Current inversion in a periodically driven two-dimensional Brownian ratchet

Strand, Nils E.; Fu, Rueih-Sheng; Gingrich, Todd R.

doi:10.1103/physreve.102.012141

Cited by 9 publications

(7 citation statements)

References 74 publications

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“…In light of that sensitivity, how should one engineer and design artificial molecular motors? Whereas physicists have studied Brownian ratchet current reversals in response to variations in one or two parameters, e.g., a noise [30,31] or driving frequency [32][33][34], biologists and chemists need ways to handle incredibly high dimensional design spaces. Protein motors can be mutated in any number of ways.…”

Section: Discussionmentioning

confidence: 99%

Current Reversal in a Molecular Motor

Albaugh¹,

Gu²,

Gingrich³

2022

Preprint

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Simulations can help unravel the complicated ways in which molecular structure determines function. Here, we use molecular simulations to show how slight alterations of a molecular motor's structure can cause the motor's typical dynamical behavior to reverse directions. Inspired by autonomous synthetic catenane motors, we study the molecular dynamics of a minimal motor model, consisting of a shuttling ring that moves along a track containing interspersed binding sites and catalytic sites. The binding sites attract the shuttling ring while the catalytic sites speed up a reaction between molecular species, which can be thought of as fuel and waste. When that fuel and waste are held in a nonequilibrium steady state, the free energy from the reaction drives directed motion of the shuttling ring along the track. Using this model and nonequilibrium molecular dynamics, we show that the shuttling ring's direction can be reversed by simply adjusting the spacing between binding and catalytic sites on the track. We present a steric mechanism behind the current reversal, supported by kinetic measurements from the simulations. These results demonstrate how molecular simulation can guide future development of artificial molecular motors.

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Section: Discussionmentioning

confidence: 99%

Current Reversal in a Molecular Motor

Albaugh¹,

Gu²,

Gingrich³

2022

Preprint

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“…In this letter and in a companion paper, we develop and apply those tensor network tools to compute steadystate currents in a multi-particle 1D ratchet. Our approach mixes the spectral large-deviation theoretic analysis of one-body ratchets we previously reported [27] with the quantum dynamics literature's tensor network methods [28,29] which are presently finding applications to classical stochastic dynamics [24,25,[30][31][32][33][34][35]. Those tensor network tools are essential for handling the manybody problem because more traditional matrix algebra techniques cannot be applied when the state space grows exponentially with the number of interacting particles.…”

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confidence: 99%

“…While we imagine a 1D flashing ratchet as being generated from turning on and off a smooth continuous potential as in Fig. 1, we immediately discretize that potential onto an N -site lattice with periodic boundary conditions, following our prior work [27,47]. Dynamics of that discrete-space model is governed by the master equation, ∂|p /∂t = W|p .…”

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confidence: 99%

“…Because the NESS tilted rate matrix shares eigenvectors with the tilted propagator e W(λ)t , the SCGF can be computed without evolving dynamics. For the time-periodic steady state, we instead compute ψ(λ) as the maximal eigenvalue of the full-period tilted propagator T ≡ e W2(λ)τ /2 e W1(λ)τ /2 , extracted using the power iteration method [27]. An arbitrary initial state vector |p is evolved via TDVP for many periods to reach a normalized steady state |π(λ) , at which point the SCGF measures the rescaling of |π(λ) under one more period of dynamics:…”

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confidence: 99%

“…Tensor network structure and methods.-For singlebody dynamics, |p may be sufficiently low dimensional that the W k (λ) are constructed as explicit matrices and the time-propagation is computed with a numerically evaluated matrix exponential [27]. As more particles are added to the ratchet model, that direct calculation becomes intractable, demanding the time evolution be executed with a tensor network approximation.…”

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Using tensor network states for multi-particle Brownian ratchets

Strand,

Vroylandt,

Gingrich

2022

Preprint

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Using tensor network states for multi-particle Brownian ratchets

Strand

Vroylandt

Gingrich

2022

The Journal of Chemical Physics

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The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet's current. To surmount the many-body problem, we employ the time-dependent variational principle (TDVP) applied to binary tree tensor networks (BTTN). Rather than propagating individual trajectories, the tensor network approach propagates a distribution over many-body configurations via a controllable variational approximation. The calculations, which reproduce Gillespie trajectory sampling, identify and explain a shift in the frequency of maximum current to higher driving frequency as the lattice occupancy increases.

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Current inversion in a periodically driven two-dimensional Brownian ratchet

Cited by 9 publications

References 74 publications

Current Reversal in a Molecular Motor

Current Reversal in a Molecular Motor

Using tensor network states for multi-particle Brownian ratchets

Using tensor network states for multi-particle Brownian ratchets

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