USE OF FLUORIDE IN BIOFILM TREATMENT
The present invention concerns materials and methods for the treatment, prevention or inhibition of biofilms.
A biofilm is a predominantly two-dimensional microbial community which forms at the interface between a liquid (typically water) and a solid surface. Primary colonising microbial cells attach to the solid surface.
Secondary colonising microbial cells then attach and with the primary organisms generate a matrix of exopolymer within which cells grow. Biofilm formation is ubiquitous; they form on any solid surface exposed to appropriate amounts of water and nutrients.
There is a need to control biofilm formation as biofilms may cause deterioration of the substrate surface. This is disadvantageous in any system where the surface has a functional role to play eg in a heat-exchange system.
Biofilms also act as reservoirs for potential pathogens. This is undesirable in eg catheters, dialysis machines, valved shunting devices, intra-cardiac valve implants, food processing implements etc. Biofilms also form on teeth, typically around gum margins. Plaque accumulation at the sites of biofilm formation causes imbalances in the native microflora, predisposing the sites to infection and disease.
To-date there is no effective method for the treatment of biofilms . They are dealt with either by discarding and replacing afflicted components or by physically scraping away the film. Bactericides are used, but are not particularly useful as they only affect the outer bacterial layers of biofilms. More information about biofilms may be found in "Bacterial Biofilms and their Control in Medicine and Industry", Edited by Julian
impenny et al published by BioLine for the British Biofilms Club, 1994.
It would be highly desirable to provide treatments which are more effective in killing off or otherwise treating bacteria in biofilms, and/or preventing or inhibiting growth or regrowth of the bacteria and biofilm. The present inventor has now found that exposure of biofilms to fluoride has effects which were not previously suspected, leading to various new techniques of practical value which are put forward herein.
Broadly, fluoride has the effect of weakening the association between neighbouring cells in a biofilm. This offers an advantage in making it easier to break up or destroy a biofilm e.g. by physical disruption. Another advantage offered is associated with an increase in extra-cellular volume which typically occurs in the film as a result of the weakened association between cells. The increased extra-cellular volume opens up the biofilm, rendering it more permeable to treatment agents used in conjunction with or subsequent to the fluoride, especially bacterially-active agents such as bactericides . Conventionally biofilms have resisted the action of such agents because of their densely-packed structure .
Fluoride is well known for topical application to teeth to reduce the solubility of teeth minerals. Teeth minerals become especially soluble in an acid environment . An oral environment of high acidity is created by bacteria in the mouth metabolising starches and sugars. Fluoride acts as a direct biocide inhibiting bacterial activity, thereby acting against the formation of the acid environment which promotes the solubilisation of teeth minerals. Secondly fluoride incorporates into the minerals of teeth as fluoroxy apatite to create a
mineral system of reduced solubility.
Calcium in plaque may serve as a reservoir which may be used to enhance remineralisation following a cariogenic episode. The work herein demonstrates that fluoride doubles the calcium binding capacity, thereby promoting this effect.
To form a biofilm the constitutive microbial cells have to be able to stick to one another. Protein bridges are partly responsible for holding the cells together via receptor anchors in the bacterial cell membranes. Bacteria also have negatively charged biochemical groups projecting from their surfaces. It is thought that Ca2+ or Mg2" bind to and cross-link adjacent bacterial cells via these negatively charged groups. EDTA, a chelating agent for Ca2+ or Mg2+ was suggested many years ago for the treatment of dental plaque. However owing to its toxicity it was never used, and analogous agents have not been researched.
The inventor's results are described later. It is thought that because fluoride is a strong anion, complexes in the form of bacteria-CaF readily form ie one +ve charge of Ca2+ is taken up by a negative charge on the bacterial cell surface and the other +ve charge by F . Sufficient F bound in this way is able to interfere significantly with the formation of Ca2+ bridges between adjacent bacteria, leading to general phenomena mentioned above. In one aspect therefore the applicant provides a method in which a non-dental biofilm, or a non-dental surface susceptible to biofilm formation, is treated with fluoride .
Non-dental biofilms and surfaces may be medical (eg as occur on catheters) or non-medical (eg as occur in a water processing plant) . They may also be of an animal
body (human and non-human) .
The fluoride treatment may be to varying degrees continuous or intermittent depending on the treatment context, and the fluoride concentration used for the treatment can be adjusted accordingly. The more prolonged the treatment, the lower the fluoride concentration that may be used. Where treatment can be prolonged or continuous, e.g. if of a water-processing appliance such as a water heater (e.g for a swimming pool), or water-treatment plant, concentrations down to 50μmol/l (lppm) can be effective. There is no particular upper limit, but a concentration above 50μmol/l would not normally be needed where the treatment is prolonged or continuous. More specifically, water in a water- processing appliance would typically include from 50 to 150μmol/l fluoride. Periodic or intermittent treatments may use more .
The treatment may use the fluoride to inhibit the onset or continuation of biofilm formation. It may use the fluoride to increase the permeability or susceptibility of existing biofilm to permeation by or activity of some secondary substance/agent used in conjunction with the fluoride e.g. simultaneously or subsequently. The secondary agent is preferably bacterially-active, and since it is often desired to prevent or destroy biofilm, the secondary substance/agent will commonly be an antibacterial or bactericide.
Such secondary substance/agent may be used in any concentration required for its effect; generally this will be conventional or easily determined by routine tests .
Suitable anti-bacterial agents include conventional ones such as chlorine, chlorine dioxide, ozone, hypochlorite
bleach, peroxide bleach, antibiotics (e.g. gentamycin, impenem, piferacillin) , chlorhexidine compounds, essential oils and triclosan. Obviously these can be selected by a skilled person taking into account the biofilm location, conditions and the type of bacteria involved. They are employed in anti-bacterially effective amounts which can be simply determined by those of skill in the art .
Any fluoride source suitable for the treatment context may be used. Simple substances containing fluoride such as metal fluorides such as KF and CaF2 are suitable. Other alternatives to prepare fluoride-providing agents are known to those skilled in the art. Substances containing F may be fully or partially water soluble. They may release fluoride ions or fluoride-containing ions in water. Further they may be substantially non-reactive with other components employed (eg other ingredients of say a dentifrice as discussed below) . Typical fluoride- releasing compounds are inorganic fluoride salts such as water-soluble alkali metal, alkaline earth metal, and heavy metal salts. Sodium and potassium fluorides have been mentioned above. Other options are sodium monofluorophosphate and stannous fluoride. The skilled person will be able to select the appropriate source of fluoride taking into account the biofilm and its location, conditions in the biofilm site and the type of bacteria involved.
A further aspect of the invention relates to the treatment of dental biofilms by using fluoride in conjunction with bactericide.
Thus the present invention provides for dentifrices such as gels and toothpastes; mouthwashes, tooth powders, mouthrinses, tooth hardeners, anti-tartar compositions, gums, tablets, lozenges; waters and dental coatings etc
comprising both fluoride and a bactericide. The base or support medium for the fluoride and bactericide of the present invention may be any conventionally employed in the field and well-known to those of skill in the art. The present invention also provides dental care and hygiene systems for the combined but sequential application of fluoride and a bactericide to the teeth. Thus a dental care and hygiene system according to the present invention may comprise a toothpaste containing fluoride and a mouthwash containing a bactericide for use pursuant to use of the toothpaste. The fluoride containing dental preparation will contain fluoride in an amount sufficient to disrupt any existing biofilm and to inhibit formation of biofilm. The bactericide containing dental preparation will contain bactericide in an amount sufficient to significantly reduce a bacterial population especially of bacteria involved in formation of the biofilm.
The bactericide may be one or more of the previously described anti-bacterial agents.
Essential oils are known bactericides and commonly used in toothpastes and mouthwashes to reduce eg gingivitis . They are aromatic compounds either derived from plants by distillation, expression or extraction or synthesised. Well-known essential oils are menthol, anethol , eugenol , eucalyptol , methyl salicylate and thymol. The latter is commonly used in compositions for oral/dental healthcare. Other suitable essential oils will be well-known to those skilled in the art as will other anti-bacterial agents (eg casein glycomacropeptide) suitable for use in the oral hygiene field.
The comments made above regarding the selection and concentration of fluoride and bactericide ingredients apply. In oral/dental care treatments are necessarily
short and intermittent . Therefore the fluoride concentration will usually be high in e.g. the range 10- 50mmol/l (1000 ppm is already the standard concentration for a toothpaste) .
Dentifrices as provided may comprise a liquid vehicle containing about 3-60% by weight of water, typically mixed with at least one humectant and a number of other ingredients. The liquid phase may comprise about 20-90% by weight of the dentifrice and generally may be about 25-80% liquid.
Suitable humectants for dentifrices include sorbitol, glycerin, propylene glycol, polyethylene glycol, sorbitan, fructose, mixtures thereof and the like.
Humectants, when employed, may be present in amounts of from about 10% to about 50%, by weight of the dentifrice composition.
Dentifrices may also contain a gelling or binding agent as a solid vehicle agent. Gelling or binding agents which may be present are alkali metal carboxymethyl cellulose, hydroxyethyl cellulose, hydroxypropyl cellulose, xanthan, thickening silicas, Irish moss, iota- carrageenan, gum tragacanth, polyethylene glycol, polyvinyl pyrrolidone, starch and mixtures thereof.
Any suitable surface active or detergent material may also be included in a dentifrice composition. Surfactants may be non- ionic, amphoteric, cationic, or anionic . Anionic surfactants include but are not limited to sodium lauryl sulfate, sodium lauryl sarcosinate, and sodium methyl cocoyl taurate, and disodium lauryl sulfosuccinate . Non-ionic surfactants include poly (oxethylene) -poly (oxypropylene) block copolymers, also known commercially as poloxamers . Poloxamer surfactants may have a Hydrophilic-Lipophilic Balance
(HLB) of between about 10 and about 30, and preferably between about 10 and about 25.
Amphoteric surfactants have the capacity to behave as either an acid or a base and include quaternized imidazole derivatives. Amphoteric agents used in the dental field include long chain (alkyl) amino-alkylene aklylated amine derivatives, also known as "Miranol", ie Miranol C2M, or N-alkyl betaine surfactants.
Cationic surfactants are surfactants which carry a positive charge. Cationic surfactants suitable include antimicrobial quaternary ammonium salts.
Sweeteners well known in the art, including natural and artificial sweeteners, may be used in dentifrice compositions. The sweetener may be selected from a wide range of materials including naturally occurring water- soluble sweeteners, artificial water-soluble sweeteners and modified water-soluble sweeteners derived from naturally occurring water-soluble sweeteners.
In general, an effective amount of sweetener is utilized to provide the level of sweetness desired in any particular product embodying the invention. This amount will vary with the sweetener selected and the final oral hygiene product .
Flavouring agents (flavours, flavourants) which may be used include those flavours known to the skilled artisan, such as natural and artificial flavours. Typical flavouring agents include mints, such as peppermint, citrus flavours such as orange and lemon, artificial vanilla, cinnamon, various fruit flavours, both singly or mixed, and the like. The amount of flavouring agent employed is normally a matter of preference subject to such factors as the type of final dentifrice composition,
the individual flavour employed, and the strength of the flavour desired.
Colouring agents (colours, colourants) may be employed in amounts effective to produce the desired colour. Colouring agents include pigments which may be incorporated in amounts up to about 6%, by weight of the composition. Titanium dioxide, may be incorporated in amounts up to about 2%, and preferably less than about 1%, by weight of the composition. A recitation of eg colourants and their corresponding chemical structures may be found in the Kirk-Othmer Encyclopaedia of Chemical Technology, 3rd Edition, in volume 5 at pages 857-884.
Suitable abrasives for use in a dentifrice include hydrated silica, calcium carbonate, calcium pyrophosphate, dicalcium phosphate dihydrate, or alkali metal meta-phosphates . Silica abrasives in the dentifrice composition may include among others, ZEODENT® (113) , manufactured by J.M. Huber Corp. and SY OID® or
SYLODENT®, manufactured by W.R. Grace Co. Abrasives may be used in amounts up to about 75.0% w/w of the composition, preferably in amounts from about 5.0% w/w to about 40% w/w of the composition, and most preferably from about 7.0% w/w to about 30.0% w/w of the composition.
Suitable buffers for use in preparation of a dentifrice include citric acid sodium citrate, acetic acid-sodium acetate, sodium saccharine-acid saccharine, and benzoic acid and benzonate in amounts up to about 1%, and preferably from about 0.05% to about 0.5%, by weight of the composition. The pH for a dentifrice of the invention may be from 3.0 to about 5.5.
Preservatives which may be employed include benzoic acid, sodium benzonate, butylated hydroxyanisole (BHA) ,
butylated hydroxytoluene (BHT) , ascorbic acid, methyl paraben, propyl paraben, tocopherols and mixtures thereof. Preservatives when used are generally present in amounts up to about 1% w/w, and preferably from about 0.1% w/w to about 1.0% w/w of the gel composition.
Various other materials may be incorporated in dentifrices. Examples thereof are opacifiers, desensitising agents, silicones and ammoniated materials such as urea, diammonium phosphate and mixtures thereof. These adjuvants are incorporated in the dentifrice in amounts which do not substantially adversely affect the desired properties and characteristics and are suitably selected and used in conventional amounts. Dentifrice compositions may be in the forms of toothpastes or dental gels. Gels describe a solid or semisolid colloid which contains considerable quantities of water. The colloid particles in a gel are linked together in a coherent meshwork which immobilises the water contained inside the meshwork. Those skilled in the art know how to formulate dentifrice compositions as paste and gels.
The final dentifrice of the present invention are readily prepared using methods generally known by those skilled in the art, as described in greater detail below.
Typically, an oral antiseptic dentifrice composition is made by first combining water, part of the humectant, one or more sweeteners, buffers and preservatives. Fluorine- releasing compounds may be added in this step. Generally the remainder of the humectant is separately combined with one or more gums, and then combined with the first mixture. Titanium dioxide and silicas are separately mixed, and combined with the other mixture previously prepared. Finally, colours, anti-bacterial agents such as antibiotics or essential oils, flavours and surfactants are added and mixed. The pH is adjusted to a pH of about 3.0 to about 5.5 with acidifiers. A vacuum
is pulled if necessary for daeration. The pH of a 25.0% w/w aqueous solution of the composition is measured using a suitable pH meter (eg Orion Research Microprocessor pH/millivolt Meter, Model 811) .
Apparatus to be used for the manufacturing process comprises mixing apparatus well known in the dental art, and therefore the selection of the specific apparatus will be apparent to the artisan.
Where it is intended that the system comprises a first preparation (eg a toothpaste) for application of fluoride and a second preparation (eg a mouthwash) for provision of a bactericide, the artisan will be able to prepare suitable preparation in accordance with standard approaches and ingredients known in the field.
These inventive proposals are now substantiated by description of experimental work done to determine the effect of fluoride as condensed (plaque-like) model biofilms and their properties.
Reference will be made to the accompanying drawing figures in which: Fig 1 is a schematic diagram showing an effusion well assembly and its use in test apparatus;
Figs 2 (a) and 2 (b) show variations of model plaque biofilm extracellular volume with [Ca2+] and [F"] at pH 7.0 and 5.0 respectively; Figs 3 (a) and 3 (b) show corresponding variations of biofilm dry/wet weight ratios;
Fig 4 shows results for effusion of labelled Ca2+ from a model plaque biofilm with and without F ;
Figs 5 (a) and 5 (b) show effective diffusion co- efficients for Ca2+ at various [Ca2+] , with and without FX at pH 7.0 and 5.0 respectively;
Figs 6 (a) and 6 (b) show the corresponding
proportions of bound Ca;
Figs 7(a) and 7(b) illustrate schemes for calcium mobility and binding in plaque in the presence and absence of fluoride respectively; Fig 8 shows effective diffusion coefficients for the effusion of labelled inulin from a similar model plaque biofilm at various F~ concentrations, and
Fig 9 shows variations in cell aggregation in the presence of Ca2+ according to whether F is present . Fig 10 shows variation in the absolute volume of a model plaque sample when treated with calcium or with fluoride and calcium together.
The following experiments were all carried out on model "plaque" biofilms of Streptococcus mutans, formed by centrifugal packing. It is generally recognised in the field of biofilms that changes of microorganisms generally have little or no effect on the behaviour of the biofilm as such, i.e. the extracellular properties. So, experiments on films of a single organism are a reliable guide to the generality of biofilms.
Materials and Methods.
Cul ture and harvesting of bacteria - Streptococcus mu tans R9 was incubated anaerobically at 37°C for three days on Todd-Hewitt agar plates supplemented with 0.4% glucose and stored at 4°C. Colonies were inoculated into 20 ml Todd-Hewitt broth supplemented with 0.4% glucose and incubated at 37°C overnight. Cells were harvested in the late exponential stage of growth (after about 17 hours) and centrifuged at 9,000 g for 30 min at 4°C. Pellets were collected, pooled and washed three times by resuspension in 15 ml of chilled, calcium-free buffer and centrifuged at 6,000 g for 10 min at 4°C. About 250 mg of the resulting pellet was transferred to a weighed Eppendorf tube and resuspended, for 30 min at 4°C, in 500 μl buffer, containing 20 μl 3H-inulin (185 kBq; Amersham
International PLC, Amersham, U.K) with variable concentrations of calcium (0, 5, 10, 15 or 20 mmol/1) and fluoride according to the experiment . Where calcium effusion was to be determined, the buffer contained lOμl 45Ca (76.2 kBq; Amersham) . For experiments at pH 7.0, the buffer used was 0.05 mol/1 dipotassium PIPES, containing 0.1 mol/1 D-glucose, while for experiments at pH 5.0 , 0.1 mol/1 MES containing 0.1 mol/1 KC1 and 0.1 mol/1 D- glucose was used. After incubation, the cells were spun at 6,000 g for 10 min. The supernatant was recovered and three 25μl samples were taken for scintillation counting (see below) . These gave the tracer concentration in equilibrium with the sample at the start of each effusion experiment ( [3H-inulin] 0 and [45Ca] 0 as appropriate) .
Effusion Experiments - Referring to Fig. 1, the sediment was transferred to a 1 mm-deep effusion well 2 of an effusion well assembly 1, spread evenly and weighed. This model plaque 3 was then covered with a high porosity alumina membrane support 4 (Anodisc 13, 0.2 μm pore size, Whatman Ltd., Maidstone, UK) as a bacterial filter which was in turn held in place with a silicone rubber 0 ' ring 5. The well assembly 1 was placed in communication with the stirred 6ml effusion chamber (10) and effusion started by addition of 6 ml of tracer-free buffer containing an equal concentration of carrier to that in the sample. Six chambers were run concurrently. 25μl samples were taken (through the top port 11) at intervals of 3 min to start with, increasing somewhat toward the end of the experiment - usually about 200 min. Samples were taken using a 25 μl glass syringe which was rinsed three times in deionised water between sampling. The samples were placed in polypropylene scintillation mini vials, mixed with 3.5 ml of scintillation fluid (LKB Optiphase 'Safe', Fisons pic, Loughborough, UK), shaken twice and counted for 300 seconds (LKB 1217 Rackbeta LKB- Wallac, Milton Keynes, UK) . Where both 3H-inulin and 45Ca
are used, windows are set for dual counting of the two isotopes. The three 25 μl samples of extracted incubating fluid described above were also counted at the same time.
Da ta analysis : correction for sample size - a volume of up to 1 ml (1/6 of the total sample volume) is removed during the experiments, so it is necessary to allow for the reduced volume and calculate corrected counts . We used a short BASIC program called ALEX, but this correction is in any event routine.
EXTRACELLULAR VOLUME
A first investigation is into the effect of fluoride on extracellular volume. Inulin is neither bound to nor taken up by, the bacteria. It does not penetrate them and is not metabolised. Since the sample volume (Vs = 20 μl) is much smaller than the clearance volume (Vx = 5-6 ml) it can be assumed that at t = ∞ all the inulin tracer has cleared into this space from the extracellular volume fraction Ve, to give an activity [3H-inulin] _, in a volume V-L . Thus :
( i :
Equation 2 below is a saturating exponential, defining counts in the clearance solution, in which C∞ is the fitted asymptotic count, Ct is the volume-corrected count at time t and α is a fitted exponential constant. It was fitted to each set of 3H-inulin effusion data using Fig.P/P.Fit software (Biosoft, Cambridge). The data were curve-fitted with a variable x-axis intercept (δ) to allow for the fact4 that the first 30% of effusion does not follow this equation (Dibdin G.H., 1988 med . Biol .
Eng Comput . 2_6, 217-221); any data points for values of Ct/C∞ less than 0.3 were also, therefore excluded from the fit.
Ct=C∞(l-e-d( +δ)) (2)
GRAVIMETRIC ANALYSIS
Bacteria were prepared as above, but without inulin.
Following incubation at the chosen pH, Ca2+ and F" concentrations, the sediment was transferred to 1 mm-deep effusion wells and weighed. These were then dried under vacuum overnight and weighed once more. Results Figs 2 (a) and 2 (b) show the variation in extracellular volume fraction with pH, calcium concentration and fluoride. Decaying exponentials (with residuals) were fitted to the data using Fig.P/P.Fit. In the absence of fluoride the maximum extracellular volume fraction (Ve max) was found to occur at zero calcium concentration, and was substantially greater at pH 7.0. The minimum extracellular volume fraction (Ve mιn) is estimated from the asymptotic residual and represents the Ve which would be achieved at an infinite calcium concentration. This was found to be lower at pH 5.0.
Fig. 3(a) and 3(b) show the effect of pH, calcium and fluoride concentrations on the dry weight/wet weight ratio of the model plaque biofilms. Although the differences were not statistically significant, the ratio was found to be greatest at pH 5.0 and proportional to the calcium concentration. Addition of fluoride to the system largely eliminated any change in the ratio with calcium concentration.
Note that the experimental protocol used in this work did not measure change in Ve, but merely established that Ve varied under different conditions. It is possible that,
in vi vo, and especially in biofilms in enclosed spaces, these effects may be manifest as a change in pressure rather than volume .
This work demonstrates that Ve was greatest (69%) at 0 mmol/1 Ca2+ and pH 7.0 and lowest (28%) at 20 mmol/1 Ca2+ and pH 5.0: similar conditions to those found during a cariogenic episode. Introduction of F" into the system raised the minimum Ve to about 49% at pH 5.0 and 20 mmol/1 Ca2+ . The gravimetric analysis represents a measure of the density of cells in the model biofilms; the dry/wet weight ratio would be expected to be higher in more densely-packed biofilms containing a greater proportion of cells per unit volume. Figure 3 demonstrates that the model biofilms are most densely packed at pH 5.0 and 20 mmol/1 calcium. By bridging adjacent cells and reducing the overall negative charge, high calcium and low pH respectively reduce the extracellular volume fraction of plaque. Notably, however, by inhibiting calcium-bridging fluoride reduces the variation in Ve to that exerted by pH alone. By increasing Ve and allowing better penetration, fluoride can form a useful adjunct to any anti-biofilm treatment .
The inventor has also demonstrated (see Fig.10) the variation in the absolute volume of a model plaque sample when treated with either calcium or calcium and fluoride together. The results as shown in Fig.10 indicate that at any calcium concentration above zero, fluoride will increase the volume of the plaque sample.
MOBILITY OF CALCIUM THROUGH A MODEL PLAQUE BIOFILM This set of experiments elucidates the effect of fluoride on the mobility of the cationic species Ca2+ through the model plaque biofilm, using labelled 45Ca2+ as mentioned previously. Unlike inulin, calcium is reversibly bound by the cells and matrix of the model plaque biofilm. The
amount cleared at t = ∞ will therefore be increased by the amount bound, which we assume occupies the sample volume Vs, with a concentration: [45Ca]bound. The mass balance equation is then:
[45Ca]bound.Vs+[45Ca]0.Ve=[45Ca]co.V1 (3)
Since Ve is now known from the inulin results (Eqn. 1) , we have, on rearranging:
[45Ca]∞.V1- [45Ca]0.Ve t45Ca] bound- v.
in which [45Ca] bound is the only unknown.
Calculation of the diffusion coefficient - Equation 2 above was fitted to each set of 5Ca and 3H-inulin effusion data using the Fig.P/P.Fit software as before
For an effusion system of the type used in this work, the exponential constant is related to the diffusion coefficient by:
4αl2
D„ =• π'
(5:
(McNee S. G. et al . , 1979 Arch. Oral. Biol . 2Λ, 359-362), (Dibdin G.H., 1993 Arch. Oral. Biol. 3_8, 251-254) . The effusion of a strongly-bound divalent cation through a bacterial plaque would have a retarded effective diffusion coefficient (rDe: (Rose & Dibdin, 1995 Arch.
Oral. Biol. 4_0, 385-391), (Dibdin, 1995 Microbial. Ecol . H/th. Dis. J3, 317-319)) because of reversible adsorption at specific sites. rDe is reduced from De (the effective diffusion coefficient) by:
D D" r e R + l
(6 in which R (Crank J., 1989 "The mathematics of diffusion" OUP) represents the ratio of bound to free calcium, i.e.
R _______
[Ca]f
(7) Where [Ca] _ is, by definition, the same as in the bathing solution and R is a constant during the experiment if, as throughout our system, [Ca] carrιer>> [45Ca] . Bound and free calcium are related by the equation (Rose & Hogg, 1995 Biochem. Biophys . Acta; 1245, 94-98):
C [Ca
[Ca]b =
Kd + [Ca]f
( 8 ) In which Cmax is the binding capacity and K d is the dissociation constant. Hence, as the free calcium concentration increases, R approaches zero and rDe approaches De . Concentration therefore affects the rate at which a front moves through the plaque or film. Although binding is not linearly related to the free calcium concentration, the use of a chosen concentration of calcium 'carrier' in this work effectively ensures that the binding ratio, R, is constant with position and time .
Results
In this type of system, the rate of calcium effusion follows a saturating exponential in which the diffusion coefficient is proportional to the exponential constant (Fig. 4) . Addition of fluoride to the system produces an increase in the height and steepness of the curve,
implying increased calcium binding and faster calcium effusion .
The calcium binding curves (Fig 5) are typical binding hyperbolas, the asymptote of which represents the capacity and the [Ca] at which sites are 50% saturated is the dissociation constant (Kd) . As predicted by our equilibrium dialysis work on streptococci in suspension, in the condensed (plaque-like) system, fluoride decreases the calcium binding affinity while approximately doubling the binding capacity. At pH 5.0, there are fewer binding sites available, and so the capacity is reduced. The calcium effusion curves (Fig. 6) are also hyperbolic, but in this case, at high free [Ca] , rDe asymptotically approaches De as the ratio of bound to free calcium (R) , tends towards zero. Since De is unaffected by binding, the asymptote does not differ significantly between the curves. The point (k) at which rDe = De/2 and [Ca]b = [Ca]f, is reached at lower [Ca] in the presence of fluoride. At low pH, k is lower and so rDe approaches De at lower calcium concentration. Hence, fluoride significantly increases calcium effusion. Discussion As predicted by our equilibrium dialysis work on streptococci in suspension, in the condensed (plaquelike) system used here, fluoride decreases the calcium binding affinity while approximately doubling the binding capacity. By decreasing the affinity, addition of fluoride increases the proportion of free calcium, hence increasing the rate of effusion, for example by 55% at pH 7.0 and 5 mmol/1 [Ca2+] . In terms of Eq. 6, addition of fluoride brings about a decrease in R, and so rDe approaches De at lower free calcium concentration.
These effects are summarized in Figs. 7(a) and 7(b) . In the absence of fluoride, calcium bridges two sites (either on the same cell, or on adjacent cells) . This
form of binding is strong, so the bound/free ratio is high. A low proportion of free calcium means slow diffusion and little potential for remineralization . When fluoride is present (Fig. 7(b)), calcium is bound by a single site and inter-cell bridging may not occur. This form of binding is weaker, so the ratio of bound/free calcium is low and a high proportion of free calcium means diffusion is fast and remineralization potential is high .
This work demonstrates that fluoride significantly increases calcium mobility in plaque. At neutral pH, while fluoride is retained in plaque, this may increase the rate at which calcium is transported between plaque and an underlying lesion, promoting remineralization.
MOBILITY OF INULIN
Using inulin data from the above experiments, and repeating them at additional fluoride concentrations of 10,15 and 20mM, the data shown in Fig 8 were obtained, namely effective diffusion coefficients through the model plaque for inulin, varying according to the amount of fluoride present. These results are interesting because inulin unlike Ca2+ is uncharged and a loop molecule. Furthermore, it does not interact significantly with the bacterial surface and so its effusion can be regarded as a useful indicator of the 'openness' of a biofilm.
The results show that the mobility of inulin, like that at Ca2" , is substantially increased when F" is present. However the increase fades above 5mM F" , presumably reflecting the possible extent of interaction of F" with cationic binding sites.
INHIBITION OF AGGREGATION
At pH 7.0, calcium is bound by bidentate chelation to plaque bacteria with a capacity of 20-40 μmol/g wet wt .
This binding allows cell aggregation and adherence (Rose RK, et al . J Dent Res 69: 850, 1990) . As observed above, Ca2+ ions also promote F" binding to plaque by acting as bridges to the bacterial. At the same time, F" breaks the usual bidentate Ca2+ chelation, reducing the calcium binding affinity and doubling the calcium binding capacity. To investigate the effect of fluoride on calcium- induced aggregation in vi tro, Strep , mu tans R9 cells were washed in calcium-free buffer, sonicated to break up chains and resuspended to 0.25 g/L in 0.05 mol/L potassium PIPES buffer containing 0 to 10 mmol/L CaCl2 and 0, 1 or 5 mmol/L KF . This suspension was incubated at 37°C for 30 min and a drop was placed on a Neubauer counting chamber. The number of free cells and the number of colony- forming units were counted on each grid square and the results expressed as the fraction of free cells. Aggregation was found to be exponentially related to the calcium concentration and was 90% complete at 10 mmol/L [Ca] , with a [Ca] 05 (the concentration which produces half of the total aggregation) of 5.2 ± 1.4 mmol/L. This aggregation was substantially inhibited by the introduction of 1 mmol/L fluoride, limiting it to 20% at 10 mmol/L [Ca] , without significantly altering the [Ca]0 5. This work demonstrates that fluoride effectively inhibits calcium-induced aggregation in streptococci. In vivo this may prevent further deposition of salivary planktonic cells on to the plaque biofilm and possibly loosen already-established plaque.