619 research outputs found
Sequence-Dependent Effects on the Properties of Semiflexible Biopolymers
Using path integral technique, we show exactly that for a semiflexible
biopolymer in constant extension ensemble, no matter how long the polymer and
how large the external force, the effects of short range correlations in the
sequence-dependent spontaneous curvatures and torsions can be incorporated into
a model with well-defined mean spontaneous curvature and torsion as well as a
renormalized persistence length. Moreover, for a long biopolymer with large
mean persistence length, the sequence-dependent persistence lengths can be
replaced by their mean. However, for a short biopolymer or for a biopolymer
with small persistence lengths, inhomogeneity in persistence lengths tends to
make physical observables very sensitive to details and therefore less
predictable
Disordered, stretched, and semiflexible biopolymers in two dimensions
We study the effects of intrinsic sequence-dependent curvature for a two
dimensional semiflexible biopolymer with short-range correlation in intrinsic
curvatures. We show exactly that when not subjected to any external force, such
a system is equivalent to a system with a well-defined intrinsic curvature and
a proper renormalized persistence length. We find the exact expression for the
distribution function of the equivalent system. However, we show that such an
equivalent system does not always exist for the polymer subjected to an
external force. We find that under an external force, the effect of
sequence-disorder depends upon the averaging order, the degree of disorder, and
the experimental conditions, such as the boundary conditions. Furthermore, a
short to moderate length biopolymer may be much softer or has a smaller
apparent persistent length than what would be expected from the "equivalent
system". Moreover, under a strong stretching force and for a long biopolymer,
the sequence-disorder is immaterial for elasticity. Finally, the effect of
sequence-disorder may depend upon the quantity considered
Elasticity of semi-flexible polymers
We present a numerical solution of the Worm-Like Chain (WLC) model for
semi-flexible polymers. We display graphs for the end-to-end distance
distribution and the force-extension relation expected from the model. We
predict the expected level of fluctuations around the mean value in
force-extension curves. Our treatment analyses the entire range of polymer
lengths and reproduces interesting qualitative features seen in recent computer
simulations for polymers of intermediate length. These results can be tested
against experiments on single molecules. This study is relevant to mechanical
properties of biological molecules.Comment: five pages revtex five figures, slightly improved version with recent
references adde
Statics and Dynamics of the Wormlike Bundle Model
Bundles of filamentous polymers are primary structural components of a broad
range of cytoskeletal structures, and their mechanical properties play key
roles in cellular functions ranging from locomotion to mechanotransduction and
fertilization. We give a detailed derivation of a wormlike bundle model as a
generic description for the statics and dynamics of polymer bundles consisting
of semiflexible polymers interconnected by crosslinking agents. The elastic
degrees of freedom include bending as well as twist deformations of the
filaments and shear deformation of the crosslinks. We show that a competition
between the elastic properties of the filaments and those of the crosslinks
leads to renormalized effective bend and twist rigidities that become
mode-number dependent. The strength and character of this dependence is found
to vary with bundle architecture, such as the arrangement of filaments in the
cross section and pretwist. We discuss two paradigmatic cases of bundle
architecture, a uniform arrangement of filaments as found in F-actin bundles
and a shell-like architecture as characteristic for microtubules. Each
architecture is found to have its own universal ratio of maximal to minimal
bending rigidity, independent of the specific type of crosslink induced
filament coupling; our predictions are in reasonable agreement with available
experimental data for microtubules. Moreover, we analyze the predictions of the
wormlike bundle model for experimental observables such as the tangent-tangent
correlation function and dynamic response and correlation functions. Finally,
we analyze the effect of pretwist (helicity) on the mechanical properties of
bundles. We predict that microtubules with different number of protofilaments
should have distinct variations in their effective bending rigidity
Getting DNA twist rigidity from single molecule experiments
We use an elastic rod model with contact to study the extension versus
rotation diagrams of single supercoiled DNA molecules. We reproduce
quantitatively the supercoiling response of overtwisted DNA and, using
experimental data, we get an estimation of the effective supercoiling radius
and of the twist rigidity of B-DNA. We find that unlike the bending rigidity,
the twist rigidity of DNA seems to vary widely with the nature and
concentration of the salt buffer in which it is immerged
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
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
Thermally induced gluten modification observed with rheology and spectroscopies
The protein vital gluten is mainly used for food while interest for non-food applications, like biodegradable materials, increases. In general, the structure and functionality of proteins is highly dependent on thermal treatments during production or modification. This study presents conformational changes and corresponding rheological effects of vital wheat gluten depending on temperature. Dry samples analyzed by X-ray photoelectron spectroscopy (XPS), Fourier-transform infrared spectroscopy (FTIR) and thermalgravimetric analysis coupled with mass spectrometry (TGA-MS) show surface compositions and conformational changes from 25 to 250 °C. Above 170 °C, XPS reveals a decreased N content at the surface while FTIR band characteristics for β-sheets prove structural changes. At 250 °C, protein denaturation accompanied by a significant mass loss due to dehydration and decarbonylation reactions is observed. Oscillatory measurements of optimally hydrated vital gluten describing network properties of the material show two structural changes along a temperature ramp from 25 to 90 °C: at 56–64 °C, the temperature necessary to trigger structural changes increases with the ratio of gliadin to total protein mass, determined by reversed-phase high performance liquid chromatography (RP-HPLC). At a temperature of 79–81 °C, complete protein denaturation occurs. FTIR confirms the denaturation process by showing band shifts with both temperature steps
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
Theory of High-Force DNA Stretching and Overstretching
Single molecule experiments on single- and double stranded DNA have sparked a
renewed interest in the force-extension of polymers. The extensible Freely
Jointed Chain (FJC) model is frequently invoked to explain the observed
behavior of single-stranded DNA. We demonstrate that this model does not
satisfactorily describe recent high-force stretching data. We instead propose a
model (the Discrete Persistent Chain, or ``DPC'') that borrows features from
both the FJC and the Wormlike Chain, and show that it resembles the data more
closely. We find that most of the high-force behavior previously attributed to
stretch elasticity is really a feature of the corrected entropic elasticity;
the true stretch compliance of single-stranded DNA is several times smaller
than that found by previous authors. Next we elaborate our model to allow
coexistence of two conformational states of DNA, each with its own stretch and
bend elastic constants. Our model is computationally simple, and gives an
excellent fit through the entire overstretching transition of nicked,
double-stranded DNA. The fit gives the first values for the elastic constants
of the stretched state. In particular we find the effective bend stiffness for
DNA in this state to be about 10 nm*kbt, a value quite different from either
B-form or single-stranded DNAComment: 33 pages, 11 figures. High-quality figures available upon reques
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