Broken Detailed Balance of Filament Dynamics in Active Networks

Gladrow, Jannes; Fakhri, Nikta; MacKintosh, F. C.; Schmidt, Christoph F.; Broedersz, Chase P.

doi:10.1103/physrevlett.116.248301

“…The philosophy underlying the analysis of mapping trajectories on kinetic model, proposed here on kinesin-1 as well as others on F 1 -ATPase [29,46], is in essence similar to the one by the recent study which has quantified circulating flux on configurational phase space (or mode space) to diagnose broken DB and non-equilibrium dynamics at mesoscopic scale [37,38]. Lastly, our study confers quantitative insights into how much of the chemical free energy supplied to active systems (enzymes, molecular motors) is converted to mechanical movement in space and eventually dissipated into heat.…”

mentioning

confidence: 97%

“…Broken DB and violation of FDT [37,38] differentiate an active system operated under non-conservative forces from a passive system in mechanical equilibrium under conservative forces. For example, the terminal velocity (V ) and diffusion constant (D) of a colloidal particle of size R in the gravitational or electric field, are mutually independent, so that regardless of V , D is always constant, obeying StokesEinstein relation D ∼ D SE ∼ k B T /ηR where η is the viscosity of media, k B is the Boltzmann constant, and T is the absolute temperature.…”

mentioning

confidence: 99%

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

Hwang

¹

,

Hyeon

²

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 philosophy underlying the analysis of mapping trajectories on kinetic model, proposed here on kinesin-1 as well as others on F 1 -ATPase [29,46], is in essence similar to the one by the recent study which has quantified circulating flux on configurational phase space (or mode space) to diagnose broken DB and non-equilibrium dynamics 4 0.14 at mesoscopic scale [37,38]. Lastly, our study confers quantitative insights into how much of the chemical free energy supplied to active systems (enzymes, molecular motors) is converted to mechanical movement in space and eventually dissipated into heat.…”

mentioning

confidence: 89%

Tight Coupling between the Heat Dissipation and Molecular Motor's Transport Properties in Nonequilibrium Steady State

Hwang

¹

,

Hyeon

²

2017

Biophysical Journal

0

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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 Fourier mode amplitudes for pairs of modes also provide information about tubule curvature over time. Transitions between states, ( , ) → ( +1 , +1 ), where denotes the amplitude of mode in frame , were interpolated and plotted in 2D coarse-grained conformational phase space (31,51,52). Figure 5A shows example phase space plots of the first two modes for various tubule conformations: straight (Figure 5Ai), sustained curvature (Figure 5Aii) and transient curvature (Figure 5Aiii and iv).…”

Section: (7)mentioning

confidence: 99%

“…The tubules of the endoplasmic reticulum provide a novel example of driven active polymeric systems that can be compared with more standard systems, such as myosin with actin networks or kinesins with microtubule networks (29)(30)(31)(32). A unique feature of the ER is its ability to experience large geometrical and morphological changes due to the elasticity of the lipid tubules e.g.…”

Section: Introductionmentioning

confidence: 99%

Network Organisation and the Dynamics of Tubules in the Endoplasmic Reticulum

Perkins

¹

,

Ducluzaux

²

,

Woodman

³

et al. 2020

Preprint

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The endoplasmic reticulum (ER) is a eukaryotic subcellular organelle composed of tubules and sheetlike areas of membrane connected at junctions. The tubule network is highly dynamic and undergoes rapid and continual rearrangement. There are currently few tools to evaluate network organisation and dynamics. We quantified ER network organisation in Vero and MRC5 cells, and developed a classification system for ER dynamics in live cells. The persistence length, tubule length, junction coordination number and angles of the network were quantified. Hallmarks of imbalances in ER tension, indications of interactions with microtubules and other subcellular organelles, and active reorganisation and dynamics were observed. Live cell ER tubule dynamics were classified using a Gaussian mixture model, defining tubule motion as active or thermal and conformational phase space analysis allowed this classification to be refined by tubule curvature states. STATEMENT OF SIGNIFICANCEThe endoplasmic reticulum (ER), a subcellular organelle, is an underexplored real-world example of active matter. Many processes essential to cell survival are performed by the ER, the efficacy of which may depend on its organisation and dynamics. Abnormal ER morphology is linked to diseases such as hereditary spastic paraplegias and it is possible that the dynamics are also implicated. Therefore, analysing the ER network in normal cells is important for the understanding of diseaserelated alterations. In this work, we outline the first thorough quantification methods for determining ER organisation and dynamics, deducing that tubule motion has a binary classification as active or thermal. Active reorganisation and dynamics along with indications of tension imbalances and membrane contact sites were observed.

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Broken Detailed Balance of Filament Dynamics in Active Networks

Cited by 90 publications

References 39 publications

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

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

Tight Coupling between the Heat Dissipation and Molecular Motor's Transport Properties in Nonequilibrium Steady State

Network Organisation and the Dynamics of Tubules in the Endoplasmic Reticulum

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