Rupture dynamics in model polymer systems

Borah, Rupam; Debnath, Pallavi

doi:10.1039/c6sm00711b

Cited by 2 publications

(10 citation statements)

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“…We are interested in one such generic model of rupture [46], initially inspired by the experiments on wood and bone with hierarchical structures exhibiting relative motion at each level of hierarchy on tensile loading [22,23,47,48]. In wood, the matrix of hemicelluloses and lignin embed the constituent tube-shaped wood cells.…”

Section: Introductionmentioning

confidence: 99%

“…The molecular-level understanding of the tensile strength in these hierarchical structures is inadequate and remains an active area of research [47,[49][50][51][52][53]. Minimally, we began by modeling the mechanical response at the single polymer level by a generic onedimensional rupture model [46], where a constant force acts on a polymeric transducer attached to a parallel rigid plate by interconnecting bonds that rupture stochastically. The polymeric transducer is a bead-spring polymer, and a two-state discreet variable describes the state of interconnecting bonds, resulting in coupled equations of motion for the bead and bond dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The polymeric transducer is a bead-spring polymer, and a two-state discreet variable describes the state of interconnecting bonds, resulting in coupled equations of motion for the bead and bond dynamics. We obtained a closed-form solution of the rupture front [46] until complete rupture without the system slipping to a steady state, as generally observed in the relative motion of surfaces, primarily because the minimal model lacked any resistance to rupture. Towards this direction, in this paper, we generalize the generic one-dimensional rupture model from our earlier work [46] to include stochastic rebinding between ruptured interconnecting bonds.…”

Section: Introductionmentioning

confidence: 99%

“…We can consider our generic rupture and rebinding model as a variant of the same earthquake model [5,6], where polymer beads replace the sliding blocks, and each bead is attached to a single interconnecting bond. Rate equations govern the rupture and rebinding events and the stochasticity by a random variable [4,46], which makes the stochastic problem intractable. We, therefore, develop a mean-field formalism (MF) [46] for analytical tractability to obtain deterministic equations of motion for (coupled) bead and bond dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Rate equations govern the rupture and rebinding events and the stochasticity by a random variable [4,46], which makes the stochastic problem intractable. We, therefore, develop a mean-field formalism (MF) [46] for analytical tractability to obtain deterministic equations of motion for (coupled) bead and bond dynamics. The resulting equation for the steady state for bead dynamics is highly nonlinear and inhomogeneous and excludes a direct numerical solution with standard methods.…”

Section: Introductionmentioning

confidence: 99%

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Solution of steady state in the model polymer system with rupture and rebinding

Shukla,

Pathak,

Debnath

2024

Phys. Scr.

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In this paper, we study the steady state attained in our model polymer system that attempts to explain the relative motion between soft rubbing surfaces at the single polymer level. We generalize our one-dimensional model [Borah et al., 2016 Soft Matter 12 4406] by including the rebinding of interconnecting bonds between a flexible transducer (bead spring polymer) and a rigid fixed plate. The interconnecting bonds described as harmonic springs rupture and rebind stochastically when a constant force pulls the flexible transducer. We obtain a distinct steady state in stochastic simulations of the model when the bead positions and the bond states (closed or open) are independent of time, analogous to creep states in frictional systems and rupture termination states in earthquakes. The simulation results of the stochastic model for specific parameter sets agree with the numerical solution to the mean-field equations developed for analytical tractability. We develop an analytical solution for the steady state within the homotopy analysis method, which converges and agrees well with the numerical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solution of steady state in the model polymer system with rupture and rebinding

Shukla,

Pathak,

Debnath

2024

Phys. Scr.

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Strength and stability of active ligand-receptor bonds: A microtubule attached to a wall by molecular motor tethers

2018

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We develop a stochastic kinetic model of a pre-formed attachment of a mictrotuble (MT) with a cell cortex, in which the MT is tethered to the cell by a group of active motor proteins. Such an attachment is a particularly unique case of ligand-receptor bonds: The MT ligand changes its length (and thus binding sites) with time by polymerization-depolymerization kinetics, while multiple motor receptors tend to walk actively along the MT length. These processes, combined with force-mediated unbinding of the motors, result in an elaborate behavior of the MT connection to the cell cortex. We present results for the strength and lifetime of the system through the well-established force-clamp and force-ramp protocols when external tension is applied to the MT. The simulation results reveal that the MT-cell attachment behaves as a catch-bond or slip-bond depending on system parameters. We provide analytical approximations of the lifetime and discuss implications of our results on in-vitro experiments.Chromosome segregation is the most important process during the mitosis phase of cell cycle [1]. In eukaryotic cells, sister chromatids, that result from chromosome replication, are segregated by a complex multi-component machine called mitotic spindle [2][3][4]. Microtubule (MT) [5], a stiff tubular filament, whose typical diameter is about 25 nm, forms a major component of the scaffolding of the spindle. A MT is a polar filament in the sense that its two ends are dissimilar; the plus end is more dynamic than the minus end. During the morphogenesis of the spindle [6,7], MTs form transient molecular joints (non-covant bonds) with specific partners. The attachments of the MTs with the chromosomes, mediated by a proteineous complex called kinetochore [8,9], has been under intense investigation in recent years. The forces exerted by these MTs on the kinetochores eventually pull the two sister chromatids apart in the late stages of mitosis thereby driving their journeys to the opposite poles of the spindle [10,11]. In contrast, another set of MTs, called astral MT, diverge from the spindle poles and their distal ends (the so-called plus ends) form contacts with the cell cortex. The kinetochore-MT attachment has been under intense investigation in recent years for the obviously important role it plays in timely and accurate segregation of the chromosomes. However, in this paper we focus exclusively on the MT-cortex attachment.Understanding the physics of the attachment formed by a single MT with the cortex is the first step in ultimately understanding how forces generated by all such attachments collectively determine the position and orientation of the spindle [12][13][14][15][16]. The studies reported in this paper are important also from the perspective of research on MTs and cytoskeletal motor proteins that use MT as the 'track' [17,18], particularly those which play crucial force-coupling roles by residing at the plus end [19][20][21]. Moreover, in spite of the simplicity of the system of our study where only a single MT is a...

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Rupture dynamics in model polymer systems

Cited by 2 publications

References 30 publications

Solution of steady state in the model polymer system with rupture and rebinding

Solution of steady state in the model polymer system with rupture and rebinding

Strength and stability of active ligand-receptor bonds: A microtubule attached to a wall by molecular motor tethers

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