Unified proportionality equation for modeling biological and pharmacological data

Introduces the modeling of biological and pharmacological data using a new mathematical concept. A wide variety of sigmoidal and bell-shaped batch data curves in the life sciences can be described by the unified proportionality equation: /spl plusmn/d(q/sup m//spl omega//sub 1/)=K(q/sup n//spl omega//sub 2/), where d is the notation of the differential and q is the notation of the logarithm, K is a proportionality constant, and m and n are the logarithmic dimensions of the geometric variables /spl omega//sub 1/ and /spl omega//sub 2/. The geometric values are defined as the linear distance in a linear measurement and the non-linear distance between an asymptote and the asymptotic curve in a non-linear measurement. The parameters m and n are non-negative integers. Proportionality graphs and characteristics of equation parameters are illustrated with simulated data in plant growth, oxygen dissociation in hemoglobin and myoglobin, and the drug action of an agonist.