Each gene locus and its corresponding classification (essential, domain essential, or nonessential) are provided.
and each eigenvalue corresponding an essential unique eigenfunction which has exactly simple zeros in and is positive near 0. Fortunately, Elias [6] developed a theory on the eigenvalue problem (1.6).
and each eigenvalue corresponding an essential unique eigenfunction ψ k which has exactly k - 1 simple zeros in (0,1) and is positive near 0. Fortunately, Elias [7] developed a theory on the eigenvalue problem ℒ y + λ h ( t ) y = 0, ( ℒ i y ) ( a ) = 0, i ∈ { i 1, …, i k }, ( ℒ j y ) ( b ) = 0, j ∈ { j 1, …, j n - k }, (1.10).
(iii) To each eigenvalue there corresponding an essential unique eigenfunction which has exactly simple zeros in and is positive near 0. (iv) Given an arbitrary subinterval of, then an eigenfunction which belongs to a sufficiently large eigenvalue change its sign in that subinterval.
Scores corresponding to essential effects are in bold.
As commented above, the data consists of knock-out and hypomorph experiments, with the latter corresponding to essential genes [ 16].
To backtrack the necessary constraints (NC, corresponding to essential parameter changes), to original parameter characterizations, we counted the total number (out of n pert) of perturbations of which have a mapped effect such that the necessary constraints (equations (24,25)) are violated.
To determine whether it is necessary to control for gene essentiality, we assess whether there is a significant difference in helix/strand density, contact density, or the evolvability index in proteins corresponding to essential versus nonessential genes (supplementary fig. S8, Supplementary Material online).
In this model, knock out of biomass production (and thus growth and survival) corresponds to "cutting" flux through at least one of the sinks corresponding to an essential biomass component.
