Curvature Induced Discontinuous Transition for Semiflexible Biopolymers

Zhou, Zicong; Lin, Fang-ting; Hung, Chin-Yi; Wu, Haoyun; Chen, Bo-Hen

doi:10.7566/jpsj.83.044802

Cited by 12 publications

(25 citation statements)

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“…There are two elastic models for a 2D intrinsically curved filament [18,[25][26][27]. The energy of the model 1 is [18,21,22,[25][26][27]…”

Section: D Modelsmentioning

confidence: 99%

“…In this model, q |˙| is curvature. These two models have very different mechanical properties [21,22,27]. Especially, model 1 shows a discontinuous change in z(L) with a varying f [21,22]; but there is no such a transition in model 2 [27].…”

Section: D Modelsmentioning

confidence: 99%

“…Meanwhile, with a long-range correlation in sequence, dsDNA develops a macroscopic (intrinsic) curvature so that WLC model fails to account for its property [18]. Moreover, an intrinsically curved filament has complete different mechanical properties from that of WLC and WLRC models [9,10,[19][20][21][22][23][24]. In 3D case, both exact theoretical analysis and experimental observation revealed that an intrinsically curved and twisted biopolymer can form a stable helix and under an applied force the extension of helix can subject to a discontinuous transition [9,10,19,20,23,24].…”

mentioning

confidence: 99%

“…In 3D case, both exact theoretical analysis and experimental observation revealed that an intrinsically curved and twisted biopolymer can form a stable helix and under an applied force the extension of helix can subject to a discontinuous transition [9,10,19,20,23,24]. On the other hand, in two-dimensional (2D) case it has been shown that a finite IC alone is enough to induce a discontinuous transition in extension for a stretched filament [21,22]. Since it is uneasy to realize an ideal 2D system, to compare with experiment it should be better to study a 3D system to check whether a nonvanishing IC alone is enough to induce the discontinuous transition.…”

mentioning

confidence: 99%

“…In this paper we answer this question. On a 2D system, we have to recall that there are two planar elastic models for an intrinsically curved filament, and they have quite different mechanical properties [18,21,22,[25][26][27]. Especially, the extension of model 1 can undergo a discontinuous transition under a stretching force [21,22]; but the extension of model 2 is always a smooth concave function of applied force [22].…”

mentioning

confidence: 99%

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Novel relationships between some coordinate systems and their effects on mechanics of an intrinsically curved filament

Zhou

2018

J. Phys. Commun.

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The fixed frame, Frenet-Serret frame and generalized Frenet-Serret frame are commonly used coordinate systems in the study of a filament or a moving rigid body. In terms of Eulerian angles, we derive some relations in these frames and apply these relations to find some significant results. Especially, we find the angle between the normal of centerline of a filament and the line of nodes which is the crossover between the horizontal plane of fixed frame and normal plane of centerline. We prove that the general solution of a set of nonlinear differential equations represents a circular helix or the corresponding filament has a unique helical ground-state configuration. We show that the effective description of a planar filament depends on the value of its torsional modulus. Finally, we find the expression of energy for a three-dimensional intrinsically curved filament when its cross-section area vanishes, and show that under an applied force the finite intrinsic curvature alone can induce a discontinuous transition in extension.The conformal and mechanical properties of a filament depend on its intrinsic properties and external physical conditions. In elastic theory, the intrinsic properties are usually characterized by some macroscopic parameters [1,2,[4][5][6][7][8][9][10], such as bending rigidity, twisting rigidity and inertia tensor. On the other hand, external conditions are often referred to as applied forces, applied torques and boundary conditions (BCs). Focusing on different physical properties results in different elastic models. The simplest model is the wormlike chain (WLC) model [11][12][13][14] which views a filament as an inextensible chain with a certain bending rigidity but a vanishing cross-section area. Owing to its slender shape, a semiflexible biopolymer is usually modeled as a filament so that the WLC model has been used to account for the entropic elasticity of some semiflexible biopolymers successfully [11][12][13][14]. Another often used model is the wormlike rod chain (WLRC) model [6,[12][13][14][15][16][17] which regards a filament as a chain with a nonvanishing intrinsic twist and a circular cross-section. The WLRC model has been applied successfully to explain supercoiling properties of some double stranded DNA (dsDNA). Both WLC and WLRC models are intrinsically straight or both of them have a vanishing IC. In other words, free of external force and torque, their ground-state configurations (GSCs, or spontaneous configurations, i.e., the configurations with the lowest energy) are a straight line and a cylinder with straight centerline, respectively. Moreover, at a finite temperature (T) the extension of both models is a smooth function of applied force.However, filaments or semiflexible biopolymers are not always intrinsically straight. For instance, for short dsDNA chains, special sequence orders favor a finite IC [33][34][35][36]. Meanwhile, with a long-range correlation in sequence, dsDNA develops a macroscopic (intrinsic) curvature so that WLC model fails to account for its propert...

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“…There are two elastic models for a 2D intrinsically curved filament [18,[25][26][27]. The energy of the model 1 is [18,21,22,[25][26][27]…”

Section: D Modelsmentioning

confidence: 99%