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Table 2 The list of symbols employed in the ordinary differential equations associated to the designs from Figure 2.

From: Avoiding transcription factor competition at promoter level increases the chances of obtaining oscillation

Symbol

Definition & Comments

A

concentration of the activator (nM)

R

concentration of the repressor (nM)

t

model time (hours)

DNA-binding constant of the activator A

DNA-binding constant of the repressor R

dimerization constant of the activator A to A2

dimerization constant of the repressor R to R2

multimerization constant of the activator A to A n

dimerization constant of the repressor R to R m

δ A

degradation rate of the activator A

δ R

degradation rate of the repressor R

Δ

δ A /δR,non-dimensional parameter of the model

x

, the nondimensional variable associated to the activator, when the activator is

a dimer

y

, the nondimensional variable associated to the repressor, when the repressor is a dimer

τ

tδ R , the nondimensional time variable of the model

α

the transcriptional synergy conferred by the activator bound to DNA

β

, the nondimensional parameter of the transcriptional response from the activator promoter, with γ A , the translation rate of the activator A; β A , the transcription rate of the mRNA of the activator; α A , activator mRNA degradation; , total activator promoter number. The root order n denotes the multimerization degree of the TF binding to DNA (i.e. n = 2, dimer; n = 4, tetramer). The subscript from , the equilibrium constant for multimer formation, also denotes its dependence on the multimerization of the binding factor.

γ

, the nondimensional parameter of the transcriptional response from the repressor promoter, similar to β. See also [18]. Notice also the multimerization degree appears here as m with similar consequences as for the β parameter.

σ

, the binding ratio of the repressor compared to the activator.