Computes the position of the point of relative concentrations on the line on which they move on in the cases of co-regulations
droite_e(tau_fun,E_ini_fun,B_fun)droite_E.Reg(tau_fun,E_ini_fun,B_fun)
droite_E.CR(tau_fun,E_ini_fun,B_fun)
droite_tau(E_fun,E_ini_fun,B_fun)
Numeric value of the position of relative enzyme concentrations on the line
Numeric vector of initial concentrations
Numeric vector of global co-regulation coefficients. Same length as E_ini_fun.
numeric vector of current concentrations on the line. Same length as E_ini_fun.
droite_e returns a numeric vector of relative concentrations
droite_E.Reg returns a numeric vector of absolute concentrations
droite_E.CR returns a numeric vector of absolute concentrations
droite_tau returns a numeric value giving the position on the line
Initial point
If tau_fun is equal to 0, droite_e returns the value of initial relative concentrations, i.e. value of E_ini_fun divided by sum(E_ini_fun);
droite_E.Reg and droite_E.CR returns the value of E_ini_fun.
If E_fun is a multiple of E_ini_fun, function droite_tau returns 0 (initial point).
End point
If tau_fun is equal to 1, droite_e returns the reverse value of B_fun;
droite_E.CR returns a multiple of the reverse value of B_fun;
droite_E.Reg returns Inf.
If E_fun is a multiple of 1/B_fun, function droite_tau returns 1 (end point).
Line becomes a point
If E_ini_fun is a multiple of 1/B_fun,droite_e returns the value of 1/B_fun;
droite_E.Reg returns an error, because concentrations E can be any multiple of 1/B_fun without variation of relative concentrations;
droite_E.CR returns E_ini_fun;
droite_tau returns an error because \(\tau\) does not exist in this case.
Line does not exist
If there only one enzyme (length of E_ini_fun is equal to 1), relative concentrations is always equal to 1.
droite_e should return 1;
droite_E.Reg, droite_E.CR and droite_tau should return an error.
In the cases of co-regulations, relative enzymes concentrations evolve along a straight line. This line is determined by to factors: initial enzyme concentrations and global co-regulation factors. The driving variable \(\tau\) is a parameter indicating the position of the relative enzyme concentrations e on this line.
Function droite_e gives the relative concentrations corresponding to the input position tau_fun.
Function droite_E.Reg gives the absolute concentrations corresponding to the input position tau_fun in case of regulation only (constraints abbreviation "RegPos" or "RegNeg").
Function droite_E.CR gives the absolute concentrations corresponding to the input position tau_fun in case of competition and regulation (constraints abbreviation "CRPos" or "CRNeg").
Function droite_tau gives the position \(\tau\) corresponding to the input enzyme concentrations E_fun.
Note that if initial relative concentrations E_ini_fun is a multiple of 1/B_fun, the line becomes a point and position \(\tau\) does not exist.
To compute global co-regulation coefficients B_fun from co-regulation matrix beta_fun, see the example or use function compute.B.from.beta.
# NOT RUN {
beta <- matrix(c(1,10,5,0.1,1,0.5,0.2,2,1),nrow=3)
B <- apply(beta,1,sumbis)
E0 <- c(30,30,30)
tau <- 0.5
droite_e(tau,E0,B)
E <- droite_E.Reg(tau,E0,B)
droite_tau(E,E0,B)
E <- droite_E.CR(tau,E0,B)
droite_tau(E,E0,B)
# }
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