The zinc ion availability (ZIA) method of analysis is presented to examine and evaluate the hypothesis that the amount of Zn2+ ions available for absorption into the oral and oropharyngeal tissues from chemically different zinc lozenges determines the extent of change in common cold duration. The present author also examined and evaluated the hypothesis that Zn2+ ions in saliva diffuse from the membranes of the oral cavity through oral-nasal tissues into the infected tissues of the nose. The ZIA method of analysis and diffusion theories were derived from Fick's laws of permeability.
The pharmacologic application of Fick's first law states that the rate of diffusion or transport of a drug across a biologic membrane is directly proportional to the surface area of the membrane and to the concentration gradient, and is inversely proportional to the thickness of the membrane.(24) The general expression for Fick's first law of diffusion is dm/dt = - DA dc/dx, where m is the quantity of drug or solute diffusing in time t, dm/dt is the rate of diffusion, D is the diffusion constant, A is the cross-sectional area of the membrane, dc is the change in concentration, and dx is the thickness of the membrane.(24) Similarly, Fick's second law of diffusion relates to diffusion through solids. A change in any of the above variables will alter the rate of drug transport over a given time. Holding both the cross-sectional area of the oral cavity and the rate of mouth-to-nose diffusion constant, and introducing lozenge dissolution times allows zinc ion ZIA values to be calculated.(25)
Zinc ion availability (ZIA) is defined as the potential for absorption of Zn2+ ions into oral and oropharyngeal mucosal membranes at pH 7.4. Mathematically, ZIA = KZiT, where K = 0.7697 (a constant used to set the Eby et al. trial(1) ZIA value at 100), Zi = initial concentration of Zn2+ ions (in mmol), and T = duration of oral contact time by zinc lozenges each day. For calculation of daily ZIA for comparative purposes between lozenge formulations, ZIA can be determined by multiplying the constant 0.7697, times lozenge zinc dosage (in mg), times fraction as Zn2+ ion at pH 7.4, times oral dissolution time (minutes) of the lozenges, X number of lozenges used per day, divided by volume of saliva (in mL) generated during each oral dissolution.
For example, The ZIA calculation for the insoluble Eby et al.(1) ZIA 100 lozenges is: 0.7697, times 23 (mg zinc per lozenge), times 0.30 (fraction of zinc as Zn2+ ion at pH 7.4), times 30 (dissolution time in minutes), times 9 (doses per day), divided by by 14.34 (mL saliva, which numerically equals the total saliva weight minus lozenge weight). Lozenge specific gravity is considered for soluble lozenges
Concentration is specified as Zi, the initial Zn2+ ion concentration. Although initial concentrations are often far above the concentration needed to have pharmacological activity in infected nasal tissues, many Zn2+ ions are made inactive by complex formation during their diffusion through tissues from interactions with diverse ligands found in saliva, blood, lymph, and tissues. Consequently, a much higher initial concentration is required to allow a few active Zn2+ ions to reach the infected superficial columnar cells of the nasal turbinate epithelium and nasopharynx. For example, the Eby et al.(1) lozenges produced a salivary Zi concentration of 7.4 mmol, while pharmacologically active concentration is only 0.1 mmol.
If Zn2+ ions are absorbed directly into oral tissues from lozenges during lozenge dissolution according to Fick's laws, the only relevant pH is 7.4, the pH of tissue, lymph, and blood (physiologic pH). This is because all acids or bases are buffered rapidly in tissue, lymph and blood to the physiologic pH during homeostatic regulation of acid-base balance.(26,27) Zn2+ ion is a Lewis acid that reacts readily with acid-labile rhinovirus coat proteins, and is capable of existing at physiologic pH 7.4.(7) Zn2+ ions are not thought to enter cells in the concentrations used.
Salivary pH was 5.5 using zinc gluconate lozenges having no other zinc chelators.(25) Salivary pH has been measured as low as pH 4.3 using zinc gluconate-citrate lozenges, and as high as 7.0 using zinc orotate and zinc aspartate lozenges.(25) In instances where salivary or infected respiratory secretion pH is lower than physiologic pH, Zn2+ ion concentration is higher, but these higher concentrations are reduced as result of being buffered to pH 7.4 upon absorption of zinc compounds into oral and oropharyngeal tissues.(25]
For example, Figure 1 shows that 60% of the zinc from zinc gluconate is available as Zn2+ ions at pH 5 to 6, while only 30% is available at pH 7.4.(28) Consequently, only those zinc gluconate species capable of existing at pH 7.4 remain. All following calculations of Zn2+ ion concentration are for physiologic pH 7.4 unless otherwise stated.
Bioavailability of metallic ions at physiologic pH depends on the first stability constant for the metal and its associated ligand. The basic solution chemistry equation CM = [M] + [ML], with [ML] = K [M] [L], becomes CM = [M] (1 + K [L]); hence [M] = CM / (1 + K [L]) shows that M (metallic ions) depend upon CM (total metal), K (the stability constant of the metal-ligand complex) and L (the free concentration of the ligand) which in turn depends upon corresponding pK and pH values (personal communication, Guy Berthon, Ph.D., Director of Research, INSERM, U-305, Toulouse, France, 1992).
Figure 1 shows Berthon's computed amount of Zn2+ ions and other zinc species available from aqueous solutions of zinc gluconate by pH. As previously stated, about 30% of the zinc from zinc gluconate is present as Zn2+ ion at physiologic pH 7.4. Speciation of zinc gluconate as shown in Figure 1 is applicable to lozenges having no water-soluble ingredients other than zinc gluconate. Because of the extremely low binding power of sweet carbohydrates for zinc,(29) Figure 1 also applies to aqueous solutions of most sweet carbohydrate-based zinc gluconate lozenges.
Results of common cold trials are usually reported for symptom severity, not symptom duration. Measurements of results have included daily clinical scores, nasal mucus weights, facial tissues used, and various subjective measures of illness.
When reduction in duration of common colds is anticipated, a uniform means of analyzing data is needed to compare results accurately. Half-lives of common colds and weighted average durations of exponentially decaying common colds have been shown to be appropriate means of analyses.(1) Historically, 50% of untreated exponentially decaying rhinovirus colds are over in 1 week, 75% are over in 2 weeks, while 87.5% last 3 weeks or less, which is an exponential decay rate.(30) Therefore, the half-life (H) of these colds is 7 days. By integrating, the average duration is half-life / ln 2.(1,25) In the case of colds having an observed half-life of 7 days, their average duration is 10 days.
Figure 1. Distribution of zinc ion and zinc-ligand complexes in the Zn2+ and gluconic acid (L) system. Curves were constructed from pK values (courtesy of Gerritt Bekendam, Akzo Chemicals BV Research Centre, Deventer, The Netherlands, 1989) shown after the reactions: Zn2+ + L- = ZnL+ (1.62) and ZnL+ + OH- = ZnL(OH)0 (8.14) at a concentration of 30 mmol zinc. The Zn2+ fraction over pH 6 is affected by the second pK value. Precipitates of zinc hydroxides result in supersaturated solutions above pH 7.4. Reprinted with permission.(28)
Methods of obtaining the average durations of colds differed slightly among trials, depending upon the reporting methods used by the researchers. Both half-life and average duration data were published for the Eby et al. zinc gluconate trial.(1) The average duration of colds in the Al-Nakib et al. zinc gluconate trial was determined from mean clinical score end-points.(2) Half-lives in the Smith et al. zinc gluconate trial were obtained from published figures and data,(31) and average durations were calculated. Average durations of colds in the zinc gluconate,(32) zinc orotate,(25) zinc aspartate,(25) zinc acetate-tartarate-carbonate,(33) and zinc gluconate-glycine(25,34) trials were stated by the authors. Average durations of colds in the zinc gluconate-citrate trial(35) were determined from day-7 symptom scores.
Zinc ion availability factors are presented in Table 1 for each zinc lozenge formulation used in clinical trials.(1,2,25,31-35) Data were obtained by direct observation, published trial reports, solution chemistry data, manufacturers' communications' and samples, and exact replications of lozenges using the original manufacturers' formulas and procedures. Oral test data was collected using manufacturers' lozenges or exact replications from healthy volunteers from 1987 through 1993 and has been published.(25) The amount of saliva resulting from lozenge dissolution was used as reported in the trial reports that contained such data.
Zinc ion availability factors were used to calculate ZIA values shown in Table 2 using the above ZIA equation.(25) Electronic charges of zinc species available at pH 7.4, and the amounts of Zn2+ ions present at pH 7.4 were determined using solution chemistry means and data from trial reports.
Evidence for the transport over long distances of metallic ions through naturally occurring biologically closed electric circuits (BCEC) was published by Nordenström of the Karolinska Institute in Stockholm in 1983. Among other findings, Nordenström showed that infected, injured, and cancerous tissues, as well as healthy muscles, generate electrical potentials that are not related to nervous system electrical activity. Nordenström also showed that metallic ions adhere to the inside of capillaries, thus changing the charge of capillary walls from negative to positive, thereby providing a conduit for other positively charged metallic ions. He also showed that Fick's laws of diffusion apply for metallic ions in a bio-electric field.(36)
Nordenström's observations suggested a search for a BCEC between the mouth and the nose as a possible explanation for the Zn2+ ion lozenge effect on colds. A volt-ohm meter was used to detect flow of electrons in the mouth-nose BCEC. Voltage was measurable only with a digital volt-ohmmeter, whereas resistance was readily measurable with either an analog or digital ohmmeter. One terminal was placed at various points within the oral cavity, and the other terminal was placed at various points within the nasal cavity. Differential resistance readings were obtained by reversing the ohmmeter leads.
Lozenge safety and adverse effects data were taken directly from the reports of clinical trials of zinc lozenges reanalyzed in the Results section.
Statistical methods used in individual common cold reports are cited as originally reported. Spearman's rank difference correlation method was used in the analysis of the relationship between lozenge ZIA values and their effects on the duration of common colds.