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. Author manuscript; available in PMC: 2017 Aug 14.
Published in final edited form as: Cell Rep. 2014 Jun 26;8(1):75–83. doi: 10.1016/j.celrep.2014.05.053

Figure 3. Mathematical Modeling of Transcriptional Response of c-Fos after Serum Induction.

Figure 3

(A) Cartoons illustrating concept of burst saturation limit. For short bursts below the saturation limit (upper plot), mRNA attached to all the loaded polymerases can be observed. For burst in the saturation limit (lower plot), only the mRNA produced by the currently loaded polymerases can be detected.

(B) Impact of burst duration on nascent mRNA distribution. Curves share same initiation rate (five mRNA/minute) and burst frequency (0.1 burst/minute) but differ in burst duration as indicated in figure legend. Values in parenthesis indicate average number of mRNAs produced per burst, i.e., the burst amplitude.

(C) Histogram of pooled nascent mRNA numbers from all induction condition (serum and zinc) except identified outliers in Figure S3C. Fit with Poisson distribution (pink solid line; log-likelihood of fit = −536) and truncated geometric distribution (dashed blue line; log-likelihood of fit = −705).

(D) Two-state model of transcription. Gene can switch between inactive (OFF) and active (ON) state. Transitions are described by rate constants kon and koff. Transcripts are produced during ON states as a Poisson process with fixed rate, kinit (vertical green bars in lower plot). Each mRNA undergoes a production period modeled as an irreversible process with fixed completion time, tprod and mature mRNA degrades as a first-order reaction with the constant γD.

(E–G) Fit with two-state model (Parameters from fit L2-8 in Table S1). (E) Fit of nascent mRNA data (green histogram) with two-state model (red line). Insets show cumulative histograms. (F) Probability for one TS to be active (black squares) together with prediction of two-state (red) and three-state model (blue). (G) Fit of mature mRNA data (green histogram) with two-state model (red line).

(H) Three-state model of transcription. A second ON state with a higher initiation frequency can be reached from the first ON state.

(I) Fits of nascent mRNA data (green histogram) with three-state model (red lines). Each line represents an individual fit with parameters defined in Table S2. Insets show cumulative histograms.

See also Figure S3.