Fluctuating nonlinear spring theory: Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra: Fluctuating Nonlinear Spring theory strength and toughness of virus particles

Farkhad Maksudov, Olga Kononova, Aida Llauró, Alvaro Ortega-Esteban, Trevor Douglas, Gabriela N. Condenzo, Carmen San Martín, Kenneth A. Marx, Gijs J.L. Wuite, Wouter H. Roos, Pedro J. de Pablo*, Valeri Barsegov

*Corresponding author for this work

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Abstract

We developed the Fluctuating Nonlinear Spring (FNS) model to describe the dynamics of mechanical deformation of biological particles, such as virus capsids. The theory interprets the force-deformation spectra in terms of the “Hertzian stiffness” (non-linear regime of a particle's small-amplitude deformations), elastic constant (large-amplitude elastic deformations), and force range in which the particle's fracture occurs. The FNS theory enables one to quantify the particles’ elasticity (Young's moduli for Hertzian and bending deformations), and the limits of their strength (critical forces, fracture toughness) and deformability (critical deformations) as well as the probability distributions of these properties, and to calculate the free energy changes for the particle's Hertzian, elastic, and plastic deformations, and eventual fracture. We applied the FNS theory to describe the protein capsids of bacteriophage P22, Human Adenovirus, and Herpes Simplex virus characterized by deformations before fracture that did not exceed 10–19% of their size. These nanoshells are soft (~1–10-GPa elastic modulus), with low ~50–480-kPa toughness – a regime of material behavior that is not well understood, and with the strength increasing while toughness decreases with their size. The particles’ fracture is stochastic, with the average values of critical forces, critical deformations, and fracture toughness comparable with their standard deviations. The FNS theory predicts 0.7-MJ/mol free energy for P22 capsid maturation, and it could be extended to describe uniaxial deformation of cylindrical microtubules and ellipsoidal cellular organelles.

Original languageEnglish
Pages (from-to)263-277
Number of pages15
JournalActa Biomaterialia
Volume122
Early online date28 Dec 2020
DOIs
Publication statusPublished - 1 Mar 2021

Funding

We thank Beate Sodeik (Medizinische Hochschule Hannover) for the collaboration on Herpes Simplex Virus and Joost Snijder (Universiteit Utrecht) for the AFM experiments on these particles. This work was supported by the NSF (grant DMR-1505316 ) and NIH (grant R01HL148227 ) to VB, by the Spanish Ministry of Economy, Industry and Competitiveness projects (FIS2017- 89549-R; “Maria de Maeztu”), Program for Units of Excellence in R&D (MDM-2014–0377 and FIS2017–90701-REDT) and Human Frontiers Science Program (HFSPO RGP0012/2018) to PJP, and by Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO) Vidi grant to WHR. CSM and GNC were supported by grants Q19PID2019–104098GB-I00/AEI/10.13039/501100011033 and BFU2016–74868-P, co-funded by the Spanish State Research Agency and the European Regional Development Fund , as well as grants BFU2013–41249-P and BIO2015–68990-REDT (Spanish Adenovirus Network, AdenoNet) from the Spanish Ministry of Economy, Industry and Competitiveness; and the Agencia Estatal CSIC (2019AEP045). The CNB-CSIC was further supported by a Severo Ochoa Excellence grant (SEV 2017–0712).

FundersFunder number
Agencia Estatal CSICSEV 2017–0712
Beate Sodeik
HFSPORGP0012/2018
Spanish Ministry of Economy, Industry and Competitiveness projectsFIS2017- 89549-R, FIS2017–90701-REDT, MDM-2014–0377
National Science FoundationDMR-1505316
National Institutes of Health
National Heart, Lung, and Blood InstituteR01HL148227
Human Frontier Science Program
Nederlandse Organisatie voor Wetenschappelijk OnderzoekBFU2016–74868-P, Q19PID2019–104098GB-I00/AEI/10.13039/501100011033
Medizinischen Hochschule Hannover
European Regional Development FundBFU2013, BFU2013–41249-P, 41249-P, 68990-REDT, BIO2015, BIO2015–68990-REDT
Ministerio de Economía, Industria y Competitividad, Gobierno de España
Agencia Estatal de Investigación2019AEP045

    Keywords

    • Fluctuating nonlinear spring (FNS) model
    • Force-deformation spectra
    • Fracture toughness
    • Probability distribution of critical deformations
    • Probability distribution of critical forces

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