Size effects on diffusion processes within agarose gels

Abstract

To investigate diffusion processes in agarose gel, nanoparticles with sizes in the range between 1 and 140 nm have been tested by means of fluorescence correlation spectroscopy. Understanding the diffusion properties in agarose gels is interesting, because such gels are good models for microbial biofilms and cells cytoplasm. The fluorescence correlation spectroscopy technique is very useful for such investigations due to its high sensitivity and selectivity, its excellent spatial resolution compared to the pore size of the gel, and its ability to probe a wide range of sizes of diffusing nanoparticles. The largest hydrodynamic radius (R(c)) of trapped particles that displayed local mobility was estimated to be 70 nm for a 1.5% agarose gel. The results showed that diffusion of particles in agarose gel is anomalous, with a diverging fractal dimension of diffusion when the large particles become entrapped in the pores of the gel. The latter situation occurs when the reduced size (R(A)/R(c)) of the diffusing particle, A, is >0.4. Variations of the fractal exponent of diffusion (d(w)) with the reduced particle size were in agreement with three-dimensional Monte Carlo simulations in porous media. Nonetheless, a systematic offset of d(w) was observed in real systems and was attributed to weak nonelastic interactions between the diffusing particles and polymer fibers, which was not considered in the Monte Carlo simulations.

FIGURE 1

The value σ (μ ≥ 10⁻²) as a function of the hydrodynamic radius R_A for HTO, □; trace metals, ♦ R6G, NB, R123, HA, ▴; proteins, ▪; latex beads, ▾; Ludox-HS30 silica (HS₃₀); and NH₂- or CO₂H-dendrimers, • (D₄R_B and D_4.5R₁₂₃, respectively). The line shows the compounds displaying only steric interactions with the gel.

FIGURE 2

Normalized FCS autocorrelation functions of diffusing particles within a 1.5% agarose gel (full lines) and in water (dashed lines). The χ² values corresponding to anomalous () and normal () diffusion models for tracer diffusion within agarose gel are given. (a) Parvalbumin: p = 6.55, and (b) R-Phycoerythrin: p = 5.44, and (c) 50-nm latex microspheres: p = 5.64, and Phosphate buffer 5 mM; pH = 7.0; T = 20.0°C.

FIGURE 3

Plot of the fractal dimension of diffusion d_w as a function of reduced particle size. Full line is simulated with the empirical Eq. 10. Dotted line simulates results obtained from MC simulations of bead diffusion in fractal polyacrylamide networks (Netz and Dorfmüller, 1995). Insert is a plot of the fractal exponent α-dependence on reduced particle size. The reduced correlation length of agarose pores has been estimated as the intercept of tangent dotted lines (arrow). Phosphate-buffered solutions; pH = 7.0; μ ≥ 10⁻²; T = 20.0°C.

FIGURE 4

Plot of the fractal exponent α-dependence on volume fraction of agarose. R6G, ▪; Parvalbumin, •. Phosphate-buffered solutions; pH = 7.0; μ ≥ 10⁻²; T = 20.0°C.