Table 2.

Theoretical values and parameter estimates for a pharmacological system described by the operational model of agonism including constitutive receptor activity (Equation 4)

Parameter	Theoretical (population mean) values	Parameter estimates Mean ± SD
Em	10	10.01 ± 0.10
log(K)	−9	−9.00 ± 0.03
log(ε)	2	2.00 ± 0.04
log(χ1)	−0.30	−0.30 ± 0.01
log(χ2)	−1	−1.00 ± 0.01
log(χ3)	−1.30	−1.30 ± 0.02
log(χ4)	−2	−2.00 ± 0.03
log(χ5)	−2.30	−2.30 ± 0.03

Fifty E/[A] data sets, each composed of five χ-varied curves and log[A] ranging between −15 and −4 with an increment of 0.5, were generated by Monte Carlo method from theoretical (population mean) values assuming normal distributions with SDs 3% of the mean. A hybrid global/local method Differential Evolution (DE)/gradient-based non-linear regression (NLR) was used for curve fitting. All parameters except E_m were assumed to be log-normally distributed. The parameter space for exploration with DE was defined as: E_m, (5,100); log(K), (−15,−3); log(ε), (0,4); log(χ₁) to log(χ₅), (−5,5). In addition, the 3-parameter DE/rand/1/bin scheme reported in (Storn and Price, 1997) was used. For a real search space of dimension D (being D the number of parameters; eight in our simulation), the population is randomly initialized with NxD vectors. In our simulations, we used the common n = 40 value. Each vector in the population is allowed to evolve by mutation and recombination operators. The mutation rate is given by a parameter F ∈ [0; 2] and the combination rate by CR ∈ [0; 1]. Following (Das and Konar, 2005), F = 0.9 and CR=0.5 parameter values were chosen for DE algorithm. All programmes were conducted under the R software environment (R Development Core Team, 2012).