Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

Abstract

Transition state theory (TST) provides a simple interpretation of many thermally activated processes. It applies successfully on timescales and length scales that differ several orders of magnitude: to chemical reactions, breaking of chemical bonds, unfolding of proteins and RNA structures and polymers crossing entropic barriers. Here we apply TST to out-of-equilibrium transport through confined environments: the thermally activated translocation of single DNA molecules over an entropic barrier helped by an external force field. Reaction pathways are effectively one dimensional and so long that they are observable in a microscope. Reaction rates are so slow that transitions are recorded on video. We find sharp transition states that are independent of the applied force, similar to chemical bond rupture, as well as transition states that change location on the reaction pathway with the strength of the applied force. The states of equilibrium and transition are separated by micrometres as compared with angstroms/nanometres for chemical bonds.

Giant Acceleration of DNA Diffusion in an Array of Entropic Barriers

“…Previous theoretical studies highlighted the entropic nature of the barriers polymers encounter in similar geometries [12,13]. Furthermore, in a pressure-driven flow, DNA hops from pit to pit with exponentially distributed dwell times in the pits and a pressure-dependent mobility; this experimentally observed behavior is consistent with thermally activated transport across entropic barriers [14,15]. Previous studies focused on the statistics [10,[16][17][18][19][20][21][22] and mobility [9,14,[22][23][24] of DNA in nanotopographies and interpreted the results in terms of the free energy in equilibrium.…”

Evolution of Nested Folding States in Compression of a Strongly Confined Semiflexible Chain

“…1,2 An intriguing question is whether such organized nonequilibrium states are specific to active ATP-burning processes in biology or could arise as well in a purely physical process such as mechanical compression or driven transport. 3,4 Nanochannels serve as an ideal model to study organizing processes in confined environments due to their simplicity, well-characterized equilibrium polymer physics, and usefulness as an experimental platform for resolving dynamic changes in polymer conformation along an effectively one-dimensional spatial axis. 5 When a semiflexible chain is confined in a "nanochannel" with a width D below its persistence length P, back-folding will be suppressed and the chain will extend to almost its full contour length L. 5 Yet, applying a sufficiently high compressive force will drive the nanochannel extended chain into a compressed configuration.…”

Modeling in food across the scales: towards a universal mass transfer simulator of small molecules in food

“…where p k eq k=c,d and c ex k=c,d are respectively the solute probability density at equilibrium and its excess chemical potentials in phase k . A more general definition of the local thermodynamical equilibrium at the interface between the macrostates/positions c and d can be envisioned within the framework of transition state theory (TST) modified by Kramers [44] and Mel'Nikov [45] and experimentally evidenced for transport of isolated molecules by Vestergaard et al [46]. According to Kramers and…”