Algebraic potential of the Hill equation as an alternative tool for plotting dose (or time)/effects relationships in toxicology: a theoretical study.
Use of the Hill equation in plotting the results of toxicological experiments offers the following advantages: 1. In dose/effect relationships, the maximum response RM can be accurately determined by means of a described new noniterative algebraic method, from both hyperbolic and sigmoidal responses expressed in natural (nontransformed) units. The Hill coefficient (n) and the dose giving 50% (f50) or X% (fX) of RM, as well as their SD, are accurately deduced. 2. In time-course experiments with sigmoidal shape, an additional set of parameters, readily available from the former basic 3, makes it possible to avoid arbitrary choices, such as the time at which a percentage or mortality is considered. The slopes of the tangents at the inflexion point (maximum rate of response) and at half-maximum effect, then the coordinates of these points and the horizontal intercept of the tangent at inflexion point (as an index of initial lag-phase) will give increasing and decreasing functions of doses, respectively, depending on RM, f50, and (n). 3. The processes described first allow the classical parameters LD50 (or LDX) and LT50 (or LTX: X%--lethality time) to be calculated with high algebraic accuracy, in addition to RM and (n), both of which are of great interest in the general case of ligand-receptor interactions. Thus, the deduced set of additional indexes, not readily available from classical "Probits-type" transformations, eliminates the mortgage of subjective operations.
Bounias
M
M
Laboratory of Biochemistry, INRA, Montfavet, France.
D004305:Dose-Response Relationship, Drug; D007928:Lethal Dose 50; D008433:Mathematics; D013997:Time Factors; D014116:Toxicology