Radial Distribution Function for Semiflexible Polymers Confined in Microchannels

An analytic expression is derived for the distribution $G(\vec{R})$ of the end-to-end distance $\vec{R}$ of semiflexible polymers in external potentials to elucidate the effect of confinement on the mechanical and statistical properties of biomolecules. For parabolic confinement the result is exact whereas for realistic potentials a self-consistent ansatz is developed, so that $G(\vec{R})$ is given explicitly even for hard wall confinement. The theoretical result is in excellent quantitative agreement with fluorescence microscopy data for actin filaments confined in rectangularly shaped microchannels. This allows an unambiguous determination of persistence length $L_P$ and the dependence of statistical properties such as Odijk's deflection length $\lambda$ on the channel width $D$. It is shown that neglecting the effect of confinement leads to a significant overestimation of bending rigidities for filaments

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.Comment: 6 pages, 3 figures, Version as published in Eur. Phys. J.

Quantitative Measurement from Vascular Casts

A review of quantitative measurements show casting materials shrink from 0.2 - 20% and have viscosities ranging from 1.4 - 100,000 centipoise. Blood vessels have highly variable mechanical properties. Some microvessels are very stiff having little change in dimensions with pressure. Larger vessels generally change diameter significantly but show highly variable changes in length with pressure. Perfusion fixation does not fix the dimensions of blood vessels. Dog carotid arteries well fixed with glutaraldehyde at physiologic dimensions retain ≈20% of their elastic recoil circumferentially and ≈30% longitudinally. We recommend vascular casting as a method of accurately measuring the vasculature if care is taken to use low shrinkage casting resins and maintain physiologic transmural pressures for the duration of any casting procedure, even if prefixation is used. We measured a ≈10% error in our method of measuring both the size and location of periorificial atherosclerotic lesions from aortic casts. Little is known about how vascular smooth muscle tone changes during casting

The distribution function of a semiflexible polymer and random walks with constraints

In studying the end-to-end distribution function $G(r,N)$ of a worm like chain by using the propagator method we have established that the combinatorial problem of counting the paths contributing to $G(r,N)$ can be mapped onto the problem of random walks with constraints, which is closely related to the representation theory of the Temperley-Lieb algebra. By using this mapping we derive an exact expression of the Fourier-Laplace transform of the distribution function, $G(k,p)$, as a matrix element of an inverse of an infinite rank matrix. Using this result we also derived a recursion relation permitting to compute $G(k,p)$ directly. We present the results of the computation of $G(k,N)$ and its moments. The moments $$ of $$ can be calculated \emph{exactly} by calculating the (1,1) matrix element of $2n$-th power of a truncated matrix of rank $n+1$.Comment: 6 pages, 2 figures, added a referenc

A Conformal Field Theory for Eternal Inflation

We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as the asymptotic distribution of bubble collisions with the domain wall of a fiducial "observation bubble" in d+2 dimensional de Sitter space. In this note we calculate the 2-,3-, and 4-point correlation functions of exponentials of the "bubble number operator" analytically in d=2. We find that these correlators, when carefully defined, are free of infrared divergences, covariant under the global conformal group, charge conserving, and transform with positive conformal dimensions that are related in a novel way to the charge. Although by themselves these operators probably do not define a full-fledged conformal field theory, one can use the partition function on a sphere to compute an approximate central charge in the 2D case. The theory in any dimension has a noninteracting limit when the nucleation rate of the bubbles in the bulk is very large. The theory in two dimensions is related to some models of continuum percolation, but it is conformal for all values of the tunneling rate.Comment: 30 pages, 8 figure

Transverse fluctuations of grafted polymers

We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and non-Gaussian for typical semiflexible polymers. The reduced distribution in the transverse direction, a Gaussian in the stiff and flexible limits, shows a double peak structure at intermediate stiffnesses. We also explore the response to a transverse force applied at the polymer free end. We identify F-Actin as an ideal benchmark for the effects discussed.Comment: 10 pages, 4 figures, submitted to Physical Review

Investigating the effects of laser beams (532 and 660 nm) in annihilation of pistachio mould fungus using spectrophotometry analysis

When moulds are illuminated by visible electromagnetic-EM radiations, several effects on nucleus materials and nucleotides can be detected. These effects have a significant influence on mould generation or destruction. This paper presents the effects and implications of a red diode laser beam (660 nm), a second-harmonics of a Nd:YAG laser emitting green beam (532 nm), or the combination of both, on the eradication of Pistachio mould fungus. Incident doses (ID) of both beams are kept identical throughout the experiment. The absorption spectrums of irradiated mouldy samples and the bright-greenish-yellow-fluorescence (BGYF) of fungus occurring in mould texture due to electronic excitation are investigated. We found that a combination of a green and a red laser beam with an ID of 0.5 J/cm^2 provides the optimal effects on Pistachio mould fungus eradication