Scanning Electron Microscopy of Early Atherosclerosis in Rabbits Using Aortic Casts

Our research involves measuring the size and location of atherosclerotic lesions on the intimal surface of arteries. To this end we have developed a new method in which scanning electron micrographs of vascular casts with impressions of these lesions on their surface are used. This method is compared with light microscopy and scanning electron microscopy of tissue with lesions. All three methods are found to detect lesions equally well. We also examine the cellular elements in the lesion to determine how the images are formed

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

Statistical mechanics of double-stranded semi-flexible polymers

We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin.Comment: 4 pages, 3 figures; final version for publication - slight modifications to text and figure

Elasticity of semiflexible polymers in two dimensions

We study theoretically the entropic elasticity of a semi-flexible polymer, such as DNA, confined to two dimensions. Using the worm-like-chain model we obtain an exact analytical expression for the partition function of the polymer pulled at one end with a constant force. The force-extension relation for the polymer is computed in the long chain limit in terms of Mathieu characteristic functions. We also present applications to the interaction between a semi-flexible polymer and a nematic field, and derive the nematic order parameter and average extension of the polymer in a strong field.Comment: 16 pages, 3 figure

Molecular elasticity and the geometric phase

We present a method for solving the Worm Like Chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4 pi. We develop an analogy between WLC elasticity and the geometric phase of a spin half system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's comments, to appear in PR

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

Topological interactions in systems of mutually interlinked polymer rings

The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined in several ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$ where $R_G$ is average size of single random walk ring, the effective topological interaction (free energy) scales $\propto R^4$.Comment: 16 pages, 3 figur

Exact theory of kinkable elastic polymers

The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the Wormlike Chain model, as well as the high-curvature softening observed in recent cyclization experiments.Comment: Revised for PRE. 40 pages, 12 figure

Two-Dimensional Fluctuating Vesicles in Linear Shear Flow

The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the constraint of constant perimeter length. These equations are solved in the low temperature limit and using a mean field approach, in which the length constraint is satisfied only on average. The constraint imposes non-trivial correlations between the lowest deformation modes at low temperature. We also simulate a vesicle in a hydrodynamic solvent by using the multi-particle collision dynamics technique, both in the quasi-circular regime and for larger deformations, and compare the stationary deformation correlation functions and the time autocorrelation functions with theoretical predictions. Good agreement between theory and simulations is obtained.Comment: 13 pages, 7 figure

Tension Dynamics and Linear Viscoelastic Behavior of a Single Semiflexible Polymer Chain

We study the dynamical response of a single semiflexible polymer chain based on the theory developed by Hallatschek et al. for the wormlike-chain model. The linear viscoelastic response under oscillatory forces acting at the two chain ends is derived analytically as a function of the oscillation frequency . We shall show that the real part of the complex compliance in the low frequency limit is consistent with the static result of Marko and Siggia whereas the imaginary part exhibits the power-law dependence +1/2. On the other hand, these compliances decrease as the power law -7/8 for the high frequency limit. These are different from those of the Rouse dynamics. A scaling argument is developed to understand these novel results.Comment: 23 pages, 6 figure