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Pensalfini M, Golde T, Trepat X, Arroyo M. Nonaffine Mechanics of Entangled Networks Inspired by Intermediate Filaments. PHYSICAL REVIEW LETTERS 2023; 131:058101. [PMID: 37595243 DOI: 10.1103/physrevlett.131.058101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 05/04/2023] [Accepted: 06/02/2023] [Indexed: 08/20/2023]
Abstract
Inspired by massive intermediate filament (IF) reorganization in superstretched epithelia, we examine computationally the principles controlling the mechanics of a set of entangled filaments whose ends slide on the cell boundary. We identify an entanglement metric and threshold beyond which random loose networks respond nonaffinely and nonlinearly to stretch by self-organizing into structurally optimal star-shaped configurations. A simple model connecting cellular and filament strains links emergent mechanics to cell geometry, network topology, and filament mechanics. We identify a safety net mechanism in IF networks and provide a framework to harness entanglement in soft fibrous materials.
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Affiliation(s)
- Marco Pensalfini
- Laboratori de Càlcul Numeric (LaCàN), Universitat Politècnica de Catalunya-BarcelonaTech, 08034 Barcelona, Spain
| | - Tom Golde
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST), 08028 Barcelona, Spain
| | - Xavier Trepat
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST), 08028 Barcelona, Spain
- Departament de Biomedicina, Facultat de Medicina, Universitat de Barcelona, 08036 Barcelona, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain
- Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 08028 Barcelona, Spain
| | - Marino Arroyo
- Laboratori de Càlcul Numeric (LaCàN), Universitat Politècnica de Catalunya-BarcelonaTech, 08034 Barcelona, Spain
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST), 08028 Barcelona, Spain
- Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), 08034 Barcelona, Spain
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Tsirigoni AM, Goktas M, Atris Z, Valleriani A, Vila Verde A, Blank KG. Chain Sliding versus β-Sheet Formation upon Shearing Single α-Helical Coiled Coils. Macromol Biosci 2023; 23:e2200563. [PMID: 36861255 DOI: 10.1002/mabi.202200563] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 02/20/2023] [Indexed: 03/03/2023]
Abstract
Coiled coils (CCs) are key building blocks of biogenic materials and determine their mechanical response to large deformations. Of particular interest is the observation that CC-based materials display a force-induced transition from α-helices to mechanically stronger β-sheets (αβT). Steered molecular dynamics simulations predict that this αβT requires a minimum, pulling speed-dependent CC length. Here, de novo designed CCs with a length between four to seven heptads are utilized to probe if the transition found in natural CCs can be mimicked with synthetic sequences. Using single-molecule force spectroscopy and molecular dynamics simulations, these CCs are mechanically loaded in shear geometry and their rupture forces and structural responses to the applied load are determined. Simulations at the highest pulling speed (0.01 nm ns-1 ) show the appearance of β-sheet structures for the five- and six-heptad CCs and a concomitant increase in mechanical strength. The αβT is less probable at a lower pulling speed of 0.001 nm ns-1 and is not observed in force spectroscopy experiments. For CCs loaded in shear geometry, the formation of β-sheets competes with interchain sliding. β-sheet formation is only possible in higher-order CC assemblies or in tensile-loading geometries where chain sliding and dissociation are prohibited.
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Affiliation(s)
- Anna-Maria Tsirigoni
- Max Planck Institute of Colloids and Interfaces, Mechano(bio)chemistry, Am Mühlenberg 1, 14476, Potsdam, Germany.,Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Am Mühlenberg 1, 14476, Potsdam, Germany
| | - Melis Goktas
- Max Planck Institute of Colloids and Interfaces, Mechano(bio)chemistry, Am Mühlenberg 1, 14476, Potsdam, Germany
| | - Zeynep Atris
- Max Planck Institute of Colloids and Interfaces, Mechano(bio)chemistry, Am Mühlenberg 1, 14476, Potsdam, Germany.,Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Am Mühlenberg 1, 14476, Potsdam, Germany
| | - Angelo Valleriani
- Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Am Mühlenberg 1, 14476, Potsdam, Germany
| | - Ana Vila Verde
- University of Duisburg-Essen, Faculty of Physics, Lotharstrasse 1, 47057, Duisburg, Germany
| | - Kerstin G Blank
- Max Planck Institute of Colloids and Interfaces, Mechano(bio)chemistry, Am Mühlenberg 1, 14476, Potsdam, Germany.,Johannes Kepler University Linz, Institute of Experimental Physics, Department of Biomolecular & Selforganizing Matter, Altenberger Strasse 69, Linz, 4040, Austria
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Huang S, Sun C, Purohit PK, Reina C. Harnessing fluctuation theorems to discover free energy and dissipation potentials from non-equilibrium data. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2021; 149:104323. [PMID: 33612859 PMCID: PMC7894616 DOI: 10.1016/j.jmps.2021.104323] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The Jarzynski relation, as an equality form of the second law of thermodynamics, represents an exact thermodynamic statement that is valid arbitrarily far away from equilibrium. This remarkable relation directly links the equilibrium free energy difference between two states and the probability distribution of the work done along a process that drives the system from one state to the other. Here, we leverage the Jarzynski equality and a local equilibrium assumption, to go beyond the calculation of free energy differences and also extract the dissipation potential from additional measurements of kinematic field variables (strain and velocity fields). The proposed strategy is exemplified over pulling experiments of mass-spring models obeying overdamped Langevin dynamics, which is a prototype for nanorods, fibrous macro-molecules and the Rouse model of polymers. Different interaction potentials, fluid viscosities and bath temperatures are studied, so as to intrinsically control how close or far away the system is from equilibrium. The data-inferred continuum models are then validated against processes governed by different pulling protocols, thereby demonstrating their predictive capability. The methods presented here represent a first step toward full material characterization from non-equilibrium data of macroscopic observables, which could potentially be obtained from experimental observations.
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Bergues-Pupo AE, Lipowsky R, Vila Verde A. Unfolding mechanism and free energy landscape of single, stable, alpha helices at low pull speeds. SOFT MATTER 2020; 16:9917-9928. [PMID: 33030193 DOI: 10.1039/d0sm01166e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Single alpha helices (SAHs) stable in isolated form are often found in motor proteins where they bridge functional domains. Understanding the mechanical response of SAHs is thus critical to understand their function. The quasi-static force-extension relation of a small number of SAHs is known from single-molecule experiments. Unknown, or still controversial, are the molecular scale details behind those observations. We show that the deformation mechanism of SAHs pulled from the termini at pull speeds approaching the quasi-static limit differs from that of typical helices found in proteins, which are stable only when interacting with other protein domains. Using molecular dynamics simulations with atomistic resolution at low pull speeds previously inaccessible to simulation, we show that SAHs start unfolding from the termini at all pull speeds we investigated. Unfolding proceeds residue-by-residue and hydrogen bond breaking is not the main event determining the barrier to unfolding. We use the molecular simulation data to test the cooperative sticky chain model. This model yields excellent fits of the force-extension curves and quantifies the distance, xE = 0.13 nm, to the transition state, the natural frequency of bond vibration, ν0 = 0.82 ns-1, and the height, V0 = 2.9 kcal mol-1, of the free energy barrier associated with the deformation of single residues. Our results demonstrate that the sticky chain model could advantageously be used to analyze experimental force-extension curves of SAHs and other biopolymers.
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Affiliation(s)
- Ana Elisa Bergues-Pupo
- Max Planck Institute of Colloids and Interfaces, Department of Theory & Bio-Systems, Am Mühlenberg 1, 14476 Potsdam, Germany.
| | - Reinhard Lipowsky
- Max Planck Institute of Colloids and Interfaces, Department of Theory & Bio-Systems, Am Mühlenberg 1, 14476 Potsdam, Germany.
| | - Ana Vila Verde
- Max Planck Institute of Colloids and Interfaces, Department of Theory & Bio-Systems, Am Mühlenberg 1, 14476 Potsdam, Germany.
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Sun C, Purohit PK. Stick-slip kinetics in a bistable bar immersed in a heat bath. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2019; 180-181:205-220. [PMID: 32831392 PMCID: PMC7442296 DOI: 10.1016/j.ijsolstr.2019.07.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Structural transitions in some rod-like biological macromolecules under tension are known to proceed by the propagation through the length of the molecule of an interface separating two phases. A continuum mechanical description of the motion of this interface, or phase boundary, takes the form of a kinetic law which relates the thermodynamic driving force across it with its velocity in the reference configuration. For biological macromolecules immersed in a heat bath, thermally activated kinetics described by the Arrhenius law is often a good choice. Here we show that 'stick-slip' kinetics, characteristic of friction, can also arise in an overdamped bistable bar immersed in a heat bath. To mimic a rod-like biomolecule we model the bar as a chain of masses and bistable springs moving in a viscous fluid. We conduct Langevin dynamics calculations on the chain and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. Our kinetic relation could be applied to rod-like biomolecules, such as, DNA and coiled-coil proteins which exhibit structural transitions that depend on both temperature and loading rate.
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Affiliation(s)
- Chuanpeng Sun
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Prashant K Purohit
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
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