Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

Godec, Aljaž; Makarov, Dmitrii E.

doi:10.1021/acs.jpclett.2c03244

Cited by 12 publications

(10 citation statements)

References 61 publications

(105 reference statements)

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“…In all cases with a Δ G ≠ 0, the directionality was underestimated by a maximum of 25%. Some underestimation is expected, as the result from Hidden Markov Modelling is only a lower limit 45 . Altogether, our findings show that we can distinguish systems in detailed balance from those with a directional flux—even if the analysed system does not show strong directionality, i.e.…”

Section: Resultsmentioning

confidence: 99%

Cochaperones convey the energy of ATP hydrolysis for directional action of Hsp90

Vollmar,

Schimpf,

Hermann

et al. 2024

Nat Commun

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The molecular chaperone and heat shock protein Hsp90 is part of many protein complexes in eukaryotic cells. Together with its cochaperones, Hsp90 is responsible for the maturation of hundreds of clients. Although having been investigated for decades, it still is largely unknown which components are necessary for a functional complex and how the energy of ATP hydrolysis is used to enable cyclic operation. Here we use single-molecule FRET to show how cochaperones introduce directionality into Hsp90’s conformational changes during its interaction with the client kinase Ste11. Three cochaperones are needed to couple ATP turnover to these conformational changes. All three are therefore essential for a functional cyclic operation, which requires coupling to an energy source. Finally, our findings show how the formation of sub-complexes in equilibrium followed by a directed selection of the functional complex can be the most energy efficient pathway for kinase maturation.

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Section: Resultsmentioning

confidence: 99%

Cochaperones convey the energy of ATP hydrolysis for directional action of Hsp90

Vollmar,

Schimpf,

Hermann

et al. 2024

Nat Commun

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“…Our goal is to find an equivalent procedure for continuous states as required for the particle on a ring. First of all, we need to identify transitions, whose crucial property is to resolve the particle's direction of motion [22]. Furthermore, if we can observe only one pair of transitions, two successive ones in the same direction should be equal to a full passage of the cycle.…”

Section: Modelmentioning

confidence: 99%

“…The entropy produced by one trajectory γ can be calculated as the sum of log-ratios between probabilities of snippets. With (22) we can replace the entropy produced by closed loops by (8). Hence, it suffices to count the times N I± (t) two successive I + and I − transitions are observed on the coarse-grained level up to time t to arrive at…”

Section: Entropy Estimatormentioning

confidence: 99%

“…One route is to lump the continuous states into discrete ones [18][19][20] using for example Kramer's rates [21]. However, except for limiting cases, state-lumping yields an effective non-Markovian dynamics, which typically prevents recovering the full entropy production [22]. Alternatively, state-like events for overdamped Langevin dynamics can be defined through milestones [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Entropy production from waiting-time distributions for overdamped Langevin dynamics

Meyberg,

Degünther,

Seifert

2024

J. Phys. A: Math. Theor.

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For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an entropy estimator, which is exact in the case of a uni-cyclic network. We adopt this framework to overdamped Langevin dynamics, where such transitions have finite duration. By introducing milestones based on the observation of a particle at at least two milestones and an additional third event, we identify an entropy estimator that becomes exact for driven motion along a one-dimensional potential.

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“…This scheme describes a projection of nonequilibrium dynamics in a N-dimensional space onto a single degree of freedom m, where-as is often the case for projected dynamics (see, e.g. [34][35][36][37][38]) -the nonequilibrium character of the underlying process is hidden, although it affects the distribution p m .…”

Section: Introducing Nowmentioning

confidence: 99%

Nonequilibrium statistical mechanics of money/energy exchange models

Miao,

Makarov,

Blom

2024

J. Phys. A: Math. Theor.

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Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations -- a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model, and its extensions, using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing “unfair” exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the ``ground state'' (i.e., with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant's wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game.

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Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

Cited by 12 publications

References 61 publications

Cochaperones convey the energy of ATP hydrolysis for directional action of Hsp90

Cochaperones convey the energy of ATP hydrolysis for directional action of Hsp90

Entropy production from waiting-time distributions for overdamped Langevin dynamics

Nonequilibrium statistical mechanics of money/energy exchange models

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