predict_grp: Prediction of equilibrium with regulation groups
In SimEvolEnzCons: Simulation of Evolution of Enzyme Under Constraints

Description Usage Arguments Details Value Special results See Also Examples

Gives the equilibrium for intra-group, inter-group and total relative concentrations at equilibrium

1	predict_grp(E_ini_fun,beta_fun,A_fun,correl_fun, tol=0.00000001)

`E_ini_fun`	Numeric vector of initial concentrations
`beta_fun`	Matrix of co-regulation coefficients
`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 intra-group e_i^q, inter-group e^q and total e_i relative concentrations, and group driving variable τ^q, and also for absolute concentrations E^i and concentrations sum in groups E^q. The equilibrium corresponds to null derivative for relative concentrations.

However, does not compute the theoretical intra-group equilibrium when there is competition, which is e_i^q = 1/B_i.

List of seven elements:

$pred_eiq: numeric vector of intra-group relative concentrations e_i^q at equilibrium. Same length as A_fun.
$pred_eq: numeric vector of inter-group relative concentrations e^q at equilibrium. The length is the number of regulation groups.
$pred_ei: numeric vector of total relative concentrations e_i at equilibrium. Same length as A_fun.
$pred_tau: numeric vector of driving variable tau^q at equilibrium. The length is the number of regulation groups.
$pred_Ei: numeric vector of enzyme absolute concentrations E_i at equilibrium. Same length as A_fun.
$pred_Eq: numeric vector of sum of absolute concentrations in groups E^q at equilibrium. The length is the number of regulation groups.
$pred_Etot: numeric value of total concentration at equilibrium.

When there are more than one positive or negative group and singletons with competition ("CRPos" or "CRNeg"), the equilibria are not predictable.

Use function activities to compute enzyme activities.

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

Use function predict_th (resp. predict_eff) to compute theoretical (resp. effective) equilibrium when there is no regulation groups (enzymes are all independent or all co-regulated).

#### For independancy "SC"
A <- c(1,10,30)
E0 <- c(30,30,30)
beta <- diag(1,3)

eq <- predict_grp(E0,beta,A,"SC")
#same results for pred_e and pred_ei
eq_th <- predict_th(A,"SC")

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

eq_grp <- predict_grp(E0,beta,A,"CRPos")
#same results for pred_e and pred_ei
eq_eff <- predict_eff(E0,B,A,"CRPos")


#Two groups: one negative group + one singleton
n <- 3
beta <- diag(1,n) 
beta[1,2] <- -0.32 
beta[2,1] <- 1/beta[1,2]

eq_grp <- predict_grp(E0,beta,A,"RegNeg")
eq_grp <- predict_grp(E0,beta,A,"CRNeg")


#Two groups: one positive group + one singleton 
n <- 3
beta <- diag(1,n) 
beta[1,2] <- 0.43 
beta[2,1] <- 1/beta[1,2]

eq_grp <- predict_grp(E0,beta,A,"RegPos")
eq_grp <- predict_grp(E0,beta,A,"CRPos")



#With saved simulation
data(data_sim_RegPos)
n <- data_sim_RegPos$param$n
num_s <- 1
pred_eq <- predict_grp(data_sim_RegPos$list_init$E0[num_s,1:n],
data_sim_RegPos$param$beta,data_sim_RegPos$list_init$A0[num_s,1:n],data_sim_RegPos$param$correl)

data(data_sim_RegNeg_1grpNeg1grpPos)
pred_eq <- predict_grp(data_sim_RegNeg_1grpNeg1grpPos$list_init$E0[num_s,],
data_sim_RegNeg_1grpNeg1grpPos$param$beta,c(1,10,30,50),"RegNeg")