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Edited by Robert H. Austin, Princeton University, Princeton, NJ, and approved November 15, 2019 (received for review June 24, 2019)
Significance
Diffusion is of fundamental relevance in physics, chemistry, and biology, to explain the transport of macromolecules in a solvent, under the action of external forces. Diffusion is fueled by temperature, resulting in thermal fluctuations. Macromolecules trapped in a potential energy well can then escape, harnessing favorable fluctuations. Such events are a priori rare nevertheless, and the so-called Arrhenius relation describes the corresponding exponential decrease of escape rates with increasing barrier heights. It therefore comes as a surprise that some potential wells, with high barriers, may help the macromolecule escape. We report experimental proof of this counterintuitive boosting effect. Optimizing theoretically the potential profile that provides maximum boost, we translate our predictions into results in automated microfluidic experiments.
Abstract
Brownian escape is key to a wealth of physico-chemical processes, including polymer folding and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates, in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under 2 different regularizations and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.
Footnotes
↵1M.C. and J.G. contributed equally to this work.
- ↵2To whom correspondence may be addressed. Email: trizac{at}lptms.u-psud.fr.
Author contributions: M.C., J.G., A.C., U.F.K., and E.T. designed research, performed research, and wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
See online for related content such as Commentaries.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1910677116/-/DCSupplemental.
Published under the PNAS license.
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Optimizing Brownian escape rates by potential shaping
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