Protein diffusion in porous gel filtration chromatography media studied by pulsed field gradient NMR spectroscopy

Investigation of Lysozyme Diffusion in Agarose Hydrogels Employing a Microfluidics-Based UV Imaging Approach

Hydrogels are polymer-based materials with a high water content. Due to their biocompatible and cell-friendly nature, they play a major role in a variety of biotechnological applications. For many of these applications, diffusibility is an essential property influencing the choice of material. We present an approach to estimate diffusion coefficients in hydrogels based on absorbance measurements of a UV area imaging system. A microfluidic chip with a y-junction was employed to generate a fluid-hydrogel interface and the diffusion of lysozyme from the fluid into the hydrogel phase was monitored. Employing automated image and data processing, analyte concentration profiles were generated from the absorbance measurements and fits with an analytical solution of Fick’s second law of diffusion were applied to estimate diffusion coefficients. As a case study, the diffusion of lysozyme in hydrogels made from different concentrations (0.5–1.5% (w/w)) of an unmodified and a low-melt agarose was investigated. The estimated diffusion coefficients for lysozyme were between 0.80 ± 0.04×10−10 m2 s−1 for 1.5% (w/w) low-melt agarose and 1.14 ± 0.02×10−10 m2 s−1 for 0.5% (w/w) unmodified agarose. The method proved sensitive enough to resolve significant differences between the diffusion coefficients in different concentrations and types of agarose. The microfluidic approach offers low consumption of analyte and hydrogel and requires only relatively simple instrumentation.

A surface flattening method for characterizing the surface stress, drained Poisson's ratio and diffusivity of poroelastic gels

When a poroelastic gel is released from a patterned mold, surface stress drives deformation and solvent migration in the gel and flattens its surface profile in a time-dependent manner. Specifically, the gel behaves like an incompressible solid immediately after removal from the mold, and becomes compressible as the solvent is able to squeeze out of the polymer network. In this work, we use the finite element method (FEM) to simulate this transient surface flattening process. We assume that the surface stress is isotropic and constant, the polymer network is linearly elastic and isotropic, and that solvent flow obeys Darcy's law. The short-time and long-time surface profiles can be used to determine the surface stress and drained Poisson's ratio of the gel. Our analysis shows that the drained Poisson's ratio and the diffusivity of the gel can be obtained using interferometry and high-speed video microscopy, without mechanical measurement.

Alternative method to study the radial dispersion in liquid chromatography columns. Part II: Experimental

The present contribution reports on the practical implementation and validation of a new experimental method to determine the radial dispersion (D_rad) in packed bed liquid chromatography columns, as well as on the results obtained with it. A first important validation was that the measured D_rad-values were independent of the applied relative central flow rate (varied from 25% to 57%). The obtained D_rad-values did not vary significantly when changing the concentration of the injected tracer to check potential mass overloading effects (25, 50 or 75 ppm of tracer for the acetophenone measurements; 12.5 and 25 ppm of tracer for the toluene measurements). And yet another important validation step was the observation that the D_rad-values clearly converged to the value of D_eff for velocities going to zero, as physically and theoretically expected. Plotting the obtained results as a plot of D_rad/D_mol versus the reduced velocity ν, a quasi-linear relationship is obtained. The slope of the curve (β = 0.38 and β = 0.46 for toluene and acetophenone, respectively) is significantly larger than the value that is most frequently cited in engineering literature. However, the obtained β-values and D_rad/D_mol-values still fall within the broad range of β- and D_rad/D_mol-values cited in literature.

Mathematical modeling of molecular diffusion through mucus

The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia.

Direct quantification of intraparticle protein diffusion in chromatographic media

Diffusion coefficients of proteins in chromatographic media are important parameters for the rational design of stationary phases and purification schemes. In contrast to free diffusion, intraparticle diffusion is hindered by the porous structure of the media. Direct intraparticle diffusion analysis (IDA) is a novel approach for the determination of intraparticle protein diffusion coefficients. IDA is based on the evaluation of spatially and temporally resolved intraparticle concentration profiles. To prevent adsorption and to study diffusion only, the chromatographic media are investigated in underivatized form. With IDA, intraparticle concentration profiles are measured in a microcolumn by confocal laser scanning microscopy (CLSM). From this dynamic data, the diffusion coefficients are determined by parameter estimation, using a spheric diffusion model. The boundary condition is given by the measured protein concentration in the bulk phase. IDA is applied to determine intraparticle diffusion coefficients of seven different proteins in Sepharose 6 FF. The results show excellent congruence of experimental data and simulation results. Moreover, the determined diffusion coefficients lie well within the range of data published in the literature. Given that the material in question allows optical analysis, IDA is a general approach for studying protein diffusion in porous particles and is easily adapted to different proteins, solution conditions and stationary phases.

The limits of the separation power of unidimensional column liquid chromatography

The practical limit of the separation power of HPLC depends on time, money, and skill. That is it depends on the time available for the analysis, on the quality and performance of the pump and hardware and particularly on the maximum pressure at which the pump can deliver the mobile phase to the column, and on the temperature at which the column can be operated. It also depends on the properties of the packing material selected (e.g., its particle size, its pore geometry, and its connectivity) and on the packing method used since it affects the coefficients of the HETP equation. Finally, it depends on the thermal stability of the sample and the packing material. The complexity of the sample also plays an important role in that it determines whether the analysis should be made under isocratic, isothermal conditions, in gradient elution, in temperature programming, or with a combination of both types of programming. The various phenomena that affect column properties and separation performance are discussed. Past achievements suggest that columns providing efficiencies in excess of a million plates in less than 1 day are within the grasp of current technology. The possibility of further advances are considered.

Measurement of Desorption Rates from Octadecylsilyl Bonded-Phase HPLC Particles and Its Characterization in Terms of Pore, Surface, and Film Diffusion

An instrument is developed to measure rates of desorption of solutes from particulate HPLC packing materials for processes that are quantitatively complete in a few tenths of a second. The instrument is a modified, pressure-driven, stopped-flow device. The major modifications include positioning a very short (0.6 mm) bed of the particles just upstream of the detector cell, eliminating the mixing chamber, and adding high-speed switching valves in order to allow sequential continuous flow of individual solutions. Instantaneous rate curves are measured for the desorption of 1,2-dimethyl-4-nitrobenzene (DMNB) from 12-microm-diameter porous particles of the bonded-phase packing Luna C-18 employing high linear velocities of the eluting solvent. The same experiment is performed for the nonsorbed compound phloroglucinol (PG) The PG rate curve is used in two ways (i.e., subtraction and deconvolution) in order to correct the observed rate curve of DMNB for experimental artifacts such as bed hold-up volume and instrument band broadening. The cumulative desorption rate curve of DMNB is obtained by integration. It is accurately described (R2 > 0.999) by a theoretical model that invokes both intraparticle diffusion (including both hindered pore diffusion and surface diffusion) and external film diffusion. The surface diffusion coefficient is (3.2 +/- 0.8) x 10(-6) cm(2)/s and the diffusion film thickness is 0.5 microm. The validity, of both the experimental technique and the theoretical model, is demonstrated by excellent agreement between a predicted and an observed chromatographic elution peak for DMNB on a 25-cm-long commercial column of Luna C-18.

Hindered convection of macromolecules in hydrogels

Hindered convection of macromolecules in gels was studied by measuring the sieving coefficient (theta) of narrow fractions of Ficoll (Stokes-Einstein radius, r(s) = 2.7-5.9 nm) in agarose and agarose-dextran membranes, along with the Darcy permeability (kappa). To provide a wide range of kappa, varying amounts of dextran (volume fractions < or = 0.011) were covalently attached to agarose gels with volume fractions of 0.040 or 0.080. As expected, theta decreased with increasing r(s) or with increasing concentrations of either agarose or dextran. For each molecular size, theta plotted as a function of kappa fell on a single curve for all gel compositions studied. The dependence of theta on kappa and r(s) was predicted well by a hydrodynamic theory based on flow normal to the axes of equally spaced, parallel fibers. Values of the convective hindrance factor (K(c), the ratio of solute to fluid velocity), calculated from Theta and previous equilibrium partitioning data, were unexpectedly large; although K(c) < or = 1.1 in the fiber theory, its apparent value ranged generally from 1.5 to 3. This seemingly anomalous result was explained on the basis of membrane heterogeneity. Convective hindrances in the synthetic gels were quite similar to those in glomerular basement membrane, when compared on the basis of similar solid volume fractions and values of kappa. Overall, the results suggest that convective hindrances can be predicted fairly well from a knowledge of kappa, even in synthetic or biological gels of complex composition.

Factors determining hydrogel permeability

Developing hydrogel membranes and coatings of appropriate permeability characteristics is key to the success of a number bioartificial organ technologies. Key principles relevant to the design and application of hydrogels for such applications were reviewed. The first key point is that permeability is a function of both transport and thermodynamic properties, the diffusion coefficient and partition coefficient, respectively, and that these parameters can be evaluated separately. Although the aspect of partitioning often emphasized is size exclusion, this review points out that many other relevant interactions come into play, especially hydrophobic and electrostatic interactions, and that these phenomena can dominate size exclusion. Similarly, while the diffusion coefficient also is strongly dependent upon size, other interactions can also cause diffusivity to deviate from theories which consider only solute size and gel swelling. For example, the heterogeneity of hydrogel networks can result in permeabilities that fail to decline as much as might be anticipated if networks were uniform.

In situ analysis of protein chromatography and column efficiency using magnetic resonance imaging

Magnetic resonance imaging has been used to visualize size-based protein separations inside operating chromatography columns. The effects of flow nonuniformity have been observed and analyzed quantitatively through concentration profiles of tracers measured inside the column. Analysis of these profiles provides local and averaged intracolumn plate height values for characterization of dispersion and flow nonuniformity. The magnetic resonance measurements compare favorably with conventional chromatographic measurements of column efficiency and provide more detailed insights into nonideal column performance.