scholarly journals SEMI-FLEXIBLE COMPACT POLYMERS IN A DISORDERED ENVIRONMENT

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Dušanka Lekić ◽  
Sunčica Elezović-Hadžić ◽  
Nataša Adžić
Keyword(s):  
Phase Transition ◽  
Molten Globule ◽  
Persistence Length ◽  
Hamiltonian Cycles ◽  
Stiffness Parameter ◽  
Bending Rigidity ◽  
Flexible Polymers ◽  
Fractal Lattice ◽  
Ring Polymer ◽  
Flexible Ring

Hamiltonian cycles with bending rigidity are studied on the first three members of the fractal family obtained by generalization of the modified rectangular (MR) fractal lattice. This model is proposed to describe conformational and thermodynamic properties of a single semi-flexible ring polymer confined in a poor and disordered (e.g. crowded) solvent. Due to the competition between temperature and polymer stiffness, there is a possibility for the phase transition between molten globule and crystal phase of a polymer to occur. The partition function of the model in the thermodynamic limit is obtained and analyzed as a function of polymer stiffness parameter s (Boltzmann weight), which for semi-flexible polymers can take on values over the interval (0,1). Other quantities, such as persistence length, specific heat and entropy, are obtained numerically and presented graphically as functions of stiffness parameter s.

scholarly journals Mechanical Response of Carbon Nanotube Bundle to Lateral Compression

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 27 ◽  
Author(s):  
Dina U. Abdullina ◽  
Elena A. Korznikova ◽  
Volodymyr I. Dubinko ◽  
Denis V. Laptev ◽  
Alexey A. Kudreyko ◽  
...  
Keyword(s):  
Phase Transition ◽  
Carbon Nanotube ◽  
Order Phase Transition ◽  
Mechanical Response ◽  
Van Der Waals ◽  
Van Der Waals Interactions ◽  
Structure Evolution ◽  
Biaxial Compression ◽  
Chain Model ◽  
Bending Rigidity

Structure evolution and mechanical response of the carbon nanotube (CNT) bundle under lateral biaxial compression is investigated in plane strain conditions using the chain model. In this model, tensile and bending rigidity of CTN walls, and the van der Waals interactions between them are taken into account. Initially the bundle in cross section is a triangular lattice of circular zigzag CNTs. Under increasing strain control compression, several structure transformations are observed. Firstly, the second-order phase transition leads to the crystalline structure with doubled translational cell. Then the first-order phase transition takes place with the appearance of collapsed CNTs. Further compression results in increase of the fraction of collapsed CNTs at nearly constant compressive stress and eventually all CNTs collapse. It is found that the potential energy of the CNT bundle during deformation changes mainly due to bending of CNT walls, while the contribution from the walls tension-compression and from the van der Waals energies is considerably smaller.

scholarly journals Phase transition of the Ising model on a fractal lattice

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
Jozef Genzor ◽  
Andrej Gendiar ◽  
Tomotoshi Nishino
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Fractal Lattice

scholarly journals DNA i-motif provides steel-like tough ends to chromosomes

2014 ◽  
Vol 1621 ◽  
pp. 135-141
Author(s):  
Raghvendra P. Singh ◽  
Ralf Blossey ◽  
Fabrizio Cleri
Keyword(s):  
Mechanical Properties ◽  
Molecular Dynamics ◽  
Tensile Strength ◽  
Mild Steel ◽  
Sampling Methods ◽  
Persistence Length ◽  
Biological Significance ◽  
Umbrella Sampling ◽  
Structural Proteins ◽  
Bending Rigidity

ABSTRACTWe studied the structure and mechanical properties of DNA i-motif nanowires by means of molecular dynamics computer simulations. We built up to 230 nm-long nanowires, based on a repeated TC5 sequence from NMR crystallographic data, fully relaxed and equilibrated in water. The unusual C●C+ stacked structure, formed by four ssDNA strands arranged in an intercalated tetramer, is here fully characterized both statically and dynamically. By applying stretching, compression and bending deformations with the steered molecular dynamics and umbrella sampling methods, we extract the apparent Young’s and bending moduli of the nanowire, as well as estimates for the tensile strength and persistence length. According to our results, i-motif nanowires share similarities with structural proteins, as far as their tensile stiffness, but are closer to nucleic acids and flexible proteins, as far as their bending rigidity is concerned. Curiously enough, their tensile strength makes such DNA fragments tough as mild steel or a nickel alloy. Besides their yet to be clarified biological significance, i-motif nanowires may qualify as interesting candidates for nanotechnology templates, due to such outstanding mechanical properties.

Characterizing titin's I-band Ig domain region as an entropic spring

1998 ◽  
Vol 111 (11) ◽  
pp. 1567-1574 ◽  
Author(s):  
W.A. Linke ◽  
M.R. Stockmeier ◽  
M. Ivemeyer ◽  
H. Hosser ◽  
P. Mundel
Keyword(s):  
Muscle Protein ◽  
Persistence Length ◽  
Thick Filament ◽  
Contour Length ◽  
Chain Model ◽  
Bending Rigidity ◽  
Force Extension ◽  
Average Force ◽  
Wormlike Chain ◽  
C Terminus

The poly-immunoglobulin domain region of titin, located within the elastic section of this giant muscle protein, determines the extensibility of relaxed myofibrils mainly at shorter physiological lengths. To elucidate this region's contribution to titin elasticity, we measured the elastic properties of the N-terminal I-band Ig region by using immunofluorescence/immunoelectron microscopy and myofibril mechanics and tried to simulate the results with a model of entropic polymer elasticity. Rat psoas myofibrils were stained with titin-specific antibodies flanking the Ig region at the N terminus and C terminus, respectively, to record the extension behaviour of that titin segment. The segment's end-to-end length increased mainly at small stretch, reaching approximately 90% of the native contour length of the Ig region at a sarcomere length of 2.8 microm. At this extension, the average force per single titin molecule, deduced from the steady-state passive length-tension relation of myofibrils, was approximately 5 or 2.5 pN, depending on whether we assumed a number of 3 or 6 titins per half thick filament. When the force-extension curve constructed for the Ig region was simulated by the wormlike chain model, best fits were obtained for a persistence length, a measure of the chain's bending rigidity, of 21 or 42 nm (for 3 or 6 titins/half thick filament), which correctly reproduced the curve for sarcomere lengths up to 3.4 microm. Systematic deviations between data and fits above that length indicated that forces of >30 pN per titin strand may induce unfolding of Ig modules. We conclude that stretches of at least 5–6 Ig domains, perhaps coinciding with known super repeat patterns of these titin modules in the I-band, may represent the unitary lengths of the wormlike chain. The poly-Ig regions might thus act as compliant entropic springs that determine the minute levels of passive tension at low extensions of a muscle fiber.

Fluctuations and Persistence Length of Charged Flexible Polymers

1995 ◽  
Vol 28 (17) ◽  
pp. 5921-5927 ◽  
Author(s):  
Hao Li ◽  
T. A. Witten
Keyword(s):  
Persistence Length ◽  
Flexible Polymers

PHASE TRANSITION OF A MODEL OF FLUID MEMBRANE

2000 ◽  
Vol 11 (03) ◽  
pp. 441-450 ◽  
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA
Keyword(s):  
Phase Transition ◽  
Piecewise Linear ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Bending Rigidity ◽  
Bending Energy ◽  
Random Surface ◽  
Spherical Surfaces ◽  
Fluid Membrane ◽  
Second Order Phase Transition

A model of fluid membrane, which is not self-avoiding, such as two-dimensional spherical random surface is studied by using Monte Carlo simulation. Spherical surfaces in R3 are discretized by piecewise linear triangle. Dynamical variables are the positions X of the vertices and the triangulation g. The action of the model is sum of area energy and bending energy times bending rigidity b. The bending energy and the specific heat are measured, and the critical exponents of the phase transitions are obtained by a finite-size scaling technique. We find that our model of fluid membrane undergoes a second order phase transition.

scholarly journals FLUCTUATIONS OF SINGLE CONFINED ACTIN FILAMENTS

2007 ◽  
Vol 02 (02) ◽  
pp. 155-166 ◽  
Author(s):  
SARAH KÖSTER ◽  
HOLGER STARK ◽  
THOMAS PFOHL ◽  
JAN KIERFELD
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Correlation Function ◽  
Monte Carlo Simulations ◽  
Actin Filaments ◽  
Persistence Length ◽  
Mesh Size ◽  
Thermal Fluctuations ◽  
Approximation Formula ◽  
Bending Rigidity

Thermal fluctuations of individual actin filaments confined in rectangular microchannels with dimensions similar to the mesh size of the cytoskeleton in eukaryotic cells are studied experimentally using fluorescence microscopy and theoretically by a combination of analytical methods and Monte Carlo simulations. Compared to freely fluctuating filaments, long filaments confined in narrow channels exhibit enhanced tangent correlations and a characteristic shape of their correlation function. The tangent correlation function is calculated analytically by approximating the confining geometry by a parabolic potential. This approximation is validated by Monte Carlo simulations. For the quantitative analysis of experimental data additional corrections for image analysis effects have to be included, for which we provide a modified analytical approximation formula which is corroborated by simulations. This allows us to obtain both the persistence length LP describing the bending rigidity of the polymer and the deflection length λ characterizing confinement effects from fits to the experimental data. Our results confirm the scaling relation λ ∝ d2/3 between the deflection length and the channel width d.

Temperature dependence of DNA condensation at high ionic concentration

2016 ◽  
Vol 30 (21) ◽  
pp. 1650298 ◽  
Author(s):  
Wei Mao ◽  
Qingqing Gao ◽  
Yanhui Liu ◽  
Yangtao Fan ◽  
Lin Hu ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
Autocorrelation Function ◽  
Persistence Length ◽  
Periodic Oscillation ◽  
Dna Condensation ◽  
Condensation Process ◽  
Bending Rigidity ◽  
Buffer Solution ◽  
Multivalent Cation ◽  
Axis Length

A series of experiments pointed out that compact states of DNA condensed by multivalent cation prefer higher temperature. The condensed DNA takes elongated coil or compact globule states and the population of the compact globule states increases with an increase in temperature. At the same time, a recent experimental work carried out in buffer solution without multivalent cation points out that DNA persistence length strongly depends on the temperature. DNA persistence length is a key parameter for quantitative interpretation of the conformational properties of DNA and related to the bending rigidity of DNA. It is necessary to revolve the effects of temperature dependence of persistence length on DNA condensation, and a model including the temperature dependence of persistence length and strong correlation of multivalent cation on DNA is provided. The autocorrelation function of the tangent vectors is found as an effective way to detect the temperature dependence of toroid conformations. With an increase in temperature, the first periodic oscillation in the autocorrelation function shifts left and the number of segments containing the first periodic oscillation decreases gradually. According to the experiments mentioned above, the long-axis length is defined to estimate the temperature dependence of condensation process further. At the temperatures defined in experiments mentioned above, the relation between long-axis length and temperature matches the experimental results.

VARIATIONAL APPROACH TO THE PHASE DIAGRAM OF RIGID MEMBRANES

1993 ◽  
Vol 07 (27) ◽  
pp. 4615-4629
Author(s):  
U. MARINI BETTOLO MARCONI ◽  
A. MARITAN
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Euclidean Space ◽  
Mean Curvature ◽  
Variational Approach ◽  
Gaussian Approximation ◽  
Dimensional Euclidean Space ◽  
Bending Rigidity ◽  
Elastic Networks ◽  
The Mean

D-dimensional elastic networks randomly embedded in a d>D dimensional euclidean space, are studied employing Hartree (Gaussian) approximation. In presence of an energy depending on the mean curvature this approach leads to the prediction of a phase transition between a flat and a crumpled regime as the bending rigidity decreases in agreement with previous approximate calculations.

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