Single-molecule tracking of polymer surface diffusion.

The dynamics of polymers adsorbed to a solid surface are important in thin-film formation, adhesion phenomena, and biosensing applications, but they are still poorly understood. Here we present tracking data that follow the dynamics of isolated poly(ethylene glycol) chains adsorbed at a hydrophobic solid-liquid interface. We found that molecules moved on the surface via a continuous-time random walk mechanism, where periods of immobilization were punctuated by desorption-mediated jumps. The dependence of the surface mobility on molecular weight (2, 5, 10, 20, and 40 kg/mol were investigated) suggested that surface-adsorbed polymers maintained effectively three-dimensional surface conformations. These results indicate that polymer surface diffusion, rather than occurring in the two dimensions of the interface, is dominated by a three-dimensional mechanism that leads to large surface displacements and significant bulk-surface coupling.

Single-molecule insights into retention at a reversed-phase chromatographic interface.

The efficiency of chromatographic separations decreases markedly when peaks exhibit asymmetry (e.g., "peak tailing"). Theoretically, these effects can arise from heterogeneous adsorption kinetics. To investigate the nature and consequences of such heterogeneity, we used a combination of single-molecule imaging and reversed-phase liquid chromatography (RPLC). In both single-molecule and macroscopic RPLC experiments, the stationary phase was hydrophobic end-capped (trimethylsilyl-functionalized) silica, which we exposed to different methanol/water solutions (50%-62% methanol), containing a fluorescent fatty acid analyte. Super-resolution maps based on single-molecule observations revealed rare, strong adsorption sites with activity that varied significantly with methanol concentration. The adsorption and desorption kinetics on the strong sites were heterogeneous and positively correlated, suggesting a broad underlying distribution of site binding energies. Adsorption equilibrium on the strong sites was more sensitive to solution conditions than overall retention measured in RPLC experiments, suggesting that the effect of strong sites on the overall adsorption kinetics should change with solution conditions. Interestingly, in RPLC experiments, peak tailing had a nonmonotonic dependence on methanol concentration within the range studied. Using the stochastic model of chromatography, we showed quantitatively that our single-molecule kinetic results were consistent with this macroscopic trend. This approach to identifying and quantifying adsorption sites should be useful for designing better chromatographic separations and for identifying the role of heterogeneous surface chemistry in molecular dynamics.

Single-molecule diffusion in a periodic potential at a solid-liquid interface.

We used single-molecule tracking experiments to observe the motion of small hydrophobic fluorescent molecules at the interface between water and a solid surface that exhibited periodic chemical patterns. The dynamics were characterized by non-ergodic, continuous time random walk statistics. The step-size distributions displayed enhanced probability of steps to periodic distances, consistent with theoretical predictions for diffusion in an atomic/molecular scale periodic potential. Surprisingly, this general behavior was observed here for surfaces exhibiting characteristic length scales three orders of magnitude larger than atomic/molecular dimensions, and may provide a new way to understand and control solid-liquid interfacial diffusion for molecular targeting applications.

Intermittent molecular hopping at the solid-liquid interface.

The mobility of molecules on a solid surface plays a key role in diverse phenomena such as friction and self-assembly and in surface-based technologies like heterogeneous catalysis and molecular targeting. To understand and control these surface processes, a universally applicable model of surface transport at solid-liquid interfaces is needed. However, unlike diffusion at a solid-gas interface, little is known about the mechanisms of diffusion at a solid-liquid interface. Using single-molecule tracking at a solid-liquid interface, we found that a diverse set of molecules underwent intermittent random walks with non-Gaussian displacements. This contrasts with the normal random walk and Gaussian statistics that are commonly assumed for molecular surface diffusion. The molecules became temporarily immobilized for random waiting times between surface displacements produced by excursions through the bulk fluid. A common power-law distribution of waiting times indicated a spectrum of binding energies. We propose that intermittent hopping is universal to molecular surface diffusion at a solid-liquid interface.

Correlating anomalous diffusion with lipid bilayer membrane structure using single molecule tracking and atomic force microscopy.

Anomalous diffusion has been observed abundantly in the plasma membrane of biological cells, but the underlying mechanisms are still unclear. In general, it has not been possible to directly image the obstacles to diffusion in membranes, which are thought to be skeleton bound proteins, protein aggregates, and lipid domains, so the dynamics of diffusing particles is used to deduce the obstacle characteristics. We present a supported lipid bilayer system in which we characterized the anomalous diffusion of lipid molecules using single molecule tracking, while at the same time imaging the obstacles to diffusion with atomic force microscopy. To explain our experimental results, we performed lattice Monte Carlo simulations of tracer diffusion in the presence of the experimentally determined obstacle configurations. We correlate the observed anomalous diffusion with obstacle area fraction, fractal dimension, and correlation length. To accurately measure an anomalous diffusion exponent, we derived an expression to account for the time-averaging inherent to all single molecule tracking experiments. We show that the length of the single molecule trajectories is critical to the determination of the anomalous diffusion exponent. We further discuss our results in the context of confinement models and the generating stochastic process.

Computational studies of Texas Red-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine-model building and applications.

Texas Red-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine (TR-DHPE) is a frequently used experimental tool in the study of lipid membranes by fluorescence microscopy techniques. Although it is usually incorporated at low concentration, several experimental studies suggest that fluorescent labels could alter the membrane's behavior. To investigate this possibility, we developed and validated a molecular dynamics model for TR-DHPE. The model was used to simulate TR-DHPE in 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bilayers of 127 lipids and 511 lipids. We also simulated a pure 128 DPPC bilayer under the same conditions and found that the results compared well with other simulations and experiments. Texas Red was found to reside in the upper acyl chain region of the bilayer. Coinciding with its position in the bilayer, we found that Texas Red decreased the upper acyl carbon order parameters of neighboring lipids. We analyzed area per lipid at varying distances from the Texas Red and discovered finite size effects in the 1:127 system. In both systems, the Texas Red bound to a DPPC lipid. The model we have developed should also be useful for other biomolecular simulations which try to mimic experimental systems.

Nanofluidic rocking Brownian motors.

Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We designed energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like-charged particles and walls. Directed transport was performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using gold spheres 60 nanometers in diameter, we investigated the physics of the motor with high spatiotemporal resolution, enabling a parameter-free comparison with theory. We fabricated a sorting device that separates 60- and 100-nanometer particles in opposing directions within seconds. Modeling suggests that the device separates particles with a radial difference of 1 nanometer.

Temporally Anticorrelated Motion of Nanoparticles at a Liquid Interface.

Quantum dots at the hexane-glycerol interface exhibited unexpected behavior including highly dynamic adsorption/desorption, where the lateral nanoparticle motion was anomalously fast immediately after adsorption and prior to desorption. At the interface, particles exhibited pseudo-Brownian lateral motion, in which the instantaneous diffusion coefficient was temporally anticorrelated, in agreement with our simulations involving fractional Brownian motion in the surface-normal direction. These phenomena suggest that, in contrast to the conventional picture for colloidal particles, nanoparticles explore a landscape of metastable interfacial positions, with different exposures to the two adjacent phases.

Hindered nanoparticle diffusion and void accessibility in a three-dimensional porous medium.

The inherent pore-scale heterogeneity of many natural and synthetic porous materials can make it difficult to model and predict porous transport because the underlying microscopic processes are often poorly understood. Here we present the results of single-particle tracking experiments in which we followed the pore-scale diffusion of individual nanoparticles, deep within a three-dimensional porous material of moderate porosity. We observed significant hydrodynamic damping of particle motion at subpore length scales, resulting in heterogeneous and spatially dependent mobility. The accessibility of the void space was strongly dependent on particle size, and related to the heterogeneous hydrodynamics. Our results suggest that pore-scale diffusion is more heterogeneous and volume accessibility more limited than previously expected. The method demonstrated here will enable studies of a broad new class of materials including porous polymers of technological interest.

Colloidal transfer printing.

Many fields of research have adopted self-assembly of colloidal spheres as an easy and reliable method to produce macroscopic structures with nanoscale periodicity. The field of soft lithography in particular has used colloidal self-assembly to fabricate lithographic masks and templates. We developed a colloidal lithography method that uses the colloidal assembly directly to produce submicrometer topographic and chemical surface patterns. The method does not require any specialized equipment, making it particularly useful in biological and chemical laboratories without lithography expertise. The technique involves the curing and solvent removal of a self-assembled colloidal crystal from an inorganic surface. The result is a triangular array of polymer features with submicrometer periodicity that covers square centimeters of surface area. The feature size and spacing is easily controlled, and the features serve as reactive sites for biomolecule immobilization.

The impact of Texas red on lipid bilayer properties.

We investigated the impact of fluorescent labeling on the properties of a lipid bilayer using atomistic molecular dynamics simulation. The system consisted of 24 Texas Red-1,2-dihexadecanoyl-sn-glycero-3-phophoethanolamine (TR-DHPE) in a bilayer of 488 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipids. We found binding between TR-DHPE and DPPC caused by electrostatic interactions. On average, TR-DHPE is bound to 1.2 DPPC molecules. Binding reduced the diffusion coefficient of TR-DHPE by 34% relative to unlabeled DPPC molecules. We estimate that binding would lead to a ∼ 5 °C increase in the liquid to liquid-ordered transition temperature of a ternary lipid system. These results emphasize the importance of considering the impact of fluorescence labeling when interpreting experimental results.