BIOPOLY MERS VOL. 15 (1976)

Method for Measurement of Charge in Collagen and Polyelec trolyte Composite Materials

INTRODUCTION

Collagen has seen increased use as a biomaterial in surgical, prosthetic, drug delivery, and other medical applications.' Such applications often require a knowledge of the effective electrical charge of both pure collagen fibers and membranes, and collagen-based composites such as skin. By effective charge, we mean that associated with the intact specimen bathed in its natural chemical environment. It is this effective charge that is reflected in measurable macroscopic properties such as resistance, transport, transmembrane potential, and me- chanical response to applied electric fields. Such information is necessary for prosthetic applications involving electrochemical or electromechanical transduction mediated by charged groups,2 and useful as a reflection of those chemical attributes which involve charged groups. Examples of the latter include crosslink density and the stability in electrolyte baths of collagen composite materials made by precipitation with other charged polyelectrolytes (e.g., colla- gen-mucopolysaccharide composites).

With respect to other charge-measuring techniques, it is known that predictions based on dilute molecular solution analysis generally do not agree with those involving intact specimens due to the consequences of structural organization (e.g., blockage of some functional groups, electrostatic interactions between groups, e t ~ ) . ~ Thus, the data from titrations of intact collagen specimens which are carried out in order to determine the total number of dissociable groups have shown discrepancies when compared to data from titrations of the same collagen in fibrillar or macromolecular s ~ l u t i o n . ~ In addition, a knowledge of only the total number of available dissociable groups does not necessarily reflect the effective charge density cor- responding to a given electrolyte environment. Static electrokinetic measurements made with biomaterials relate solely to hydrodynamically effective charge densities: as they reflect only that portion of electrolyte counterion charge in the mobile region of the electrical double layer. Further, they are plagued by the inability to distinguish rate processes associated with electrodes and electrolyte bath from those of the specimen. (A new dynamic measuring technique has alleviated some of the latter problem^.^)

This communication concerns the measurement of transmembrane diffusion potentials as a relatively simple technique for charge and transport characterization of many biomaterials in their natural state. Data is presented concerning measured transmembrane potentials VO, and the corresponding calculated effective fixed-charge densities p , of collagen membranes in an imposed concentration gradient, over a range of pH and neutral salt concentration. A form of the Teorell-Meyer-Sievers theory6 is used to calculate p m from the measured VO a t any given pH and neutral salt condition. While the calculated p , is presented here as a guideline for the interpretation and utility of the measured VO, in practice it is the comparison of VO or p m from sample to sample, or for the same sample undergoing successive stages of chemical processing, that can be very useful in material design.

Studies of steady state VO versus pH and ionic strength have been made with many synthetic nonswelling membrane^^.^ and with some simple protein filmsg To our knowledge, this technique has not yet been applied to the study of collagen over an extended pH range, or to the general area of collagen-polyelectrolyte composites. In addition, data presented here suggests the usefulness of real time or continuous monitoring of Vo(t) as a technique for fol- lowing the time course of chemical reactions involving membrane-charged groups. Such information can help to shed light on the various rate processes involved. This application of membrane potential measurements has not been stressed in the literature.

MATERIALS AND METHODS

Collagen films (dry thickness -1.8 mil) were made from a dispersion of hide corium collagen as described by Liebermanlo and kindly donated to us by Dr. T. Tsuzuki, Devro, Inc., Som- erville, New Jersey. The films were extrusion cast and then crosslinked in 0.1% glutaraldehyde

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0 1976 by John Wiley & Sons, Inc.

1846 BIOPOLYMERS VOL. 15 (1976)

v +-

I-

Fig. 1. Measurement configuration: (a) membrane of thickness 6, (b) poly(methy1 meth- acrylate) chamber, (c) Ag/AgCl electrodes, (d) ports for addition of reagents and monitoring of pH and temperature, (e) magnetic stirring bars, (f) rubber stoppers. c' and c" are bulk so- lution concentrations; A@; A@; and A@diff are the two interfacial Donnan potentials and the diffusion potential, respectively, having the polarities indicated; VO is the total measured potential difference.

for 30 min; no plasticizing agent was used. The total amount of impurities in the final preparation (primarily natural fats) was less than 0.5 wt %.ll These films were among several samples previously used in our laboratory for studying electromechanical transduction properties of ~ollagen.~ (Preliminary experiments have been performed with other specimens including films cast from rat tail tendon collagen and collagen-mucopolysaccharide com- posites. More extensive data concerning the latter films, which are being developed by Yannas and co-workers*2 for use as a skin substitute, will be reported in a future paper.)

Collagen membranes were mounted in a poly(methy1 methacrylate) chamber, as shown in Figure 1, resulting in an active membrane area of 13.4 cm2. Each half-cell compartment, having a volume of -540 cm3, contained ports for initial filling with electrolyte bath, additional pipetting of reagents during an experiment, and continuous monitoring of bath temperatures and pH. Ag/AgCl electrodes, made by procedures described by were used to measure transmembrane potentials, which were continuously monitored and recorded by a Keithley 610B electrometer and a Heathkit EUW chart recorder. Vigorous stirring was accomplished via magnetic stirrers.

The membrane chamber was initially filled with electrolytes such that a gradient in neutral salt concentration was imposed across the membrane. The pH was equal on both sides throughout the course of an experiment, but was changed from an initial value of -11.5(3.0) to a final value of -3.0 (11.5) hy pipetting in successive increments of HCl (NaOH) each within less than 5 sec, into the stirred baths. The curves of Figure 2 typify the change in measured poteotial Vo(t) accompanying such step changes in pH in both the low and high pH regions away from the central isoelectric regime. The pH was continuously monitored with a Radi- ometer digital pH meter PHM-63 which gave reproducible readings to f O . O 1 pH units and had been calibrated with standard buffers. All solutions added to the bath were prepared from reagent grade chemicals and were standardized as necessary. All measurements were made at 23'C.

In order to calculate pm from the measured VO, the latter was modeled (using the Teorell- Meyer-Sievers approach) as the sum of a diffusion potential A@diff internal to the membrane, two Donnan potentials A@D at the membrane electrolyte interfaces (defined in Fig. 1) and two electrode-electrolyte potentials A@e, respectively,

where a& and a&- are ion activities in the bulk solutions, and the last term is A@,. The calculations presented here incorporate the Henderson model6 for A@diff, written for univalent ions as

COMMUNICATIONS TO THE EDITOR

I I I I I I pH 4 62

6 - -

n + 0 - > 5 - E

-

>O

4 -

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5 10 15 20 25 30

TIME , m i n u t e s

Fig. 2. Transmembrane potential VO vs. time resulting from step decreases in pH (equal on both sides) for a collagen membrane in an imposed concentration gradient; C & C ~ = 0.06 M , c;,~, = 0.03 M . The pH values indicated in the figure are the steady state values prior to the next addition of acid. Data corresponds to the experiment of Fig. 3 (open circles).

RT - (EL/,?,) (E‘” -G;) c B a;

ii, 5;

In - (2) F L

A@’d,ff =

x k - (a -!” - a,) -’ 1 I

where ii, and ii, denote ion activities and mobilities of the permeable species inside the membrane. (Equation (2) is based on the usual Teorell-Meyer-Sievers assumption that ionic mobilities and activity coefficients do not vary across the membrane.) The relation between a, and ti, is determined by the requirement of bulk electroneutrality in the membrane, as embodied in the Donnan equilibrium; thus a t the left-hand interface6

RT F

A@; = - -In r‘

(3)

(4)

r’ = ([I + (fim/2a’)2I1/2 - (fim/2a’)] (5)

where the quantity a’ in Eq. (5) is in general equal to Z, a;+ = 8, a;- (the latter equality fol- lowing from electroneutrality). Relations analagous to Eqs. (3)-(5) also apply to the right- hand interface. The assumption of electroneutrality is justified since the membrane thickness 6 is much greater than a Debye length 11~ for the experiments discussed.

RESULTS AND DISCUSSION

Representative results of transmembrane potential measurements appear in Figure 3. The two sets of data represent steady state values of V O after the successive increments of acid or base (as in Fig. 2) for the same hide corium collagen membrane. In one experiment, a 2:l concentration ratio of NaCl was used (c’ = 0.06 M ; c” = 0.03 M ) and the pH was decreased from 11.5 to 3. Thus, the change in total bath ionic strength due to addition of base was less than 10%. In the other experiment, the NaCl concentrations were c’ = 0.003 M and c” = 0.001 M , and the pH was raised from 3 to 11.5. Here, the ratio of ionic strengths (initially 21 at pH 3) changed measurably over the course of the experiment. However, the final ionic strengths on each side were still an order of magnitude less than those of the first experiment. (Collagen primary charge is known to change with pH, but is also affected by changes in total bath ionic ~ t r e n g t h . ~ )

1848 BIOPOLYMERS VOL. 15 (1976)

I " ' I I.1o.' I 22

20

18-

16

14 - 12

E 10

-

-

-

n -

> - >" 0 -

6 -

4 -

2 -

0 -

0

0

0

0 0

0

0 000

0 0 .

0 0.0

3 4 5 6 7 8 9 10 II 12

P H

Fig. 3. Steady-state transmembrane potential VO vs. bath pH for a single hide corium collagen membrane. Open circles: initial NaCl concentrations were chat, = 0.06 M and chat, = 0.03 M and the pH was decreased in steps from -11.5 to -3. Closed circles: initial con- centrations were ch.~, = 0.003 M, ch.~, = 0.001 M and the pH was increased from -3 to -11.5.

The water content of the same membrane was determined as a function of pH after the method of Ginzburg and Katcha1~ky.I~ Measurements were made using the identical bath ionic strength conditions and pH range as that of the two experiments of Figure 3. For the high ionic strength case, the water content varied from a minimum of 65% by weight in the pH region 7-9 to maxima of 71% at pH 11.3 and 72% at pH 3.0. For the low ionic strength case the corresponding values were 67,72, and 74%, respectively. At a given pH, water content was higher for the low ionic strength case.

The data of Figure 4 represent the calculated prn corresponding to the measured VO of Figure 3. The calculation was accomplished via an iterative technique based on Eqs. (1)-(5) in terms of the unknowns Pm and EL. With Aadiffinitidy set to zero in Eq. (l), an initial value for (A& - A@;) was found in terms of A@, and the measured VO at each pH (the A a e was calculated from the imposed bulk concentration eel-). Equations (4) and (5) and their analogs at the right interface were then rearranged so as to solve for an initial value of p m in terms of (A*; - A@;), a', and a". The P m in turn was used to initialize Ei and then Aadiff in Eq. (3) and (2), respectively. A new value of (A@; - A%) was then found using Eq. (1) with the calculated value of A@diff. Five iterations were generally sufficient for convergence.

With regard to the values of the parameters used in Eqs. (1)-(5), the a' (and a") were ap- proximated as constant and due to NaCl alone for the high NaCl concentration case. For the low concentration case, activities were approximated by concentrations but the u' - c' (and a" - c" ) were updated at each point to account for the addition of base. In keeping with the Teorell-Meyer-Sievers approach, the Ei in Eq. (2) was assumed to be the same as that in bulk solution. However, the Ez were treated as unknowns along with Pm, to be deter- mined by the Donnan theory via the iterative technique outlined above. Changes in the measured VO due to changes in membrane swelling would thus be reflected in the calculated values of p m and EL. Detailed corrections to the original Teorell-MeyerSievers model have been derived to account for nonideal ion mobility within a membrane.4J5 However, they

COMMUNICATIONS TO T H E EDITOR 1849

L al c ._ - In al 0 - E E

40

30

20

10

0

- 10

20

30

3 4 5 6 7 8 9 K) II 12

PH

Fig. 4. Calculated collagen net fixed-charge densityp, vs. pH, based on the measured VO of Fig. 3 and Eqs. (1)-(4) (see text).

either apply only to nonswelling membranes or require (in the present context) an independent nondestructive determination of the total number of available dissociable groups in the same intact specimen. The latter requirement, is presently being studied; for the purposes of the present work, however, such corrections have not been included.

The effect of osmotic and electroosmotic water transport across the membrane on VO, which is neglected in the Teorell-Meyer-Sievers theory has been assumed negligible for the case a t hand, based on independent measurements of steady state hydrodynamic and electrokinetic transport properties of the collagen membrane.5 Finally, the calculation of p , was based on the assumption that solution volumes were sufficiently large so that changes in external concentration could be neglected over the course of an experiment. As there was yet no provision for bath recirculation, subsequent measurements were made of the decay (from diffusion) of an imposed concentration gradient for both charged and neutral membranes. From these measurements it was estimated that a decay of less than 10% had occurred by the end of a VO versus pH experiment (Fig. 3), leading to an underestimate of the open-circle &,, a t very low pH and of the closed-circle I p , I a t very high pH (Fig. 4).

Several conclusions concerning the collagen film used here may first be drawn by inter- preting Figures 3 and 4 in terms of fixed-charge membrane theory. We note that measured potentials VO directly reflect collagen charge density, bath ionic strength, and the degree of collagen swelling or porosity consistent with both. In general, the higher the ratio of p , to bath ionic strength, the closer V O should approach the value attained by Eq. (1) for the limit of an ideal semipermeable membrane where co-ion transport becomes negligibly small (-0 mV and - (RT/F) [-In (a&/a&) - In (ahe+/aka+)] for a positive and negative membrane, respectively). Often interpreted in terms of Donnan exclusion, this effect is seen in Figure 3 as expected, where the VO (which includes the electrode potentials) for the low ionic strength case is smaller a t low pH and larger a t high pH than that of the higher ionic strength case. This does not necessitate a higher p m a t low ionic strength; in fact just the opposite is seen here in Figure 4. The reversal of VO a t high pH (closed circles) is due primarily to the significant perturbation in ionic strength and change in total concentration gradient due to the addition of base, another indication that VO is sensitive to an effective rather than stoichiometric charge density.

Of course, the exact value of pm in Figure 4 will reflect the assumptions and limitations of

1850 BIOPOLYMERS VOL. 15 (1976)

the model used in the calculation. While the assumptions of the Teorell-Meyer-Sievers theory may be violated to a greater or lesser extent in a given experiment, the major point to be stressed is that the trends of the VO and the pm thus calculated as well as comparative data for different membranes and experimental conditions can be quite instructive as a guide in material design. With these limitations in mind, we note that the p , of Figure 4 show charging trends which are characteristic of the few titration curves of intact collagen specimens available for comparison in the literature.I6 One notable trend is the increase in I p m 1 with bath ionic strength at a fixed pH in the low and high pH regions. This may be interpreted in terms of Donnan exclusion, and the Debye screening effect of the neutral salt. Such an interpretation is equivalent to and consistent with that based on the effect of ionic strength on osmotic swelling. That the isoelectric pH is found not to be constant with changes in ionic strength has also been seen in titration work.17

The utility of a diffusion potential measurement rests not only with its ease, but with the added possibility of following the time course of chemical reactions and other processes in- volving the dissociable groups. For example, the data of Figure 2 show the time course of Vo(t) in response to step changes in pH at approximately constant ionic strength, which re- flects the combined effects of diffusion (of added reagent into the membrane) and chemical reaction. In an attempt to distinguish between reaction and diffusion, Vo(t) was measured in response to step changes in bath ionic strength while keeping the pH and the overall con- centration gradient c ’ h ” constant. Bath conditions were chosen such that those changes in ionic strength were known to leave essentially unperturbed the total number of ionized grohps2 (though changes in Vo(t) and prn would follow from variations in membrane water content). The resulting 1040% rise times of these Vo(t) were typically an order of magnitude less than those of Figure 2; in magnitude they were on the order of the time for diffusion of ions across a distance equal to that of the swollen membrane. One might hypothesize that the two groups of experiments were rate limited by diffusion-controlled reaction (Fig. 2) and diffusion processes, respectively. This would he consistent with the known experimental conditions.

Finally, our preliminary experiments with other hide collagen films have shown first that transmembrane potentials vary with the degree of crosslinking (induced thermally or by means of glutaraldehyde) in a manner consistent with the belief that crosslinks involve charged groups. Second, the measured VO has been found to be sensitive to the binding of the mu- copolysaccharide chondroitin-6-sulfate to these same collagen films. In this case, VO reflects an average pm for the composite material. The additional negative groups of the muco- polysaccharide have been detected by the potential measurement over a wide range of pH.

This work was supported by National Science Foundation Grant #ENG74-09744. It is based in part on the SB Thesis of M. A. P. The authors would like to thank Professors I. V. Yannas and J. R. Melcher for helpful discussions and suggestions.

References

1. Chvapil, M., Kronenthal, R. L. & Van Winkle, W. (1973) in International Review of Connective Tissue Research, vol. 6, Hall, D. A. and Jackson, D. S., Eds., Academic Press, New York, pp. 1-62.

2. Yannas, I. V. & Grodzinsky, A. J. (1973) J. Mechanochem. Cell Motility, 113-125. 3. Veis, A. (1967) in Treatise on Collagen, vol. 1, Ramachandran, G. N., Ed., Academic

4. Kobatake, Y. & Kamo, N. (1973) in Progress in Polymer Science Japan, Murahashi,

5. Grodzinsky, A. J. & Melcher, J. R., (1976) ZEEE Trans. Biomed. Eng., in press. 6. Plonsey, R. (1969) in Bioelectric Phenomena, McGraw Hill, New York, pp. 78-112. 7. Sollner, K. (1969) J. Macromol. Sci.-Chem. A 3,1-84. 8. Jacobson, H. (1962) J. Phys. Chem. 66,570-572. 9. Petri, E. M. & Staverman, A. J. (1953) Disc. Faraday SOC. 13,151-159.

Press, New York, pp. 367-439.

I., Ed., John Wiley, New York, pp. 257-302.

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10. Lieberman, E. R. U S . Patent #3,123,482, “Edible collagen casings and process of

11. Dr. T . Tsuzuki, personal communication, Devro, Inc., Somerville, N.J. 12. Yannas, I. V., Burke, J. F., Huang, C. & Gordon, P. L. (1975) Polym. Prepr. 16 (21,

13. Ives, D. J. G. & J a m , G. J. (1961) in Reference Electrodes, Academic Press, New York,

14. Ginzburg, B. Z. & Katchalsky, A. J . Gen. Phys. 47 403-418. 15. Lakshminarayanaiah, N. (1975) J. Membrane Biology 21,175-189. 16. Gustavson, K. H. (1956) in The Chemistry and Reactiuity of Collagen, Academic Press,

17. Veis, A. (1964) in The Macromolecular Chemistry of Gelatin, Academic Press, New

manufacturing the same,” March 3, 1964.

209-214.

pp. 179-230.

New York, pp. 87-132.

York, pp. 99-123.

MICHAEL A. PICHENY ALAN J. GRODZINSKY

Department of Electrical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139

Received January 15,1976 Returned for revision February 20,1976 Accepted March 31,1976