Chlorine Dioxide Is a Size-Selective Antimicrobial Agent

Background / Aims ClO2, the so-called “ideal biocide”, could also be applied as an antiseptic if it was understood why the solution killing microbes rapidly does not cause any harm to humans or to animals. Our aim was to find the source of that selectivity by studying its reaction-diffusion mechanism both theoretically and experimentally. Methods ClO2 permeation measurements through protein membranes were performed and the time delay of ClO2 transport due to reaction and diffusion was determined. To calculate ClO2 penetration depths and estimate bacterial killing times, approximate solutions of the reaction-diffusion equation were derived. In these calculations evaporation rates of ClO2 were also measured and taken into account. Results The rate law of the reaction-diffusion model predicts that the killing time is proportional to the square of the characteristic size (e.g. diameter) of a body, thus, small ones will be killed extremely fast. For example, the killing time for a bacterium is on the order of milliseconds in a 300 ppm ClO2 solution. Thus, a few minutes of contact time (limited by the volatility of ClO2) is quite enough to kill all bacteria, but short enough to keep ClO2 penetration into the living tissues of a greater organism safely below 0.1 mm, minimizing cytotoxic effects when applying it as an antiseptic. Additional properties of ClO2, advantageous for an antiseptic, are also discussed. Most importantly, that bacteria are not able to develop resistance against ClO2 as it reacts with biological thiols which play a vital role in all living organisms. Conclusion Selectivity of ClO2 between humans and bacteria is based not on their different biochemistry, but on their different size. We hope initiating clinical applications of this promising local antiseptic.


A reaction-diffusion (RD) model for the transport of ClO 2 in a medium containing reactive proteins
A general RD equation for ClO 2 The following partial differential equation (usually called reaction-diffusion equation [1]) holds for the local ClO 2 concentration c (c is a function of the time t and of the space coordinates) when ClO 2 diffuses through a medium containing various components which can react with it: (S1) In equation (S1) t c   is the time derivative of the local ClO 2 concentration, R i is the rate of the ClO 2 consumption due to the i-th reaction at the same location, N is the number of the various ClO 2 consuming reactions, D is the diffusion coefficient of ClO 2 in the medium, and c 2  is the Laplacian of c, which, applying a three dimensional Descartes coordinate system with spatial coordinates x, y, and z, can be written in the following form: Equation (S1) is a balance equation for ClO 2 where the two terms on the right hand side stand, successively, for the effect of the chemical reactions and of diffusional transport [1].
A simplified RD equation for ClO 2 . The effective substrate concentration As it was discussed previously there are four different amino acids and amino acid residues which can react with ClO 2 rapidly. In living tissue, however, there are even more chemical components [2] which are also able to react with ClO 2 by a slower but still measurable rate. A simple model cannot deal with all the ClO 2 reducing substrates of a complex biological system individually. To simplify the model the concept of the effective substrate concentration s will be introduced, which represents the local ClO 2 reducing capacity of all the various substrates in an integrated form.
To develop a definition for s, let us write the stoichiometry of the i-th reaction (the reaction of the i-th substrate S i with ClO 2 ) in the following simplified form: The stoichiometric coefficient  i shows how many ClO 2 moles can be reduced by one mole of S i . For example, when the substrate contains an SH (sulfhydryl or thiol) group as cysteine does, the stoichiometric equation around pH 7 for a fast initial reaction [3] can be written as 2 ClO 2 + 2 CSH  CSSC + 2 ClO 2  + 2 H + , (R2) where CSH stands for cysteine and CSSC is its oxidation product, a disulfide, called cystine. (One of the products, ClO 2  (chlorite) is actually an intermediate because it can react further with cysteine, but only with a rate which is 6 orders of magnitude slower than the first step of the ClO 2 /CSH reaction [3].) Thus, if we regard only the fast initial reaction then  CSH = 1, because 1 mole CSH removes 1 mole ClO 2 in (R2). For tyrosine [4] and tryptophane [5], a simplified scheme would suggest  TYR =  TRP = 2. Even in these relatively simple cases of pure amino acids, however, the effect of various parallel and consecutive reactions [3,4,5] can make it rather difficult to calculate  very precisely, not to mention when these amino acids are residues in proteins or peptides.
For the definition of s, however, it is enough to assume that there is such a stoichiometric coefficient for each component. Then s, the effective substrate concentration of the medium, can be defined as a weighted sum of the individual s i substrate concentrations, where  i plays the role of a "weight factor": (S3) Moreover, as a further simplification, it will be assumed that R i , the rate of the i-th reaction, follows mass action kinetics, that is the rate of ClO 2 reduction due to the i-th reaction can be written as a bilinear function of s i and c: where k i is the second order rate constant of the i-th reaction. Next, introducing an "effective rate constant" k by the definition: equation (S1) has the following simple form: Simplified balance equations for fixed substrates We will also assume all the substrates are fixed to the medium, and it is only the ClO 2 which is able to diffuse. This approximation is reasonable, if the RD medium is a human or an animal tissue having a cellular structure. Amino acid residues are usually parts of large protein molecules, the diffusion of which is very slow. Smaller peptidesespecially glutathioneand free amino acids can diffuse but only within a cell because the outer membrane of the cell is not permeable for them. Thus, from the point of a long range transport through an animal or human tissue, even these small substrates can be regarded as fixed ones. This way, the general RD equation for a substrate as all D i = 0. If we multiply both sides of equation (S8) with  i , and then summarize all such type of equations then we obtain the balance equation for the effective substrate concentration in the following simple form: When the medium contains the very reactive SH groups in a significant concentration then it can be proven that (S6) and (S9) can be simplified further: the form of the equations remains the same but the effective rate constant can be approximated as SH k k  (S10) where k SH is the rate constant of the ClO 2 -SH group reaction, and the effective substrate concentration is SH s s  (S11) where s SH is the concentration of the sulfhydryl groups in the medium.

Approximate solutions of the simplified RD equations
If the simplified RD equations (S6) and (S9) are accepted as a starting point, then the logical next step is to find a solution for these equations, that is to find the functions c=c(t,x,y,z) and s=s(t,x,y,z) while taking into account the given initial and boundary conditions. However, to find exact analytical solutions for nonlinear partial differential equations is usually not possible, and in this work we did not want to apply numerical solutions either. Thus, our aim here should be to find and apply approximate solutions with simple mathematical formulas which can be easily applied for the interpretation of our experimental results.
One type of approximation can be applied when the rate constant k is very high, as in the case of substrates containing SH groups or tyrosine residues. In this case, a sharp reaction front propagates through the medium, and the solution of the reaction-diffusion problem can be approximated with "parabolic rate law" type equations.
The other approximation is valid for low k values. In this case, the smooth concentration profiles are determined mostly by the diffusion, and modified only slightly by the reaction which can be distributed in the whole medium (no sharp front). When the medium is finite, as in the case of a membrane, an approximate steady state can be reached after some transition time.

Quasi steady state solution of the RD equations when the ClO 2 -substrate reaction is fast
Preconditions of the parabolic rate law The so-called parabolic rate law [6] holds for certain reaction-diffusion problems where the rate limiting step of an otherwise fast irreversible reaction (R3) C + S  P (R3) between the mobile reactant C and the fixed substrate S giving the product P is not the reaction itself but the diffusion of the reactant C to reach S. In our case C is ClO 2 and S is the reactive side group of an amino acid. The most important reactant in this respect is the SH group of the cysteine [3].
An important player in the process is the medium M immobilizing the substrate S but permeable for C at the same time. In our case the medium M is the hydrogel of the living tissues which is permeable for ClO 2 . Lipid membranes of the cells in the tissue do not form barriers for ClO 2 either, as it is very soluble in organic phases as well. The reactive amino acids, on the other handbeing mostly building blocks of various proteinsare immobilized in that hydrogel.
The parabolic rate law in one dimension for a slab of thickness d The simplest geometry giving a parabolic rate law is a situation where the concentration of C is kept constant, [C] = c 0 at the flat boundary of a slab e.g. at its left hand side, while [C] = 0 at the right hand side of the slab. The material of the slab is a medium containing the fixed substrate S in a homogeneous initial concentration s 0 (see Fig. S1). The thickness of the slab is d.

Figure S1. Schematic ClO 2 and substrate concentration profiles in a hydrogel slab of thickness d at an intermediate time t ( 0 < t < T ). p is the penetration depth.
When C is ClO 2 and ClO 2 is fed from one side of the slab, a sharp reaction front propagates from one side to the other. There is a measurable ClO 2 concentration only behind the front thus disinfection of the slab is completed only when the reaction front reaches the other side of the slab. The characteristic time T required for that can be calculated by the parabolic rate law. The result: That is the characteristic time T is proportional with the square of the thickness for a given set of non-geometrical parameters s 0 , c 0 , and D. Here D is the diffusion coefficient of C in M. Alternatively, the penetration depth p of a sharp reaction is proportional with the square root of the time t: Naturally the above formula gives the right p value only when T t  or when d is infinitely long.

S5
Derivation of the parabolic rate law for a slab (or membrane) As the concentration profile in Fig. S1 shows, it is assumed that the reaction occurs only in the plane x = p. This can be a good approximation if most of the reaction takes place in a narrow reaction zone much thinner than d (which is valid for a fast reaction combined with a relatively slow diffusion). The ClO 2 current I C across the slab with cross-section A in the region 0 < x < p can be given by Fick's law of diffusion: (S14) (I C is positive when the ClO 2 flow points from left to right in Fig. S1).
In a quasi steady state which is the parabolic rate law in one dimension for a slab.
The parabolic rate law for an infinitely long cylinder of radius R In this case the characteristic time T is when the sharp reaction front starting from the surface propagating inward reaches the symmetry axis of the cylinder.

S6
We shall regard concentration distributions with cylindrical symmetry where the local concentration c is a function of the radius r onlythat is c=c(r)and independent of the azimuthal angle  and the height z. In an analogy to the one dimensional case where H is the height of the cylinder. We will assume a quasi steady state concentration in the zone of R > r > R-p where p is the penetration depth. If I C is independent of r in this region then const dr dc r   . Regarding the boundary conditions: c(R-p) = 0 and c(R) = c 0 the steady state concentration profile in this region can be written as: Thus, with the above quasi steady state approximation The negative sign shows that I C points inward: it is negative when dr dc > 0.
The parabolic rate law in three dimensions for a sphere of radius R We shall regard concentration distributions with spherical symmetry where the local concentration c is a function of the radius r onlythat is c=c(r)and independent of the azimuthal angle  and the polar angle  . In an analogy to the one dimensional case, We will assume a quasi steady state concentration in the zone of R > r > R-p where p is the penetration depth. If I C is independent of r in this region then const dr dc r  