Activation Energy for Mobility of Dyes and Proteins in Polymer Solutions: From Diffusion of Single Particles to Macroscale Flow

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Abstract

We measure the activation energy Ea for the diffusion of molecular probes (dyes and proteins of radii from 0.52 to 6.9 nm) and for macroscopic flow in a model complex liquid-aqueous solutions of polyethylene glycol. We cover a broad range of polymer molecular weights, concentrations, and temperatures. Fluorescence correlation spectroscopy and rheometry experiments reveal a relationship between the excess of the activation energy in polymer solutions over the one in pure solvent ΔEa and simple parameters describing the structure of the system: probe radius, polymer hydrodynamic radius, and correlation length. ΔEa varies by more than an order of magnitude in the investigated systems (in the range of ca. 1-15 kJ/mol) and for probes significantly larger than the polymer hydrodynamic radius approaches the value measured for macroscopic flow. We develop an explicit formula describing the smooth transition of ΔEa from the diffusion of molecular probes to macroscopic flow. This formula is a reference for the quantitative analysis of specific interactions of moving nano-objects with their environment as well as active transport. For instance, the power developed by a molecular motor moving at constant velocity u is proportional to u2exp(Ea/RT).

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Probing transcription factor dynamics at the single-molecule level in a living cell.

Johan Elf, Gene-Wei Li, X Sunney Xie (2007)

Transcription factors regulate gene expression through their binding to DNA. In a living Escherichia coli cell, we directly observed specific binding of a lac repressor, labeled with a fluorescent protein, to a chromosomal lac operator. Using single-molecule detection techniques, we measured the kinetics of binding and dissociation of the repressor in response to metabolic signals. Furthermore, we characterized the nonspecific binding to DNA, one-dimensional (1D) diffusion along DNA segments, and 3D translocation among segments through cytoplasm at the single-molecule level. In searching for the operator, a lac repressor spends approximately 90% of time nonspecifically bound to and diffusing along DNA with a residence time of <5 milliseconds. The methods and findings can be generalized to other nucleic acid binding proteins.

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Scaling Concepts in Polymer Physics

P de Gennes, Thomas A. Witten (1980)

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Artificial Brownian motors: Controlling transport on the nanoscale

Fabio Marchesoni, Peter Hänggi (2008)

In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases, one speaks of "Brownian motors". In this review the constructive role of Brownian motion is exemplified for various one-dimensional setups, mostly inspired by the cell molecular machinery: working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are reviewed with particular attention to transport in artificial nanopores and optical traps, where single particle currents have been first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented hereby. Another area with promising potential for realization of artificial Brownian motors are microfluidic or granular set-ups.....