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Di Terlizzi I, Gironella M, Herraez-Aguilar D, Betz T, Monroy F, Baiesi M, Ritort F. Variance sum rule for entropy production. Science 2024; 383:971-976. [PMID: 38422150 DOI: 10.1126/science.adh1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 01/09/2024] [Indexed: 03/02/2024]
Abstract
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.
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Affiliation(s)
- I Di Terlizzi
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - M Gironella
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 40530 Gothenburg, Sweden
| | - D Herraez-Aguilar
- Facultad de Ciencias Experimentales, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - T Betz
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), University of Göttingen, Göttingen, Germany
| | - F Monroy
- Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía, 28041 Madrid, Spain
| | - M Baiesi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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Salinas-Almaguer S, Mell M, Almendro-Vedia VG, Calero M, Robledo-Sánchez KCM, Ruiz-Suarez C, Alarcón T, Barrio RA, Hernández-Machado A, Monroy F. Membrane rigidity regulates E. coli proliferation rates. Sci Rep 2022; 12:933. [PMID: 35042922 PMCID: PMC8766614 DOI: 10.1038/s41598-022-04970-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2021] [Accepted: 01/04/2022] [Indexed: 12/23/2022] Open
Abstract
Combining single cell experiments, population dynamics and theoretical methods of membrane mechanics, we put forward that the rate of cell proliferation in E. coli colonies can be regulated by modifiers of the mechanical properties of the bacterial membrane. Bacterial proliferation was modelled as mediated by cell division through a membrane constriction divisome based on FtsZ, a mechanically competent protein at elastic interaction against membrane rigidity. Using membrane fluctuation spectroscopy in the single cells, we revealed either membrane stiffening when considering hydrophobic long chain fatty substances, or membrane softening if short-chained hydrophilic molecules are used. Membrane stiffeners caused hindered growth under normal division in the microbial cultures, as expected for membrane rigidification. Membrane softeners, however, altered regular cell division causing persistent microbes that abnormally grow as long filamentous cells proliferating apparently faster. We invoke the concept of effective growth rate under the assumption of a heterogeneous population structure composed by distinguishable individuals with different FtsZ-content leading the possible forms of cell proliferation, from regular division in two normal daughters to continuous growing filamentation and budding. The results settle altogether into a master plot that captures a universal scaling between membrane rigidity and the divisional instability mediated by FtsZ at the onset of membrane constriction.
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Affiliation(s)
- Samuel Salinas-Almaguer
- Centro de Investigación y de Estudios Avanzados, Unidad Monterrey, Vía del Conocimiento 201, PIIT, 66600, Apodaca, NL, Mexico
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense S/N, 28040, Madrid, Spain
| | - Michael Mell
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense S/N, 28040, Madrid, Spain
| | - Victor G Almendro-Vedia
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense S/N, 28040, Madrid, Spain
| | - Macarena Calero
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense S/N, 28040, Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía S/N, 28041, Madrid, Spain
| | | | - Carlos Ruiz-Suarez
- Centro de Investigación y de Estudios Avanzados, Unidad Monterrey, Vía del Conocimiento 201, PIIT, 66600, Apodaca, NL, Mexico
| | - Tomás Alarcón
- ICREA, Pg. Lluís Companys 23, 08010, Barcelona, Spain
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193, Bellaterra, Barcelona, Spain
- Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain
- Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain
| | - Rafael A Barrio
- Instituto de Fisica, U.N.A.M., Apartado Postal 20-364, 01000, Mexico, D.F., Mexico
| | - Aurora Hernández-Machado
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193, Bellaterra, Barcelona, Spain.
- Departament Fisica de la Materia Condensada, Facultat de Fisica, Universitat de Barcelona, Diagonal 645, 08028, Barcelona, Spain.
- Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain.
| | - Francisco Monroy
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense S/N, 28040, Madrid, Spain.
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía S/N, 28041, Madrid, Spain.
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