Figure 2. A test model with different... | Rockefeller University Press

Figure 2.

$Figure 2. A test model with different sets of constraints. (A) A simple kinetic mechanism that generates voltage-gated sodium channel-like currents (see Fig. 3). All rate constants are as described by Eq. 1 in the companion paper (Salari et al., 2018; k ij = k ij 0 × e k ij 1 ×V ); a1 is an allosteric factor, and NC is the number of channels. (B) Six sets of constraints were applied to the model to test the algorithms (see Figs. 4 and 5). Runs I and II test linear parameter constraints implemented with linear algebra–based methods that convert model parameters into free parameters, and vice versa. Run I implements only linear relationships, whereas run II adds two inequalities. Runs III through VI test arbitrary parameter constraints and behavioral constraints implemented with the penalty mechanism. Run III tests a parameter range constraint, whereas runs IV through VI test constraints that enforce model properties and behavior: the maximum open probability during a depolarization step (PO, run IV and VI) and the recovered fraction of available channels at 50 ms after a 5-ms inactivation step (fR, runs V and VI). The PO and fR quantities are obtained as shown.$

A test model with different sets of constraints. (A) A simple kinetic mechanism that generates voltage-gated sodium channel-like currents (see Fig. 3). All rate constants are as described by Eq. 1 in the companion paper (Salari et al., 2018; $k_{ij} = k_{ij}^{0} \times e^{k_{ij}^{1} \times V}$ ⁠); a₁ is an allosteric factor, and N_C is the number of channels. (B) Six sets of constraints were applied to the model to test the algorithms (see Figs. 4 and 5). Runs I and II test linear parameter constraints implemented with linear algebra–based methods that convert model parameters into free parameters, and vice versa. Run I implements only linear relationships, whereas run II adds two inequalities. Runs III through VI test arbitrary parameter constraints and behavioral constraints implemented with the penalty mechanism. Run III tests a parameter range constraint, whereas runs IV through VI test constraints that enforce model properties and behavior: the maximum open probability during a depolarization step (P_O, run IV and VI) and the recovered fraction of available channels at 50 ms after a 5-ms inactivation step (f_R, runs V and VI). The P_O and f_R quantities are obtained as shown.