Rediscovering Hydrogel-Based Double-Diffusion Systems for Studying Biomineralization

Abstract

For those seeking to model biomineralization in vitro, hydrogels can serve as excellent models of the extracellular matrix (ECM) microenvironment. A major challenge posed in implementing such systems is the logistics involved, from fundamental engineering to experimental design. For the study of calcium phosphate (e.g., hydroxyapatite) formation, many researchers use hydrogel-based double-diffusion systems (DDSs). The various designs of these DDSs are seemingly as unique as their applications. In this Highlight, we present a survey of four distinct types of double-diffusion systems and evaluate them in the context of fundamental diffusion theory. Based upon this analysis, we present the design and evaluation of an optimized system. The techniques and framework for the evaluation and construction of a DDS presented here can be applied to any DDS that a researcher may want to implement for their particular studies of biomineralization.

Fig. 1

Representative illustrations of gels used in both static and dynamic double diffusion systems (DDS), the corresponding Fickian relations, and the characteristic plots of concentration, c vs. position, x. a) Static DDSs utilize Fick’s 1^st Law, where the flux, j, of ions is constant and c only varies with x. b) Dynamic DDSs utilize Fick’s 2^nd Law, where j changes with time and therefore c changes with both x and the time, t.

Fig. 2

The Static Dual-Membrane Nested Tube DDS is used to study the effect various hydrogels have on the growth of calcium phosphate crystals. The nested tube design has a calcium reservoir nested within a phosphate reservoir, with the 15 μL hydrogel separated from the two reservoirs by a dialysis or ion-exchange membrane. Both reservoirs are set at a fixed volume and concentration (5–10 mM) at the beginning of the experiment, while the reaction occurs at 37°C. The concentrations of the reservoirs are chosen such that the supersaturation threshold condition is exceeded. The types of gels and proteins tested in this system have included: gelatin (bovine skin collagen, Type B 75 Bloom, 10%), bovine serum albumin (1%, 5%, 10%) poly(acrylamide) (10% with 0.5% crosslinker), agarose (0.5%), amelogenins (1%, 5%, 10%).^{, , , –, –}

Fig. 3

The Flowing Infinite Reservoir DDS is used to study the effects of extracellular matrix molecules on the nucleation of hydroxyapatite crystals. With an infinite reservoir design both the phosphate and calcium reservoirs are cycled using peristaltic pumps (1 per set of 3 assemblies) along the opposite boundaries of three separate, 1 cm long hydrogels. As the solution from the reservoirs flow past the hydrogel interface they empty into a waste collector at 1 mL/h per gel. The hydrogel is maintained in a steady state condition by the two reservoirs with a calcium concentration of 5.5–7.5 mM and a phosphate concentration of 5.5–7.5 mM. The interface between the hydrogel and the reservoirs is separated by dialysis membranes to keep target proteins within the hydrogel. The reaction takes place over the course of 5 days at pH 7.4 (Tris-buffer or HEPES buffer) at 37°C, and variety of hydrogels have been used (agarose 1% and 2%, type I native collagen 0.2%).^{, –}

Fig. 4

A Thin Film Source DDS was used to examine the evolution of calcium pyrophosphate growth given various changes in mineralization conditions such as path length, pH (6–8), and starting concentrations. Experiments were run in test tubes 22 mm x 200 mm, with four layers of gel (275 Bloom gelatin 3–15% w/v), ~15 mL in volume (unless otherwise specified). One layer at either end serves as thin film sources for the ions of (calcium and pyrophosphate, 0.001–0.1 M) in the experiment with two ion-free layers of gel in the middle dictating the path length.^{, –}

Fig. 5

The Circulating Semi-Infinite Reservoir DDS is used to study the effect of biomacromolecules sandwiched in a 10 w/v % gelatin hydrogel on the nucleation and growth of hydroxyapatite. 3 mL of a 10% w/v 275 Bloom Type A gelatin hydrogel in a pH 7.4 Tris buffer is cast into a 6 cm long pipette tube set between two 3–4 L reservoirs of constant volume. Each 3–4 L reservoir is circulated and degassed using either dry, CO₂-scrubbed air or compressed nitrogen, to maintain a constant concentration of 100 mM calcium and 100 mM phosphate. Each reservoir and ion circuit is of sufficient volume that they can be modeled as semi-infinite sources in the time frame of the 5 day experiment. The circuit tubing is constructed of vinyl tubing with polypropylene connectors. The connection of the gel tubes to the circuit are made with thin walled vinyl tubing that is pre-stretched to provide a snug connection with the larger diameter gel filled diffusion tube.^{, , , –}

Fig. 6

The swelling and shrinking of the gel/solution interface has an effect on the boundary conditons of the system. With changes in x, the calculated effective values of t and D can also change.

Fig. 7

Optimized construction of the Circulating Semi-Infinite Reservoir Design. To create and maintain turbulent mixing, peristaltic pumps circulate each reservoir (42 mL/min) and stir plates (350 rpm) are placed under each reservoir. The reservoirs are constructed from 1 L media bottles modified with stopcocks attached at a 10° angle.

Fig. 8

Timing in the onset of precipitation bands from the start of the experiment, in four different DDSs, Condition A: No reservoir circulation, no pre-hydration of the hydrogel; Condition B: No reservoir circulation, pre-hydration of the hydrogel; Condition C: Reservoir circulation, no pre-hydration of the hydrogel; Condition D: Reservoir circulation, pre-hydration of the hydrogel. All systems used 225 Bloom Type-A gelatin 10% w/v. The mode of the precipitation events for each condition is plotted with a horizontal line, with the error bars representing the maximum and minimum timing of precipitation in the tubes (12 each) under each condition.

Fig. 9

Plot of the measured ( )and calculated ( ) values of calcium and phosphate concentration in the end sections of two different lengths of diffusion tubes (6 cm and 8 cm) compared to the calculated value of c at x = L ( ) and the targeted theoretical value of 0.1% of c₀ shown as lines. ( calcium, phosphate). When the measured and calculated values are within error of each other, then the data are self-consistent and the assumed condition is considered valid (8 cm calcium and phosphate). When the measured value is equal to or less than the targeted value line, but the calculated value for c at x = L is greater than the targeted value line, the condition is considered quasi-infinite (not seen here). When both the calculated value 47 for c at x = L and the measured value at the end section are equal to or less than the targeted value line, then the condition can be considered semi-infinite (ex., calcium and phosphate 8 cm).

Fig. 10

Scans of diffusion gels, cast from 10 w/v % 225 Bloom Type-A gelatin, from a Circulating Semi-infinite Reservoir DDS (run using Condition D). (a) Mineralized control gel with a dense mineral band formed after 5 days, (b) gels with the initial precipitation band seen at 71.43 hours, (c) gels removed ~1 hour before precipitation was seen and then left to sit for 45 minutes after being removed from the system, (d) gels removed ~2 hours before precipitation was seen (the faintest bands are circled for easy spotting) and then left to sit for 45 minutes after being removed from the system, (e) blank gel as cast and not placed on a DDS.

Fig. 11

Measured calcium ( ) and phosphate ( ) values for the optimized (condition D) and un-optimized (condition A) systems in the circulating semi-infinite reservoir design after 69.36 hours (2 ± 0.1 hours before precipitation was expected). Values for calcium and phosphate from the SD tubes in both conditions were statistically similar. The main difference between the two conditions is the measured calcium concentrations for the DD tubes in each case. (: The values for phosphate are within error of each other.)

Fig. 12

Values of ion products (Ca x P) about location x = 3 cm. Shown are the average values of the ion product as calculated (Condition AC and DC) from concentrations in SD tubes and the values of the ion product as measured (Condition AM and DM) directly from DD tubes. The error bars represent the maximum and minimum possible (based on the standard deviation of the concentration values measured) values of the ion product. The average values for both the calculated and measured ion products for Condition D are within the supersaturation threshold window while only the maximum possible value for the ion product for Condition AM, falls within the supersaturation threshold.