2927559.pdf

The document contains additional details on the models and data analysis methods used, description of experimental details, illumination and detection profile visualizations, as well as supplementary experimental results

Nanoscopic Approach to Quantification of Equilibrium and Rate Constants of Complex Formation at Single-Molecule Level

Equilibrium and rate constants are key descriptors of complex-formation processes in a variety of chemical and biological reactions. However, these parameters are difficult to quantify, especially in the locally confined, heterogeneous, and dynamically changing living matter. Herein, we address this challenge by combining stimulated emission depletion (STED) nanoscopy with fluorescence correlation spectroscopy (FCS). STED reduces the length-scale of observation to tens of nanometres (2D)/attoliters (3D) and the time-scale to microseconds, with direct, gradual control. This allows one to distinguish diffusional and binding processes of complex-formation, even at reaction rates higher by an order of magnitude than in confocal FCS. We provide analytical autocorrelation formulas for probes undergoing diffusion-reaction processes under STED condition. We support the theoretical analysis of experimental STED-FCS data on a model system of dye–micelle, where we retrieve the equilibrium and rates constants. Our work paves a promising way toward quantitative characterization of molecular interactions <i>in vivo</i>

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

<div><p>We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales—from diffusion of molecular probes to macroscopic viscous flow—we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid.</p></div

Comparison with the theoretical model.

<p>Bulk viscosity data for all the investigated solutions of a) PMAANa and b) PSSNa plotted according to Dobrynin’s theoretical model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref047" target="_blank">47</a>] based on de Gennes’ concept of scaling of electrostatic blobs [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref060" target="_blank">60</a>]—<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e007" target="_blank">Eq 5</a>. Panel b) includes also data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref061" target="_blank">61</a>]. Despite some deviations, the model seems to describe the data acceptably well.</p

Macroviscosity measurements.

<p>Results of measurements of macroscopic viscosity (rotational rheometry) of aqueous solutions of a) PMAANa and b) PSSNa at ionic strength of 0.154 M and pH of 7.4. Good conformity with the model originally developed for neutral polymer solutions (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e003" target="_blank">Eq 3</a>, solid line) is observed in both cases. In panel b) literature data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref061" target="_blank">61</a>] are included (empty symbols). These data correspond to viscosity measurements on a 1200 kDa PSSNa sample at 0.01 M NaCl. This still falls within the high salt regime and the results follow the model proposed hereby.</p

Nanoviscosity measurements.

<p>Results of fluorescence correlation spectroscopy (FCS) measurements of probe diffusion rates in solutions of PMAANa of different molecular masses. The probes used were rhodamine dyes, apoferritin and TAMRA-labelled dextrans. Ionic strength was kept at 0.154 M. Diffusion coefficients were translated to effective viscosities experienced by the probes via <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e008" target="_blank">Eq 6</a>. The data are plotted according to the model from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e003" target="_blank">Eq 3</a>. All the probes are of neutral or negative electric charge (no electrostatic attraction to the polyelectrolyte chains).</p

Hydrodynamic radii of the probes used throughout the FCS experiments (<i>r</i>_p), along with the probe charges at the pH of phosphate buffer (7.4).

<p>Hydrodynamic radii of the probes used throughout the FCS experiments (<i>r</i>_p), along with the probe charges at the pH of phosphate buffer (7.4).</p

Scaling Equation for Viscosity of Polymer Mixtures in Solutions with Application to Diffusion of Molecular Probes

We measured macroscopic viscosity as well as nanoviscosity experienced by molecular probes diffusing in solutions containing two polymer species vastly differing in the molecular weight. On this basis we postulated a scaling equation for viscosity of complex liquids characterized by two distinct length-scales. As an experimental model, we used aqueous solutions of low-polydispersity poly­(ethylene glycol) and poly­(ethylene oxide) with molecular weight ranging from 6 to 1000 kg/mol, polymer concentrations from 0.25% up to 50%, and viscosity up to 500 mPa·s. The proposed model distinguishes between the contributions to the total viscosity stemming from the mesoscopic structure of the complex liquid and from the magnitude of interactions dictated by the chemical nature of its constituents. It allows to predict diffusion rates of nanoscaled probes in polymer solution mixtures and can be adapted to various multilength-scale complex systems

Anomalous Effect of Flow Rate on the Electrochemical Behavior at a Liquid|Liquid Interface under Microfluidic Conditions

We have investigated the oxidation of ferrocene at a flowing organic solvent|aqueous electrolyte|solid electrode junction in a microfluidic setup using cyclic voltammetry and fluorescent laser scanning confocal microscopy. At low flow rates the oxidation current decreases with increasing flow, contrary to the Levich equation, but at higher flow rates the current increases linearly with the cube root of the flow rate. This behavior is explained using a simple model postulating a smallest effective width of the three-phase junction, which after fitting to the data comes to be ca. 20 μm. The fluorescence microscopy reveals mixing of the two phases close to the PDMS cover, but the liquid|liquid junction is stable close to the glass support. This study shows the importance of the solid|liquid|liquid junctions for the behavior of multiphase systems under microfluidic conditions