Thin PA gels were polymerized while sandwiched between ATCS-functionalized and non-functionalized glass coverslips (). Each gel was prepared from 4µl of acrylamide plus cross linker at 3.6% and 6% w/v monomer concentration, with nominal elasticities of 1 and 10 kPa (recall ) that mimic the microelasticity of brain(1
) and muscle(4
) respectively (). Gel thickness was nominally controlled at the micron scale with 0.5 µm and 1 µm monodispersed silica microspheres, serving as physical spacers between the glasses. Thicker gels were also prepared with no spacer beads. After polymerization, gels were immersed in water for a few hours which allowed for easy detachment of the top coverslip.
Figure 4 Preparation of thin PA gels. (A) Thin PA gels were polymerized between an ATCS-treated coverslip and a clean coverslip. To control gel thickness, micron-scale bead spacers were included in the gels and pressed between the glass substrates using a weight. (more ...)
Gel thickness was evaluated from z-stack fluorescence images obtained by a laser-scanning confocal microscope. To fluorescently label the gels, allylamine was included during polymerization (1% of acrylamide mol/mol); allylamine is a small molecule similar in size to acrylamide and is thus unlikely to modify the mechanical properties of the gels, especially since it is almost completely protonated (NH3+) in water (amine pKa = 9.5) while acrylamide remains neutral (amide pKa = 0.5). The calculated mean distance between adjacent charged amine groups is 5.8 nm for 6% w/v gels and 7.3 nm for 3.6% w/v gels; these length scales are both larger than the Debye length (for electrostatic interactions) in physiologically buffered solution. Gels were conjugated with fluorescein-isothiocyanate (FITC) fluorophores that bind via the allylamine-flanking primary amines; FITC conjugation was carried out after gel polymerization and not during gel polymerization to minimize steric alterations to the structure of the gels. FITC possesses a carboxyl group which is negatively charged at neutral pH, and so the charge arguments above apply to the dye as well. Microelasticity measurements below will ultimately validate the expectation that labeling perturbations have negligible effect on gel mechanics. Imaging of the fluorescently labeled gels showed laterally homogeneous fluorescence, consistent with gels of uniform thickness and no obvious cracks or wrinkles to affect cell-matrix interactions.
Cross sections of soft (3.6% w/v) and stiff (6% w/v) gels were obtained by confocal microcopy (). Gel thickness was obtained for each gel at randomly chosen sites (> 5 sites) using an edge detector (). Z-stack images of parallel slices with submicron thickness (0.25 – 0.67µm) were scanned slice by slice. Fluorescence intensity as a function of z (scanning window position) was generated by a convolution of the gel intensity profile and the scanning laser window (middle). At a first approximation, which holds true for small numerical aperture objective lenses and for homogeneous objective-sample immersion coupling, the laser intensity has a symmetric squared-sinc profile, gel edges (z1, z2) can be easily obtained from the z-derivative (right). This derivative-based edge-detector method for evaluating gel thickness remained valid also for gels with non-rectangular intensity gradients that are shallow as compared with the slopes of the convolution curve at vicinity of the gels edges ().
To assess the origins of intensity gradients and address photo-bleaching effects, gels were scanned both bottom-up and top-down. The differences between fluorescence profiles that were obtained in opposite directions are illustrated for a thick, soft gel (). Bottom-up scans in which the top of the gel was exposed to laser excitation during the entire scan prior to being imaged showed ~30% decrease in intensity relative to the glass-gel interface. In the opposite scanning direction, the top of the gel was imaged first and thus underwent minimal bleaching relative to lower sections. In this case, the fluorescence intensity at the top of the gel was only ~10% lower than the gel bottom. Similar fluorescence gradients were obtained for top-to-bottom and for bottom-to-top scans using non-immersion objective lenses as were observed with oil-immersion objective lenses. While both objective lenses reveal a modest non-homogeneous density profile through the gel thickness, the refractive index of air is smaller than the specimen (water) in opposite to oil, thus arguing against the notion that the observed gradients are optical aberrations. Based on an average of the normalized top-down and bottom-up intensity profiles, gel density decreases monotonically with z, reaching 80% PA density at the top of the gel relative to the bottom (for soft gels). This suggests non-uniform swelling of the gels in water, and the degree of swelling relative to the spacer beads is seen to vary from 1.6 to 12.3 fold ().
Thickness measurements for gels (±SEM).
To estimate the effects that the rigid substrate has on the effective stiffness that cells are likely to sense when cultured on thin matrices, the microelasticity of thin PA gels was measured using AFM. The characteristic forces and gel deformations that are exerted by AFM amount to tens-to-hundreds pN and extend over a few microns – which are typical of cell-induced stresses and strains(28
). Gel E
was thus evaluated from the force-indentation relations by fitting to the z-parabolic variant of the classical Hertz model(29
) that was adjusted to a spherical cone geometry as a model of a pyramidal tip (, inset). We assume a Poisson ratio ν = 0.5, in accord with our stretching measurements of PA gels (). Fitting of force-indentation curves is generally subjected to a choice of the indentation range to be fitted. We find that the evaluation of E
is highly dependent on the choice, with three regimes corresponding to fitting over increasing indentation regimes that start at gel-tip contact points. Importantly, this contact point was evaluated analytically from the increase in the slope of the force-indentation curve and was verified using the relation between the indentation and the tip deflection in the vicinity of the contact point(30
). With increasing range of indentation, E
decreases sharply, reaches a plateau at ~500 nm and then remains unchanged up to ~1 µm range, above which it increases again. The quality of the fit was quantified by the RMS-deviation from the experimental curve and proves to be minimal in the middle regime of the fitting range (). We find that the patterns described here for the fitting of E and for the RMS-deviation of the fit from the experimental curve were both consistent for all gels with varying nominal elasticity and thickness. We therefore estimated the apparent gel elasticity in the middle regime which satisfies two requirements: (i
) the fitted E
is robust to changes in the fitting range, and (ii
) the mean root-mean-square deviation of the fit from the experimental data per data point is minimal. Both of these conditions are satisfied in respectively for the fit range that is illustrated by green brackets.
Figure 5 Apparent elasticity of thin gels as evaluated from force-indentation analyses with AFM. (A) Force-indentation curves were fitted (inset) by a variant of the classical Hertz model adjusted for pyramidal (cone-like) tip geometry. (B) E was estimated in (more ...)
The apparent elasticity measured for thin gels differed from expected values, both for 1 and 10 kPa gel formulations (). Thin gels proved to be softer than bulk gels consistent with swelling and density thinning at the top of the gels ( and ). The effects of the bottom surface on the apparent elasticity of the gels are likely reflected in the increased stiffness of the thinnest gels as compared with the intermediate thickness and thick gels.
To summarize, we present thin PA gels of soft and stiff elasticity and of controlled thickness that range from a few microns to ~10 µm and ~20 µm as nominally set by spacer beads or by limiting volume of the gel precursor. Despite their hydrophobicity, uniform films are formed on the ATCS-derivatized glass substrates onto which the gels bind covalently. Variations in gel thickness and in local micro-elasticity were assessed with AFM measurements at 7–10 randomly chosen sites per gel and for gel duplicates and are presented by the error bars shown in . While trends in gel thickness as a function of spacer size and/or gel precursor volume are conserved, gel thickness measurements should be carried out separately for each experiment to obtain absolute values. We find also that the type and brand of glass used both as gel substrates and as overlying coverslips may alter gel thickness even when the same spacer beads are used, so that careful measurement of these systems is probably wise.
Mechanical properties of PA gels are determined at first order by the polymer-to-crosslinker ratio and are related to pore size. Pore sizes in PA gels are typically tens of nanometers and are thus well below the various length scales of relevance, including gel thickness, cell spread area and focal adhesion size. The thin gel are therefore continuous substrata with well defined elasticity. Confocal images suggest a surface roughness of thin gels is ~0.5 µm (not shown) and within 100-by-100 µm2 fields of view irregularities of 1–2 µm height are rare. Only for the thinnest gels here is such roughness non-negligible and likely to give rise to an increased variability in gel micro-elasticity (per ). However, over surface areas that correspond to either the area of spread cells (>1000 µm2) or the area of focal adhesions (~1–10 µm2), the characteristic roughness of the gel surfaces seems unimportant. Taken together, thin PA gel films seem well defined in terms of structure and effective micro-elasticity, which are both necessary and sufficient for describing the mechanical interactions between surface-immobilized compliant matrices of finite thickness and adhesive and contractile cells.