predict_eff: Prediction of effective equilibrium
In SimEvolEnzCons: Simulation of Evolution of Enzyme Under Constraints

Description Usage Arguments Details Value Special results References See Also Examples

Gives the effective equilibrium for relative concentrations

1	predict_eff(E_ini_fun,B_fun,A_fun,correl_fun, tol=0.00000001)

`E_ini_fun`	Numeric vector of initial concentrations
`B_fun`	Numeric vector of global co-regulation coefficients. Same length as `E_ini_fun`.
`A_fun`	Numeric vector of activities
`correl_fun`	Character string indicating the abbreviation of the constraint applied on the system
`tol`	Tolerance for function `uniroot`

Gives values at effective equilibrium for relative concentrations and corresponding driving variable τ. This equilibrium corresponds to null derivative of relative concentrations, with a maximum for flux.

Effective equilibrium is found by searching the zero for response coefficients. The R function uses in this objective is uniroot.

Note that sum of 1/B_fun need to be equal to 1.

When there are regulation groups, preferably use predict_grp.

List of three elements:

$pred_e: numeric vector of relative concentrations at effective equilibrium. Same length as A_fun
$pred_tau: numeric value of driving variable tau at effective equilibrium
$pred_E: numeric vector of absolute concentrations at effective equilibrium. Same length as A_fun

In case of independence (correl_fun="SC") or positive regulation (correl_fun="RegPos"), there is no effective equilibrium, and function predict_eff stops.

In case of competition (correl_fun="Comp"), effective and theoretical equilibria are confounded. Function predict_eff also stops, so use preferably function predict_th to compute equilibrium.

If E_ini_fun is a multiple of 1/B_fun, effective equilibrium is confounded with theoretical equilibrium and initial point (see droites for details). Function predict_eff returns E_ini_fun for $pred_E and 0 for $pred_tau, with a warning message.

Coton et al. (2021)

Use function activities to compute enzyme activities.

Use function is.correl.authorized to see allowed constraints for correl_fun.

Use function predict_th to compute theoretical equilibrium.

Use function predict_grp to predict equilibria when there are co-regulation groups.

###### In presence of competition plus regulation
A <- c(1,10,30)
E0 <- c(30,30,30)
beta <- matrix(c(1,10,5,0.1,1,0.5,0.2,2,1),nrow=3)
B <- apply(beta,1,sumbis) 

eq_eff <- predict_eff(E0,B,A,"CRPos")

eq_eff$pred_e
eq_eff$pred_tau
eq_eff$pred_E