Diffusion-limited encounter rate in a three-dimensional lattice of connected compartments studied by Brownian-dynamics simulations.

We considered the rate at which a diffusing particle encounters a target in a three-dimensional lattice of compartments with semipermeable walls. This work expands a previous theory [Li et al., Phys. Rev. Lett. 113, 028303 (2014)] for the encounter rate in the dilute limit of targets to the general case of any density of targets. We also used Brownian dynamics simulations to evaluate the approximations in the analytical theory. We find that the largest errors in the analytical theory are on the order of 10%. This work therefore demonstrates an analytical theory capable of describing the encounter rates in compartmentalized environments for any level of confinement and any target density.

Effects of macromolecular crowding on the structure of a protein complex: a small-angle scattering study of superoxide dismutase.

Macromolecular crowding can alter the structure and function of biological macromolecules. We used small-angle scattering to measure the effects of macromolecular crowding on the size of a protein complex, SOD (superoxide dismutase). Crowding was induced using 400 MW PEG (polyethylene glycol),TEG (triethylene glycol), α-MG (methyl-α-glucoside), and TMAO (trimethylamine n-oxide). Parallel small-angle neutron scattering and small-angle x-ray scattering allowed us to unambiguously attribute apparent changes in radius of gyration to changes in the structure of SOD. For a 40% PEG solution, we find that the volume of SOD was reduced by 9%. Considering the osmotic pressure due to PEG, this deformation corresponds to a highly compressible structure. Small-angle x-ray scattering done in the presence of TEG suggests that for further deformation-beyond a 9% decrease in volume-the resistance to deformation may increase dramatically.

Size-Dependent Diffusion of Dextrans in Excised Porcine Corneal Stroma.

Delivery of therapeutic agents to the eye requires efficient transport through cellular and extracellular barriers. We evaluated the rate of diffusive transport in excised porcine corneal stroma using fluorescently labeled dextran molecules with hydrodynamic radii ranging from 1.3 to 34 nm. Fluorescence correlation spectroscopy (FCS) was used to measure diffusion coefficients of dextran molecules in the excised porcine corneal stroma. The preferential sensitivity of FCS to diffusion along two dimensions was used to differentially probe diffusion along the directions parallel to and perpendicular to the collagen lamellae of the corneal stroma. In order to develop an understanding of how size affects diffusion in cornea, diffusion coefficients in cornea were compared to diffusion coefficients measured in a simple buffer solution. Dextran molecules diffuse more slowly in cornea as compared to buffer solution. The reduction in diffusion coefficient is modest however (67% smaller), and is uniform over the range of sizes that we measured. This indicates that, for dextrans in the 1.3 to 34 nm range, the diffusion landscape of corneal stroma can be represented as a simple liquid with a viscosity approximately 1.5 times that of water. Diffusion coefficients measured parallel vs. perpendicular to the collagen lamellae were indistinguishable. This indicates that diffusion in the corneal stroma is not highly anisotropic. Our results support the notion that the corneal stroma is highly permeable and isotropic to transport of hydrophilic molecules and particles with hydrodynamic radii up to at least 34 nm.

Calculated rates of diffusion-limited reactions in a three-dimensional network of connected compartments: application to porous catalysts and biological systems.

We describe the diffusion limit for reaction rates in a three-dimensional system of connected compartments. This model exhibits the length-scale dependent diffusion that can be observed in many heterogeneous environments, such as porous catalysts and biological environments. We obtain a simple analytical expression for the diffusion limit applicable to any scale of the compartment confinement. This diffusion limit exceeds the classic Smoluchowski diffusion limit that was derived for homogeneous environments but is often applied to biological reactions in heterogeneous environments. We expect our new diffusion limit to provide a more appropriate upper bound on reaction rates in biological systems, porous structures, and other heterogeneous environments where obstacles create local confinement.

Multivalent ion screening of charged glass surface studied by streaming potential measurements.

We used streaming potential technique to measure ζ potentials for glass as a function of Co(NH3)6Cl3 concentration, KCl concentration, and pH. Charge inversion was observed only at high surface charge densities and was inhibited by increased KCl concentration. Measured ζ potentials were compared with predictions from a recent theory by dos Santos et al. [J. Chem. Phys. 132, 104105 (2010)] that models multivalent ions adsorbed to the charged surface as a strong coupled liquid (SCL). The location of shear plane was determined independent of the SCL theory, allowing a rigorous experimental test of the theory with no fitting parameters. We found that SCL predictions agree quantitatively with our experimental data.

Kinetics of loop formation in worm-like chain polymers.

A common theoretical approach to calculating reaction kinetics is to approximate a high-dimensional conformational search with a one-dimensional diffusion along an effective reaction coordinate. We employed Brownian dynamics simulations to test the validity of this approximation for loop formation kinetics in the worm-like chain polymer model. This model is often used to describe polymers that exhibit backbone stiffness beyond the monomer length scale. We find that one-dimensional diffusion models overestimate the looping time and do not predict the quantitatively correct dependence of looping time on chain length or capture radius. Our findings highlight the difficulty of describing high-dimensional polymers with simple kinetic theories.

Separability of electrostatic and hydrodynamic forces in particle electrophoresis.

By use of optical tweezers we explicitly measure the electrostatic and hydrodynamic forces that determine the electrophoretic mobility of a charged colloidal particle. We test the ansatz of O'Brien and White [J. Chem. Soc. Faraday II 74, 1607 (1978)] that the electrostatically and hydrodynamically coupled electrophoresis problem is separable into two simpler problems: (1) a particle held fixed in an applied electric field with no flow field and (2) a particle held fixed in a flow field with no applied electric field. For a system in the Helmholtz-Smoluchowski and Debye-Hückel regimes, we find that the electrostatic and hydrodynamic forces measured independently accurately predict the electrophoretic mobility within our measurement precision of 7%; the O'Brien and White ansatz holds under the conditions of our experiment.

DNA stretching and multivalent-cation-induced condensation.

Motivated by measurements on stretched double-stranded DNA in the presence of multivalent cations, we develop a statistical mechanical model for the compaction of an insoluble semiflexible polymer under tension. Using a mean-field approach, we determine the order of the extended-to-compact transition and provide an interpretation for the magnitude and interval of tensions over which compaction takes place. In the simplest thermodynamic limit of an infinitely long homogeneous polymer, compaction is a first-order transition that occurs at a single value of tension. For finite length chains or for heterogeneous polymers, the transition progresses over an interval of tension. Our theory provides an interpretation for the result of single-molecule experiments in terms of microscopic parameters such as persistence length and free energy of condensation.

Electrostatic exclusion of neutral solutes from condensed DNA and other charged phases.

Motivated by experiments on condensed DNA phases in binary mixtures of water and a low-dielectric solute, we develop a theory for the electrostatic contribution to solute exclusion from a highly charged phase, within the continuum approximation of the medium. Because the electric field is maximum at the surface of each ion, the electrostatic energy is dominated by the Born energy; interactions between charges are of secondary importance. Neglecting interactions and considering only the competition between the Born energy and the free energy of mixing, we predict that low dielectric solutes are excluded from condensed DNA phases in water-cosolvent mixtures. This suggests that the traditional continuum electrostatic approach of modeling binary mixtures with a uniform dielectric constant needs to be modified. The linking of solute exclusion to solute dielectric properties also suggests a mechanism for predicting the electrostatic contribution to preferential hydration of polar and charged surfaces.

Attractive forces between cation condensed DNA double helices.

By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 +/- 0.1 A characteristic decay length and the attractive component of the free energy is always 2.3 +/- 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 +/- 0.5 A characteristic decay length for intermolecular attractions between condensed DNA molecules.

Interplay of ion binding and attraction in DNA condensed by multivalent cations.

We have measured forces generated by multivalent cation-induced DNA condensation using single-molecule magnetic tweezers. In the presence of cobalt hexammine, spermidine, or spermine, stretched DNA exhibits an abrupt configurational change from extended to condensed. This occurs at a well-defined condensation force that is nearly equal to the condensation free energy per unit length. The multivalent cation concentration dependence for this condensation force gives the apparent number of multivalent cations that bind DNA upon condensation. The measurements show that the lower critical concentration for cobalt hexammine as compared to spermidine is due to a difference in ion binding, not a difference in the electrostatic energy of the condensed state as previously thought. We also show that the resolubilization of condensed DNA can be described using a traditional Manning-Oosawa cation adsorption model, provided that cation-anion pairing at high electrolyte concentrations is taken into account. Neither overcharging nor significant alterations in the condensed state are required to describe the resolubilization of condensed DNA. The same model also describes the spermidine3+/Na+ phase diagram measured previously.

Probing the limits of the Derjaguin approximation with scanning force microscopy.

We have measured the interaction force between a silicon nitride scanning force microscopy (SFM) probe and the basal plane of highly oriented pyrolitic graphite as a function of pH and ionic concentration in aqueous solutions. Forces in the range +/- 50 pN were reconstructed from measured signals using dynamical analysis of the cantilever. We modeled the force-separation data using a flat plate electric double-layer interaction and assumed the Derjaguin approximation to adapt the flat plate geometry for the SFM probe shape. Measured forces were well modeled by the theory at high ionic concentrations (10 and 100 mM), where Debye lengths were 3.0 and 0.96 nm, respectively. The theory failed to model forces at a lower ionic concentration (1 mM), where the Debye length was 9.6 nm. To investigate this, we calibrated the SFM probe geometry using blind reconstruction and obtained an apex radius of 7 nm. This value suggested that failure of the theory was due to an invalidation of the Derjaguin approximation at long Debye lengths, where the characteristic length scale for the interaction was larger than the size of the SFM probe. The errors were reduced by replacing the Derjaguin approximation with a surface element integration. The result experimentally demonstrates the limitations of the Derjaguin approximation for predicting interactions of nanoscale colloids.

Connecting nanoscale images of proteins with their genetic sequences.

We present a technique for reconstructing biomolecular structures from scanning force microscope data. The technique works by iteratively refining model molecules by comparison of simulated and experimental images. It can remove instrument artifacts to yield accurate dimensional measurements from tip-broadened data. The result of the reconstruction is a model that can be chosen to include the physically significant parameters for the system at hand. We demonstrate this by reconstructing scanning force microscope images of the cartilage proteoglycan aggrecan. By explicitly including the protein backbone in the model, we are able to associate measured three-dimensional structures with sites in the protein primary structure. The distribution of aggrecan core protein lengths that we measure suggests that 48% of aggrecan molecules found in vivo have been partially catabolized at either the E(1480)-(1481)G or E(1667)-(1668)G aggrecanase cleavage site.