Out of equilibrium generalized Stokes–Einstein relation: determination of the effective temperature of an aging medium

Pottier, N.

doi:10.1016/j.physa.2004.07.019

Cited by 14 publications

(18 citation statements)

References 12 publications

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“…To quantify the deviation from equilibrium in evolving systems, it has been proposed [25], [28] to replace the temperature in Eq. 1 (FDT) by a frequency-dependent effective temperature, T eff (ω).…”

Section: Discussionmentioning

confidence: 99%

In Vivo Determination of Fluctuating Forces during Endosome Trafficking Using a Combination of Active and Passive Microrheology

et al. 2010

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BackgroundRegulation of intracellular trafficking is a central issue in cell biology. The forces acting on intracellular vesicles (endosomes) can be assessed in living cells by using a combination of active and passive microrheology.Methodology/Principal FindingsThis dual approach is based on endosome labeling with magnetic nanoparticles. The resulting magnetic endosomes act both as probes that can be manipulated with external magnetic fields to infer the viscoelastic modulus of their surrounding microenvironment, and as biological vehicles that are trafficked along the microtubule network by means of forces generated by molecular motors. The intracellular viscoelastic modulus exhibits power law dependence with frequency, which is microtubule and actin-dependent. The mean square displacements of endosomes do not follow the predictions of the fluctuation-dissipation theorem, which offers evidence for active force generation. Microtubule disruption brings the intracellular medium closer to thermal equilibrium: active forces acting on the endosomes depend on microtubule-associated motors. The power spectra of these active forces, deduced through the use of a generalized Langevin equation, show a power law decrease with frequency and reveal an actin-dependent persistence of the force with time. Experimental spectra have been reproduced by a simple model consisting in a series of force steps power-law distributed in time. This model enlightens the role of the cytoskeleton dependent force exerted on endosomes to perform intracellular trafficking.Conclusions/SignificanceIn this work, the influence of cytoskeleton components and molecular motors on intracellular viscoelasticity and transport is addressed. The use of an original probe, the magnetic endosome, allows retrieving the power spectrum of active forces on these organelles thanks to interrelated active and passive measures.Finally a computational model gives estimates of the force itself and hence of the number of the motors pulling on endosomes.

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Section: Discussionmentioning

confidence: 99%

In Vivo Determination of Fluctuating Forces during Endosome Trafficking Using a Combination of Active and Passive Microrheology

et al. 2010

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“…To quantify the deviation from the in-equilibrium situation, it has been proposed to replace the bath temperature T in Eqs. (2) and (3) by a frequencydependent effective temperature T eff [17]. T eff !…”

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confidence: 99%

Out-of-Equilibrium Microrheology inside Living Cells

2008

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Both forced and spontaneous motions of magnetic microbeads engulfed by Dictyostelium cells have served as experimental probes of intracellular dynamics. The complex shear modulus G*(omega), determined from active oscillatory measurements, has a power-law dynamics and increases with the probe size, reflecting intracellular structural complexity. The combined use of passive microrheology allows one to derive the power spectrum of active forces acting on intracellular phagosomes and to test the validity of the fluctuation-dissipation theorem inside living cells.

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“…If the cell is alive it will produce much more kinetic entropy to compensate the active entropy flow from the environment and keep the stationary state of life. Hence, the temperament will be much higher than B kT, which will reflect in more intensive Brownian motion and higher diffusion constant D [30]. Indeed, the corresponding effective temperature, estimated by the Stokes-Einstein formula 6 RD    from experimental values of the cell diffusion constant, is several orders of magnitude higher than the thermodynamic one [28,29].…”

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confidence: 94%

Brownian Motion and the Temperament of Living Cells

Tsekov

Lensen

2013

Chinese Phys. Lett.

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The migration of living cells obeys usually the laws of Brownian motion. While the latter is due to the thermal motion of surrounding matter, the cells locomotion is generally associated to their vitality. In the present paper the concept of cell temperament is introduced, being analogous to thermodynamic temperature and related to the cell entropy production. A heuristic expression for the diffusion coefficient of cell on structured surfaces is derived as well. The cell locomemory is also studied via the generalized Langevin equation.Tissue cells (e.g. fibroblasts) are anchorage dependent, implying that they need an interface to adhere to. If a substrate with a sufficient rigidity is not available, those cells are not viable, even in the presence of extracellular matrix proteins. Successful initial adhesion is followed by cell spreading and eventually active migration, involving intricate mechano-transduction and biochemical signalling processes. Consequently, the cell migration is dependent on physical, chemical and mechanical cues, among others. This has inspired many researchers over the years to predict and control the cell migration, for example by administering increasing concentrations of nutrients to lure cells in a certain direction, which is denoted chemotaxis [1], or directing them to move up a gradient of substrate elasticity, a process called durotaxis [2,3].Controlling cell migration is a very important task in the biomedical field and in tissue engineering, since it determines for example the eventual integration of implants and plays an important role in cancer metastasis, where individual cells come loose from the tumour tissue and go out to settle at another suitable interface (e.g. in arteries). We have analysed the motility of single cells cultured on polymeric gel substrates, i.e. hydrogels, with variable rigidities. Our preliminary unpublished results show that both the mean square displacement and the average speed are larger on stiffer gels, while the mean square displacement scaled linearly with time, implying Brownian motion. Finally the persistence (angle of directional movement between subsequent steps) appeared larger on the softest gel, an observation that could however be affected inherently by the slower speed. Thus, it seems that cell motility and active migration are correlated to the substrate stiffness [2,3], besides other factors such as the ones mentioned above. Nevertheless, from single cell observations it becomes clear that cells are individual entities and do not behave all identically, whereas the chemical or mechanical cues are supposedly homogeneous and act upon all cells similarly. We are interested to unravel other driving forces that dictate cellular behaviour and wish to find out more about cell individual characteristics. In a sense, we are searching for biophysical factors besides the well-known chemical and mechanical pa-

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Out of equilibrium generalized Stokes–Einstein relation: determination of the effective temperature of an aging medium

Cited by 14 publications

References 12 publications

In Vivo Determination of Fluctuating Forces during Endosome Trafficking Using a Combination of Active and Passive Microrheology

In Vivo Determination of Fluctuating Forces during Endosome Trafficking Using a Combination of Active and Passive Microrheology

Out-of-Equilibrium Microrheology inside Living Cells

Brownian Motion and the Temperament of Living Cells

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