Premium
ALGEBRAIC POTENTIAL OF THE HILL EQUATION AS AN ALTERNATIVE TOOL FOR PLOTTING DOSE (OR TIME)/EFFECTS RELATIONSHIPS IN TOXICOLOGY: A THEORETICAL STUDY
Author(s) -
BOUNIAS M.
Publication year - 1989
Publication title -
fundamental and clinical pharmacology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.655
H-Index - 73
eISSN - 1472-8206
pISSN - 0767-3981
DOI - 10.1111/j.1472-8206.1989.tb00024.x
Subject(s) - tangent , inflection point , sigmoid function , mathematics , algebraic number , point (geometry) , set (abstract data type) , algebraic equation , hyperbolic function , mathematical analysis , statistics , geometry , computer science , physics , nonlinear system , quantum mechanics , machine learning , artificial neural network , programming language
Summary— Use of the Hill equation in plotting the results of toxicological experiments offers the following advantages:1 In dose/effect relationships, the maximum response R M 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% (f 50 ) or X% (f x ) of R M , 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 R M , f 50 , and ( n ). 3 The processes described first allow the classical parameters LD 50 (or LD x ) and LT 50 (or LT x : X%‐lethality time) to be calculated with high algebraic accuracy, in addition to R M 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.