Metastable intermediates in the condensation of semiflexible polymers

Schnurr, Bernhard; Gittes, Frederick; MacKintosh, F. C.

doi:10.1103/physreve.65.061904

Cited by 74 publications

(117 citation statements)

References 37 publications

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“…Also, the scaling property r c ∼ L 1 5 matches the one in [4,7,8]. Similarly, the mean radius of the toroidal cross section can be calculated for the complete hexagonal cross section with a side of (n + 1) monomers [5]:…”

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confidence: 58%

Effect of interaction shape on the condensed toroid of the semiflexible chain

Ishimoto

Kikuchi

2008

The Journal of Chemical Physics

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Abstract. -We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviours of the mean toroidal and cross sectional radii, rc and rcross, as functions of the contour length L:) for the van der Waals type, ν = (− ) for the Coulomb type, ν = (−1, 1) for the delta function type attractions in the asymptotic limit. For the toroids with finite winding number Nc = 100 ∼ 400, we find ν ≃ 0 for the Yukawa interaction with screening parameter κ = 0.5 ∼ 1.0, and ν = 0.1 ∼ 0.13 for the van der Waals type interactions. These findings could provide possible explanation for the experimentally well known observation ν ≃ 0 of the condensed DNA toroids. Conformational transitions are also discussed.Condensed DNA toroid and its conformational properties have been of great interest, for instance, as a possible candidate for gene delivery in gene therapy [1,2]. Although condensed DNA toroids have been heavily investigated in experiment and theory ( [3-5] and the references therein), it remains unclear what physical factors determine the toroidal sizes [2]. In fact, there is experimentally well known observation that the radius of DNA toroid r c is independent of chain contour length L = 400−50, 000bp (132.8 nm−16.6 µm): r c ∼ L ν with ν ≃ 0 [6]. In most analytic works, phenomenological free energy models balance the bending and surface free energies to estimate toroidal properties. The predicted scaling relation for the mean toroid radius is r c ∼ L ν with ν = 1 5 for large L [4, 7, 8]. This is however inconsistent to the experimental observation.In this letter, we show how different microscopic interactions qualitatively modifies physical properties of the toroid, in particular, the mean toroidal and cross sectional radii. To achieve this, we first propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. We then specify the explicit forms of attractive interactions, namely delta-function, van der Waals, and Yukawa (screened Coulomb) type interactions. We show exponents of the mean toroidal and cross sectional radii in the large L (or equivalently large dominant winding number N c ) limit are categorised into three distinct groups for different interactions. For experimentally realistic winding numbers N c = 100 ∼ 400, we find ν ≃ 0 for the Yukawa interaction with inverse screening length κ = 0.5 ∼ 1.0 and ν = 0.1 ∼ 0.13 for the van der Waals type interactions. We also describe conformational transitions.Theory. -We propose the general Hamiltonian of a tightly packed toroid, with any type of short/long-range attractive interactions between segments:Gap(N ) . l denotes the persistence length of the semiflexible polymer chain of total contour length L. l is assumed to be large enough relative to the bond length l b to realise its ...

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confidence: 58%

Effect of interaction shape on the condensed toroid of the semiflexible chain

Ishimoto

Kikuchi

2008

The Journal of Chemical Physics

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“…Section 3.2 presents a more quantitative description of the collapsed states in term of the correlation function between tangent vectors along the chain and of the energy levels associated with each different collapsed state, which confirm that the toroid is the stable configuration, and show how the collapse proceeds through a cascade of subsequently more energetic favorable metastable states -the various multiple headed racquets shapes, as predicted from theory [23]. The decay rate of uncollapsed states is investigated as a function of a proper combination of L, L 0 and L p in Section 3.3, together with a statistical analysis of the preferred collapsed configurations.…”

Section: Resultsmentioning

confidence: 87%

“…Flexible chains expand in shear flow, i.e., the average end to end distance increases while the molecules tend to orient with the flow; the effect of the flow is therefore counteracting that of the attractive forces, which tend to form compact globula. Stiff semiflexible chains, with L p ≥ L shrink in shear flow, due to a buckling instability [25]; such rigid chain however would not collapse to form tori and multiple racquets in bad solvent, as the open, rod-like shape is stable at equilibrium [23]. In this work, we consider the collapse dynamics of less stiff semiflexible molecules: is not clear a priori what to expect for the collapse dynamics under shear flow.…”

Section: Effect Of Shear Flowmentioning

confidence: 99%

Collapse of a semiflexible polymer in poor solvent

2004

Self Cite

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We investigate the dynamics and the pathways of the collapse of a single, semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations. Earlier work indicates that the condensation of semiflexible polymers generically proceeds via a cascade through metastable racquet-shaped, longlived intermediates towards the stable torus state. We investigate the rate of decay of uncollapsed states, analyze the preferential pathways of condensation, and describe likelihood and lifespan of the different metastable states. The simulation are performed with a bead-stiff spring model with excluded volume interaction and exponentially decaying attractive potential. The semiflexible chain collapse is studied as functions of the three relevant length scales of the phenomenon, i.e., the total chain length L, the persistence length Lp and the condensation length L0 = kBT Lp/u0, where u0 is a measure of the attractive potential per unit length. Two dimensionless ratios, L/Lp and L0/Lp, suffice to describe the decay rate of uncollapsed states, which appears to scale as (L/Lp) 1/3 (L0/Lp). The condensation sequence is described in terms of the time series of the well separated energy levels associated with each metastable collapsed state. The collapsed states are described quantitatively through the spatial correlation of tangent vectors along the chain. We also compare the results obtained with a locally inextensible bead-rod chain and with a phantom bead-spring model. Finally, we show preliminary results on the effects of steady shear flow on the kinetics of collapse.

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“…1 d and e). After completing our analysis, we became aware of recent work on the role of this shape in the collapse of semiflexible polymer chains (36,37). Here we will consider only the zero-temperature aspects of this problem.…”

Section: Racketsmentioning

confidence: 99%

Kinks, rings, and rackets in filamentous structures

Cohen

Mahadevan

2003

Proc. Natl. Acad. Sci. U.S.A.

178

170

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Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and ''tennis racket'' shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important determinant of the morphology than any molecular details. Our mesoscopic continuum theory is capable of quantifying observations of these structures and is suggestive of their occurrence in other filamentous assemblies as well.S mall self-assembled structures are common in biology, chemistry, and condensed matter physics. The rich morphology that these structures exhibit arises from a combination of shortand long-range forces, often mediated by the presence of thermal fluctuations and hydrodynamic forces. From a geometrical perspective, the simplest self-assembling structures arise from the interaction between particles (monomers) and lead to the formation of globules and filaments. At the next level of complexity, filaments can aggregate into higher-order structures such as helices, rings, tapes, sheets, etc. At the mesoscopic level, the interactions within a filament may be represented by longwavelength elastic deformations due to stretching, bending, and shear, whereas the complex interactions between filaments can be replaced by a simple short-range adhesive potential. In a variety of systems such as organic and inorganic nanotubes as well as stiff biopolymers, the stretching and shear deformation modes are energetically expensive relative to the bending modes, so that the filaments may be approximated as inextensible. In such cases, the competition between bending elasticity and adhesion is sufficient to explain the shapes seen in filamentous aggregates. We address the equilibrium morphologies of kinks, rings, and rackets in these systems.First we review the linear mechanics of thin rods and consider the conditions under which a classical description suffices. The stiffness of a rod is measured by its bending constant, YI, where Y [N͞m 2 ] is the Young's modulus of the material, and I[m 4 ] is the area moment of inertia given by the second moment of the mass distribution in a cross-section perpendicular to the axis of symmetry. § The bending energy per unit length is YI 2 ͞2, where is the curvature.Thermal fluctuations bend a rod on the scale of its persistence length, l p ϭ YI͞k B T. These are the approximate room temperature persistence lengths of the rods considered below: Limulus acrosome, 2.7 m; single-walled carbon nanotube (SWNT), 45 m; sickle-cell hemoglobin (S hemoglobin) fiber, 240 m; microtubule, 6 mm. The persistence length of a multiwalled carbon nanotube (MWNT) depends on the number of shells but is always much greater than that of a SWNT. In each case, the persistence length is much greater than the actual length of the rod, so thermal fluctuations are negligible. Thermal fluctuations may be introduced as a weak perturbation in these systems (1), but we do not do so here. KinksWe start by examining kinked helices in MWNTs and in the acrosome of horseshoe c...

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Metastable intermediates in the condensation of semiflexible polymers

Cited by 74 publications

References 37 publications

Effect of interaction shape on the condensed toroid of the semiflexible chain

Effect of interaction shape on the condensed toroid of the semiflexible chain

Collapse of a semiflexible polymer in poor solvent

Kinks, rings, and rackets in filamentous structures

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