Nonequilibrium Mechanics of Active Cytoskeletal Networks

Mizuno, Daisuke; Tardin, Catherine; Schmidt, Christoph F.; MacKintosh, F. C.

doi:10.1126/science.1134404

Cited by 873 publications

(1,163 citation statements)

References 25 publications

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“…By measuring the response function and spontaneous fluctuations for the same system and for the same experimental conditions, it is possible to assert directly the presence of " 2 non-equilibrium processes, as recently demonstrated in vitro for hair bundles 29 , active gels 30 and suspended bone cells 31 . A series of techniques allow the measurement of cellular mechanics 32 , and the RBC membrane response was measured previously using micropipette aspiration 33 , electric fields 34 , or optical tweezers 10,35 , but never compared directly to the fluctuations in the same cell.…”

Section: Main Textmentioning

confidence: 99%

Equilibrium physics breakdown reveals the active nature of red blood cell flickering

et al. 2016

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Section: Main Textmentioning

confidence: 99%

Equilibrium physics breakdown reveals the active nature of red blood cell flickering

et al. 2016

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“…If the mean duration of locomotion is τ r and the bacterium tumbles occasionally with a rotational diffusion constant D R for time τ t , the effective diffusion constant of the bacterium at time t much greater than τ s and τ t is estimated D eff ∼ V 2 b τ r /6D R τ t [41,42]. In this case, V b or D eff of bacterium is affected not by the ambient temperature but by the amount of food, also violating the conventional FDT (D eff k B T /ηR) [37,43,44].…”

mentioning

confidence: 99%

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Hwang

Hyeon

2016

Preprint

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Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related to each other. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1 whose dynamics is confined on one-dimensional tracks is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers thermodynamic basis to understand the heat enhanced self-diffusion of exothermic enzymes.Together with recent studies [1][2][3][4], Riedel et al. [5] have demonstrated a rather surprising result, from a perspective of equilibrium statistical mechanics: Diffusion constants (D) of exothermic enzymes, measured from fluorescence correlation spectroscopy (FCS), increase linearly with their catalytic turnover rates V cat , so that the enhancement of diffusivity at maximal activity (maximum V cat ) is as large aswhere D 0 and D max are the diffusion constants measured by FCS at V cat = 0 and maximal V cat , respectively. Their enigmatic observation [5] has called much attention of biophysics community to the physical origin of the activity-dependent diffusivity of a single enzyme. Golestanian [6] considered four distinct scenarios (self-thermophoresis, boost in kinetic energy, stochastic swimming, collective heating) to account for this observation quantitatively; however, the extent of enhancement observed in the experiment was still orders of magnitude greater than the theoretical estimates from the suggested mechanisms. Bai et al.[7] also drew a similar conclusion by considering hydrodynamic coupling between the conformational change of enzyme and surrounding media. The experimental demonstration of enzymes' enhanced diffusion with multiple control experiments in Ref.[5] is straightforward; however, physical insight of the observed phenomena is currently missing [5,6,8,9].While seemingly entirely different from freely diffusing enzymes, kinesin-1 [10-15] is also a substrate-catalyzing enzyme. Conformational dynamics of kinesin-1, induced by ATP hydrolysis and thermal fluctuations, is rectified into a unidirectional movement with a high fidelity [16,17]; hydrolysis of a single ATP almost always leads to 8 nm step [18]. Every step of kinesin-1 along 1D tracks, an outcome of cyclic chemical reaction, can be mapped (2)µ, ..., (N )µ denote distinc...

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“…The effective temperature can be estimated in terms of the mean motor force F , motor step length L , and k B as T a = F L k B . Using known experimental values for kinesin -average motor force, F = 5pN and average motor step length, L = 8 nm [42] -we estimate the effective temperature to be 3000 K (approximately 10 times room temperature), which is consistent with [28,43].…”

Section: Semi-dilute Solution Model Formulation and Associated Fokkerplmentioning

confidence: 54%

“…(4.4), are necessary to describe fluctuations in non-equilibrium systems of active motors that can potentially induce an effective temperature larger than the equilibrium (thermodynamic) temperature [24,25,28,43]. Experiments in actinmyosin mixtures [28] showed strong deviations from thermodynamic equilibrium behavior due to motor fluctuations. We assume ξ i (t) = 0 and 6) for i, j = 1..N .…”

Section: Semi-dilute Solution Model Formulation and Associated Fokkerplmentioning

confidence: 99%

Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions

Swaminathan

Ziebert

Aranson

et al. 2010

Math. Model. Nat. Phenom.

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Abstract. We study molecular motor-induced microtubule self-organization in dilute and semidilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.

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Nonequilibrium Mechanics of Active Cytoskeletal Networks

Cited by 873 publications

References 25 publications

Equilibrium physics breakdown reveals the active nature of red blood cell flickering

Equilibrium physics breakdown reveals the active nature of red blood cell flickering

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions

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