SimEvolEnzCons (version 2.0.0)

predict_grp: Prediction of equilibrium with regulation groups

Description

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

Usage

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

Arguments

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

Value

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.

Special results

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

Details

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 \(\tau^q\), 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 \(e_i^q = 1/B_i\).

See Also

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).

Examples

# NOT RUN {
#### 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")


# }
# NOT RUN {
#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")

# }
# NOT RUN {
# }