Caries Res. 13: 154-162 (1979)
Diffusion of Radiotracers in Human Dental Plaque A. Tatevossian Physiology Department, University College, Cardiff
Keywords. Bicarbonate ■Carbohydrates • Carboxylic acids - Diffusion • Plaque • Tracers
In a study of the local factors in dental caries, Dobbs [1932] showed differences in the rate of diffusion of salt solutions through ‘dental plaque’ removed from teeth by their immersion in 5% hydrochloric acid containing some potassium aluminium sul phate, which was added ‘to prevent protein in the plaques from swelling’. He concluded that mouthwashes containing sodium bicar bonate or phosphate, or salivary bicarbon ate, would be of little importance in con trolling the acids produced in dental plaque
because their diffusion in this system was relatively restricted and, with phosphates, prevented. Although the organic material dissolved off the teeth was described as a membrane, its morphology was not exam ined to establish whether an intact microbial layer was present. Straljors [1950] was unable to apply Fick’s diffusion equations to a system where the diffusion of glucose occurred from a stirred bulk solution into columns of agar gel containing bacteria obtained from broth
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Abstract. A method for the determination of the diffusion coefficient, D, of solutes in the separated aqueous and residual phases of 24-hour human dental plaque is described. The separated plaque components were placed in tubing (inner diameter 0.49 mm), pulsed at one end with radiotracer, and horizontal diffusion was continued at 37 or 5 °C for 5-17 h. The results indicate that the diffusion of 14C-sucrose and 14C-inulin in plaque fluid was similar to that in water, while the diffusion of 14C-starch was unexpectedly greater than in water. The D values for the three carbohydrates studied were inversely related to their molecular weights. In plaque fluid, the diffusion of ionic species, bicarbonate, acetate, lactate, butyrate as sodium salts, was less than in water. In the plaque residue, the diffusion was restricted in relation to the packing density of the residue. While the diffusion into plaque of readily fermentable carbohydrate was not restricted, that of their bacterial meta bolic products was impeded, consistent with the rapid fall and slow rise in plaque pH, known to occur after exposure to fermentable carbohydrate.
Tracer Diffusion in Plaque
ability to produce glucan from sucrose. The two strains showed no significant difference in lactic acid production from glucose at pH 4.0-7.0 when tested. The relevance of diffusion processes in relation to the pathogenesis of dental caries has been discussed by Kleinberg [1970] and Higuchi [1974], and in relation to the aver age concentration of some solutes in plaque fluid, which are higher than in saliva, by Tatevossian and Gould [1976], Quantitative data on diffusion in dental plaque are lack ing, although recent attempts have been made to obtain them [Geddes, 1977; Melsen et al., 1977]. The development of a method for separating the aqueous and residual phases in dental plaque allows a simple ex perimental approach for measuring the dif fusion of solutes in these plaque compo nents under well-defined boundary condi tions.
Materials and Methods Plaque Collection and Phase Separation Dental plaque was collected from a pool of about 90 dental students aged 18-24 years who were instructed to refrain front toothbrushing dur ing the previous 24 h. Collections were made in the mornings, at least 1 h after the mid-morning snack, using specially co n stru cted p erspex spatu-
lae and avoiding the lingual anterior lower re gion and areas where caries or gingival inflamma tion was observed. Individual frozen plaque sam ples from 10-40 subjects were pooled in a cold room at 5 °C and the aqueous phase was separat ed after centrifugation (5,000 g for 15 min at 2 °C), and stored at -20 °C in a sealed tube. The sealed tubes containing plaque fluid were centri fuged (5,000 g for 5 min at 2°C ) to sediment any bacterial aggregates which may have been resus pended from the residue during the procedure for withdrawing the fluid from above the residual phase.
Downloaded by: Univ. of California Santa Barbara 128.111.121.42 - 3/5/2018 1:58:30 PM
culture. A pH indicator was included in the gel, and diffusion of glucose into the gel was seen as the colour change induced by the bacterial acid produced. In this complex system, the diffusion of glucose into the gel, and of bacterial acid metabolites out of the gel, was modified by variations in the rate of acid produced as a function of the change in pH within the gel. Strdlfors [1950] mea sured the diffusion of lactic acid in agar gel when no microorganisms were incorporated into the gel and derived quantitative data in relation to his ‘acid production-diffusion’ theory of caries on the assumption that the diffusion coefficient for lactic acid was of a similar order of magnitude to that in plaque. Manly [1958] reported that the activity of a range of chemicals inhibiting glycolysis was related to the thickness of the films of salivary sediment exposed to the inhibitors. Huh et al. [1959] determined the passage of glucose through a disc of packed salivary sediment and concluded that the distribu tion of glucose in the sediment was depend ent on the density of packing and the rate of utilisation of the substrate. Although it would have been possible to calculate the apparent diffusion coefficient for glucose in these preparations, this was not quantitated by the authors. Kelstrup and Funder-Nielsen [1972] dis cussed the unpredictable effect of polymers in the plaque extracellular phase on the ac tivity of levan sucrose and levan hydrolase and suggested that these effects may be re lated to the diffusion of substrate and prod uct in the vicinity of enzyme molecules. Hojo et al. [1976] concluded that extracel lular glucan reduced diffusion in the plaque. They found that, compared with the native strain of Streptococcus mutans PK1, the pH fall was smaller in a mutant with a reduced
155
156
where d = diameter, v = volume and h - length of fluid column. The gravimetric data were used to calculate the mean diameter, taking the density of water as 1.00. Diffusion Studies The method described by Redwood et al. [1974] was used, with modifications. Samples of deionised water, plaque fluid or plaque residual phase were introduced into the Portex tubing to form a column 1-3 cm long, depending on the ex pected diffusion rate of the tracer to be studied. Plaque residue was introduced into the tubing and packed by centrifugal force at values indicated in ‘Results’. Stainless-steel plugs were constructed to fit tightly into the inner diameter of the Portex tubing. A collar allowed the plug to project 1.0 mm into the tubing until the end of the tubing came to rest against the collar. The portion inside the tubing presented a polished plane surface at right angles to the long axis of the tubing and provided a defined starting point for the diffusing tracer which was placed as a solution onto the polished end of the plug and evaporated to dry ness. After the plug was inserted, the other end of the tubing was sealed with clay and the tubes, maintained in a horizontal position by inserting them into glass tubing, were incubated in a Petri dish in an air incubator (37 °C) or refrigerator (5 °C), as indicated in ‘Results’. After 5-17 h, the diffusion was terminated by placing the samples in a deep-freeze, which froze the samples within 5 sec. After removing the stainless-steel plug, each tube was placed in a brass holder, pre-cooled to maintain the tube in a frozen state, and the entire
tubing was sliced into 1-mm segments using a pre cooled sheer carrying 40 stainless-steel blades spaced at 1-mm intervals. This apparatus, de signed and constructed in the Physiology Depart ment, Cardiff, will be described in a separate re port. The radioactivity in each slice was counted in a Nuclear Enterprises liquid scintillation count er using a Dioxan-based scintillant solution (NE 250, Nuclear Enterprises). The counting efficiency of this system for UC, using a standard solution of I4C-sodium acetate, was > 70% at the window set tings used for counting the experimental samples. Calculation of the Tracer Diffusion Coefficient, D The experimental conditions correspond to one-dimensional semi-infinite diffusion, which is described by the relationship (Crank, 1957; Red wood et al., 1974): c = m0 (7!Dt)"1/2exp (-x2/4Dt),
(1)
where c = concentration of tracer (cpm cm'3) at distance x (cm) and time t (sec), and m0 = initial amount of tracer per cross-sectional area at the origin (cpm cm'2). The logarithm of this relationship is: In c = In m0 (rrDt)-l'2- x 2/4Dt,
(2)
thus a plot of log c against x2 is a straight line, with a slope of l/4Dt, and if x2w = diffusion half distance squared, and th (hours) = 3,600 t, substituting in equation 2 and solving for D gives the relation: D = 0.10019 (r W ta ) x 10‘5 cm2 sec-1.
(3)
Thus the diffusion coefficient was a function of the square of the distance over which lognc falls to a half of the previous value. In these experiments, the regression of the logo radioactivity (cpm) in each slice minus the background (cpm) as a function of 0.1 n - i
- [0.1/2]2 was
calculated by linear least squares regression analysis, where n was the ordinal number of the corresponding slice. The value of the *2i/2 so derived was substi tuted in equation 3, together with the time during which diffusion occurred (hours), in order to obtain the tracer diffusion coefficient, D.
Downloaded by: Univ. of California Santa Barbara 128.111.121.42 - 3/5/2018 1:58:30 PM
Tubing Diameter Portex® tubing of uniform bore was used. To test the uniformity of the bore, 20 pieces 2.0 cm in length were cut and weighed empty to + 200 fig, 3.0 fi\ of distilled water were introduced, and the length of the resulting column of fluid was measured to + 0.1 mm. The tubing was then completely filled with water and weighed at room temperature. The average diameter for each 2.0 cm length was calculated from the volumetric data using
Tatevossian
Tracer Diffusion in Plaque
157
Radiochemicals [U-14C]-sucrose, [U-I4C]-inulin, [U-14C]-starch (soluble), sodium salts of [U-l4C]-acetic, DL-[114C]-lactic and n-[l-,4C]-butyric acids, and sodium [14C]-bicarbonate were obtained from The Radio chemical Centre, Amersham, England.
Results Tubing Diameter The standard deviations of the results in table I confirm that the inner diameter of the tubing was uniform over 2-cm lengths from sample to sample. There was good agreement between the calculated diameters based on volumetric and gravimetric analy sis. The larger standard deviation and smaller mean value obtained by the gravi metric method was expected because more evaporation would be expected to take Table I. Uniformity of tube inner diameter
Mean SD
Length of Calculated Weight of 2 cm wa3 /d water inner cm diameter ter, mg mm
Calculated inner diameter mm
1.53 0.02
0.4925 0.0063
0.4995 0.0040
3.81 0.10
place in the liquid column when it complete ly filled the tube. Tracer Diffusion Coefficients of Ionic Species The diffusion coefficients for sodium [I4C]-bicarbonate and the carboxylic acids tested are shown in table II. The diffusion of sodium [I4C]-bicarbonate and sodium [l-14C]-Z)L-lactate was significantly slower in plaque fluid than in water, and a similar effect was seen with the sodium salts of the other carboxylic acids tested, although with sodium [U-14C]-acetate, the standard devia tion of the D values in water was high, so that the differences were not statistically sig nificant. In the plaque residues centrifuged at 5,000 g, D values were significantly lower than in water. Compared to plaque fluid, the diffusion coefficients were significantly lower in the residues for bicarbonate (p < 0.001), acetate (p < 0.01), lactate (p < 0.02), but not butyrate (p < 0.1). These differences are more clearly illustrat ed by the ratio of the diffusion coefficient in the sample, compared to that of water, the diffusivity ratio (table III). Although the diffusivity ratios for the ionic species were similar in the plaque residues centrifuged at 5,000 g, there is a gradual increase in the
Sodium[14C]-bicarbonate Sodium[U-14C]-acetate Sodium[l-14C]-DL-lactate Sodium[l-14C]-n-butyrate
Water
Plaque fluid
Plaque residue (5,000 g)
1.202(0.220) 1.059(0.912) 1.012(0.251) 0.811 (0.041)
0.276 (0.32)** 0.324 (0.078) 0.338(0.177)*** 0.506 (0.288)
0.094(0.015)*** 0.129 (0.022)* 0.142(0.016)*** 0.096 (0.016)***
t values compared to water: ***p
Diffusion of Radiotracers in Human Dental Plaque A. Tatevossian Physiology Department, University College, Cardiff
Keywords. Bicarbonate ■Carbohydrates • Carboxylic acids - Diffusion • Plaque • Tracers
In a study of the local factors in dental caries, Dobbs [1932] showed differences in the rate of diffusion of salt solutions through ‘dental plaque’ removed from teeth by their immersion in 5% hydrochloric acid containing some potassium aluminium sul phate, which was added ‘to prevent protein in the plaques from swelling’. He concluded that mouthwashes containing sodium bicar bonate or phosphate, or salivary bicarbon ate, would be of little importance in con trolling the acids produced in dental plaque
because their diffusion in this system was relatively restricted and, with phosphates, prevented. Although the organic material dissolved off the teeth was described as a membrane, its morphology was not exam ined to establish whether an intact microbial layer was present. Straljors [1950] was unable to apply Fick’s diffusion equations to a system where the diffusion of glucose occurred from a stirred bulk solution into columns of agar gel containing bacteria obtained from broth
Downloaded by: Univ. of California Santa Barbara 128.111.121.42 - 3/5/2018 1:58:30 PM
Abstract. A method for the determination of the diffusion coefficient, D, of solutes in the separated aqueous and residual phases of 24-hour human dental plaque is described. The separated plaque components were placed in tubing (inner diameter 0.49 mm), pulsed at one end with radiotracer, and horizontal diffusion was continued at 37 or 5 °C for 5-17 h. The results indicate that the diffusion of 14C-sucrose and 14C-inulin in plaque fluid was similar to that in water, while the diffusion of 14C-starch was unexpectedly greater than in water. The D values for the three carbohydrates studied were inversely related to their molecular weights. In plaque fluid, the diffusion of ionic species, bicarbonate, acetate, lactate, butyrate as sodium salts, was less than in water. In the plaque residue, the diffusion was restricted in relation to the packing density of the residue. While the diffusion into plaque of readily fermentable carbohydrate was not restricted, that of their bacterial meta bolic products was impeded, consistent with the rapid fall and slow rise in plaque pH, known to occur after exposure to fermentable carbohydrate.
Tracer Diffusion in Plaque
ability to produce glucan from sucrose. The two strains showed no significant difference in lactic acid production from glucose at pH 4.0-7.0 when tested. The relevance of diffusion processes in relation to the pathogenesis of dental caries has been discussed by Kleinberg [1970] and Higuchi [1974], and in relation to the aver age concentration of some solutes in plaque fluid, which are higher than in saliva, by Tatevossian and Gould [1976], Quantitative data on diffusion in dental plaque are lack ing, although recent attempts have been made to obtain them [Geddes, 1977; Melsen et al., 1977]. The development of a method for separating the aqueous and residual phases in dental plaque allows a simple ex perimental approach for measuring the dif fusion of solutes in these plaque compo nents under well-defined boundary condi tions.
Materials and Methods Plaque Collection and Phase Separation Dental plaque was collected from a pool of about 90 dental students aged 18-24 years who were instructed to refrain front toothbrushing dur ing the previous 24 h. Collections were made in the mornings, at least 1 h after the mid-morning snack, using specially co n stru cted p erspex spatu-
lae and avoiding the lingual anterior lower re gion and areas where caries or gingival inflamma tion was observed. Individual frozen plaque sam ples from 10-40 subjects were pooled in a cold room at 5 °C and the aqueous phase was separat ed after centrifugation (5,000 g for 15 min at 2 °C), and stored at -20 °C in a sealed tube. The sealed tubes containing plaque fluid were centri fuged (5,000 g for 5 min at 2°C ) to sediment any bacterial aggregates which may have been resus pended from the residue during the procedure for withdrawing the fluid from above the residual phase.
Downloaded by: Univ. of California Santa Barbara 128.111.121.42 - 3/5/2018 1:58:30 PM
culture. A pH indicator was included in the gel, and diffusion of glucose into the gel was seen as the colour change induced by the bacterial acid produced. In this complex system, the diffusion of glucose into the gel, and of bacterial acid metabolites out of the gel, was modified by variations in the rate of acid produced as a function of the change in pH within the gel. Strdlfors [1950] mea sured the diffusion of lactic acid in agar gel when no microorganisms were incorporated into the gel and derived quantitative data in relation to his ‘acid production-diffusion’ theory of caries on the assumption that the diffusion coefficient for lactic acid was of a similar order of magnitude to that in plaque. Manly [1958] reported that the activity of a range of chemicals inhibiting glycolysis was related to the thickness of the films of salivary sediment exposed to the inhibitors. Huh et al. [1959] determined the passage of glucose through a disc of packed salivary sediment and concluded that the distribu tion of glucose in the sediment was depend ent on the density of packing and the rate of utilisation of the substrate. Although it would have been possible to calculate the apparent diffusion coefficient for glucose in these preparations, this was not quantitated by the authors. Kelstrup and Funder-Nielsen [1972] dis cussed the unpredictable effect of polymers in the plaque extracellular phase on the ac tivity of levan sucrose and levan hydrolase and suggested that these effects may be re lated to the diffusion of substrate and prod uct in the vicinity of enzyme molecules. Hojo et al. [1976] concluded that extracel lular glucan reduced diffusion in the plaque. They found that, compared with the native strain of Streptococcus mutans PK1, the pH fall was smaller in a mutant with a reduced
155
156
where d = diameter, v = volume and h - length of fluid column. The gravimetric data were used to calculate the mean diameter, taking the density of water as 1.00. Diffusion Studies The method described by Redwood et al. [1974] was used, with modifications. Samples of deionised water, plaque fluid or plaque residual phase were introduced into the Portex tubing to form a column 1-3 cm long, depending on the ex pected diffusion rate of the tracer to be studied. Plaque residue was introduced into the tubing and packed by centrifugal force at values indicated in ‘Results’. Stainless-steel plugs were constructed to fit tightly into the inner diameter of the Portex tubing. A collar allowed the plug to project 1.0 mm into the tubing until the end of the tubing came to rest against the collar. The portion inside the tubing presented a polished plane surface at right angles to the long axis of the tubing and provided a defined starting point for the diffusing tracer which was placed as a solution onto the polished end of the plug and evaporated to dry ness. After the plug was inserted, the other end of the tubing was sealed with clay and the tubes, maintained in a horizontal position by inserting them into glass tubing, were incubated in a Petri dish in an air incubator (37 °C) or refrigerator (5 °C), as indicated in ‘Results’. After 5-17 h, the diffusion was terminated by placing the samples in a deep-freeze, which froze the samples within 5 sec. After removing the stainless-steel plug, each tube was placed in a brass holder, pre-cooled to maintain the tube in a frozen state, and the entire
tubing was sliced into 1-mm segments using a pre cooled sheer carrying 40 stainless-steel blades spaced at 1-mm intervals. This apparatus, de signed and constructed in the Physiology Depart ment, Cardiff, will be described in a separate re port. The radioactivity in each slice was counted in a Nuclear Enterprises liquid scintillation count er using a Dioxan-based scintillant solution (NE 250, Nuclear Enterprises). The counting efficiency of this system for UC, using a standard solution of I4C-sodium acetate, was > 70% at the window set tings used for counting the experimental samples. Calculation of the Tracer Diffusion Coefficient, D The experimental conditions correspond to one-dimensional semi-infinite diffusion, which is described by the relationship (Crank, 1957; Red wood et al., 1974): c = m0 (7!Dt)"1/2exp (-x2/4Dt),
(1)
where c = concentration of tracer (cpm cm'3) at distance x (cm) and time t (sec), and m0 = initial amount of tracer per cross-sectional area at the origin (cpm cm'2). The logarithm of this relationship is: In c = In m0 (rrDt)-l'2- x 2/4Dt,
(2)
thus a plot of log c against x2 is a straight line, with a slope of l/4Dt, and if x2w = diffusion half distance squared, and th (hours) = 3,600 t, substituting in equation 2 and solving for D gives the relation: D = 0.10019 (r W ta ) x 10‘5 cm2 sec-1.
(3)
Thus the diffusion coefficient was a function of the square of the distance over which lognc falls to a half of the previous value. In these experiments, the regression of the logo radioactivity (cpm) in each slice minus the background (cpm) as a function of 0.1 n - i
- [0.1/2]2 was
calculated by linear least squares regression analysis, where n was the ordinal number of the corresponding slice. The value of the *2i/2 so derived was substi tuted in equation 3, together with the time during which diffusion occurred (hours), in order to obtain the tracer diffusion coefficient, D.
Downloaded by: Univ. of California Santa Barbara 128.111.121.42 - 3/5/2018 1:58:30 PM
Tubing Diameter Portex® tubing of uniform bore was used. To test the uniformity of the bore, 20 pieces 2.0 cm in length were cut and weighed empty to + 200 fig, 3.0 fi\ of distilled water were introduced, and the length of the resulting column of fluid was measured to + 0.1 mm. The tubing was then completely filled with water and weighed at room temperature. The average diameter for each 2.0 cm length was calculated from the volumetric data using
Tatevossian
Tracer Diffusion in Plaque
157
Radiochemicals [U-14C]-sucrose, [U-I4C]-inulin, [U-14C]-starch (soluble), sodium salts of [U-l4C]-acetic, DL-[114C]-lactic and n-[l-,4C]-butyric acids, and sodium [14C]-bicarbonate were obtained from The Radio chemical Centre, Amersham, England.
Results Tubing Diameter The standard deviations of the results in table I confirm that the inner diameter of the tubing was uniform over 2-cm lengths from sample to sample. There was good agreement between the calculated diameters based on volumetric and gravimetric analy sis. The larger standard deviation and smaller mean value obtained by the gravi metric method was expected because more evaporation would be expected to take Table I. Uniformity of tube inner diameter
Mean SD
Length of Calculated Weight of 2 cm wa3 /d water inner cm diameter ter, mg mm
Calculated inner diameter mm
1.53 0.02
0.4925 0.0063
0.4995 0.0040
3.81 0.10
place in the liquid column when it complete ly filled the tube. Tracer Diffusion Coefficients of Ionic Species The diffusion coefficients for sodium [I4C]-bicarbonate and the carboxylic acids tested are shown in table II. The diffusion of sodium [I4C]-bicarbonate and sodium [l-14C]-Z)L-lactate was significantly slower in plaque fluid than in water, and a similar effect was seen with the sodium salts of the other carboxylic acids tested, although with sodium [U-14C]-acetate, the standard devia tion of the D values in water was high, so that the differences were not statistically sig nificant. In the plaque residues centrifuged at 5,000 g, D values were significantly lower than in water. Compared to plaque fluid, the diffusion coefficients were significantly lower in the residues for bicarbonate (p < 0.001), acetate (p < 0.01), lactate (p < 0.02), but not butyrate (p < 0.1). These differences are more clearly illustrat ed by the ratio of the diffusion coefficient in the sample, compared to that of water, the diffusivity ratio (table III). Although the diffusivity ratios for the ionic species were similar in the plaque residues centrifuged at 5,000 g, there is a gradual increase in the
Sodium[14C]-bicarbonate Sodium[U-14C]-acetate Sodium[l-14C]-DL-lactate Sodium[l-14C]-n-butyrate
Water
Plaque fluid
Plaque residue (5,000 g)
1.202(0.220) 1.059(0.912) 1.012(0.251) 0.811 (0.041)
0.276 (0.32)** 0.324 (0.078) 0.338(0.177)*** 0.506 (0.288)
0.094(0.015)*** 0.129 (0.022)* 0.142(0.016)*** 0.096 (0.016)***
t values compared to water: ***p
