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Viot P, Argun A, Volpe G, Imparato A, Rondoni L, Oshanin G. Destructive effect of fluctuations on the performance of a Brownian gyrator. SOFT MATTER 2024; 20:3154-3160. [PMID: 38512337 DOI: 10.1039/d3sm01606d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/22/2024]
Abstract
The Brownian gyrator (BG) is often called a minimal model of a nano-engine performing a rotational motion, judging solely upon the fact that in non-equilibrium conditions its torque, specific angular momentum and specific angular velocity have non-zero mean values. For a time-discretised (with time-step δt) model we calculate here the previously unknown probability density functions (PDFs) of and . We show that for finite δt, the PDF of has exponential tails and all moments are therefore well-defined. At the same time, this PDF appears to be effectively broad - the noise-to-signal ratio is generically bigger than unity meaning that is strongly not self-averaging. Concurrently, the PDF of exhibits heavy power-law tails and its mean is the only existing moment. The BG is therefore not an engine in the common sense: it does not exhibit regular rotations on each run and its fluctuations are not only a minor nuisance - on contrary, their effect is completely destructive for the performance. Our theoretical predictions are confirmed by numerical simulations and experimental data. We discuss some plausible improvements of the model which may result in a more systematic rotational motion.
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Affiliation(s)
- Pascal Viot
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 Place Jussieu, Paris 75252, Cedex 05, France.
| | - Aykut Argun
- Physics Department, University of Gothenburg, Gothenburg 412 96, Sweden
| | - Giovanni Volpe
- Physics Department, University of Gothenburg, Gothenburg 412 96, Sweden
| | - Alberto Imparato
- Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, Building 1520, Aarhus C DK-8000, Denmark
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 Place Jussieu, Paris 75252, Cedex 05, France.
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Bryant SJ, Machta BB. Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit. PHYSICAL REVIEW LETTERS 2023; 131:068401. [PMID: 37625074 PMCID: PMC11146629 DOI: 10.1103/physrevlett.131.068401] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Revised: 03/20/2023] [Accepted: 06/09/2023] [Indexed: 08/27/2023]
Abstract
Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in k_{B}T/bit, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.
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Affiliation(s)
- Samuel J. Bryant
- Department of Physics, Yale University, New Haven, Connecticut 06511, USA
| | - Benjamin B. Machta
- Department of Physics, Yale University and Quantitative Biology Institute, Yale University, New Haven, Connecticut 06511, USA
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Cerasoli S, Ciliberto S, Marinari E, Oshanin G, Peliti L, Rondoni L. Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator. Phys Rev E 2022; 106:014137. [PMID: 35974646 DOI: 10.1103/physreve.106.014137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally relevant model of such a system-the so-called Brownian gyrator-a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under nonequilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in nonequilibrium. We show that indeed one can conclusively distinguish between equilibrium and nonequilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a nonequilibrium dynamics.
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Affiliation(s)
- Sara Cerasoli
- Department of Civil and Environmental Engineering, Princeton University, Princeton New Jersey 08544, USA
| | - Sergio Ciliberto
- Laboratoire de Physique (UMR CNRS 567246), Ecole Normale Supérieure, Allée d'Italie, 69364 Lyon, France
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Luca Peliti
- Santa Marinella Research Institute, Santa Marinella, Italy
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
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Pilkiewicz KR, Lemasson BH, Rowland MA, Hein A, Sun J, Berdahl A, Mayo ML, Moehlis J, Porfiri M, Fernández-Juricic E, Garnier S, Bollt EM, Carlson JM, Tarampi MR, Macuga KL, Rossi L, Shen CC. Decoding collective communications using information theory tools. J R Soc Interface 2020; 17:20190563. [PMID: 32183638 PMCID: PMC7115225 DOI: 10.1098/rsif.2019.0563] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2019] [Accepted: 02/28/2020] [Indexed: 02/03/2023] Open
Abstract
Organisms have evolved sensory mechanisms to extract pertinent information from their environment, enabling them to assess their situation and act accordingly. For social organisms travelling in groups, like the fish in a school or the birds in a flock, sharing information can further improve their situational awareness and reaction times. Data on the benefits and costs of social coordination, however, have largely allowed our understanding of why collective behaviours have evolved to outpace our mechanistic knowledge of how they arise. Recent studies have begun to correct this imbalance through fine-scale analyses of group movement data. One approach that has received renewed attention is the use of information theoretic (IT) tools like mutual information, transfer entropy and causation entropy, which can help identify causal interactions in the type of complex, dynamical patterns often on display when organisms act collectively. Yet, there is a communications gap between studies focused on the ecological constraints and solutions of collective action with those demonstrating the promise of IT tools in this arena. We attempt to bridge this divide through a series of ecologically motivated examples designed to illustrate the benefits and challenges of using IT tools to extract deeper insights into the interaction patterns governing group-level dynamics. We summarize some of the approaches taken thus far to circumvent existing challenges in this area and we conclude with an optimistic, yet cautionary perspective.
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Affiliation(s)
- K. R. Pilkiewicz
- Environmental Laboratory, U.S. Army Engineer Research and Development Center (EL-ERDC), Vicksburg, MS, USA
| | | | - M. A. Rowland
- Environmental Laboratory, U.S. Army Engineer Research and Development Center (EL-ERDC), Vicksburg, MS, USA
| | - A. Hein
- National Oceanic and Atmospheric Administration, Santa Cruz, CA, USA
- University of California, Santa Cruz, CA, USA
| | - J. Sun
- Department of Mathematics, Clarkson University, Potsdam, NY, USA
| | - A. Berdahl
- School of Aquatic and Fishery Sciences, University of Washington, Seattle, WA, USA
| | - M. L. Mayo
- Environmental Laboratory, U.S. Army Engineer Research and Development Center (EL-ERDC), Vicksburg, MS, USA
| | - J. Moehlis
- Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA
| | - M. Porfiri
- Department of Mechanical and Aerospace Engineering and Department of Biomedical Engineering, New York University Tandon School of Engineering, Brooklyn, NY, USA
| | | | - S. Garnier
- Department of Biological Sciences, New Jersey Institute of Technology, Newark, NJ, USA
| | - E. M. Bollt
- Department of Mathematics, Clarkson University, Potsdam, NY, USA
| | - J. M. Carlson
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - M. R. Tarampi
- Department of Psychology, University of Hartford, West Hartford, CT, USA
| | - K. L. Macuga
- School of Psychological Science, Oregon State University, Corvallis, OR, USA
| | - L. Rossi
- Department of Mathematical Sciences, University of Delaware, Newark, DE, USA
| | - C.-C. Shen
- Department of Computer and Information Sciences, University of Delaware, Newark, DE, USA
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