Supplemental Methods

Mathematical Modeling and Numerical Simulations

We based our numerical simulations on the framework of two coupled modules. As described previously, the first module consists of two coupled differential delay equations (Goodwin 1965; Lewis 2003; Monk 2003).

(1)

(2)

The description and values of the parameters used are presented here in Supplemental Table 1. The chosen values were either measured (protein and mRNA stability) or estimated to be within physiological ranges (Lewis 2003; Monk 2003).

For simulations that incorporated stochastic elements, this model was adapted for discrete numerical simulations with time steps of 0.001 min and space steps equivalent to 10 bp (relevant for producing elongation bursts). The simulation time was 1,800 min.

We implemented an explicit Euler integration scheme to simulate the model numerically, where the character of k was obtained from a second numerical module. This module contributed the explicit simulation of either RNA polymerase II initiating events or transcription elongation across the gene. In particular, we considered:

description / values / unit
a / rate constant of protein production / 4.5 / 1/min
Tp / protein time delay / 30 / min
b / protein degradation rate constant of / 0.017 / 1/min
k / maximal transcription initiation rate / 60 / molecules/min
Tm / mRNA time delay / 30, 37, 47 / min
po / Hill constant / 1000 / molecules
n / Hill coefficient / 2
c / mRNA degradation rate constant / 0.017 / 1/min

Supplemental Table 1: Values used in simulations.

(1)For simulations with random transcription initiation events, we set the time intervals between two initiation events to stochastically follow a Gaussian distribution with different standard deviations. The precision of the periods was robust, even when the standard deviation of the Gaussian distribution exceeded the mean.

(2)Promoter burst simulations: k was substituted by a description of RNA bursting consistent with previous observations in E. coli: an exponential distribution of “on times” with a mean of 6 min, an exponential distribution of “off times” with a mean of 37 min, and an exponential distribution of burst sizes with a mean of 2.2 (Golding et al. 2005).

(3)Elongation burst simulations: k was substituted by burst distributions that we generated by a numerical simulation of RNA polymerase II traffic. To produce traffic bursting, objects were simulated to move along vector spaces equivalent to either 3, 10, or 19 kb (units were accounted for in vector space to maintain equivalent elongation rates and gene lengths). The simulated polymerase objects initiated at a rate equivalent to 60 events per min. Once elongating, the polymerase objects transcribed at constant velocities sampled from a Gaussian distribution with a mean velocity of 1 kb/min and a standard deviation of 0.225 kb/min (adapted from experiments with bacterial RNA polymerase) (Adelman et al. 2002; Tolic-Norrelykke et al. 2004). In our simulations, when a faster polymerase object catches up to a slower polymerase object they both acquire the velocity of the slow leader. While it is not clear what the collective behavior is for polymerases on the same gene, our traffic rule is based on prior ideas concerning transcription kinetics (MacDonald et al. 1968; Golding et al. 2005). This simulation resulted in burst distributions that served as the transcription initiation events in the model (i.e. replacing k).

Image and Data Analysis

All time-lapse microscopy images were analyzed with custom-written MATLAB (The Mathworks, Natick, MA) scripts in combination with the commercially available MATLAB Image Processing Toolbox, similar to previous approaches (Rosenfeld et al. 2005; Neumann et al. 2006; Sigal et al. 2006). Broadly, the method consists of segmentation of individual nuclei by taking advantage of the bright Histone-mCherry nuclear marker, tracking of these nuclei over time, and quantification of the respective nuclear TetR-Venus YFP signals.

The images were loaded into MATLAB in the MetaMorph Stack (STK) file format with tiffread2.m, a freely available MATLAB function developed by the Laboratory of Francois Nedelec at EMBL ( Automated segmentation was performed exclusively on the RFP images to detect individual nuclei using standard techniques including global gray-level thresholding by Otsu's method and watershed segmentation (Eddins; Gonzalez 2004). The binary version of the RFP images was used to determine the size, boundary and position of the nuclei. Objects with an area smaller than 100 pixels and image-border-touching nuclei were discarded. The resulting nuclear regions were transferred to the respective YFP and phase images for quantification and visualization purposes, respectively.

Nuclei centroids were tracked from image i to image i-1 by connecting each nucleus to the nucleus in the previous frame that exhibited the smallest deviation in centroid position. Cell division resulted in two nuclei merging into the same object when viewed in this reverse order. These events were detectable by an abrupt decrease in the nuclear area and the total RFP fluorescence intensity. The performance of the automated image segmentation and nuclei tracking procedures were manually checked for all single-cell trajectories (N = 152). Tracking and segmentation errors were either corrected, or the corresponding data points were excluded from further analysis.

The average background YFP fluorescence intensity was estimated for each YFP frame and used for background subtraction. All fluorescence intensity measurements were performed on the background-corrected YFP images. Correction for photo-bleaching was unnecessary because of the rapid turnover of our YFP reporter. The average fluorescence intensity (i.e. the average pixel intensity) within each nucleus was computed as the total nuclear fluorescence intensity divided by the area of the nucleus and plotted as a function of time to visualize the dynamics of our reporter gene.

Cloning and construct assembly

The mouse -actin promoter, spanning minus 1000 base pairs to the second exon, was cloned by PCR using mouse genomic DNA as a template with the following primers

sis16: gcgGGTACCCTGTGGCTGCACATAATAAATAGAGGATAG

sis17: gcgatcGATATCGTCATCCATGGCGAACTATCA

Tet-operators were cloned using an annealed oligo (each containing a pair of operators). The operators were cloned sequentially into blunted unique sites in the -actin promoter: BsrG I, Afl II, and Bsu36 I. The oligo was supplied in excess and clones with multiple inserts were selected. The BsrG I site received a total of two operators, the Afl II site received four operator sequences, and the Bsu36 I site received 6 operators.

sis34: tccctatcagtgatagagattgacatccctatcagtgataga

The modular intron sequence was cloned from the first intron of the human PIP4k1a gene into an Age I site in the first intron of the -actin gene (see above). This destination site was chosen because it is away from obvious critical locations in the intron, it is unique in the cloning scheme, and the sequence conservation is relatively low at this locus. The intron of PIP4k1a was chosen because our previous genomic work on RNA polymerase pausing and RNA processing factor genome associations suggest that there is no detectable pausing or obvious RNA processing in the cloned portion of this intron. Additionally, the gene is highly expressed in HeLa cells, there is relatively low sequence conservation in portion of this intron we cloned. The genome position that spans the largest intron cloned is chr1:149,438,287-149,455,112 (March, 2006 assembly of the human genome). Parts of the intron were cloned directly from a BAC containing the intron. Additionally, fragments were cloned with the following pairs of PCR primers:

sis23:acatcaATGCATACC GGTAAGTGGGCGCGAG

sis24.2:TTGGGAAGCTGAAGCAGGAG

sis23.2: CCAACTTCCTAATTCCTCTGGTACC

sis24:gcgTTAATTAACCGGTGTCATGGCAGAAATAAATCGATCAGAAGC

sis25:gcgGCTTCTGATCGATTTATTTCTGCCATGAC

sis26:gcgTTAATTAACCGGTGGATCCGAGGTGGGCAGATCACGAGGTTAG

sis27:gcgGGATCCTAACCTCGTGATCTGCCCACCTC

sis28.2: GTG GCT CAC GCG TAT AAT CCC AG

sis 27.2: TTT ACC ATG TTG GCC AGG ATG GTC TTG

sis28:gcgTTAATTAACCGGTCATCAGATCTACCTCTCTTACCACTGACC

Venus YFP was sublconed with the following PCR primers:

sis9b:gcg ATCGAT CTCGAG ATG GTG AGC AAG GGC GAG GA

sis10b:gcg GGATCCCTT GTA CAG CTC GTC CAT GCC G

A mutant version of mouse ornithine decarboxylase PEST sequence was cloned by annealing oligos:

GGAtccAGCCATGGCTTCCCTCCTGCCGTGGCCGCCCAGGATGATGGCACCCTGCCCATGTCTTGTGCCCAGGAGAGCGGGATGGACAGGCACCCTGCAGCCTGTGCTTCTGCTAGGATCAATGTGGGATCC

The tetracycline repressor was cloned from a humanized repressor generated and kindly provided by A. Francis Stewart and Konstantinos Anastassiadis (Anastassiadis et al. 2002). The following primers were used to sublcone the repressor into the construct as outlined in Figure 1A.

sis32: gcg CTCGAGATG TCC AGA CTG GAC AAG AGC A

sis70: gcg cctcaggctgct GAGGTT gccgtcgcc CAC GTG AGA GCC AGA CTC AC

A SV40 NLS was cloned with annealed oligos:

AGCAGCCTGAGGCCTCCCAAGAAGAAGAGAAAGGTGTGA

A standard globin 3’-UTR was subcloned with the following primers

sis3: gcgGAATTCTTAATTAAGATCTTTTTCCCTCTGCC AAA AAT TAT GGG G

sis4: gcgACTAGTCTG CTT TAA TAA GAT CTT CAT AAG AGA AGA GGG

Previously described, optimized AU-rich elements were cloned into the 3’ UTR with annealed oligos:

TTTATTTATTTATTTATTTAATTTATTTATTTATTTATTTA

The final arrangement of the gene is below. To find a portion of the gene using the above primers, search with the 3’-ends of the oligos because the 5’-ends often contain restriction sites lost in the cloning process. The gene’s sequence from promoter to 3’-UTR and ARE (minus the 16kb of intron) is:

AGATCCGGGGCAGGGGATATCTGGAGGCATCTTCTTGCAACACCTCCAGTTATTGGACCACTGGGGCTCGCCCTATGCTTGGGATAGGATGGtCTTGAGTCTCTAAGAGGTCAAGATCCATGAAAACCTCTCCAACCAGAGTTCTGCTTCCAAGTTGAACCCCAACACACCTAGCAAATTAGAACCACAGCAGAAGGGGCCCCCCCGGATCTGGCTTTCCGGCTATTGCTAGCAATTGCTAGCAAGGGGGAGTGACTCTCTGTCCATTCAATCCAGGCCCCGCGTGTCCCTCAAACAAGAGGCCACACAAATAGGGTCCGGGCCTCGATGCTGACCCTCATCCACTTAATCCCTATCAGTGATAGAGATTGACATCCCTATCAGTGATAGATCCCTATCAGTGATAGAGATTGACATCCCTATCAGTGATAGAttaaGTGCTCGATATCCACGTGACATCCACACCCAGAGGGTCCTGGGGTGGTTGGGTGACCCCCAGAATGCAGGCCTAGTAACCGAGACATTGAATGGGGCAGTGTCCACAAGGGCGGAGGCTATTCCTGTACTCCCTATCAGTGATAGAGATTGACATCCCTATCAGTGATAGAtacATCTGGGCCTACGGAGCCAGCACCCATCGCCAAAACTCTTCATCCTCTTCCTCAATCTCGCTTTCTCTCTCGCTTTTTTTTTTTTTCTTCTTCTTTTTTTTTTTTTTTTttTCAAAAGGAGGGGAGAGGGGGTAAAAAAATGCTGCACTGTGCGGCGAGGCCGGTGAGTGAGCGACGCGGAGCCAATCAGCGCCCGCCGTTCCGAAAGTTGCCTTTTATGGCTCGAGTGGCCGCTgTGGCGTCCTATAAAACCCGGCGGCGCAACGCGCAGCCACTGTCGAGTCGCGTCCACCCGCGAGCACAGCTTCTTTGCAGCTCCTTCGTTGCCGGTCCACACCCGCCACCAGGTAAGCAGGGACGCCGGGCCCAGCGGGCCTTCGCTCTCTCGTGGCTAGTACCTCACTGCAGGGTCCTgaTCCCTATCAGTGATAGAGATTGACATCCCTATCAGTGATAGATCCCTATCAGTGATAGAGATTGACATCCCTATCAGTGATAGATCCCTATCAGTGATAGAGATTGACATCCCTATCAGTGATAGAtGAGGATCACTCAGAACGGACACCATGGGCGGGTGGAGGGTGGTGCCGGGCCGCGGAGCGGACACTGGCACAGCCAACTTTACGCCTAGCGTGTAGACTCTTTGCAGCCACATTCCCGCGGTGTAGACACTCGTGGGCCCGCTCCCGCTCGGTGCGTGGGGCTTGGGGACACACTAGGGTCGCGGTGTGGGCATTTGATGAGCCGGTGCGGCTTGCGGGTGTTAAAAGCCGTATTAGGTCCATCTTGAGAGTACACAGTATTGGGAACCAGACGCTACGATCACGCCTCAATGGCCTCTGGGTCTTTGTCCAAACCGGTTTGCCTATTCGGCTTGCCGGGCGGGCGGGCGGGCGGGCGGGCGCGGCAGGGCCGGCTCGGCCGGGTGGGGGCTGGGATGCCACTGCGCGTGCGCTCTCTATCACTGGGCATCGAGGCGCGTGTGCGCTAGGGAGGGAGCTCTTCCTCTCCCCCTCTTCCTAGTTAGCTGCGCGTGCGTATTGAGGCTGGGAGCGCGGCTGCCCGGGGTTGGGCGAGGGCGGGGCCGTTGTCCGGAAGGGGCGGGGTCACAGTGGCACGGGCGCCTTGTTTGCGCTTCCTGCTGGGTGTGGTCGCCTCCCGCGCGCGCACAAGCCGCCCGTCGGCGCAGTGTAGGCGGAGCTTGCGCCCGTTTGGGGAGGGGGCGGAGGTCTGGCTTCCTGCCCTAGGTCCGCCTCCGGGCCAGCGTTTGCCTTTTATGGTAATAATGCGGCCGGTCTGCGCTTCCTTTGTCCCCTGAGCTTGGGCGCGCGCCCCCTGGCGGCTCGAGCCCGCGGCTTGCCGGAAGTGGGCAGGGCGGCAGCGGCTGCTCTTGGCGGCCCCGAGGTGACTATAGCCTTCTTTTGTGTCTTGATAGTTCGCCATGGATGACGATATCGCTGCGCTGGTCATGCATctcgaggaattcATGGTGAGCAAGGGCGAGGAGCTGTTCACCGGGGTGGTGCCCATCCTGGTCGAGCTGGACGGCGACGTAAACGGCCACAAGTTCAGCGTGTCCGGCGAGGGCGAGGGCGATGCCACCTACGGCAAGCTGACCCTGAAGCTGATCTGCACCACCGGCAAGCTGCCCGTGCCCTGGCCCACCCTCGTGACCACCCTGGGCTACGGCCTGCAGTGCTTCGCCCGCTACCCCGACCACATGAAGCAGCACGACTTCTTCAAGTCCGCCATGCCCGAAGGCTACGTCCAGGAGCGCACCATCTTCTTCAAGGACGACGGCAACTACAAGACCCGCGCCGAGGTGAAGTTCGAGGGCGACACCCTGGTGAACCGCATCGAGCTGAAGGGCATCGACTTCAAGGAGGACGGCAACATCCTGGGGCACAAGCTGGAGTACAACTACAACAGCCACAACGTCTATATCACCGCCGACAAGCAGAAGAACGGCATCAAGGCCAACTTCAAGATCCGCCACAACATCGAGGACGGCGGCGTGCAGCTCGCCGACCACTACCAGCAGAACACCCCCATCGGCGACGGCCCCGTGCTGCTGCCCGACAACCACTACCTGAGCTACCAGTCCGCCCTGAGCAAAGACCCCAACGAGAAGCGCGATCACATGGTCCTGCTGGAGTTCGTGACCGCCGCCGGGATCACTCTCGGCATGGACGAGCTGTACaagGGAtccAGCCATGGCTTCCCTCCTGCCGTGGCCGCCCAGGATGATGGCACCCTGCCCATGTCTTGTGCCCAGGAGAGCGGGATGGACAGGCACCCTGCAGCCTGTGCTTCTGCTAGGATCAATGTGGGATCCcttaagAGCAGCCTGAGGCCTCCCAAGAAGAAGAGAAAGGTGTGATTAATTAAGATCTTTTTCCCTCTGCCAAAAATTATGGGGACATCATGAAGCCCCTTGAGCATCTGACTTCTGGCTAATAAAGGAAATTTATTTTCATTGCAATAGTGTGTTGGAATTTTTTGTGTCTCTCACTCGGAAGGACATATGGGAGGGCAAATCATTTAAAACATCAGAATGAGTATTTGGTTTAGAGTTTGGCAACATATGCCcATATGCTGGCTGCCATGAACAAAGGTGGCTATAAAGAGGTCATCAGTATATGAAACAGCCCCCTGCTGTCCATTCCTTATTCCATAGAAAAGCCTTGACTTGAGGTTAGATTTTTTTTATATTTTGTTTTGTGTTATTTTTTTCTTTAACATCCCTAAAATTTTCCTTACATGTTTTACTAGCCAGATTTTTCCTCCTCTCCTGACTACTCCCAGTCATAGCTGTCCCTCTTCTCTTATGAAGATCTTATTAAAGCAGACTAGATTTATTTATTTATTTATTTAATTTATTTATTTATTTATTTA

Supplemental References

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