10 MHz and for hydration levels from wet powder (>0.35 h) to the low hydration limit (h.) where the evaporation rate is zero under these experimental conditions. The data were analyzed previously for the high hydration region, h > 0.2 (1). In this paper we analyze a similar body of data for the low hydration region.For display and analysis, the dielectric properties are presented as a function of hydration level, h. During the measurements the hydration of each sample was varied from the starting conditions, a wet powder obtained by isopiestic equilibration against pure water, to the final limiting low hydration, h.. The dielectric data were collected continuously. Hydra...
The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power α, is analytically computed. It is also shown how to compute a rescaling function that allows to reduce the model, for any d-dimensional lattice and for any α < d, to the mean field (α = 0) model. PACS: 05.20.-y, 05.70.Ce, 05.10.-a
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which first occurred in Wuhan (China) in December of 2019, causes a severe acute respiratory illness with a high mortality rate, and has spread around the world. To gain an understanding of the evolution of the newly emerging SARS-CoV-2, we herein analyzed the codon usage pattern of SARS-CoV-2. For this purpose, we compared the codon usage of SARS-CoV-2 with that of other viruses belonging to the subfamily of Orthocoronavirinae. We found that SARS-CoV-2 has a high AU content that strongly influences its codon usage, which appears to be better adapted to the human host. We also studied the evolutionary pressures that influence the codon usage of five conserved coronavirus genes encoding the viral replicase, spike, envelope, membrane and nucleocapsid proteins. We found different patterns of both mutational bias and natural selection that affect the codon usage of these genes. Moreover, we show here that the two integral membrane proteins (matrix and envelope) tend to evolve slowly by accumulating nucleotide mutations on their corresponding genes. Conversely, genes encoding nucleocapsid (N), viral replicase and spike proteins (S), although they are regarded as are important targets for the development of vaccines and antiviral drugs, tend to evolve faster in comparison to the two genes mentioned above. Overall, our results suggest that the higher divergence observed for the latter three genes could represent a significant barrier in the development of antiviral therapeutics against SARS-CoV-2.
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