RNV.size.at.equilibr: Plot and linear model of RNV size at equilibrium
In SimEvolEnzCons: Simulation of Evolution of Enzyme Under Constraints

Description Usage Arguments Details Value See Also Examples

Gives a plot and computes a linear model of the RNV size at equilibrium against the activities and the RNV-ranking-order factor

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RNV.size.at.equilibr(n_fun,correl_fun,N_fun,A_fun=NA,B_fun=NA,E0_fun=NA,
Etot_0=sum(E0_fun),Etot_eq=100,A_lim=c(0.001,10000),inv_B_lim=c(0,100),E0_lim=c(1,100),
RNV.by.E=FALSE,show.plot=TRUE,enz.lab=FALSE,...)

`n_fun`	Integer number indicating the number of enzymes.
`correl_fun`	Character string indicating the abbreviation of the constraint applied on the system
`N_fun`	Numeric. Population size
`A_fun, B_fun, E0_fun`	Numeric vectors (length `n_fun`) of activities, global co-regulation coefficients and initial concentrations respectively. If `NA` (default), values are randomly chosen.
`Etot_0`	Numeric value of initial total concentration. `E0_fun` is rescaled to have `sum(E0_fun)=Etot_0`.
`Etot_eq`	Numeric value of total concentration at equilibrium for cases `"SC"` and `"RegPos"`. Default is `100`.
`A_lim`	Numeric vector of the two limits between which activities are chosen if `A_fun=NA`.
`inv_B_lim`	Numeric vector of the two limits between which inverse of global co-regulations `B` are chosen if `B_fun=NA`.
`E0_lim`	Numeric vector of the two limits between which initial concentrations `E0` are chosen if `E0_fun=NA`.
`RNV.by.E`	Logical. Show RNV divided by Ei rather than RNV size?
`show.plot`	Logical. Show plot of RNV in relation to RNV-ranking-order factor?
`enz.lab`	Logical. Add enzyme name above points in graphics?
`...`	Arguments to be passed to `plot` function, such `cex` or `cex.lab`

Function RNV.size.at.equilibr gives a plot of RNV size in relation to activities, and then a plot of RNV size in relation to RNV-ranking-order-factor.

RNV size is computed at equilibrium with function RNV.for.simul. Only "near" RNV (small mutations) is used.

WARNING! This function is not adapted or regulation groups (1<sum(1/B)<n).

Factors governing ranking order of RNV

RNV-ranking-order factor depends on constraint. See function RNV.ranking.order.factor.

Random variables

Input parameters A_fun, B_fun, E0_fun are chosen randomly if not specified (default NA).

Activities A_fun are taken in a uniform law between limits given by A_lim.

Initial concentrations E0_fun are taken in a uniform law between limits given by E0_lim, then leveled to have sum of E0_fun equal to Etot_fun.

Global co-regulation coefficients B_fun are chosen differently. The inverse of B are taken between limits given by inv_B_lim. If correl_fun is equal to "RegNeg" or "CRNeg" (negative co-regulations), sign are randomly chosen. Then these inverse values are leveled to have sum of 1/B equal to 1. Thus B are computed by the reverse operation, and therefore the matrix of beta by function compute.beta.from.B.

Equilibrium

RNV is computed at equilibrium, theoretical one for cases "SC", "Comp" and "RegPos", and effective one for cases "RegNeg", "CRPos" and "CRNeg".

Graphics

If RNV.by.E=TRUE, RNV size divided by its corresponding enzyme concentration is plotted, rather than RNV size.

Invisible list of 12 elements:

$RNV_size: matrix of one or two rows and n columns indicating the RNV size of every enzymes (in columns) and current RNV (near or far, in rows). See output $RNV_size of function RNV.for.simul;
$lm_RNV: linear model of RNV size in relation to the ranking-order variable;
$E_eq: numeric vector (length n) of concentrations at equilibrium;
$e_eq: numeric vector (length n) of relative concentrations at equilibrium;
$A: numeric vector (length n) of activities;
$B: numeric vector (length n) of global co-regulation coefficients;
$beta: numeric matrix of n rows and n columns indicating the co-regulation coefficients;
$E0: numeric vector (length n) of initial concentrations;
$rank_var: list of 2 elements:
- $value: numeric vector (length n) of the RNV-ranking-order factor values for each enzyme (see details);
- $name: character string indicating the name of the RNV-ranking-order factor.
$N, $n, $correl: numeric value of population size, number enzymes and applied constraints respectively (respectively input value of N_fun, n_fun and correl_fun)

RNV is computed with the function RNV.for.simul.

See function RNV.ranking.order.factor to have further details on RNV-ranking-order.

RNV.size.at.equilibr(20,"Comp",1000)
RNV.size.at.equilibr(100,"CRNeg",1000)
RNV.size.at.equilibr(3,"SC",1000,c(1,10,30),NA,c(30,30,30),100,200)
 #in this case, sum(E0)=100 and sum(E*)=200