Modeling Brownian Microparticle Trajectories in Lab-on-a-Chip Devices with Time Varying Dielectrophoretic or Optical Forces

Lab-on-a-chip (LOC) devices capable of manipulating micro/nano-sized samples have spurred advances in biotechnology and chemistry. Designing and analyzing new and more advanced LOCs require accurate modeling and simulation of sample/particle dynamics inside such devices. In this work, we present a generalized computational physics model to simulate particle/sample trajectories under the influence of dielectrophoretic or optical forces inside LOC devices. The model takes into account time varying applied forces, Brownian motion, fluid flow, collision mechanics, and hindered diffusion caused by hydrodynamic interactions. We develop a numerical solver incorporating the aforementioned physics and use it to simulate two example cases: first, an optical trapping experiment, and second, a dielectrophoretic cell sorter device. In both cases, the numerical results are found to be consistent with experimental observations, thus proving the generality of the model. The numerical solver can simulate time evolution of the positions and velocities of an arbitrarily large number of particles simultaneously. This allows us to characterize and optimize a wide range of LOCs. The developed numerical solver is made freely available through a GitHub repository so that researchers can use it to develop and simulate new designs.

Cage effects control the mechanism of methane hydroxylation in zeolites

Catalytic conversion of methane to methanol remains an economically tantalizing but fundamentally challenging goal. Current technologies based on zeolites deactivate too rapidly for practical application. We found that similar active sites hosted in different zeolite lattices can exhibit markedly different reactivity with methane, depending on the size of the zeolite pore apertures. Whereas zeolite with large pore apertures deactivates completely after a single turnover, 40% of active sites in zeolite with small pore apertures are regenerated, enabling a catalytic cycle. Detailed spectroscopic characterization of reaction intermediates and density functional theory calculations show that hindered diffusion through small pore apertures disfavors premature release of CH3 radicals from the active site after C-H activation, thereby promoting radical recombination to form methanol rather than deactivated Fe-OCH3 centers elsewhere in the lattice.

Measurement of hindered diffusion in complex geometries for high-speed studies of single-molecule forces

In a high-speed single-molecule experiment with a force probe, a protein is tethered between two substrates that are manipulated to exert force on the system. To avoid nonspecific interactions between the protein and nearby substrates, the protein is usually attached to the substrates through long, flexible linkers. This approach precludes measurements of mechanical properties with high spatial and temporal resolution, for rapidly exerted forces are dissipated into the linkers. Because mammalian hearing operates at frequencies reaching tens to hundreds of kilohertz, the mechanical processes that occur during transduction are of very short duration. Single-molecule experiments on the relevant proteins therefore cannot involve long tethers. We previously characterized the mechanical properties of protocadherin 15 (PCDH15), a protein essential for human hearing, by tethering an individual monomer through very short linkers between a probe bead held in an optical trap and a pedestal bead immobilized on a glass coverslip. Because the two confining surfaces were separated by only the length of the tethered protein, hydrodynamic coupling between those surfaces complicated the interpretation of the data. To facilitate our experiments, we characterize here the anisotropic and position-dependent diffusion coefficient of a probe in the presence of an effectively infinite wall, the coverslip, and of the immobile pedestal.

Binding Revisited—Avidity in Cellular Function and Signaling

When characterizing biomolecular interactions, avidity, is an umbrella term used to describe the accumulated strength of multiple specific and unspecific interactions between two or more interaction partners. In contrast to the affinity, which is often sufficient to describe monovalent interactions in solution and where the binding strength can be accurately determined by considering only the relationship between the microscopic association and dissociation rates, the avidity is a phenomenological macroscopic parameter linked to several microscopic events. Avidity also covers potential effects of reduced dimensionality and/or hindered diffusion observed at or near surfaces e.g., at the cell membrane. Avidity is often used to describe the discrepancy or the “extra on top” when cellular interactions display binding that are several orders of magnitude stronger than those estimated in vitro. Here we review the principles and theoretical frameworks governing avidity in biological systems and the methods for predicting and simulating avidity. While the avidity and effects thereof are well-understood for extracellular biomolecular interactions, we present here examples of, and discuss how, avidity and the underlying kinetics influences intracellular signaling processes.

Measurement of hindered diffusion in complex geometries for high-speed single-molecule experiments

In a high-speed single-molecule experiment, a protein is tethered between two substrates that are manipulated to exert force on the system. To avoid nonspecific interactions between the protein and nearby substrates, the protein is usually attached to the substrates through long, flexible linkers. This approach precludes measurements of mechanical properties with high spatial and temporal resolution, for rapidly exerted forces are dissipated into the linkers. Because mammalian hearing operates at frequencies reaching tens to hundreds of kilohertz, the mechanical processes that occur during transduction are of very short duration. Single-molecule experiments on the relevant proteins therefore cannot involve long tethers. We previously characterized the mechanical properties of protocadherin 15 (PCDH15), a protein essential for human hearing, by tethering an individual monomer through very short linkers between a probe bead held in an optical trap and a pedestal bead immobilized on a glass coverslip. Because the two confining surfaces were separated by only the length of the tethered protein, hydrodynamic coupling between those surfaces complicated the interpretation of the data. To facilitate our experiments, we characterize here the anisotropic and position-dependent diffusion coefficient of a probe in the presence of an effectively infinite wall, the coverslip, and of the immobile pedestal.

A Fractal-Based Correlation for Time-Dependent Surface Diffusivity in Porous Adsorbents

Fluid–solid adsorption processes are mostly governed by the adsorbate transport in the solid phase and surface diffusion is often the limiting step of the overall process in microporous materials such as zeolites. This work starts from a concise review of concepts and models for surface transport and variable surface diffusivity. It emerges that the phenomenon of hindered surface diffusion for monolayer adsorption, which is common in zeolites, and models able to fit a non-monotonic trend of surface diffusivity against adsorbate solid phase concentration, have received limited attention. This work contributes to the literature of hindered diffusion by formulating a time-dependent equation for surface diffusivity based on fractal dynamics concepts. The proposed equation takes into account the contributions of both fractal-like diffusion (a time-decreasing term) and hopping diffusion (a time-increasing term). The equation is discussed and numerically analyzed to testify its ability to reproduce the possible different patterns of surface diffusivity vs. time.

Moisture Absorption of Carbon/Epoxy Nanocomposites

Moisture absorption of composites with nanoscale carbon additives such as carbon nanotubes, carbon nanofibers, graphite nanoplatelets, and carbon black is investigated using thermogravimetric data and a non-Fickian hindered diffusion (Langmuir-type) model. The moisture absorption parameters are determined using this model for six different types of carbon/epoxy nanocomposites. The absorption behaviors obtained at different humidity levels and thermal environments are recovered by minimizing the error between the experimental data and model predictions, thus enabling the accurate determination of the moisture equilibrium level. The absorption behavior and the weight gain of all nanocomposites are shown to be accurately represented by this model over the entire absorption period. The presence of carbon nanomaterials is found to induce varying levels of non-Fickian behavior, governed by the nondimensional hindrance coefficient. This behavior is enhanced with the nanomaterial content and separate from the slight non-Fickian behavior of all neat epoxy samples. The molecular bonding during diffusion, as well as the interfacial moisture storage, could be among the reasons for non-Fickian behavior and should be included in the absorption models for accurate characterization of carbon/epoxy nanocomposites.