The mean velocity of the reaction rate is $$\eta = \frac{VS}{K_m(1 + \frac{I}{Kic}) + S(1 + \frac{I}{Kiu})}.$$ Here, \(S\) is the substrate concentration, \(I\) is the inhibitor concentration, \(V\) is the maximum velocity of the enzyme, \(K_{ic}\) and \(K_{iu}\) are the dissociation constants and \(K_m\) is the Michaelis-Menten constant. Any design point is of the form \((S, I)\).
FIM_mixed_inhibition(S, I, w, param)vector of S component of design points. S is the substrate concentration.
vector of I component of design points. I is the inhibitor concentration.
vector of corresponding weights for each design point. Its length must be equal to the length of I and S, and sum(w) should be 1.
vector of model parameters \((V, K_m, K_{ic}, K_{iu})\).
Fisher information matrix of design.
The model has an analytical solution for the locally D-optimal design. See Bogacka et al. (2011) for details. The optimal design does not depend on parameter \(V\).
Bogacka, B., Patan, M., Johnson, P. J., Youdim, K., & Atkinson, A. C. (2011). Optimum design of experiments for enzyme inhibition kinetic models. Journal of biopharmaceutical statistics, 21(3), 555-572.
Other FIM: FIM_comp_inhibition,
FIM_emax_3par, FIM_exp_2par,
FIM_exp_3par,
FIM_logisitic_1par,
FIM_logistic_4par,
FIM_logistic, FIM_loglin,
FIM_michaelis,
FIM_noncomp_inhibition,
FIM_power_logistic,
FIM_uncomp_inhibition