droites: Line of relative enzyme concentrations (co-regulations cases)
In SimEvolEnzCons: Simulation of Evolution of Enzyme Under Constraints

Description Usage Arguments Details Value Special results See Also Examples

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)

`tau_fun`	Numeric value of the position of relative enzyme concentrations on the line
`E_ini_fun`	Numeric vector of initial concentrations
`B_fun`	Numeric vector of global co-regulation coefficients. Same length as `E_ini_fun`.
`E_fun`	numeric vector of current concentrations on the line. Same length as `E_ini_fun`.

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 τ 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 τ 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 τ does not exist.

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 τ 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.

To compute global co-regulation coefficients B_fun from co-regulation matrix beta_fun, see the example or use function compute.B.from.beta.

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)