Benefit of redundant gating variable definitions in EasyML?

Question

In the Grandi model, the h and j gating variables seem to have redundant definitions where they have both (alpha_X, beta_X) and (tau_X, X_inf) pairs, which the EasyML tutorial warns against.

What would be the benefit of redundant definitions in this case? Do the ternary definitions of (alpha_X, beta_X) help "constrain" the equation better? And how would the redundancy be handled?

ah = ((V >= -40)
      ? 0 
      : (0.057 * exp( -(V + 80) / 6.8 ))
      );
bh = ((V >= -40)
      ? (0.77 / (0.13*(1 + exp( -(V + 10.66) / 11.1 ))))
      : ((2.7 * exp( 0.079 * V) + 3.1e5 * exp(0.3485 * V)))
      );
tau_h = 1 / (ah + bh); 
hss_factor = (1 + exp( (V + 71.55)/7.43 ));
h_infinity = 1 / (hss_factor*hss_factor);
 
aj = ((V >= -40)
      ? (0)
      : (((-2.5428 * 10e4*exp(0.2444*V) - 6.948e-6 * exp(-0.04391*V)) * (V + 37.78)) / 
         (1 + exp( 0.311 * (V + 79.23) )))
      );
bj = ((V >= -40)
      ? ((0.6 * exp( 0.057 * V)) / (1 + exp( -0.1 * (V + 32) )))
      : ((0.02424 * exp( -0.01052 * V )) / (1 + exp( -0.1378 * (V + 40.14) )))
      );
tau_j = 1 / (aj + bj);
jss_factor = (1 + exp( (V + 71.55)/7.43 ));
j_infinity = 1 / (jss_factor*jss_factor);    

Answer 1

Hi Chang,

While it might seem so at first glance, the Grandi et al. .model file does not use both methods.

ah and bh are interpreted as regular variables. They would only be interpreted as alphas and betas if they were called a_h or alpha_h etc.

For future reference, the details are documented here: https://opencarp.org/documentation/examples/01_ep_single_cell/05_easyml#gate_vars