SimEvolEnzCons: SimEvolEnzCons: Simulation of Enzyme Evolution Under...

In SimEvolEnzCons: Simulation of Evolution of Enzyme Under Constraints

Description

Simulate the evolution of enzyme concentrations under constraints in a metabolic pathway, in accordance to the theoretical background developed in Coton et al. (2021).

The functions are divided in five sections. Succinct definitions are given below. There is also a section about the correct use of recurrent function parameters.

In version 2.0.0 and more, some functions have been added or modified to take account of regulation groups. Most important modifications are listed in section Regulation groups.

Informations about recurrent parameters

Integer numbers

n_fun (or n) is the number of enzymes in he pathway.

nsim is the number of simulations.

Allowed constraints

correl_fun is used to indicate the constraint applied on the system. Possible constraints and their corresponding abbreviation to pass in correl_fun are listed below:

• "SC": independence between all enzymes

• "Comp": competition for resources

• "RegPos": positive regulation

• "RegNeg": negative regulation

• "CRPos": competition plus positive regulation

• "CRNeg": competition plus negative regulation

name.correl helps to find the correct abbreviation, and is.correl.authorized verifies the abbreviation.

Co-regulation coefficients

For cases with co-regulations (i.e. correl_fun value is "RegPos", "RegNeg", "CRPos" or "CRNeg"), beta_fun or B_fun is obligatory. In other cases (i.e. correl_fun value is "SC" or "Comp"), beta_fun and B_fun are ignored, that is why default is NULL.

beta_fun is a square matrix of size n*n, indicating co-regulation coefficients. B_fun is vector of length n, indicating global co-regulation coefficients.

compute.beta.from.B and compute.B.from.beta help to compute beta_fun and B_fun from another.

Initial concentrations E_ini_fun is used in the same way as B_fun

Basic functions

Basic functions used for other functions.

• flux: computes flux depending on A, E and X

• activities: computes pseudo-activities depending on kinetic parameters and equilibrium constants

• alpha_ij: computes redistribution coefficients

• coef_rep: computes response coefficients

• coef_sel.continue: computes selection coefficient from expression s_i = R_i δ_i/E_i

• coef_sel.discrete: computes selection coefficient from expression s_i = (J^m - J^r)/J^r

• compute.delta: computes the actual effect δ of a mutation

• droite_e, droite_E.CR, droite_E.Reg and droite_tau: gives respectively relative concentrations e, concentrations E (competition + regulation), concentrations E (regulation only) and driving variable tau when there is regulation

• range_delta: bounds of δ_i for mutant concentrations E_j between 0 and Etot

• range_tau: bounds of driving variable tau for relative concentrations between 0 and 1

• name.correl: gives abbreviation of constraint names

Equilibrium

Functions used to find equilibrium of relative concentrations.

• predict_th: computes theoretical equilibrium

• predict_eff: computes effective equilibrium

• predict_eff_allE0: computes effective equilibrium for various initial concentrations

Graphics

Functions for drawing figures.

• flux.dome.graph3D: gives dome of flux in a 3D-plot

• flux.dome.projections: gives projection on plane of relative concentrations of the flux dome in a triangular plot

• graph.simul.by.time.by.enz and graph.simul.by.time.by.sim: illustrations of simulation results. Give different plots with time in x-axis, and color pattern depends on enzymes and simulation numbers respectively

• graph.simul.by.time.RNV: various plots of RNVs, computing from simulation results

• graph.simul.triangle.diagram.e: gives a triangular diagram of relative concentrations from simulation results

• RNV.graph.double.at.eq: RNV size and relative concentrations depending on activities at equilibrium

Simulation

Functions for simulations of enzyme evolution.

• simul.evol.enz.one: evolution of enzyme concentrations (one simulation)

• simul.evol.enz.multiple: evolution of enzyme concentrations (multiple simulations)

RNV

Functions for computing Range of Neutral Variation of enzyme concentrations.

• RNV.delta.all.enz: computes δ_i at limits of neutral zone for each enzyme

• RNV.for.simul: computes RNV in the simulations

• RNV.mean.simul: computes mean of RNV size in the simulations

• RNV.ranking.order.factor: gives the name and the value of of the factor that influences the ranking order of RNV

• RNV.size.at.equilibr: computes RNV at equilibrium, then plots RNV size against the ranking-order factor

• graph.simul.by.time.RNV: various plots of RNVs, computing from simulation results

Informations about Range of Neutral Variations (RNV)

The Range of Neutral Variations (RNV) are mutant concentration values such as coefficient selection is between 1/(2N) and -1/(2N).

Inferior (resp. superior) bound of RNV corresponds to selection coefficient equal to -1/(2N) (resp. 1/(2N)).

Depending on applied constraint correl_fun, it exists 1 or 2 RNV. In case of independence ("SC") or positive regulation between all enzymes ("RegPos"), flux has no limit and there is only one RNV. In other cases (competition and/or negative regulation), because flux can reach a maximum, there is two RNV: a "near" one, for small mutations, and a "far" one for big mutations that put mutants on the other side of flux dome.

The RNV size is the absolute value of δ_i^sup minus δ_i^inf. If there is no superior bounds but there is two RNVs, RNV size is obtained by the difference of the two δ_i^inf.

Regulation groups

In version 2.0.0 and more, some functions have been added or modified to take account of regulation groups. Most important new functions are listed below, with function section in parenthesis:

• class_group (basic): classifies enzymes in regulation groups from the co-regulation matrix

• group_types (basic): gives types of regulation groups, aka negative group, positive group or singleton, from co-regulation matrix

• predict_grp (equilibrium): computes equilibrium for the different relative concentrations when there are regulation groups

• apparent.activities.Aq (equilibrium): computes apparent activities at equilibrium for regulation groups

• graph.simul.group (graphics): gives graphics of the different kind of relative enzyme concentrations through time when there are regulation groups

• extract.tabEtot (simulation): extracts table of enzyme concentration from simulation results and computes sum of concentrations in a group. Useful to compute the different kind of relative concentrations.

Other graphics function have been modified to take account of equilibrium for regulation groups.

Two new datasets have been added, to have examples when there are regulation groups.

However, RNV.size.at.equilibr and RNV.ranking.order.factor have not been modified, as we cannot determine the relative RNV at equilibrium where there are regulation groups. Moreover, simulations simul.evol.enz.one do not compute equilibrium when there are regulation groups.

References

Coton, C., Talbot, G., Le Louarn, M., Dillmann, C., de Vienne, D., 2021. Evolution of enzyme levels in metabolic pathways: A theoretical approach. bioRxiv 2021.05.04.442631. https://doi.org/10.1101/2021.05.04.442631

Version 2: Coton, C., Dillmann, C., de Vienne, D., 2021. Evolution of enzyme levels in metabolic pathways: A theoretical approach. Part 2.

SimEvolEnzCons documentation built on Oct. 29, 2021, 1:07 a.m.