Reliability of rectified transport: Coherence and reproducibility of transport by open-loop and feedback-controlled Brownian ratchets

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Amer Physical Soc
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Brownian ratchets are small-scale systems which rectify thermal fluctuations to produce a net current of particles. They have inspired many models of molecular motors that perform transport in the noisy environment of living cells. For the most common ratchet systems, this rectification is achieved by means of the switching of a periodic and spatially asymmetric potential (flashing ratchets) or by means of a rocking force (rocking ratchets). The rectification mechanism can be applied without information on the state of the system (open-loop ratchets) or using information on the state of the system (feedback or closed-loop ratchets). In order to characterize the transport, the most used quantity is the mean velocity of the center of mass of the system. However, another important transport attribute that has not received much attention is its quality. Here we analyze the quality of transport by studying the coherence and reproducibility of the transport induced by several representative open-and closed-loop rectification protocols under the maximum mean velocity conditions. We find that for few-particle systems, the best protocol is the rocked feedback protocol, producing the transport of particles with the highest coherence and reproducibility per distance traveled at the maximum mean velocity, while for larger systems it is overtaken by its open-loop counterpart. Our results also show that protocols with similar maximum mean velocities can have quite different coherences and reproducibilities. This highlights the importance of studying the reliability of rectified transport to develop performant synthetic rectification devices. These contributions to the emerging field of reliable transport in noisy environments are expected also to provide insight into the performance of natural molecular motors.
©2018 American Physical Society. We acknowledge Ana Asenjo for her early impulse to do this research. J.J. acknowledges financial support from Ministerio de Educación, Cultura y Deportes (MECD; Spain) through Grant No. FPU13/02934. F.J.C. acknowledges financial support through Grant No. FIS2010-17440 from Ministerio de Ciencia e Innovación (MICINN; Spain) and Grants No. GR35/14-920911, No. GR35/10-A-920911, and No. GR58/08-920911 from Universidad Complutense de Madrid and Banco de Santander (Spain). J.P.G. and F.J.C. also acknowledge Grant No. FIS2006-05895 (MINECO/FEDER) from Ministerio de Economía y Competitividad (MINECO; Spain) and the European Regional Development Fund (ERDF). The computations in this work were performed at EOLO, the HPC of Climate Change at the International Campus of Excellence of Moncloa (CEI Moncloa), funded by Ministerio de Educación, Cultura y Deportes (MECD) and Ministerio de Ciencia e Innovación (MICINN).
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