I. Principles of cytochemical staining methods

Advances that could accrue from the introduction of photometric methods into cytochemical staining practice include the investigation, by cytophotometry, of the mechanism of enzyme action in situ and the possible identification of closely similar enzymes by the direct determination of their Michaelis-Menten constants in the cell or tissue. After brief mention of the fundamental limitations of stain cytochemistry associated with (i) enzyme specificity, and (ii) the need for preliminary treatment such as fixation, a study is made of the theoretical basis of those staining methods which can be classified under the scheme $\text{substrate}$ $\underset \text{reaction}\to{\overset \text{enzymic}\to{\rightarrow}}$ $\underset \text{precursor}\to{\overset \text{stain}\to{}}$ $\underset \text{with developing agent}\to{\overset \text{`capture reaction\text{'}}\to{\rightarrow}}$ $\text{stain}$. These are considered in relation to a radially symmetrical model in which the enzyme is taken to be uniformly distributed in a spherical site, selected as the simplest that approximates to many actual sites. The overall process is simplified, without undue error, by division into stages. A brief survey of substrate penetration is followed by detailed study of the production, diffusion, and chemical removal of the stain precursor. Little is known about the mechanism of stain immobilization, but on the assumption of non-diffusibility, the stain density patterns are given for various values of the (first order) velocity constant of the capture reaction, diffusion coefficient of the stain precursor, and enzyme-site radius. A localization factor (degree of localization, F) is defined, which gives an indication of the intrinsic localization possibilities of any cytochemical method. This has value in both theoretical and experimental study. Values for F have been calculated, corresponding to the kinetic and geometrical parameters mentioned above. In order to satisfy the objective requirements that emerge from the theory, certain generalizations may be made concerning the properties of prospective substrates. The substrate itself should not associate with protein, except possibly the specific enzyme species, but it should yield a stain precursor and a stain, both of which should associate strongly with protein, i.e. be highly substantive molecules. Unless precursor-protein association occurs, extremely high capture reaction velocities are necessary for precise enzyme mapping in small sites.