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

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

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

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

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

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

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The Effect of Probes’ Polydispersity

This work, based on <i>in vivo</i> and <i>in vitro</i> measurements, as well as <i>in silico</i> simulations, provides a consistent analysis of diffusion of polydisperse nanoparticles in the cytoplasm of living cells. Using the example of fluorescence correlation spectroscopy (FCS), we show the effect of polydispersity of probes on the experimental results. Although individual probes undergo normal diffusion, in the ensemble of probes, an effective broadening of the distribution of diffusion times occurssimilar to anomalous diffusion. We introduced fluorescently labeled dextrans into the cytoplasm of HeLa cells and found that cytoplasmic hydrodynamic drag, exponentially dependent on probe size, extraordinarily broadens the distribution of diffusion times across the focal volume. As a result, the <i>in vivo</i> FCS data were effectively fitted with the anomalous subdiffusion model while for a monodisperse probe the normal diffusion model was most suitable. Diffusion time obtained from the anomalous diffusion model corresponds to a probe whose size is determined by the weight-average molecular weight of the polymer. The apparent anomaly exponent decreases with increasing polydispersity of the probes. Our results and methodology can be applied in intracellular studies of the mobility of nanoparticles, polymers, or oligomerizing proteins