Templated Pores in Hydrogels for Improved Size Selectivity in Gel

AC Research

Anal. Chem. 1998, 70, 2433-2438

Accelerated Articles

Templated Pores in Hydrogels for Improved Size Selectivity in Gel Permeation Chromatography Randolph L. Rill,*,† David H. Van Winkle,‡ and Bruce R. Locke§

Department of Chemistry and Institute of Molecular Biophysics and Department of Physics and Center for Materials Research and Technology, The Florida State University, and Department of Chemical Engineering, Florida A&M University and Florida State University College of Engineering, The Florida State University, Tallahassee, Florida 32306

The pore structures of cross-linked polyacrylamide gels can be altered by polymerizing in the presence of high concentrations of unreactive, micellar surfactant cosolutes which act as “templates”. Removal of surfactant after polymerization is expected to leave pores with the approximate shape and dimensions of the surfactant micelles. A simple model was developed to simulate gel permeation chromatography (GPC) separations of globular proteins on templated gels. The model assumes that the partition coefficient for sieving of a protein is equal to the fraction of gel volume accessible to a sphere with a radius equal to the protein Stokes radius. The total gel volume is considered to include a fraction that is a conventional, random gel matrix and a remaining fraction contributed by templated pores. The pore size distribution of the conventional gel was estimated using the Ogston equation, which approximates the matrix as a random collection of long, thin, rigid fibers. Templated pores were assumed to have a Gaussian distribution of radii centered about some mean determined by the micelle radius. In comparison to conventional media, gels with templated pores are predicted to exhibit more sharply defined exclusion limits and improved resolution over a narrow size range centered on the mean templated pore size. Selectivity and resolution are expected to increase as the volume fraction of templated pores is increased and as the dispersion of templated pore radius is decreased. Small changes in template radius lead to large changes in the molecular weight range of optimal separation of globular proteins. It should be possible to create a series of GPC media that collectively offer high S0003-2700(98)00274-1 CCC: $15.00 Published on Web 05/13/1998

© 1998 American Chemical Society

resolution over the molecular weight range of most globular proteins of interest.

Hydrogels are cross-linked, completely interconnected polymer networks combining high water content with high porosity for macromolecules and reasonable mechanical strength. The biocompatability of hydrogels leads to important applications as media for separations of proteins and nucleic acids and as biomaterials including contact lenses and controlled-release devices. Common hydrogel types are “chemical gels” such as polyacrylamide, prepared by polymerization of chain monomers with a crosslinking agent, and “physical” gels such as agarose, created by noncovalent cross-linking of preexisting polymer chains. Both gel classes are intrinsically random chain networks. Gel permeation chromatography (GPC) on uncharged hydrogels relies on differential permeabilities of the gel to molecules of different sizes. Molecular sieving separations of globular proteins on hydrogels are predicted well by treating the proteins as spheres with radii equal to the Stokes radii and assuming that partition coefficients are proportional to the fractional gel volumes accessible to spheres of different radii.1-11 The gel is commonly * Correspondence (tel) 850-644-1768; (fax) 850-644-8281; (e-mail) [email protected]. † Department of Chemistry and Institute of Molecular Physics, The Florida State University. ‡ Department of Physics and Center for Materials Research and Technology, The Florida State University. § Department of Chemical Engineering, Florida A&M University and The Florida State University. (1) Laurent, T. C.; Killander, J. J. Chromatogr. 1964, 14, 317-330. (2) Fawcett, J. S.; Morris, C. J. Sep. Sci. Technol. 1966, 1, 9-26. (3) Siegel, L. M.; Monty, K. J. Biochim. Biophys. Acta 1966, 112, 346-362. (4) Morris, C. J. Protides of the Biological Fluids, 14th Colloquium; Peeters, H., Ed.; Elsevier: New York, 1967; pp 543-551. (5) Morris, C. J.; Morris, P. Biochem. J. 1971, 124, 517-528.

Analytical Chemistry, Vol. 70, No. 13, July 1, 1998 2433

modeled according to Ogston12 as a collection of randomly oriented, long rigid fibers (see also below). The random structures of conventional hydrogels ensure broad distributions of pore sizes. Broad pore size distributions allow for separations over wide molecular weight ranges, but with poor definition of the size exclusion limitsthe largest spheres that can access some internal gel volume (see below). Though beneficial in certain contexts, these attributes prevent highly size-selective separations. Further, the mechanical properties of hydrogels are directly linked to size separation range. The mean pore size is increased by decreasing the polymer content, hence the mechanical strength. The loss of gel rigidity above a certain mean pore size ultimately places a practical limit on the accessible size separation range of a given material. Templating approaches have been proposed to create pores of a defined size within an otherwise normal, cross-linked chemical hydrogel matrix.13-16 Polymerization is conducted in the presence of high concentrations of macromolecules or surfactant micelles intended to limit the possible directions of local chain network growth. Removal of the templating agent after gelation is expected to leave cavities or pores approximating the size and dimensions of the template. Previous studies showed that templating gels with sodium dodecyl sulfate (SDS) at concentrations up to 20% altered the electrophoretic separations of SDS-protein complexes in a manner consistent with the creation of pores by SDS micelles.16 Anderson and Strom14 demonstrated templating of poly(methyl methacrolate) gels by the bicontinuous phase of didodecyldimethylammonium bromide (DDAB) but did not investigate separations on these media. Templated pores were proposed to increase the size selectivity of molecular sieving by hydrogels.16 The templating process is expected to partially decouple pore size from mechanical strength of the gel. Anderson15 noted that such decoupling is expected because the shear modulus of a normal hydrogel is a steeply decreasing, nonlinear function of the water content, but the shear modulus of a macroporous material depends linearly on the macroporosity. This effect can be understood in terms of the large decrease in cross-link concentration in a normal gel with increasing water content (porosity). Analogies can be made to the strategy of putting holes in high-strength construction materials to reduce weight with only a modest reduction in strength. A higher strength-to-weight ratio is obtained than the alternative of using a thinner piece of the same material without holes. (6) Rodbard, D.; Chrambach, A. Proc. Natl. Acad. Sci. U.S.A. 1970, 65, 970977. (7) Rodbard, D.; Chrambach, A. Anal. Biochem. 1971, 40, 95-134. (8) Felgenhauer, K. Hoppe Seylers Z. Physiol. Chem. 1974, 355, 1281-1290. (9) Kuga, S. J. Chromatogr. 1981, 206, 449-461. (10) Smisek, E. L. Electrophoresis 1995, 16, 2094-2099. (11) Tong, J.; Anderson, J. L. Biophys. J. 1996, 70, 1505-1513. (12) Ogston, A. G. Trans. Faraday Soc. 1958, 54, 1754-1757. (13) de Gennes, P. G. Phys. Lett. 1969, 28A, 715-726. (14) Anderson, D. M.; Strom, P. In Polymer Association Structures: Microemulsions and Liquid Crystals, El.-Nokaly, M. A., Ed.; American Symposium Series 384; American Chemical Society: Washington, DC, 1989; pp 204224. (15) Anderson, D. M. Preparation of a polymeric hydrogel containing micropores and macropores for use as a cell culture substrate, U.S. Patent 5,244, 799, 1993. (16) Rill, R. L.; Locke, B. R.; Liu, Y.; Dharia, J.; Van Winkle, D. Electrophoresis 1996, 17, 1304-1312.

2434 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

A method to simulate GPC separations of native proteins on templated gels was desired to examine the potential advantages of templating and conditions required to obtain desirable templating effects. A simple, but well-precedented, model was adopted based on the approach first suggested by Laurent and Killander1 to describe solute partitioning in GPC. This model has been elaborated and extended to describe sieving during electrophoresis as well as chromatography.2,6,8,11,17-20 The fundamental assumption equates the partition coefficient of a globular protein to the fraction of total gel volume available to an equivalent sphere with a radius usually equated to the Stokes radius.1 The Ogston model12 of the gel matrix as a random collection of rodlike fibers has generally been assumed in calculations of the dependence of accessible volume on radius. Slater and Guo19-21 have modeled sieving on nonrandom gels during electrophoresis and pointed out limitations of the Ogston model in this context. The simulations described here assume, by analogy, that the partition coefficient for a globular protein in a templated gel is equal to the fractional volume accessible to the protein within the templated pores plus their surrounding “normal” gel matrix. Templated pores are described in terms of a mean radius with a Gaussian dispersion about the mean, while the pore size distribution within the “normal” gel regions is described by the Ogston equation.12 This approach demonstrates that gels with moderate contents of templated pores can significantly improve size selectivity in molecular sieving, providing more sharply defined exclusion limits and higher resolution over narrow separation ranges than can be attained on conventional gels. Size selectivity increases with increasing fraction of templated volume and decreasing dispersion of the templated pore radius, while the size range of optimal resolution is determined by the mean templated pore size. A following report shows that this model successfully describes GPC of globular proteins and oligonucleotide standards on 20% polyacrylamide gels templated with SDS and confirms that SDS micelles can template pores with radii of about 2 nm (B. Patterson, Y. Liu, D. H. Van Winkle, B. R. Locke, R. L. Rill, in preparation). METHODS Simulation of GPC on Templated and Conventional Gels. As described above, this model follows Laurent and Killander1 (see also refs 6 and 18) in assuming that partition coefficients of molecules due to sieving during GPC are proportional to the fraction of internal volume accessible to equivalent spheres of different radii. Ogston12 showed that the fractional volume, F(R), accessible to a sphere of radius R within a gel modeled as a collection of randomly oriented, rodlike fibers, is given most generally by

4 F(R) ) exp - 2πνL(R + r)2 + πν(R + r)3 3

[(

)]

(1)

where ν is the number of fibers per unit volume, L is the fiber length, and r is the fiber radius. The first term in the exponent (17) (18) (19) (20) (21)

Morris, C. J. Protides Biol. Fluids 1966, 14, 543-551. Richards, E. G.; Temple, C. J. Nature Phys. Sci. 1971, 230, 92-96. Slater, G. W.; Guo, H. L. Electrophoresis 1996, 17, 977-988. Slater, G. W.; Guo, H. L. Electrophoresis 1996, 17, 1407-1415. Slater, G. W.; Guo, H. L. Electrophoresis 1995, 16, 11-15.

dominates when gel fibers are thin and extremely long relative to R, while the second term dominates if the fibers are short and thick. It is convenient to recast eq 1 in terms of T, the mass percentage of polymer in the gel matrix (T ) 100 × mass polymer/mass polymer + solvent) as

F(R) ) exp[-(RT(R + r)2 + βT(R + r)3)]

(2)

where R and β are coefficients. This form of the Ogston equation was chosen for simplicity. Other formulations have been described which take additional features of the gel, e.g., the crosslinker concentration, into account explicitly in alternative expressions for R and β.6,18 Other types of pore size distributions have been described (reviewed in ref 22) which could also be considered within the context of the approach given here. The templating process is assumed to create pores with a Gaussian distribution of radii centered about a mean radius, F, and a dispersion characterized by σ. The probability that a sphere of radius R will fit within a templated pore is then given by

P(R) )

( )

1 1 Q 2πσ

∫

Rmax

R

[

exp -

]

(x - F)2 2σ2

dx

Kav,i )

Ve,i - V0 Vt - V0

(5)

The model assumes that this partition coefficient for a particle with radius Ri is equal to the fractional volume available to a sphere of that radius calculated as above, ie., Φ(Ri) ) Kav,i. The dependence of predicted partition coefficient on the molecular weight of a globular protein was approximated from the radius of an equivalent sphere using the relationship

Mi )

4πNAvRi3 3(vji + 0.25)

(6)

where NAv is Avogadro’s number, vji is the protein partial specific volume (set at 0.73 cm3/g), and the factor of 0.25 approximates an average contribution of hydration and asymmetry to the effective protein volume.23 All calculations were done on a Macintosh Performa 6110 using programs written in Mathcad 3.1 (MathSoft).

(3)

where ft is the fraction of the total gel volume contained within templated pores. Like the original Ogston model, this model intrinsically assumes that any porestemplated or notsis accessible to solutes with radii equal or smaller than the pore radius. The accessibility assumption will not be true if the size distributions of normal and templated pores do not overlap sufficiently (see further discussion below). F(R) was calculated for the limiting case of long, thin fibers; ie., the second term in the Ogston equation was set to zero. The parameter R was adjusted so that the mean pore size for a given T and ratio of bisacrylamide to acrylamide, C, matched the pore sizes reported by Faucett and Morris.2 The experimentally determined partition coefficient for a given solute, Kav,i, is defined for GPC in terms of the total column volume, Vt, the volume between gel particles or “excluded volume”, V0, and the elution volume, Ve,i, as

RESULTS AND DISCUSSION Initial simulations were performed for gels with T ) 20%, and varying volume fractions, ft, of templated pores up to ft ) 0.4. A high acrylamide concentration was chosen in the simulation and in practice16 to accentuate the templating effects by casting templated pores in a background of tight matrix pores. Limits on the degree of templating possible have not been established and will depend on the specific surfactant and polymer, but we suspect that values of ft > 0.4 will be difficult to achieve. A template radius of F ) 2.0 nm was chosen to roughly approximate the dimensions of SDS micelles. The dispersion was arbitrarily set at σ ) 0.1F ) 0.2 nm. The pore size distributions generated by this approach, and corresponding predicted dependence of Kav(R) on particle radius, are illustrated in Figure 1A,B. The difference in Kav(R) between templated gels and a conventional gel with the same T is illustrated in Figure 1C. Although this model is simplistic, we expect the simulations to convey the essential performance features of templated gels. The most fundamental effects of templating are to (1) substantially increase the gel porosity (Kav) for particles of radii approximating the mean radius of templated pores and (2) more sharply define the size exclusion limit. (The latter effect will be observed only when the mean templated pore size is significantly larger than the mean radius of background poresssee below.) The change in ∆Kav with increasing particle radius is gradual (Figure 1C), reaching a maximum when the particle radius is slightly greater than the minimum size of the templated pores (Figure 1A). This corresponds to the crossing point of the size distributions of the background “normal” pores and templated pores. Particles of this size have limited access to the background gel matrix but greater access to the templated pore volume than particles with larger R.

(22) Rodbard, D. In Methods of Protein Separation; Catsimpoolas, N., Ed.; Plenum Press: New York, 1976; Vol. 2, pp 145-179.

(23) Tanford, C. Physical Chemistry of Macromolecules; John Wiley: New York, 1961; p 336.

where Q is a normalization factor obtained by integrating from R ) 0 to Rmax. Rmax was scaled with the mean templated pore radius and was chosen to be sufficiently large that particles of this radius had essentially zero probability of fitting within a templated pore. Values varied from Rmax ) 3.0 nm when F ) 2.0 nm to Rmax ) 5.0 nm when F ) 3.5 nm. The simulation describes the volume fraction, Φ(R), within a templated gel that is accessible to a particle of radius R as a weighted sum of contributions from the normal and templated pores, F(R) and P(R),

Φ(R) ) (1 - ft)F(R) + ftP(R)

(4)

Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

2435

Figure 1. Influence of templated pores on partitioning coefficients of globular proteins with effective radius R. (A) The calculated pore size distribution, dΦ(R) ) Φ(Ri) - Φ(Ri-1) versus Ri, as a function of fractional gel volume in templated pores, ft. Templated pores are assumed to have a radius F ) 2.0 nm with a dispersion σ ) 0.1F ) 0.2 nm. T ) 20% for the conventional gel matrix (ft ) 0) and the background gel matrix of templated gels. The mean pore radius of the normal gel matrix is 0.64 nm. (B) Predicted partitioning coefficients, Kav, for spheres with radius R for normal and templated gels with increasing ft. (C) The difference in Kav between templated gels and a normal gel with the same local polymer density, T, in the gel matrix.

When the simulated fraction of templated pores is reasonably large, the predicted Kav decreases sharply as the particle radius approaches, then exceeds, the mean templated pore radius. Such templated gels should have much more narrowly defined size exclusion limits than conventional gels. The region where Kav drops steeply with increasing radius also represents a narrow size range where high resolution is uniquely possible on templated gels. The molecular weight range of enhanced resolution of globular proteins is predicted to depend on the mean templated pore size and its dispersion. For the postulated mean templated pore radius F ) 2.0 nm and dispersion σ ) 0.2 nm (illustrated in Figure 1), this range is estimated to be about 14 000-27 000 (Figure 2). Kav varied from about 0.32 to 0.08 over this range for ft ) 0.4. The potential ability of templated gels to provide high resolution of proteins over a narrow size range can be appreciated more easily by reference to simulated chromatograms. Figure 3 simulates the separations of nine proteins from 10 500 to 35 600 in size, differing by equal increments in radius, on a normal T ) 10% gel and the above templated gel with ft ) 0.4, F ) 2.0 nm, and σ ) 0.2 nm. Chromatograms were approximated as a sum of nine Gaussian curves of equal area and dispersion, each centered about the predicted Kav of a protein of the indicated molecular weight. Despite the assumption of significant band broadening, a characteristic of GPC, the templated gel is predicted to provide excellent separation of the five proteins from 15 000 to 27 400 2436 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

Figure 2. Predicted molecular weight dependence of partitioning coefficients, Kav, of globular proteins on normal and templated gels. Conditions (T ) 20%, F ) 2.0 nm, σ ) 0.2 nm) are the same as in Figure 1.

Figure 3. Simulated GPC separations of nine globular proteins on a templated gel (as in Figures 1 and 2: ft ) 0.4, T ) 20%, F ) 2.0 nm, σ ) 0.2 nm) and a normal gel (T ) 10%). Protein molecular weights (indicated in thousands) range from 10 500 to 35 600. The proteins differ by equal increments in radius. Assumed bandwidths (arbitrary) are identical for all proteins and both simulations. A normal gel with T ) 10% and a mean pore size of 1.62 nm was simulated because the smallest component (10 500) had approximately the same calculated Kav on the two gels.

(Figure 3, top). Little or no separation is expected for proteins larger than 30 000 or smaller than 13 000. By contrast, a 10% conventional gel should partially separate all components, but with poor resolution over the entire range (Figure 3, bottom). A T ) 10% gel was chosen for comparison because the predicted Kav for

Figure 4. Simulated influence of degree of templating, ft (expressed here as a percent), on GPC separations of nine globular proteins on templated gels (as in Figures 1 and 2: T ) 20%, F ) 2.0 nm, σ ) 0.2 nm).

the 10 500 protein was about the same on this conventional gel and the templated gel. The exclusion limit of a conventional gel with T ) 20% is too low to permit separation of proteins in this size range. The separation predicted for the conventional 10% gel is consistent with published data (e.g., see ref 2). The sharpness of the molecular weight cutoff, the breadth of the size range of enhanced resolution, and the resolving power of a templated gel in the range of particle radii near the mean templated pore radius are dependent on two factors. These are the volume fraction, ft, and the size distribution (represented by σ) of templated pores. These dependencies are easily understood. The spread in Kav values, hence the resolving potential, over the size separation range of templated pores is directly determined by the volume fraction ft. Figure 4 shows the effects on simulated chromatograms if ft is reduced, while keeping other parameters the same as in Figure 3. Although reducing ft progressively narrows the size range of enhanced separation, unique separations should be possible, even for low degrees of templating. The three intermediate size proteins in this group (17 700, 20 600, and 23 800) are predicted to be reasonably well resolved from others for ft ) 0.3. On the gel with ft ) 0.2 the same proteins, particularly the 20 000 Kda component, are still predicted to be resolved somewhat better than on the normal 10% gel. The ft ) 0.1 gel is not predicted to resolve any of the individual components, but to cleanly separate the four larger components (23 800-35 600), eluting in the void volume peak, from the three smallest components (10 500-15 000) eluting in the second peak. This degree of discrimination is not expected on any conventional gel. The size exclusion limit would be infinitely sharp if there were no dispersion in the size of templated pores, since particles even slightly larger than the pores could not enter the gel. In this extreme, the size separation range would be infinitely narrow, and the resolution or difference in Kav for particles that could barely enter the pores and those that could not would simply be Kav ) ft. Dispersion of the templated pore size broadens the separation range related to templating at the expense of resolution, as illustrated in Figure 5. Increasing the volume fraction of templated pores with constant dispersion increases the range of Kav influenced by templating and, hence, increases the resolution (Figure 2). The simple model used to simulate the behaviors of templated gels makes the critical assumption that particles have access to all templated pores through the background gel matrix. That is,

Figure 5. Predicted influence of the dispersion, σ, of templated pore size on the molecular weight dependence of partitioning coefficients, Kav, of globular proteins on templated gels. Other conditions (ft ) 0.4, T ) 20%, F ) 2.0 nm) are the same as in Figure 2. (Top) Calculated pore size distributions. (Bottom) Predicted dependence of Kav on molecular weight.

it is assumed that continuous paths through the gel exist for molecules with radii approaching the radii of the largest pores and that all large pores are accessible through such paths. These assumptions are not strictly true in conventional gels21 and will not be the case for templated pores if the concentration of polymer in the background matrix is so high that there are vanishingly few “normal” pores with the dimensions of templated pores. Calculation of the limiting polymer concentration would require a substantially more detailed model. Since the probability that templated pores will be accessible can be increased by decreasing the background gel concentration, we examined the dependence of Kav predicted from the simple model on the polymer concentration, T, in the background matrix. Kav values were calculated for a mean templated pore size of 2.0 nm and decreasing values of T. These simulations predict that templating should improve resolution of proteins within a narrow size range determined primarily by the templated pore diameters, not the background matrix concentration (Figure 6, top). The predicted size range of optimal separation in normal gels increased progressively with decreasing T, as expected (Figure 6, bottom). For example, reducing the acrylamide concentration of templated gels from 20 to 12%, which increases the calculated mean pore radius of the background matrix from 0.64 to 1.16 nm, is predicted to have little effect on either the exclusion limit or size range of optimal separation and may slightly improve resolution by increasing the spread of Kav within this range. Increased connectivity of templated pores at lower T values, a factor not included in the model, would also tend to improve performance. Further increasing the mean pore radius to 1.62 (T ) 10%) or 2.03 nm (T ) 8%) overlaps the optimal separation ranges of the conventional gels and templated gels. This overlap degrades the definition of the size exclusion limit but does not diminish the enhanced resolution over a narrow size range expected from the templating process. Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

2437

Figure 6. Predicted influence of the polyacrylamide concentration in the normal gel matrix on the molecular weight dependence of partitioning coefficients, Kav, of globular proteins on templated and normal gels. Other conditions (ft ) 0.4, F ) 2.0 nm, σ ) 0.2 nm) are the same as in Figure 2. Mean pore sizes of the normal gels are 0.64 (T ) 20%), 0.85 (T ) 15%), 1.16 (T ) 12%), 1.62 (T ) 10%), and 2.03 nm (T ) 8%).

There are many surfactants of different chain lengths and headgroup compositions that might be used to tune the dimensions of templated pores. Micelle size depends intimately on surfactant structure. Since the molecular weights of globular proteins scale approximately with the cube of the radius, small variations in templated pore radius are expected to cause large changes in the protein size range for optimal separation (Figure 7). Simulations illustrated in Figure 7 were performed for T ) 20%, ft ) 0.4, and σ ) 0.1F. Based on these constraints, increasing the mean templated pore radius from 2.0 to 3.5 nm in increments of 0.5 nm increases the size range of optimal separation from about 15 000-30 000 (F ) 2.0 nm) to 30 000-50 000 (F ) 2.5 nm), 50 000-90 000 (F ) 3.0 nm), or 80 000-140 000 (F ) 3.5 nm). Surfactants forming micelles with radii as large (and larger) than 3.5 nm are available. It may be possible to create a series of GPC media that offer high resolution of proteins within narrow molecular weight ranges and collectively span the molecular weight range of a large majority of proteins. CONCLUSIONS These simulations predict that gels containing a subset of templated pores having a narrow size distribution should yield significantly improved size selectivity in molecular sieving in comparison to conventional gels. Templated gels are expected to provide both more sharply defined exclusion limits and improved resolution over narrow size ranges. Size selectivity increases with increasing volume fraction of the gel contained in

2438 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

Figure 7. Predicted influence of the mean templated pore size on the molecular weight dependence of partitioning coefficients, Kav, of globular proteins on templated gels. Other conditions (ft ) 0.4, T ) 20%, σ ) 0.2 nm) are the same as in Figure 2.

templated pores and decreasing dispersion of the templated pore radius. The size range of optimal resolution centers around the mean templated pore size. Even low degrees of templating may produce useful changes in separations if the size distribution of templated pores is narrow. The templating process is expected to provide the additional advantage of partially decoupled mechanical strength of a gel from its porosity. Small changes in template radius can lead to large changes in the molecular weight range of optimal separation of roughly spherical, globular proteins because their molecular weight increases as R3. It should be possible to use different surfactants as templates to create a series of GPC media that collectively offer high resolution over the molecular weight range of most globular proteins of interest. Such media may be particularly useful in biotechnology for large-scale purification of a specific expressed protein. ACKNOWLEDGMENT This work was supported in part by NSF Grant BES-951381 and the FSU Center for Materials Research and Technology (MARTECH). We thank Hank Henricks for technical support and our students Yingjie Liu and Brian Patterson for discussions and experimental support of these concepts. Received for review March 10, 1998. Accepted April 22, 1998. AC980274T