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Transcriptional burst frequency and burst size are equally modulated across the human genome

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Gene expression occurs either as an episodic process, characterized by pulsatile bursts, or as a constitutive process, characterized by a Poisson-like accumulation of gene products. It is not clear which mode of gene expression (constitutive versus bursty) predominates across a genome or how transcriptional dynamics are influenced by genomic position and promoter sequence. Here, we use time-lapse fluorescence microscopy to analyze 8,000 individual human genomic loci and find that at virtually all loci, episodic bursting-as opposed to constitutive expression-is the predominant mode of expression. Quantitative analysis of the expression dynamics at these 8,000 loci indicates that both the frequency and size of the transcriptional bursts varies equally across the human genome, independent of promoter sequence. Strikingly, weaker expression loci modulate burst frequency to increase activity, whereas stronger expression loci modulate burst size to increase activity. Transcriptional activators such as trichostatin A (TSA) and tumor necrosis factor α (TNF) only modulate burst size and frequency along a constrained trend line governed by the promoter. In summary, transcriptional bursting dominates across the human genome, both burst frequency and burst size vary by chromosomal location, and transcriptional activators alter burst frequency and burst size, depending on the expression level of the locus.
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Transcriptional burst frequency and burst size are
equally modulated across the human genome
Roy D. Dara,b,c,1, Brandon S. Razookya,d,e,1, Abhyudai Singhd,2, Thomas V. Trimelonif, James M. McCollumf,
Chris D. Coxg,h, Michael L. Simpsonb,I,3, and Leor S. Weinbergera,d,j,3
aGladstone Institutes, San Francisco, CA 94158; bCenter for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831;
cDepartment of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996; dDepartment of Chemistry and Biochemistry, University of California
at San Diego, La Jolla, CA 92093; eBiophysics Graduate Group, University of California, San Francisco, CA 94158; gCenter for Environmental Biotechnology,
University of Tennessee, Knoxville, TN 37996;hDepartment of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN 37996;
IDepartment of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996; jDepartment of Biochemistry and Biophysics, University
of California, San Francisco, CA 94158; and fDepartment of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, VA
232843072
Edited by Jonathan S. Weissman, University of California, San Francisco, CA, and approved September 13, 2012 (received for review August 8, 2012)
Gene expression occurs either as an episodic process, characterized
by pulsatile bursts, or as a constitutive process, characterized by
a Poisson-like accumulation of gene products. It is not clear which
mode of gene expression (constitutive versus bursty) predomi-
nates across a genome or how transcriptional dynamics are influ-
enced by genomic position and promoter sequence. Here, we use
time-lapse fluorescence microscopy to analyze 8,000 individual
human genomic loci and find that at virtually all loci, episodic
burstingas opposed to constitutive expressionis the predomi-
nant mode of expression. Quantitative analysis of the expression
dynamics at these 8,000 loci indicates that both the frequency
and size of the transcriptional bursts varies equally across the
human genome, independent of promoter sequence. Strikingly,
weaker expression loci modulate burst frequency to increase
activity, whereas stronger expression loci modulate burst size to
increase activity. Transcriptional activators such as trichostatin A
(TSA) and tumor necrosis factor α(TNF) only modulate burst size
and frequency along a constrained trend line governed by the
promoter. In summary, transcriptional bursting dominates across
the human genome, both burst frequency and burst size vary by
chromosomal location, and transcriptional activators alter burst
frequency and burst size, depending on the expression level of
the locus.
stochastic noise automated single-cell imaging human
immunodeficiency virus long terminal repeat promoter
There exists conflicting evidence over the predominant mode
of gene expression in both prokaryotes and eukaryotes. The
classical view of gene expression as a constitutive, Poisson-like
accumulation of gene products (Fig. 1A) is supported by a com-
prehensive large-scale study in bacteria, demonstrating that >400
genes appear to follow constitutive (or Poisson-like) gene expres-
sion (1). Constitutive expression has also been reported for
subsets of human genes (2). Conversely, several elegant studies
showed that specific promoters in bacteria and yeast express
gene products in an episodic process (Fig. 1B), characterized by
pulsatile bursts in transcription (39). Given this conflicting evi-
dence, it remains unclear if episodic bursting is the predominant
mode of gene expression across a genome or just a highlighted
exception. If bursting is predominant, it is not clear if or how it
depends on genomic location.
To globally determine if constitutive Poisson-like expression
or episodic bursty expression dominates throughout the human
genome, we capitalize on a recently proposed theoretical frame-
work (10) for extracting the details of gene regulation from the
time-resolved structure of fluctuations (i.e., noise) in gene expres-
sion. This analysis quantifies time-lapse expression trajectories to
obtain three orthogonal measures of expression: the average
expression level, the magnitude of expression fluctuations (as
measured by the coefficient of variation squared, CV2), and the
autocorrelation time of expression fluctuations (as measured
by the noise autocorrelation time at half of its initial value, τ12)
(11, 12) (Fig. 1C). Although this three-dimensional noise space is
impractical to analyze directly, different two-dimensional projec-
tions of noise space allow the quantification of rate parameters
in gene-regulatory models and provide a convenient method to
differentiate between underlying gene-expression mechanisms,
such as constitutive versus bursty transcription (Fig. 1C). For
example, transcriptional bursting increases both noise magnitude
and noise autocorrelation time and shifts points in the CV2
versus τ12plane to the upper right quadrant relative to a con-
stitutive expression model (Fig. 1C,Bottom Left). Conversely,
translational bursting shifts noise magnitude, but not the auto-
correlation time (10, 13).
Importantly, analysis of the τ12axis is critical to fully parame-
terize two-state transcriptional bursting models (Fig. 1C), which
always include at least three unknown parameters: the rate of
transition to a transcriptionally active state (kon), the rate of tran-
sitioning to a transcriptionally inactive state (koff ), and the rate
of transcription once in the active state (km) (13, 14). Analyses
of a single two-dimensional plane (e.g., CV2versus expression
level) cannot fully determine these three rate parameters. Con-
versely, analyses of CV2versus expression level and τ12versus
expression level allow the determination of these three para-
meters, and analysis of CV2-versus-τ12facilitates direct compar-
isons of data containing widely varying expression levels, because
it removes the reciprocal dependence of noise magnitude on
expression level (10).
The ability to accurately quantify these transcriptional rate
parameters is essential for answering basic questions about the
mechanisms that regulate transcription. Previous studies ele-
gantly applied flow cytometry (6, 7) and time-lapse microscopy
(1, 15, 16) to analyze gene-expression noise in large subsets of
genes. However, a tedious experimental bottleneck of subcloning
and expansion of isogenic populations necessarily limits the
throughput of these noise-analysis approaches. Here, we circum-
vent this subcloning requirement to globally apply the analytical
Author contributions: R.D.D., B.S.R., C.D.C., M.L.S., and L.S.W. designed research; R.D.D.,
B.S.R., T.V.T., and J.M.M. performed research; R.D.D., B.S.R., C.D.C., M.L.S., and L.S.W.
contributed new reagents/analytic tools; R.D.D., B.S.R., A.S., T.V.T., J.M.M., M.L.S., and
L.S.W. analyzed data; and R.D.D., B.S.R., C.D.C., M.L.S., and L.S.W. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1R.D.D. and B.S.R. contributed equally to this work.
2Present address: Department of Electrical and Computer Engineering, University of
Delaware, Newark, DE 19716.
3To whom correspondence may be addressed: E-mail: simpsonml1@ornl.gov or
leor.weinberger@gladstone.ucsf.edu.
This article contains supporting information online at www.pnas.org/lookup/suppl/
doi:10.1073/pnas.1213530109/-/DCSupplemental.
1745417459 PNAS October 23, 2012 vol. 109 no. 43 www.pnas.org/cgi/doi/10.1073/pnas.1213530109
framework of noise space across the human genome and quantify
these transcriptional rate parameters. The analysis addresses two
specific questions regarding transcriptional regulation in human
cells. (i) Does constitutive (Poisson-like) expression or episodic
(bursty) expression dominate throughout the human genome?
(ii) Does genomic location influence either mode of expression?
For example, if bursting is operant, does genomic location influ-
ence burst size or burst frequency, and which is predominantly
influenced? Recent studies (1719) have tackled these questions
for specific genes, but no clear and broad consensus has yet
emerged.
Results
To globally apply the analytical framework of noise space to
screen for constitutive versus bursty expression across the human
genome, we capitalized on the semirandom pattern of integration
exhibited by the HIV-1 lentivirus, where the majority of integra-
tions (approximately 69%) occur within transcriptionally active
regions (20, 21). Jurkat T lymphocytes were infected with HIV-
based lentiviral vectors encoding a short-lived, two-hour half-life
version of green fluorescent protein (referred to as d2GFP), to
generate a library of cells in which the vector is integrated at a
different genomic position in each individual cell (i.e., a poly-
clonal library) (Fig. 2A). To focus on measuring the intrinsic fluc-
tuation dynamics of the genomic region surrounding the vector-
integration site, we utilized a vector encoding the HIV-1 LTR
promoter, which is relatively weak and heavily influenced by the
expression dynamics of the local chromatin environment (22).
Initially, the analytical framework for distinguishing bursty
expression was applied to five isoclonal populations: Each popu-
lation was grown from a single parent cell, and all daughter
cells, therefore, share the same LTR genomic integration site
(Fig. 2 AD). Cell fluorescence was then imaged for 18 h, and the
resulting fluorescence intensity trajectories were used to con-
struct a three-dimensional noise space with three axes: noise mag-
nitude as measured by the coefficient of variation squared (CV2),
noise autocorrelation represented by the half-autocorrelation
time (τ12), and mean expression level (hGFPi) (Fig. 2 BCand
SI Appendix). Analysis of these trajectories in the noise space
allows comparisons between isoclonal populations and differen-
tiation between isoclones that exhibit constitutive transcription
versus episodic bursts of transcription (Fig. 2D). To generate an
initial baseline origin for noise-space analysis of the single-cell
data, we identified isoclones that were the most Poissonian in
their expression fluctuation profiles from a library of isoclonal
populations (17) (SI Appendix). Two isoclonal populations exhi-
biting the fastest fluctuation autocorrelation decays (i.e., shortest
autocorrelation times) were selected as the most Poissonian and
used to establish an origin of the CV2-versus-τ12noise map
(Fig. 2D, clones 1 and 2). The isoclone heat map represents the
probability of where a randomly chosen single cell would land on
the noise map (Fig. 2D).
Importantly, nontranscriptional phenomena that influence
noise behavior (e.g., protein and mRNA lifetimes, GFP matura-
tion, extrinsic noise) are already embedded in the noise of these
isoclonal populations, specifically the most Poissonian reference
clones. Thus, comparison between these necessarily precludes the
possibility that noise-map shifts are due to these nontranscrip-
tional phenomena. In addition, the high-frequency noise-proces-
sing technique minimizes extrinsic noise effects (SI Appendix)
(12). Because it is likely that these two isoclones are somewhat
bursty in their expression (SI Appendix), comparisons to these iso-
clones represent a highly conservative assay for bursty expression.
Nevertheless, the results show that even in a small panel of five
clones, there are marked changes in both noise magnitude and
autocorrelation time of approximately 1.5-fold in normalized
space (Fig. 2D). Clones 4 and 5 show significant changes in auto-
correlation time with smaller differences in noise magnitude.
These differences in noise magnitude were validated against con-
ventional flow cytometry measurements (SI Appendix, Fig. S1).
The agreement between data from the 1218 h microscopy
experiments and flow cytometry demonstrates that this CV2-ver-
sus-τ12analysis has the fidelity to differentiate transcriptional
dynamics between different isoclones.
We next extended the analysis to image polyclonal populations
consisting of thousands of integration sites (Fig. 3A)to glob-
ally apply the analytical framework of noise space to screen for
constitutive versus bursty expression across the human genome.
We analyzed more than 8,000 distinct genomic loci with three
different promoters integrated throughout the genome by ima-
ging cells for 1218 h (Fig. 3B). The constitutive expression origin
of the CV2-versus-τ12noise map previously determined for
the most-Poissonian isoclones (Fig. 2Dand SI Appendix) was
compared to the 8,000 loci. To control for LTR-specific or vector-
specific artifacts, we also tested self-inactivating lentiviral vectors
Fig. 1. Fluctuations in gene expression to differentiate between alternate
models of transcription across the genome. (Aand B) Schematics of the con-
stitutive, Poisson-expression model and the episodic, bursty gene-expression
model, together with three expression trajectories from hypothetical geno-
mic loci. Sites that exhibit constitutive (i.e., Poisson) expression exhibit small
and relatively fast fluctuations in gene products over time. Alternatively,
loci that exhibit episodic expression bursts generate large, slow fluctuations
in gene expression. (C) The principle of noise space. The three-dimensional
noise space consists of noise magnitude, noise autocorrelation, and mean
expression level. Small, fast fluctuations have a small noise magnitude and
short autocorrelation times and thus cluster (after normalization) at the
origin of the noise magnitude-autocorrelation plane (gray region, Lower
Left). Large, slow (i.e., bursty) fluctuations have expanded noise magnitude
and extended autocorrelation times (red ovals). The three-dimensional
space can be decomposed into two additional two-dimensional projections
of noise magnitude and noise autocorrelation versus mean expression level
(Lower Center and Lower Right). For episodic-bursty expression, a trajectorys
noise-space coordinates are invariably shifted away from the constitutive
model into the burst model space depending on changes to their transcrip-
tional parameters (10).
Dar et al. PNAS October 23, 2012 vol. 109 no. 43 17455
BIOPHYSICS AND
COMPUTATIONAL BIOLOGY
that encode either promoters for human elongation factor 1α
(EF1A) or human ubiquitin C (UBC) that in turn drive d2GFP.
UBC and EF1A are promoters that drive essential cellular
housekeeping genes: UBC promotes the ubiquitinization cascade
by marking proteins for proteosomal degradation, and EF1A
promotes the GTP-dependent binding of an aminoacyl-tRNA to
ribosomes. UBC and EF1A are among the most abundant pro-
teins in eukaryotic cells, and their promoters exhibit robust high-
level expression across integration sites in different cell types
(23, 24). Virtually all examined genomic loci for all promoters
exhibit noise-map shifts to the upper right (Fig. 3B), indicating
significant bursting in gene expression at virtually all genomic loci.
Similar widespread bursting is also observed in the THP-1 human
monocyte cell line and compared to a constitutive simulation (SI
Appendix,Fig.S2). Both synchronized and unsynchronized cells
exhibit similar shifts in noise space (SI Appendix, Fig. S3), indicat-
ing that transcriptional bursts appear to be common throughout
the cell cycle, as reported (25).
The UBC and EF1A promoters showed markedly lower CV2
values than the LTR promoter (Fig. 3Band SI Appendix, Fig. S4),
which is consistent with our previous study (17) showing that the
LTR promoter displays relatively higher levels of noise than other
eukaryotic promoters in yeast (6, 7). This shift in noise magnitude
is consistent with the well-known transcriptional elongation stall
that characterizes LTR expression (26). This stall results in
Fig. 2. Extracting transcriptional parameters from
the noise space. In individualisoclones, burst dynamics
vary with genomic location. (A)Cellsareinfectedwith
a lentiviral vector expressing a 2-h half-life GFP repor-
ter (d2GFP) at a low multiplicity of infection (moi) to
ensure a single semirandom integration in each cell.
Individual single cells are isolated, grown (creating
isoclone populations), and imaged by time-lapse
fluorescence microscopy. (Band C) Single-cells are
tracked for 1218 h, and an individual cells mean ex-
pression level, variance (σ2), and autocorrelation time
(τ12) are extracted from the time trace (e.g., the
green circle represents a single cells noise space coor-
dinate). A constitutive model of gene expression that
displays abundance dependence (bold red arrows
from black model lines) was used to normalize each
cells noise magnitude (CV2) and autocorrelation
(τ12). The normalized noise magnitudes and autocor-
relations are plotted in a Δlog CV2Δlog τ12noise
map (Left). (D) Consistent shifts to the Upper Right
quadrant in ΔlogCV 2Δlog τ12space observed
for three LTR isoclones (clones 3, 4, and 5), are indica-
tive of transcriptional bursting relative to the least
bursty isoclones (clones 1 and 2). Bursting dynamics
varies between different clones as evidenced by
shifts in both noise autocorrelation and magnitude.
The isoclonal signature is taken from 18 h trajectories
of 400 cells.
Fig. 3. Episodic-bursty expression dominates across the human genome. (A)
To create the polyclonal population, cells are infected with a lentiviral vector
expressing d2GFP so that each cell represents a unique clone harboring a sin-
gle semirandom integration of reporter. (B) Resultant noise maps for over
8,000 individual cell trajectories for the HIV-1 LTR promoter, EF1A promoter,
and UBC promoter. The constitutive origin is derived from Fig. 2D(18 h).
17456 www.pnas.org/cgi/doi/10.1073/pnas.1213530109 Dar et al.
delayed switching to the transcriptional ON state in a two-state
transcription model (17) and predicts that noise frequency (not
only noise magnitude) (27) is modulated in different genomic or
chromatin environments (SI Appendix). In agreement with this
prediction, the distribution of points in the LTR noise map indi-
cates significant differences from the UBC and EF1A noise maps.
In further support, an alternate representation of the noise-map
distribution that converts the distributions to centroids (with
error bars) can be used to conveniently visualize these differences
between promoters (SI Appendix, Fig. S4) (11).
Given conflicting reports on whether burst frequency varies
with genomic location (1719, 28), we next determined if tran-
scriptional burst size, burst frequency, or both changed across the
genome (Fig. 4A). As mentioned above, transcriptional bursting
can be quantified by a two-state model of transcription (13, 14) in
which switching between the two states occurs at rates kon and
koff , and transcription only occurs in the ON state with a rate
km(Eqs. 13and Materials and Methods). The burst size, or num-
ber of mRNAs generated per activity pulse, is typically defined
as kmkoff and, in the limit of koff kon, the burst frequency
is defined as kon (Fig. 4A) (17). To directly test if transcriptional
burst frequency changes across genome location, we analyzed the
polyclonal three-dimensional noise-space data to fit values for
km,koff , and kon. LTR polyclonal trajectories are subclustered
into groupings of approximately 60 cells, so that each subcluster
represents cells in a specific range of gene-expression levels (SI
Appendix, Fig. S5), and average noise autocorrelation is calcu-
lated for each subcluster by autocorrelation analysis (12). To
validate this subclustering approach, we verified that CV2values
from subclustered polyclonal trajectories agree with CV2from
conventional flow cytometry data from isoclonal populations
(Compare Fig. 4Cto SI Appendix, Figs. S1 and S6) . Thus, each
polyclonal subcluster corresponds to an isoclonal population in
terms of average expression level (SI Appendix, Fig. S6). Strik-
ingly, this genome-wide data demonstrate that autocorrelation
time first increases with increasing expression and once an ex-
pression threshold is reached (gray line, Fig. 4B), autocorrelation
time decreases as expression level increases (Fig. 4B). This pat-
tern of concavity is inconsistent with constant burst frequency
(i.e., constant kon) across genomic locations and provides a
genome-wide measurement of kon and koff changes that is inde-
pendent of km(10).
Conventional approaches to quantify transcriptional burst
kinetics analyze noise magnitude (CV2-versus-hGFPi) (6, 7) and
the polyclonal data from Fig. 3 can also be analyzed in terms of
noise magnitude on the CV2-versus-hGFPiplane of noise space
(Fig. 4C). This noise magnitude analysis shows a strong initial
decrease in CV2at low expression levels (Fig. 4C). Then when
an expression threshold is reached (gray line, Fig. 4C) a leveling
off of CV2is observed for higher expression levels (Fig. 4C).
However, noise magnitude is insufficient to uniquely parameter-
ize the two-state model. Because burst size couples kmand koff ,
it is only through the τ12measurement, which is not influenced
by km, that the two parameters can be differentiated from one
another. Note, that the gray line in Fig. 4 Band Ccorrespond to
the same expression threshold.
Fitting of the two-state model in the polyclonal three-dimen-
sional noise map space shows a strong initial increase in burst
frequency at low expression levels, whereas burst size remains
almost constant (Fig. 4 Dand E). Upon reaching a threshold
expression level (gray vertical line in Fig. 4D), a switch in burst
dynamics occurs, and burst size increases, whereas burst fre-
quency remains constant (Fig. 4 Dand E). The fold change in
transcriptional burst size and burst frequency values reveals that
both vary equally across genomic loci (Fig. 4Fand SI Appendix,
Fig. S6). In addition, the measured burst-size range predicts an
average mRNA level of 110 molecules per cell, which is consis-
tent with previous measurements that used single-molecule
mRNA fluorescent in situ hybridization (29, 30). The success of
fitting the three-dimensional noise space is reflected in the close
agreement between a simulated autocorrelation curve and the
experimental trend (Fig. 4B) with the fit model parameters. This
fit shows that the assumed two-state model is sufficient to de-
scribe the measured system (SI Appendix). Much like LTR,
UBC, and EF1A display similar fold changes in burst size and
frequency and exhibit a similar pattern of increasing burst fre-
quency, followed by increasing burst size (Fig. 4G). These data
indicate that integration site influences burst kinetics, irrespective
of promoter type (i.e., cis sequence). However, UBC and EF1A
exhibit almost constant τ12at the highest expression levels indi-
cating increases in only kmat these levels (SI Appendix, Fig. S7).
Interestingly, these two strong promoters individually span the
range of burst frequencies recently reported for a variety of
mammalian genes (18) (SI Appendix, Fig. S7), whereas the LTR
functions at much lower burst frequencies (Fig. 4).
To test how transcriptional activators influence burst dynamics
(Fig. 4), transcription was perturbed with transcriptional
activators, including the histone deacetylase inhibitor (HDAC)
trichostatin A (TSA), and the cell-signaling molecule tumor ne-
crosis factor α(TNF). TNF enhances expression by stimulating
Fig. 4. Transcriptional burst frequency and burst size vary equally across
the genome and are strongly dependent on expression level. (A) Schematic
of the two-state model of transcriptional bursting, where the promoter
switches between ON and OFF states at rates kon and koff and transcribes at
rate kmin the ON state. Transcriptional dynamics are modulated through
changes in burst size, burst frequency, or both. (B) Noise autocorrelation,
noise magnitude (C), burst frequency (D), and burst size (E) versus abundance
for polyclonal subclusters of 2,000 12-h Ld2G single-cell trajectories. Low and
high abundance domains are separated by a solid gray threshold line which
indicates the changes in the trends of noise autocorrelation, noise magni-
tude, and hence burst size and burst frequency is observed. (Fand G)Asa
function of hGFPi, fold changes in burst size and frequency are comparable,
with an initial increase of frequency in all promoters investigated.
Dar et al. PNAS October 23, 2012 vol. 109 no. 43 17457
BIOPHYSICS AND
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recruitment of a p50-RelA heterodimer to nuclear factor κB
(NFκB) binding sites (31) and the HIV-1 LTR encodes multiple
NFκB binding sites and is potently activated by TNF (22). We
previously reported that TNF only changes burst frequency of
the LTR while conserving burst size in a limited number of
isoclones (17), and were interested to see how widespread this
phenomena was across the genome. The τ12-versus-hGFPiana-
lysis of TNF stimulation shows a significant decrease in τ12with
increasing expression level (Fig. 5A). Here, τ12decrease with
increasing abundance is a direct indication of kinetic changes
and demonstrates that increasing expression level cannot be
explained solely by modulations of km(SI Appendix, Eq. S1)
(10, 13).
Fitting of the different two-dimensional planes of three-
dimensional noise space upon TNF induction (Fig. 5 Aand B)
demonstrates that both burst frequency and size significantly
increase as expression levels increase, with burst frequency
increasing at low expression levels and burst size increasing at
higher expression levels (Fig. 5 Cand D). Interestingly, there
appears to be a threshold in expression level, above which kon
plateaus to values observed before adding TNF, and koff appears
to decrease. These data and analysis are corroborated by con-
ventional flow cytometry measurements of 35 isoclonal popula-
tions (SI Appendix, Fig. S6). Overall, these results suggest that
TNF induces expression from the LTR along existing burst trends
(Fig. 5Cand D), and the use of TSA, which induces expression
through a different mechanism than TNF (32), corroborates this
observation (SI Appendix). This observed decrease in koff with
TNF induction leads to extended duration of bursts and is con-
sistent with the reported inhibition of p50-HDAC1 repressive-
complex formation at LTR NFκB sites by p50/RelA heterodimers
(33)the successful formation of HDAC1 leads to weakened
recruitment of RNA polymerase II and weakened transcriptional
initiation (34). The observed increases in kon are also consistent
with increased recruitment of RNA polymerase II to the LTR
promoter NFκB sites induced by TNF (35, 36). Fitted parameter
estimates of LTR residency time in the presence of TNF were
used to represent an average over the first 12 h of stimulation
given the dynamic nonlinear nature of the NFκBresponse(37,
38). Collectively, these results enable estimation of LTR residency
time in the transcriptional ON and OFF states and show that TNF
extends duration in the ON state up to eightfold (Fig. 5E).
Discussion
The analysis of noise space presented here provides a high-through-
put method to dynamically profile gene-regulatory mechanisms
and the effects of perturbations on gene expression. A significant
methodological advantage of analyzing three dimensions of noise
space is the ability to more accurately constrain two-state transcrip-
tional burst models and the polyclonal nature of the approach en-
ables shotgun mapping of gene regulation dynamics on a genome-
wide scale.
The resulting genome-wide data demonstrate that constitutive
transcription is rare across the human genome. Instead, the
overwhelming majority of human genomic loci appear to stochas-
tically fire in episodic bursts. Analysis of noise space demon-
strated that both transcriptional burst frequency and burst size
vary in roughly equal degree across the human genome
(Fig. 4 DG). Intriguingly, there appears to be a threshold expres-
sion level below which integrations modulate only transcriptional
burst frequency and above which only burst size is modulated
(Fig. 4 BGand SI Appendix, Figs. S6 and S7). This transition
could result from recently reported refractory periods inherent to
bursting kinetics (18, 39). Burst frequency can be increased at
loci where transcriptional bursts are infrequent, but as frequency
increases, the refractory period temporally precludes further
increases in frequency. Therefore, once this frequency ceiling is
reached, the only way to increase expression is to increase the
transcription rate or extend the duration of each burst.
As proposed (40), widespread episodic bursting may allow
limited transcriptional resources within the cell to be efficiently
allocated to achieve high-level transcription across large numbers
of loci. This efficient allocation of resources may be the biological
analog of time-domain multiplexing approaches used to effi-
ciently transmit data in signal processing applications.
Materials and Methods
Lentiviral Vectors. Lentiviral vectors were cloned as described (41) and used to
infect 5×105Jurkat cells at a multiplicity of infection <0.1, resulting in
25,00050,000 infected cells each with a unique integration site. Cells were
then sorted by FACS and fluorescently imaged on glass-bottom dishes in RPMI
medium 1640 with 10% fetal calf serum and 1% penicillin-streptomycin.
Imaging. Imaging was performed in humidified conditions at 37 °C and 5%
CO2for 1224 h with a 40X (1.2 N.A.) oil-immersion objective on an Olympus
DSU microscope equipped with an automated linear-encoded X-Y stage, as
described in refs. (12) and (42). Image processing and cell tracking were
performed in Matlab with an in-house algorithm (12) and a single 12-h
experiment could generate up to 1,000 trajectories for analysis.
Calculations. For each trajectory, noise autocorrelation (τ12) and noise mag-
nitude (CV2) were calculat ed using an established noise-processing algorithm
(11, 12). A reported theory (10, 13) of the two-state transcriptional bursting
model yields analytical expressions for both the autocorrelation of the noise,
τ12, and the noise magnitude, CV2(see SI Appendix, Materials and Methods).
Detailed discussion of the noise-mapping approach, including analytical
arguments and stochastic simulations (of Poissonian gene expression) by
the Gillespie algorithm (43, 44), are described in detail in SI Appendix.
Transcriptional burst dynamics are quantified by deriving analytical ex-
pressions for burst size and burst frequency with formulations from previous
analyses (13, 14, 17) and low promoter activity assumptions where koff kon,
koff km,koff γpand kmðγmþγpÞ):
CV2¼C1ð1þBSÞ
hpi;hpBF ·BS ·kp
γm·γp
;
C1¼kp
ðγmþγpÞkp
γp
or b[1]
Fig. 5. Transcriptional burst size and frequency are altered by transcrip-
tional activators. (AD) TNF addition (filled red circles) shifts the measured
integration sites to the higher abundance and burst dynamic domain along
the nondrug curve (empty circles). Large autocorrelation shifts implicate
changes in burst kinetics. (E) Estimated residence times in the active (ON)
and inactive (OFF) states.
17458 www.pnas.org/cgi/doi/10.1073/pnas.1213530109 Dar et al.
BS ¼CV2·hpi
C1
1[2]
BF ¼hpi
BS ·C1·C2
;C
2¼ðγmþγpÞ
γm·γp
1
γp
;[3]
where BS is the burst size, BF is the burst frequency, kmis the transcription
rate, kpis the translation rate, γmand γpare the mRNA and protein decay
rates, respectively, hPiis the mean protein abundance, and bis the transla-
tional burst rate. hPi, or the mean number of GFP molecules in the measure-
ments, is assumed to be directly proportional to hFLi, the mean fluorescence
intensity. Eqs. 2and 3reveal that measurements of CV2and hFLiare sufficient
to quantify burst size and burst frequency within a constant, which is only
dependent on the translation rate and decay rates of mRNA and protein.
Assuming these remain constant, while varying integration site or promoter
sequence, an abundance-dependent burst size and frequency trend can be
directly resolved.
Note. Full decomposition of koff,kon , and kmcan only be performed through
the use of the full 3D noise space.
ACKNOWLEDGMENTS. We thank Hana El-Samad, Ido Golding, Jim Kadonaga,
Laurie Boyer, Alex Hoffmann, John Cooke, David Karig, and members of the
Weinberger and Simpson labs for helpful comments. B.S.R. was supported by
National Science Foundation Graduate Research Fellowship Grant 1144247
and by National Institutes of Health (NIH) Molecular Biophysics Training
Grant GM08326. L.S.W. acknowledges support from the Pew Scholars Pro-
gram in the Biomedical Sciences and the Alfred P. Sloan Research Fellowship
Program. This work was supported by the NIH Directors New Innovator
Award (OD006677) (to L.S.W.), the in-house research program at the Center
for Nanophase Materials Sciences at Oak Ridge National Laboratory (spon-
sored by the Office of Basic Energy Sciences, US Department of Energy)
(to R.D.D. and M.L.S.), and by the National Institute of General Medical
Sciences National Systems Biology Centers at University of California at
San Diego (P50 GM085764) and University of California, San Francisco (P50
GM081879).
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Dar et al. PNAS October 23, 2012 vol. 109 no. 43 17459
BIOPHYSICS AND
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An exact method is presented for numerically calculating, within the framework of the stochastic formulation of chemical kinetics, the time evolution of any spatially homogeneous mixture of molecular species which interreact through a specified set of coupled chemical reaction channels. The method is a compact, computer-oriented, Monte Carlo simulation procedure. It should be particularly useful for modeling the transient behavior of well-mixed gas-phase systems in which many molecular species participate in many highly coupled chemical reactions. For “ordinary” chemical systems in which fluctuations and correlations play no significant role, the method stands as an alternative to the traditional procedure of numerically solving the deterministic reaction rate equations. For nonlinear systems near chemical instabilities, where fluctuations and correlations may invalidate the deterministic equations, the method constitutes an efficient way of numerically examining the predictions of the stochastic master equation. Although fully equivalent to the spatially homogeneous master equation, the numerical simulation algorithm presented here is more directly based on a newly defined entity called “the reaction probability density function.” The purpose of this article is to describe the mechanics of the simulation algorithm, and to establish in a rigorous, a priori manner its physical and mathematical validity; numerical applications to specific chemical systems will be presented in subsequent publications.
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In both prokaryotes and eukaryotes, transcription has been described as being temporally discontinuous, most genes being active mainly during short activity windows interspersed by silent periods. In mammalian cells, recent studies performed at the single cell level have revealed that transcriptional kinetics are highly gene-specific and constrained by the presence of refractory periods of inactivity before a gene can be turned on again. While the underlying mechanisms generating gene-specific kinetic characteristics remain unclear, various biological consequences of transcriptional discontinuity have been unravelled during the past few years. Here we review recent advances on understanding transcriptional kinetics of individual genes at the single cell level and discuss its possible origins and consequences.