Fig 1.
Simulation of enhancer models and calculation of transcriptional noise and fidelity.
(A) A computational representation of the Drosophila embryo showing the region of Kruppel expression [20]. (B) Cartoon depicting a reaction network model of Kruppel shadow enhancers [20]. (C) Sample stochastic traces of mRNA from simulations of the model in (B) and their average over time E[R] which estimates the mean mRNA concentration. The values of E[R] and the standard deviation σR can also be approximated by moment closure techniques and be used to estimate the transcriptional noise and fidelity of the modeled enhancer system.
Table 1.
Parameter values that were fitted to Kruppel expression data.
Fig 2.
Under additive assumptions, transcriptional fidelity and noise are independent on enhancer number but depend on TF binding site number.
(A) Different enhancer models used in the simulations. Each model has different total binding sites for T1, total binding sites for T2, distribution of binding sites, and number of enhancers. (B) Simulations for the models in (A) show that fidelity and noise are independent of the number of enhancers and the distribution of binding sites. The noise broadly decreases as a function of total TF binding sites, while fidelity with respect to T1 increases with the number of T1 binding sites. The table on the right shows the fidelity and noise values for two different configurations of TF binding sites among two enhancers. (C) Noise calculated as functions of the total binding sites for T1 or T2. As the total number of binding sites increases, the noise generally decreases.
Fig 3.
In subadditive enhancers, noise increases with enhancer number but fidelity is broadly unchanged.
(A) Subadditivity is implemented in our model by linearly decreasing kon rates and linearly increasing koff rates. In this case d1, the rate of decrease for kon, was chosen to be 0.04 for T1 and 0.02 for T2. Meanwhile d2, the rate of increase for koff, was chosen to be 0.75 for both T1 and T2. (B) Systems with more subadditive enhancers tend to exhibit higher noise, while the fidelity is broadly independent of enhancer number. Noise and fidelity are also independent of binding site distribution but vary with respect to the number of binding sites. (C) Plots showing the relationship between binding site numbers and transcriptional noise for two subadditive enhancers.
Fig 4.
In superadditive networks, more enhancers decrease noise and fidelity.
(A) Superadditivity is implemented in our model by linearly increasing kon rates and linearly decreasing koff rates. In this case d2, the rate of decrease for koff, was chosen to be 0.4 for T1 and 0.3 for T2. Meanwhile d1, the rate of increase for kon, was chosen to be 0.01 for both T1 and T2 (B) Unlike in the subadditive case, enhancer numbers decrease transcriptional fidelity and also decrease noise. The distribution of binding sites does not affect either the noise or the fidelity all else being constant. (C) Plots showing the relationship between binding site numbers and transcriptional noise for two superadditive enhancers. Increasing binding site numbers leads to less noise in gene expression.
Fig 5.
Saturating and synergistic enhancer interactions lead to different trends in noise and fidelity.
A saturated system yields mRNA at the same rate for any positive number of enhancers bound. On the other hand, a synergistic system becomes active only when all enhancers are bound to the promoter. The resulting plots of fidelity and noise corresponding to these systems show inverse relationships between noise and fidelity. In the saturating regime, low noise and high fidelity are achieved with higher enhancer numbers, while in the synergistic regime, low noise and high fidelity occur with lower enhancer numbers.
Fig 6.
Duplication of subadditive enhancers can increase transcriptional fidelity and reduce noise.
(A) Single enhancer models and those that result from repeated enhancer duplications. (B) Plots showing the relationship between total binding sites and enhancers for the case of enhancer splitting and enhancer duplication. Splitting does not affect total binding site numbers while it increases enhancer numbers. On the other hand, duplication increases both enhancer numbers and total binding sites at different rates. (C) Plots depicting transcriptional fidelity and noise for subadditive versions of the models in (A). Enhancer duplications increase transcriptional fidelity while the noise generally decreases.