Abstract:
Using the criterion that the mechanical unzipping transition in a bound homopolymer is triggered when the average force exerted by the single unbound strands on the first base pair in the bound section exceeds the force binding the pair together, the temperature dependence of the critical unzipping force is obtained. In the resulting phase diagram, the critical force decreases monotonically with increasing temperature, from a finite value at zero Kelvin to zero at the critical temperature.

Abstract:
A conceptual difficulty in the Hooke's-law description of ideal Gaussian polymer-chain elasticity is sometimes apparent in analyses of experimental data or in physical models designed to simulate the behavior of biopolymers. The problem, the tendency of a chain to collapse in the absence of external forces, is examined in the following examples: DNA-stretching experiments, gel electrophoresis, and protein folding. We demonstrate that the application of a statistical-mechanically derived repulsive force, acting between the chain ends, whose magnitude is proportional to the absolute temperature and inversely proportional to the scalar end separation removes this difficulty.

Abstract:
Recognition that certain forces arising from the averaging of the multiple impacts of a solute particle by the surrounding solvent particles undergoing random thermal motion can be of an entropic nature has led to the incorporation of these forces and their related entropies into theoretical protocols ranging from molecular-dynamics simulations to the modeling of quarkonium suppression in particle physics. Here we present a rigorous derivation of this Brownian entropic force by means of the classical Gibbs canonical partition function and in so doing provide a heuristic demonstration of its kinetic origin.

Abstract:
Taking into account the nonequivalence of fixed-force and fixed-length ensembles in the weak-force regime, equations of state are derived that describe the equilibrium extension or compression of an ideal Gaussian polymer chain in response to an applied force in such a manner that the calculated unstretched scalar end-to-end separation is the random-coil size rather than zero. The entropy-spring model for a polymer chain is thereby modified so that for calculational purposes, the spring is of finite rather than zero unstretched length. These force laws are shown to be consistent with observations from stretching experiments performed on single DNA molecules, wherein the measured extension approaches a non-zero limit as the external force is reduced. When used to describe single-chain dynamics, this approach yields a single exponential relaxation expression for a short Gaussian chain (bead-spring dumbbell), which when initially compressed or extended relaxes into a state having the random-coil end separation, in agreement with the Rouse-model result. An equation is derived that describes the elongational response of a charged, tethered chain to a weak electric field (as might occur in electrophoresis), a calculation not feasible with the traditional approach. Finally, an expression for the entropic work required to bring the ends of a chain together, starting from the random-coil configuration, is derived and compared with the Hookean result.

Abstract:
The Helmholtz free-energy W is calculated as a function of separation distance for two molecules in a fluid, A and B, whose mutual interaction is described by a spherically symmetric potential. For the equilibrium A + B = AB occurring in a dilute solution or gas, W is used to evaluate the association constant K, which for ionic A and B is identical to the Bjerrum result. The criterion defining the bound species is not arbitrary; i.e., the cutoff separation distance in the configuration integral used to calculate K arises directly from the definition of W. For a one-component dense fluid, W permits the derivation of the phase-condensation temperature, which for a gas is the critical temperature and for a liquid the freezing temperature. For ionic A and B (e.g., Sodium and Chloride ions in molten NaCl), an expression for the freezing temperature is obtained, which is similar to the expression for the melting temperature derived by Kosterlitz and Thouless for two-dimensional systems.

Abstract:
We show that the simple analytical model proposed by Zhang and Marko (Phys. Rev. E 77, 031916 (2008)) to illustrate Maxwell relations for single-DNA experiments can be improved by including the zero-force entropy of a Gaussian chain. The resulting model is in excellent agreement with the discrete persistent-chain model and is in a form convenient for analyzing experimental data.

Abstract:
A broad spectrum of beneficial effects has been ascribed to creatine (Cr), phosphocreatine (PCr) and their cyclic analogues cyclo-(cCr) and phospho-cyclocreatine (PcCr). Cr is widely used as nutritional supplement in sports and increasingly also as adjuvant treatment for pathologies such as myopathies and a plethora of neurodegenerative diseases. Additionally, Cr and its cyclic analogues have been proposed for anti-cancer treatment. The mechanisms involved in these pleiotropic effects are still controversial and far from being understood. The reversible conversion of Cr and ATP into PCr and ADP by creatine kinase, generating highly diffusible PCr energy reserves, is certainly an important element. However, some protective effects of Cr and analogues cannot be satisfactorily explained solely by effects on the cellular energy state. Here we used mainly liposome model systems to provide evidence for interaction of PCr and PcCr with different zwitterionic phospholipids by applying four independent, complementary biochemical and biophysical assays: (i) chemical binding assay, (ii) surface plasmon resonance spectroscopy (SPR), (iii) solid-state 31P-NMR, and (iv) differential scanning calorimetry (DSC). SPR revealed low affinity PCr/phospholipid interaction that additionally induced changes in liposome shape as indicated by NMR and SPR. Additionally, DSC revealed evidence for membrane packing effects by PCr, as seen by altered lipid phase transition. Finally, PCr efficiently protected against membrane permeabilization in two different model systems: liposome-permeabilization by the membrane-active peptide melittin, and erythrocyte hemolysis by the oxidative drug doxorubicin, hypoosmotic stress or the mild detergent saponin. These findings suggest a new molecular basis for non-energy related functions of PCr and its cyclic analogue. PCr/phospholipid interaction and alteration of membrane structure may not only protect cellular membranes against various insults, but could have more general implications for many physiological membrane-related functions that are relevant for health and disease.

Background: It has been postulated that elliptical cutaneous excisions must possess a length-to-width ratio of 3 to 4 and a vertex angle of 30o or less in order to be closed primarily without creating a “dog ear”. These dimensions became axiomatic in cutaneous surgery and have been taught in the apprenticeship model for years. The present article examines the validity of that paradigm. Methods: We collected data from two sources: ellipses described in the literature (57 cases); and elliptical excisions performed at the authors’ outpatient clinic (83 cases). The surgical ellipse lengths, widths, and vertex angles were analyzed, and the data were compared to a mathematical formula used to generate a fusiform ellipse. Results: The length-to-width ratio of 3 - 4 was found to be inconsistent with the recommended vertex angle of 30o. In fact, a length-to-width ratio of 3 - 4 determines a vertex angle of 48o - 63o. A 30o vertex angle is only feasible with long length-to-width ration of about 7.5. Conclusions: The paradigm that surgical ellipses should have a vertex angle of 30o with length-to-width ratio of 3 - 4 is incorrect. Evidence from actual surgical practice and from mathematical formulation shows that either the length-to-width ratio must be larger than 3 - 4 or the vertex angle must be larger than 30 degrees.

Abstract:
We present ROSAT HRI data of the distant and X-ray luminous (L_x(bol)=2.6^ {+0.4}_{-0.2} 10^{45}erg/sec) cluster of galaxies 3C 295. We fit both a one-dimensional and a two-dimensional isothermal beta-model to the data, the latter one taking into account the effects of the point spread function (PSF). For the error analysis of the parameters of the two-dimensional model we introduce a Monte-Carlo technique. Applying a substructure analysis, by subtracting a cluster model from the data, we find no evidence for a merger, but we see a decrement in emission South-East of the center of the cluster, which might be due to absorption. We confirm previous results by Henry & Henriksen(1986) that 3C 295 hosts a cooling flow. The equations for the simple and idealized cooling flow analysis presented here are solely based on the isothermal beta-model, which fits the data very well, including the center of the cluster. We determine a cooling flow radius of 60-120kpc and mass accretion rates of dot{M}=400-900 Msun/y, depending on the applied model and temperature profile. We also investigate the effects of the ROSAT PSF on our estimate of dot{M}, which tends to lead to a small overestimate of this quantity if not taken into account. This increase of dot{M} (10-25%) can be explained by a shallower gravitational potential inferred by the broader overall profile caused by the PSF, which diminishes the efficiency of mass accretion. We also determine the total mass of the cluster using the hydrostatic approach. At a radius of 2.1 Mpc, we estimate the total mass of the cluster (M{tot}) to be (9.2 +/- 2.7) 10^{14}Msun. For the gas to total mass ratio we get M{gas}/M{tot} =0.17-0.31, in very good agreement with the results for other clusters of galaxies, giving strong evidence for a low density universe.

Abstract:
A topology τ on the vertices of a comparability graph G is said to be compatible with G if each subgraph H of G is graph-connected if and only if it is a connected subspace of (G,τ). In two previous papers we considered the problem of finding compatible topologies for a given comparability graph and we proved that the nonexistence of infinite paths was a necessary and sufficient condition for the existence of a compact compatible topology on a tree (that is to say, a connected graph without cycles) and we asked whether this condition characterized the existence of a compact compatible topology on a comparability graph in which all cycles are of length at most n. Here we prove an extension of the above-mentioned theorem to graphs whose cycles are all of length at most five and we show that this is the best possible result by exhibiting a comparability graph in which all cycles are of length 6, with no infinite paths, but which has no compact compatible topology.