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Article
Single Mammalian Cells Compensate for Differences
in Cellular Volume and DNA Copy Number through
Independent Global Transcriptional Mechanisms
Graphical Abstract
Authors
Olivia Padovan-Merhar,
Gautham P. Nair, ..., Abhyudai Singh,
Arjun Raj
Correspondence
rajlaboratory@gmail.com
In Brief
Padovan-Merhar et al. combine singlemolecule transcript counting with
computational measurement of cellular
volume, showing that single cells
maintain transcript abundance despite
variability in cell size. Large cells have
greater transcriptional burst size,
whereas burst frequency halves upon
DNA replication.
Highlights
d
Transcription scales with cell volume to maintain transcript
concentration
d
Cell fusion shows that increasing cellular content can
increase transcription
d
Transcriptional burst size changes with cell volume and burst
frequency with cell cycle
d
The burst frequency mechanism allows for proper
transcription during early S phase
Padovan-Merhar et al., 2015, Molecular Cell 58, 1–14
April 16, 2015 ª2015 Elsevier Inc.
http://dx.doi.org/10.1016/j.molcel.2015.03.005
Accession Numbers
GSE66053
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
Molecular Cell
Article
Single Mammalian Cells Compensate for Differences
in Cellular Volume and DNA Copy Number through
Independent Global Transcriptional Mechanisms
Olivia Padovan-Merhar,1 Gautham P. Nair,2 Andrew G. Biaesch,2 Andreas Mayer,3 Steven Scarfone,1 Shawn W. Foley,4
Angela R. Wu,5 L. Stirling Churchman,3 Abhyudai Singh,6 and Arjun Raj2,*
1Department
of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
3Department of Genetics, Harvard Medical School, Boston, MA 02115, USA
4Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
5Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
6Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
*Correspondence: rajlaboratory@gmail.com
http://dx.doi.org/10.1016/j.molcel.2015.03.005
2Department
SUMMARY
Individual mammalian cells exhibit large variability in
cellular volume, even with the same absolute DNA
content, and so must compensate for differences
in DNA concentration in order to maintain constant
concentration of gene expression products. Using
single-molecule counting and computational image
analysis, we show that transcript abundance correlates with cellular volume at the single-cell level due
to increased global transcription in larger cells. Cell
fusion experiments establish that increased cellular
content itself can directly increase transcription.
Quantitative analysis shows that this mechanism
measures the ratio of cellular volume to DNA content,
most likely through sequestration of a transcriptional
factor to DNA. Analysis of transcriptional bursts reveals a separate mechanism for gene dosage compensation after DNA replication that enables proper
transcriptional output during early and late S phase.
Our results provide a framework for quantitatively
understanding the relationships among DNA content, cell size, and gene expression variability in single cells.
INTRODUCTION
Within a population, individual mammalian cells can vary greatly
in their volume, often independently of their position in the cell
cycle (Bryan et al., 2014; Crissman and Steinkamp, 1973; Tzur
et al., 2009). Biochemical reaction rates, however, depend on
the concentration of reactants and enzymes. Thus, to maintain
proper cellular function, most molecules must be present in the
same concentration despite these volume variations, meaning
that the absolute numbers of molecules would have to scale
roughly linearly with cellular volume (see Marguerat and Ba¨hler,
2012 for an excellent review).
One critical molecule whose concentration need not scale with
cellular volume, however, is DNA. Most mammalian cells have
two or four copies of the genome per cell, and even cells with
the same number of genomes can differ widely in size; thus,
DNA concentration can vary dramatically from cell to cell. This
poses a problem: if two otherwise identical cells with the same
DNA content had different volumes, then the larger cell must
somehow maintain a higher absolute number of biomolecules
despite them being expressed from the same amount of DNA.
Previous efforts to resolve this puzzle have largely focused on
analyzing bulk population measurements of size-altering mutants. A number of such studies have shown that the amount
of both RNA and protein generally scales with cellular volume
(Marguerat and Ba¨hler, 2012; Marguerat et al., 2012; Schmidt
and Schibler, 1995; Watanabe et al., 2007; Zhurinsky et al.,
2010) and ploidy (Wu et al., 2010), with some further finding
that transcription changes in mutants with larger or smaller cell
volumes (Fraser and Nurse, 1979; Schmidt and Schibler, 1995;
Zhurinsky et al., 2010). Most of these studies utilized yeast,
with a few notable exceptions (Miettinen et al., 2014; Schmidt
and Schibler, 1995; Watanabe et al., 2007).
These experiments do not, however, establish a causal relationship between cellular volume changes and transcript abundance. Causality could change the interpretation of gene expression measurements because, if cellular volume changes can in
and of themselves change global expression levels, observations of changes in global expression levels in response to
various perturbations may actually be the indirect consequence
of changes to cellular volume rather than resulting from direct
global transcriptional responses to the perturbations, per se.
Also unclear is how or even whether these mechanisms manifest in individual cells. Much recent evidence has shown that
individual transcripts levels can vary from cell to cell due to stochastic effects in gene expression (Raj and van Oudenaarden,
2008, 2009; Sanchez and Golding, 2013) such as transcriptional
bursts (Chubb et al., 2006; Golding et al., 2005; Raj et al., 2006;
Suter et al., 2011; Zenklusen et al., 2008). Yet it remains unclear
how differences in cellular volume affect the interpretation of
such measurements or whether transcriptional measurements
can reveal further characteristics of homeostatic mechanisms.
Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc. 1
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
We used single-molecule RNA imaging and computational
image analysis to measure transcript abundance and cellular
volume simultaneously in individual human cells. Cell fusion
experiments showed that cellular size can directly and globally
affect gene expression by modulating transcription. Quantitative
analysis of these experiments revealed that the mechanism underlying this global regulation does not merely sense cellular volume but rather integrates both DNA content and cellular volume
to produce the appropriate amount of RNA for a cell of a given
size, consistent with a model in which a factor limiting for transcription is sequestered to the DNA, either through direct titration by DNA or restriction to the nuclear compartment. We also
provide a quantitative framework for interpreting gene expression variability in single cells and extended this framework
to genome-wide single-cell RNA-sequencing analysis, showing
that cell-type-specific genes are more variable than ubiquitously
expressed genes.
RESULTS
mRNA Counts Scale with Cellular Volume in Single
Mammalian Cells
We first looked at the number of mRNA molecules in individual
primary fibroblast cells (human primary foreskin fibroblasts,
CRL2097) within a population to see whether mRNA counts
scale with cellular volume at the single-cell level. We measured
both mRNA abundance and volume simultaneously using single-molecule multicolor mRNA fluorescence in situ hybridization
(RNA FISH; Femino et al., 1998; Raj et al., 2008), which allowed
us to detect the positions of individual mRNAs in three dimensions as fluorescent spots in the microscope (Figure 1A). We
measured the abundance of a particular mRNA (e.g., TBCB)
labeled with one color and then calculated the volume of the
cell using the 3D positions of mRNA from a ‘‘volume guide’’
gene labeled with another color to define the cellular boundary
(Figure 1B; Experimental Procedures). The cell volumes we
measured varied over a 6-fold range, agreeing with other estimates (Bryan et al., 2014; Tzur et al., 2009), and are robust to
choice of guide gene and the fixation procedure itself (Figure S1).
We ultimately measured the abundance of 25 to 30 different
mRNA species in both this primary fibroblast line and a lung cancer line (A549).
For most genes, mRNA counts and volumes in single cells exhibited a strongly positive, linear correlation (e.g., Figure 1C; see
Figure S2 for all genes examined). Because larger cells had proportionally more transcripts than did smaller cells, the mRNA
concentration remained relatively constant from cell to cell
despite considerable variation in absolute mRNA numbers. This
scaling property was not confined to high-abundance mRNAs
such as GAPDH and EEF2—genes expressing as few as 10 to
20 mRNA per cell such as ZNF444 and KDM5A scaled similarly,
as did rRNA (Figure S2). We also observed the same behavior
for short-lived mRNA such as UBC and IER2 mRNA, whose
half-lives are 2.9 and 2.2 hr, respectively (Tani et al., 2012).
We checked whether the scaling of mRNA count with volume
depended on cell-cycle progression or cell growth. We costained cells with cell-cycle markers (Eward et al., 2004; Levesque and Raj, 2013; Robertson et al., 2000; Whitfield et al.,
2 Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc.
2002) to classify them as being in the G1, S, or G2 phases of
the cell cycle (Figure S3). Cell volume varied as much for cells
in individual phases of the cell cycle as the population overall,
with a shift in the distribution toward G2 cells being larger, and
the linear relationship between mRNA count and volume did
not depend on cell-cycle phase (Figure 1D), showing that
mRNA count did not depend on DNA content of the cell. We
also note that the primary fibroblast cells exhibit normal ploidy
(Levesque and Raj, 2013), so our results are not simply explained
by differences in ploidy. We also found that nuclear size
increased somewhat with cellular volume and that nuclear size
increased in later stages of the cell cycle (Figure S3). To check
whether progression through the cell cycle or cell growth is
responsible for maintaining scaling, we grew the primary fibroblasts for 7 days in medium lacking serum, making them quiescent. Despite growth and cell cycle arrest, we found that mRNA
count and volume still scaled strongly for all genes examined,
showing that neither progression through cell cycle nor continual
cell growth is required for mRNA count to scale with cellular volume (Figure 1F). Interestingly, we found that although the mean
count of mRNA decreased in quiescent cells as compared with
proliferating cells, the cells maintained a similar concentration
of GAPDH and other mRNA between the two conditions (Figures
1G–1H and S1).
We also checked whether we could observe similar behavior in
intact organisms. We looked at both RNA and DNA density in the
heads and gonads of adult nematodes, comparing measurements from both wild-type worms and worms with mutations
leading to decreased organismal size but with roughly the
same number of cells (Figures 2A–2B) (Watanabe et al., 2007).
We found that the RNA concentrations were roughly the same
between the two strains and that the number of RNA per molecule of DNA decreased by a factor similar to that of the volume
differences between the strains (Figures 2C–2D), verifying that
our observations can hold in vivo.
It is important to note that although the mRNA abundance is
strongly correlated with cellular volume, the y intercept (a) of a
line fit to the data (mRNA = a + bV) was nonzero, indicating
that mRNA count in individual cells has a volume-independent
component in addition to the volume-correlated component.
Quantifying the relative fractions of mRNA that are volume correlated versus volume independent in a cell of average volume
(Figure 1E) [i.e., a / (a + bVavg) versus bVavg / (a + bVavg)] revealed
a range of values for different genes (Figure S1), although the volume-dependent fraction was dominant for most genes examined. Thus, the mRNA concentration is actually somewhat
greater in smaller cells than in larger ones; for most genes, the
smallest cells have an mRNA concentration 1.2 to 3 times greater
than that of the largest cells (Figure S2). We later describe a
mathematical model providing a potential explanation for this
increased concentration based on nuclear volume measurements (see Supplemental Information).
Transcriptional Activity, Not mRNA Degradation, Scales
Globally with Cellular Volume
These data show that larger cells have a proportionally higher
number of mRNA than smaller cells, even if they have the
same absolute number of DNA molecules. To maintain this
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
C
B
D
E
F
G
H
Figure 1. mRNA from Many Genes Scales with Cellular Volume
(A) Single-molecule RNA FISH. The DAPI stain is in blue, and the TBCB mRNA FISH probe is in white.
(B) Representative outline of a primary fibroblast cell found using our volume calculation algorithm.
(C) mRNA versus volume for EEF2, LMNA, and TBCB. Each point represents one single-cell measurement. Each dataset is a combination of at least two biological
replicates, with at least 30 cells per replicate.
(D) GAPDH mRNA and volume in primary fibroblast cells. Marginal histograms show volume and mRNA distributions. Colors indicate cell-cycle stage determined
by Cyclin A2 (CCNA2) mRNA count. Dashed diagonal line is the best linear fit of RNA versus volume. Vavg indicates the average primary fibroblast volume. We
determined volume-independent and -dependent transcript levels using the linear fit and Vavg. Data are a 15% subset of 1,868 cells spanning >30 biological
replicates.
(E) Fraction of volume-independent and -dependent RNA expression from the linear fit of RNA versus volume for 21 genes in primary fibroblast cells (we omitted
highly variable genes whose volume-independent fractions were less than zero). Data for each gene are a combination of at least two biological replicates, with at
least 30 cells per replicate.
(F) GAPDH mRNA versus volume in cycling and quiescent primary fibroblast cells. Dashed lines are best fit line for GAPDH in cycling cells. Data are an 8% subset
of 1,868 cells spanning >30 biological replicates for cycling cells and 10% subset of 1,105 cells for quiescent. We only analyzed quiescent cells that had less than
20 CCNA2 mRNA.
(G and H) Mean GAPDH mRNA count (G) and concentration (H) in different growth conditions for data from (F).
All error bars represent SEM. See also Figures S1–S3.
Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc. 3
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
C
B
D
Figure 2. mRNA Scales with Volume In Vivo
(A) Images of the two C. elegans strains.
(B) Quantification of the relative sizes of the two strains (n = 24 for N2, n = 20 for
CB502).
(C) Number of mRNA molecules per cell in the gonad region for each type of
worm for genes ama-1 and arf-3. We estimated the number of cells in each
segment by counting nuclei stained with DAPI. Each bar is a compilation of
three biological replicates, with >3 worms per replicate.
(D) Concentration of mRNA in the gonad region. All scale bars represent 10 mm.
All error bars represent SEM.
proportionality, larger cells must either transcribe more mRNA
from the same number of DNA molecules or degrade those
mRNA more slowly. To distinguish these possibilities, we determined the rate of mRNA degradation in cells of different sizes by
measuring volumes and mRNA counts for UBC and IER2 after a
period of 4 hr of transcriptional inhibition (transcriptional inhibition did not affect cell volume; Figure 3D). By measuring mRNA
counts before and after transcription inhibition (Figures 3A–3B,
inset; see Experimental Procedures for details), we calculated
the effective decay constant for each measured cell (Figures
3A–3B). We found that the degradation rate was the same in cells
of all volumes, showing that slower degradation is not responsible for the increased number of mRNA in larger cells.
We next checked whether larger cells transcribe more than
smaller cells (as observed in bulk populations; Fraser and Nurse,
1979; Schmidt and Schibler, 1995; Zhurinsky et al., 2010). We inferred global transcription rate by incorporating a labeled uridine
into all newly synthesized RNA produced during a 60-min time
window (Figure 3C), which we then rendered fluorescent via click
chemistry (Jao and Salic, 2008). The intensity of fluorescence is
equivalent to the global transcription rate. We found that transcription rate is linearly proportional to volume, thus showing
that individual cells vary in their overall transcription (das Neves
et al., 2010), and these variations correlate strongly with volume.
We conclude that larger cells maintain proportionally higher
levels of RNA by increased transcription rather than decreased
degradation as compared to smaller cells. Also, quantification
of fluorescence from probes targeting the internal transcribed
spacer of the rRNA (the ‘‘intronic’’ sequence of rRNA) showed
4 Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc.
that transcription of rRNA also scales linearly with volume (Figure S2), indicating that RNA polymerase I transcription is also
volume dependent.
The scaling of transcription with cellular volume could be due to
global factors regulating transcription of all genes in a volumecorrelated manner, or it could be that gene regulatory networks
sense deviations in each particular gene’s protein concentration
and modulate transcription to restore concentration. In the latter
case, reducing protein concentration of any one gene would
result in increased transcription to compensate, whereas in the
global scenario, reducing the concentration of any one gene
would not appreciably affect the cellular volume, thus leaving
the gene’s transcription unchanged. We tested this by reducing
the level of lamin A/C mRNA and protein in the cell via small interfering RNA (siRNA) (Figures 3E and 3F); we chose lamin A/C
because its expression scales strongly with volume (Figure 1C)
and is thought to be tightly regulated (Swift et al., 2013). To measure the transcriptional response, we took advantage of the fact
that transcription occurs in bursts (Chubb et al., 2006; Dar et al.,
2012; Golding et al., 2005; Suter et al., 2011; Vargas et al., 2005;
Zenklusen et al., 2008), and genes that are actively undergoing a
transcriptional burst have bright accumulations of nascent RNA
at the site of transcription itself (Levesque and Raj, 2013; Levsky
et al., 2002; Raj et al., 2006; Zenklusen et al., 2008) (note that
siRNA does not affect nuclear RNA; Maamar et al., 2013). We
measured both the average number of active lamin A/C transcription sites per cell and the intensity of those transcription sites,
finding both metrics unchanged upon reduction of lamin A/C protein levels (Figure 3G). We conclude that increased mRNA counts
in larger cells result from a global difference in transcription rather
than the activity of a particular gene network that regulates the
concentration of lamin A/C. There may be other situations in
which mRNA levels are regulated by specific networks.
A Diffusible trans Factor Sensing DNA Content and
Volume Links Cellular Volume and Transcription
What links volume and transcription? One possibility is that the
total cellular content itself exerts a global influence on transcription, thus making transcription scale with cellular volume; alternatively, transcription may affect cellular volume. To distinguish
these possibilities, we fused a small human melanoma cell that
expressed GFP mRNA (WM983b-GFP-NLS) at constant density
to the larger fibroblasts that do not express GFP (Figure 4A) to
form heterokaryons (Pomerantz et al., 2009). We found that absolute GFP mRNA counts increased in fused cells as compared
to the original small cells (Figure 4B), showing that increasing total cellular content is by itself sufficient to increase absolute
mRNA abundance. Moreover, the GFP mRNA counts scaled
with heterokaryon volume (Figure 4C), suggesting that the rate
of GFP transcription scaled with the ultimate volume of the fused
cell. The fact that the nucleus from the WM983b-GFP-NLS cell
could change its overall transcriptional activity showed that the
modulation occurs via the activity of a diffusible trans factor.
How might such a factor transmit volume information to the
GFP gene in order to increase its transcription concordantly
with the increase in cellular volume? There are two broad categories of mechanism: (1) the factor acts as a ‘‘volume sensor’’
and does not know about the amount of DNA in the cell. An
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
C
B
D
E
F
G
Figure 3. Cells Exhibit Global Volume-Dependent Transcriptional Control over mRNA Abundance
(A and B) We inhibited transcription in primary fibroblast cells using actinomycin D for 4 hr and allowed UBC (A) and IER2 (B) mRNA to degrade. Inset shows mRNA
before and after inhibition. Each point represents a single-cell measurement. We calculated the decay constant for each cell using the best-fit line before inhibition
(see Experimental Procedures). Blue line shows fit if degradation were volume-dependent; red line shows fit if transcription were volume-dependent. Data
represent one of two biological replicates.
(C) We fluorescently labeled nascent RNA produced in 1 hr using the Click-iT eU assay in primary fibroblast cells and quantified the total fluorescence intensity by
imaging the nuclei of single cells. Inset shows raw micrograph data. Blue line shows fit for volume-dependent degradation; red line shows fit for volumedependent transcription. Data shown are from quiescent cells and are one of three biological replicates.
(D) Distribution of cell volumes before and after transcription inhibition.
(E) We performed siRNA treatment for 72 hr in primary fibroblast cells using either a control siRNA (left) or an siRNA targeting LMNA mRNA (right). DAPI stain is
shown in purple, and LMNA mRNA FISH probe is shown in white. White arrows indicate active transcription sites.
(F) Quantification of cytoplasmic LMNA mRNA knockdown by RNA FISH. Inset shows protein knockdown.
(G) Comparison of the number of LMNA transcription sites and transcription site intensity in siRNA control and LMNA knockdown conditions. We detected
transcription sites through intron/exon colocalization using RNA FISH. All error bars represent SEM. Data in (D) and (E) are a combination of two biological
replicates, n = 323 cells for control siRNA and 284 cells for LMNA siRNA.
example could be a modifiable global transcription factor protein
whose degree of modification/activity is proportional to cellular
size (Figure 4D, left). Or (2) the factor acts as a ‘‘volume/DNA
sensor’’ whose activity depends on both cellular volume and
DNA content. One such mechanism is the existence of a general
transcription factor of limiting abundance relative to the number
of binding sites in the DNA (limiting factor). Here, the DNA
‘‘counts’’ how big the cell is by binding all available factor molecules (Figure 4D, right), thus increasing transcription in bigger
cells as more factor binds to DNA. Another possibility is
Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc. 5
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
B
C
Prediction for volume
sensor hypothesis
D
Figure 4. A trans-Acting Limiting Factor Links Gene Expression to Volume
(A) Representative image of fused cells (heterokaryon, left) and unfused cells (WM983b, primary fibroblast, right). DAPI stain is in orange, GFP mRNA is in green,
and GAS6 mRNA is in white. White arrows indicate transcription sites.
(B) Quantification of GFP mRNA in unfused and fused cells. Box extends to first and third quartiles, and whiskers extend to the maximum-distance points within
1.5 interquartile ranges of the box. Data are a combination of two biological replicates.
(C) GFP versus volume for fused and unfused cells. Upper dashed line represents fit for unfused cells. Lower dashed line has a slope that is half of the upper fit line.
(D) Schematic of transcriptional output of fused cells if the scaling of expression with volume were mediated by a volume sensor or a volume/DNA sensor. All error
bars represent SEM.
sequestration of the factor to the nucleus, which can also
achieve the same volume/DNA-sensing behavior if nuclear volume is only weakly dependent on cellular volume (see Supplemental Information).
We distinguished these two alternatives by comparing the
concentration of GFP mRNA in the fused and unfused cells (Figure 4C). In the volume sensor scenario, the fusion cell will have
the same concentration of GFP mRNA as the original small cells
because the factor transmits the volume information to the GFP
gene independent of the number of nuclei in the cell. In the volume/DNA sensor scenario, the fusion cell will have half the concentration of GFP mRNA because the factor senses both the
increased volume and the two nuclei (for example, a limiting
factor would be diluted between the two nuclei in the fused
cell). We found that the concentration of GFP mRNA in the fused
cells is strictly less than and very close to half the concentration
in unfused cells. We conclude that the factor responsible for
increased transcription in smaller cells is not a volume sensor
but responds to both the size and DNA content. These results
also suggest that perturbations that change cell size will indirectly change global transcript counts per cell through this
generic mechanism.
6 Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc.
Transcriptional Burst Size Increases in Larger Cells
We next sought to characterize this mechanism further by
examining the relationship between volume and transcription
of individual genes. mRNA is produced in bursts, marked by
bright accumulations of nascent mRNA at the site of transcription. We characterize this bursting behavior through burst size
(how much RNA is produced during a single burst) and burst
fraction (how often a gene is actively transcribing, which is
related to burst frequency; Levesque and Raj, 2013). To quantify
burst size, we measured the intensity of transcription sites for
four genes in our fibroblasts and found higher intensity transcription sites in larger cells (Figure 5A). We verified that the intensity of transcription sites reflected the degree of transcriptional activity by treating primary fibroblast cells with 100 nM
triptolide, which targets RNA polymerase II for degradation
(Bensaude, 2011), reducing its levels (Figure 5D). After 1 hr,
we saw a reduction of bright transcription sites for two different
genes, showing that transcription site intensity depends directly
on the amount of transcriptional machinery available. This intensity is often proportional to burst size (Levesque and Raj, 2013;
Senecal et al., 2014). Interestingly, transcription site intensity
did not depend on cell-cycle stage (Figure 5B). We concluded
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
B
C
Figure 5. Transcriptional Burst Size Increases in Larger Cells
(A) Transcription site intensity and volume in primary fibroblast cells for genes UBC, MYC, EEF2,
and TUSC3. Each data point represents the mean
transcription site intensity per cell for a quartile of
cells classified by volume or GAPDH. We detected
transcription sites through intron/exon colocalization using RNA FISH. We calculated volume for
EEF2 data using EEF2 as a guide and volume for
MYC data using GAPDH. We use GAPDH as a
proxy for volume for UBC and TUSC3.
(B) Transcription site intensity and cell-cycle stage
in primary fibroblast cells. We determined cell-cycle
stage by Cyclin A2 and the histone 1H4E mRNA
counts (see Experimental Procedures and Figure S3). For intensity measurements, data for UBC,
MYC, and EEF2 are from one of two biological
replicates (EEF2: n = 190, UBC: n = 202, and MYC:
n = 103 transcription sites). Data for TUSC3 are
combined from two biological replicates (n = 255
transcription sites).
(C) Western blot analysis reveals that >99% of the
C-terminal domain hyperphosphorylated form of
RNA polymerase II (IIO) is present in the chromatin
fraction. The hypophosphorylated form of Pol II (IIA)
is captured in all cellular fractions. We generated
subcellular lysates from the same batch of primary
fibroblast cells and probed with the F-12 antibody
(Santa Cruz Biotechnology) that is directed against
the N-terminal region of RPB1, the largest subunit
of RNA polymerase II. We adjusted sample volumes
so that western blot signals of the subcellular
fractions are comparable.
(D) Quantification of transcription site intensity
before and after treatment with 100 nM triptolide for
1 hr. p value represents the probability of randomly
finding the distributions of bright transcription
sites (values to the right of the black line) in each
condition.
All error bars represent SEM. See also Figures S3
and S4.
D
that the factor connecting gene expression and cellular volume
affected mRNA abundance through modulation of transcriptional burst size.
What might this factor be? In order to
formalize the possibilities, we developed
a mathematical model for how this factor
may act (see Supplemental Information),
assuming that the factor is almost purely
nuclear and that the total amount of factor
in the cell is proportional to cellular volume.
Our model of perfect linear scaling of transcription with volume requires that either
(1) the volume of the nucleus remains fixed
between cells irrespective of cytoplasmic
volume or (2) the factor has such a high affinity for DNA that it is essentially titrated by
DNA (or both). In both scenarios, either the
nucleus or the DNA ‘‘counts’’ the amount
of factor in the cell to modify transcription,
thus making transcription proportional to the total amount, rather
than concentration, of the factor. Further, in scenario 1, it predicts
that if nuclear volume changes with cell size, it will manifest as a
Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc. 7
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
deviation from pure linear scaling of transcription with cellular volume. Our data cannot distinguish these two possibilities, but our
analysis did predict that in scenario 1, the slight increase in nuclear volume we saw in larger cells (Figure S3) could lead to a
slight decrease in mRNA concentration, manifesting as a nonzero
intercept when fitting RNA abundance to volume, as observed in
Figure 1D. Indeed, the quantitative magnitude of the increased
concentration at low cell volumes matches what our model
predicts based on our measured relationship between nuclear
volume and cellular volume (see Supplemental Information),
perhaps favoring the model in which transcriptional scaling
results from sequestration of this factor to the nucleus over a
pure titration mechanism. It is possible that the factor is some
component of the general transcriptional machinery, which is
94% nuclear based on fractionation (Figure 5C) (A.M. and
L.S.C., unpublished data).
A DNA-Linked cis-Acting Factor Reduces Transcription
Frequency, Not Burst Size, Immediately after DNA
Replication
We have shown that cells in the G1 and G2 phases of the cell cycle can have the same volume and same mRNA density, although
cells in G2 have twice the DNA content as those in G1. How, then,
do two cells of the same size produce the same amount of mRNA,
despite having different amounts of DNA?
We already found that transcriptional burst size does not
change dramatically between phases of the cell cycle (Figure 5B),
so we now measured burst fraction. To measure transcriptional
burst fraction, we counted active transcription sites in each cell
and divided by the total number of gene copies for each stage
of the cell cycle (two copies in G1, four copies in G2). For all of
the genes we measured, the number of active sites per gene
copy in G2 was approximately half of that in G1 (Figure 6A).
This is not due to repression of replicated copies of DNA, as
we observed G2 cells with four transcription sites (Figure S4).
This showed that the cell has a mechanism to precisely reduce
transcription fraction in G2 to keep overall transcription constant
across the G1 and G2 phases of the cell cycle. Burst fraction did
not depend on cell volume (Figure 6B), showing that the mechanism is distinct from the volume-compensating mechanism
described above.
We were surprised that the mechanism for cell cycle was
different from the one compensating for volume. In principle,
limiting factor models that may be responsible for volume conservation would also compensate for increased gene copy number due to DNA replication. However, these models predict an
inappropriate boost in transcription for genes that replicate early
in S phase because a limiting factor would distribute itself over all
the DNA, essentially ‘‘double counting’’ the small percentage of
genes that replicate considerably earlier than the majority of DNA
(Figure 6C). To see whether this was the case, we measured
transcriptional burst fraction for early-replicating genes in S
phase (EEF2, MYC, UBC; see Figure S4 for replication timing).
These genes all showed the same number of active transcription
sites per gene copy in S and G2, ruling out the possibility that a
factor simply gets diluted between copies of replicated DNA.
This leaves two alternatives for burst fraction reduction
between G1 and G2. Transcription fraction could universally
8 Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc.
decrease by a factor of two upon the initiation of S phase,
but this would potentially cause the opposite problem—genes
that replicate late in S phase would be under-transcribed for
the majority of S phase. Alternatively, transcription fraction could
decrease on a gene-by-gene basis (i.e., in cis) immediately upon
DNA replication. To test between these alternatives, we imaged
transcription of a gene that replicates very late in S phase
(TUSC3; Figure S4). If transcription fraction was universally
reduced by a factor of two at the beginning of S phase, this
gene would have the same transcription fraction in S and G2.
However, we found that this late-replicating gene maintains G1
levels of transcription through S phase and does not reduce transcription fraction until G2. Therefore, we conclude that there exists a mechanism whereby transcription fraction is reduced by a
factor of two immediately upon replication of that gene, with
different timing for different genes. Candidates for a mechanism
include the partitioning or modification of DNA-linked factors,
such as histones with particular modifications, upon DNA replication, resulting in half the transcriptional burst fraction as before
replication.
Together, our data demonstrate the existence of two separate
transcriptional mechanisms that allow cells to maintain RNA
concentration homeostasis despite changes in DNA content
and cellular volume. Cells modulate transcriptional burst size
through a trans mechanism to allow larger cells to produce
more mRNA from the same amount of DNA and modulate burst
frequency over the cell cycle in cis to maintain RNA concentration despite changes in DNA content.
Single-Cell RNA Sequencing Reveals that Cell-TypeSpecific Genes Are ‘‘Noisier’’ Than Ubiquitously
Expressed Genes
Our RNA FISH data revealed that, although the expression of
most genes was consistent with a volume-dependent transcription rate, many of the genes also showed strong variability in
transcript concentration from cell to cell (Li and Xie, 2011; Raj
and van Oudenaarden, 2009; Raj et al., 2008; Sanchez and Golding, 2013).
To accurately quantify gene expression noise while accounting for cell volume, we developed a metric we call volume-corrected noise measure (Nm; Figure 7A), defined as (Bowsher
and Swain, 2012; Johnston et al., 2012; Swain et al., 2002)
follows:
bhVi
Covðm; VÞ
;
Nm = CVm2 a + bhVi
hmihVi
where
CVm =
sm
;
hmi
and a and b indicate the intercept and slope of a best-fit line for
mRNA and volume,
hmi = a + bhVi:
Volume-corrected noise measure is in principle similar to the
squared coefficient of variation of mRNA concentration but accounts for volume-independent transcription (Figure S5).
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
B
Figure 6. A cis-Acting Factor Decreases
Transcription Frequency Immediately upon
DNA Replication
(A) Number of transcription sites by cell-cycle stage
in primary fibroblast cells. We determined cell-cycle
stage by Cyclin A2 and histone 1H4E mRNA counts.
Dashed lines represent half the number of transcription sites in G1. We normalize all G1 data to two
gene copies and all G2 data to four gene copies. For
EEF2, MYC, and UBC (early replicators), we
normalize S-phase data to four gene copies. For
TUSC3 (late replicator), we normalize S-phase data
to two gene copies.
(B) Number of transcription sites per gene copy
classified by volume in primary fibroblast cells. Each
data point represents the mean number of transcription sites for a quartile of cells classified by
volume. We calculated volume for EEF2 data using
EEF2 as a guide and volume for MYC data using
GAPDH. We use GAPDH as a proxy for volume for
UBC and TUSC3. For frequency measurements,
data for EEF2, UBC, and TUSC3 are a combination
of two biological replicates (EEF2: n = 516, UBC: n =
332, and TUSC3: n = 255 transcription sites). Data
for MYC is from one of two biological replicates
(MYC: n = 103 transcription sites).
(C) Schematic depicting different potential mechanisms for changing gene expression with cell cycle.
All error bars represent SEM. See also Figures S3
and S4.
C
We evaluated Nm for all of the genes we measured by RNA
FISH. A standard measure of gene noise is the coefficient of variation (CV; standard deviation divided by mean), which takes into
account only the spread and the mean of the expression data.
With such a measurement, most of the genes we measured by
RNA FISH would be deemed ‘‘noisy,’’ or far from Poisson noise
levels (Figure S5). However, when we instead measured Nm
for each of our RNA FISH genes, we saw that many of them
displayed levels of variability near to or
indistinguishable from Poisson (Figure 7B)
once we accounted for measurement error
(upper bound of approximately 15%) (Raj
et al., 2006).
To quantify this variability genome-wide,
we performed single-cell RNA sequencing
(Brennecke et al., 2013; Gru¨n et al., 2014;
Shalek et al., 2013) on human foreskin
fibroblast cells, calibrating the sequencing
data using our RNA FISH results (Figures
7C and S6) and adding synthetic RNA at
known concentrations to estimate cell
volume. Briefly, we used the ratio of
RNA-sequencing reads mapping to the
transcriptome to the reads mapping to
spiked-in RNA from the External RNA
Controls Consortium (ERCCs) (Devonshire
et al., 2010) to estimate the total relative
amount of RNA in the cell (Marinov et al.,
2014; Wu et al., 2014), dropping a small
number of cells that were qualitatively inconsistent with the
rest (Figure S7). We used the measured relationship between
GAPDH mRNA count and cellular volume from RNA FISH to
convert total RNA to relative cellular volume, matching this to
our measured volume distribution to obtain cellular volumes.
We then used the correlation between FPKM (fragments per kilobase per million fragments mapped) and RNA FISH counts for
our gene panel to provide estimates of absolute RNA counts
Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc. 9
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
A
B
C
D
F
E
Figure 7. Connection between Single-Cell RNA Sequencing and RNA FISH Reveals that Cell-Type-Specific Genes Exhibit Higher Noise
Levels
(A) RNA FISH data. TBCB mRNA abundance and volume in primary fibroblast cells. Each point represents a single-cell measurement. Histogram indicates mRNA
distribution. Arrow indicates volume-corrected noise measure. Gray line is best linear fit.
(B) Volume-corrected noise measure values for different genes in primary fibroblast cells. Each data point represents a collection of single-cell measurements for
one gene. The straight gray line represents the Poisson limit. The curved gray line is the Poisson limit plus our experimental noise limit, a combination of the
Poisson limit and a 15% measurement error. Data for each gene is a combination of at least two biological replicates, with at least 30 cells per replicate.
(C) Pipeline for converting FPKM from single-cell sequencing to RNA-FISH-equivalent counts and cellular volume in picoliters.
(D) Qualitative comparison of count versus volume from RNA FISH and single-cell RNA sequencing. Example low-Nm (GAPDH) and high-Nm genes (MYC).
(E) Comparison between Nm calculated from RNA FISH data and single-cell RNA-seq data. Each point represents a single gene. Nm is calculated by bootstrapping.
(F) Breakdown of high- and low-noise genes into ubiquitously expressing genes and genes that express in a cell-type-dependent manner.
All error bars represent 95% confidence intervals as calculated by bootstrapping. See also Figures S5–S7.
for all genes in individual cells. (It is important to note, however,
that there is substantial variance in this relationship and that the
relationship is nonlinear.) We found that both RNA FISH and single-cell mRNA sequencing yielded similar results for noisy and
non-noisy genes (Figures 7D and 7E).
Upon quantifying Nm for the genes in our RNA FISH experiments in both human foreskin fibroblast and lung cancer cells,
we noticed that three of the four genes (ICAM1, LUM, and
ACTA2) with the strongest degree of cell-type specificity were
also the three genes with the highest noise measure of all the
genes in our study (Figure S7). To see whether this trend held
more generally, we used our single-cell RNA-sequencing data
to explore noise measure across all genes. We selected genes
with high or low noise measures and looked for enrichment in
genes exhibiting cell-type-specific expression between human
lung cancer cell and foreskin fibroblast cell data. We found that
10 Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc.
the set of high noise measure genes contained a significantly
higher proportion of cell-type-specific genes than did the set of
low noise genes (Figure 7F; see Figure S7 for classification details). Such findings mirror those showing that more ubiquitously
expressed ‘‘housekeeping’’ genes typically exhibit lower levels
of noise than other types of genes, although the notion of celltype specificity is more difficult to relate to studies performed
in single-celled organisms (Bar-Even et al., 2006; Newman
et al., 2006; Taniguchi et al., 2010).
DISCUSSION
We have shown that individual cells globally control transcription
to compensate for variability in the ratio of DNA to cellular
content. Our results point to two independent mechanisms:
one that compensates for cell size fluctuations and one that
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
compensates for DNA content changes during the cell cycle.
These compensatory mechanisms help to maintain the concentration of mRNA in the cell, which is presumably useful from the
perspective of the cell because the rates of most chemical reactions in the cell depend on concentration rather than absolute
number. Importantly, the fact that these mechanisms seem to
be global in nature, and not gene-specific, means that other
specific forms of transcriptional regulation, for instance, during
development or in response to particular cues, can still function
properly in both large and small cells without the need for a
complex interplay between the specific regulation and the
mechanism governing concentrational homeostasis; indeed,
the expression of most genes is likely not specifically compensated to maintain concentration (Springer et al., 2010). This is
not to say that the concentration of most gene expression products is arbitrary and unregulated. Rather, these global mechanisms provide a means by which any such regulation may operate
to achieve said concentration without having to take into account
differences in DNA content due to cellular volume or DNA content
differences. This is important in a number of biological contexts
such as development and embryogenesis, in which rapid cell divisions lead to an exponential decrease in individual cell volume,
but the organism must maintain the concentration of most proteins while still enabling dynamic transcriptional programs to
occur (Nair et al., 2013).
Our work also highlights the importance of taking cellular volume into account when interpreting gene expression data and
points to the significance of global factors in studying single
cell expression in general (Elowitz et al., 2002; das Neves
et al., 2010; Volfson et al., 2006). In particular, our cell fusion experiments show that changing the amount of cellular content in
and of itself can lead to changes in total RNA abundance,
whereas previous experiments largely relied on cell-size mutants
that make inferences of cause and effect more difficult (Fraser
and Nurse, 1979; Miettinen et al., 2014; Schmidt and Schibler,
1995; Zhurinsky et al., 2010). These cell fusion experiments
directly establish that any perturbation that changes overall
cellular volume may result in global changes in overall transcript
abundance as a secondary rather than primary effect per the
generic mechanism of a diffusible trans factor that senses an
increased ratio of volume to DNA. Thus, we believe one must
take care in interpreting experiments showing global changes
in transcript abundance (Lin et al., 2012; Nie et al., 2012), both
from the perspective of establishing causal relationships, given
that cellular volume/content can by itself change transcription
rates, and in the interpretation of the functional significance,
given that the concentration of many transcripts will remain
roughly the same despite these overall changes. Our study
does not, however, address the question of why cells have
different volumes and how expression plays a role in that heterogeneity—such questions necessarily involve the examination of
mechanisms regulating cell growth and proliferation. Rather,
our results show how cells may globally cope with such changes
to maintain biomolecule concentration.
We do not yet know the factor (or factors) linking the ratio of
cellular volume to DNA content to the amount of transcription.
One potential candidate is some element of the general transcription machinery, such as the RNA polymerase II holoen-
zyme. We have shown that RNA polymerase II is almost completely nuclear, and it is required for transcription; indeed, its
reduction changes burst size, much as reduced volume does.
Its transcription also scales with volume (Figure S4). Other
studies (Marguerat and Ba¨hler, 2012; Zhurinsky et al., 2010)
have speculated that RNA polymerase II holoenzyme may act
as a limiting factor titrated by DNA, but various studies (Kimura
et al., 1999, 2002) show that RNA polymerase II is directly associated with DNA only for short periods of time. Thus, we believe
that the scenario in which the factor remains in the nucleus and
nuclear volume scales only weakly with cell size is the most plausible given our current evidence (see Supplemental Information).
Indeed, our model shows that the weak scaling of nuclear volume with cell size we observe can also explain why we observed
higher mRNA concentrations in smaller cells, sometimes by a
factor of two or more, further supporting this view, although
more experiments will be required to establish this model.
Regardless of the origin of the effect, it is clear that mRNA concentration is typically higher in smaller cells. We do not know the
consequences of this effect, in particular on cell growth, or how it
may vary in different cell types and contexts. One practical
consequence of this finding is that the time-honored practice
of normalizing transcript levels to GAPDH mRNA abundance,
although largely sound, does not fully account for differences
in mRNA concentration between small and large cells. This
suggests that new strategies may be required for measuring
cellular volume when interpreting single-cell RNA-sequencing
experiments.
We found it striking that the volume compensation mechanism
is distinct from the one that compensates for changes in DNA
content as the cell cycle progresses. We found that the burst frequency appears to decrease upon DNA replication for each gene
rather than at a particular time in the cell cycle for all genes. One
plausible explanation for this feature is to ensure proper transcriptional output regardless of whether a gene is replicated
early or late in S phase, which can proceed for many hours.
The molecular underpinnings of this mechanism remain unclear,
although our results demonstrate that it must be a factor that remains bound to DNA and changes in character during DNA replication. A likely candidate may be a DNA or histone modification
that completely coats the DNA during G1 but that is diluted by a
factor of two upon DNA replication in S phase.
Together, these findings provide a deeper quantitative understanding of single-cell gene expression and its role in maintaining cellular homeostasis. Further work may elucidate how
these homeostatic mechanisms for maintaining biomolecule
concentration manifest themselves in biological contexts and
whether they are an important point of dysregulation in disease
processes.
EXPERIMENTAL PROCEDURES
Cell Culture
We grew primary human foreskin fibroblast cells (CCD-1079Sk, ATCC CRL2097) and A549 cells (human lung carcinoma, A549, ATCC CCL-185)
in Dulbecco’s Modified Eagle Medium supplemented with 10% FBS and
50 U/mL penicillin and streptomycin (Pen/Strep). To create quiescent cells,
we grew primary fibroblast cells in DMEM with Pen/Strep, without FBS for
7 days. We cultured WM983b-GFP-NLS cells (melanoma cell line from the
Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc. 11
Please cite this article in press as: Padovan-Merhar et al., Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy
Number through Independent Global Transcriptional Mechanisms, Molecular Cell (2015), http://dx.doi.org/10.1016/j.molcel.2015.03.005
lab of Meenhard Herlyn) in Tu 2% media. The WM983b-GFP-NLS contains
EGFP fused to a nuclear localization signal driven by a cytomegalovirus promoter that we stably transfected into the parental cell line.
RNA Fluorescence In Situ Hybridization and Imaging
We performed single-molecule RNA FISH on the samples as described previously (Femino et al., 1998; Raj and Tyagi, 2010; Raj et al., 2008). We co-stained
the actin cytoskeleton with Phalloidin-Alexa 488 (Life Technologies) to detect
cell boundaries.
We used Cyclin A2 mRNA to specifically label cells in S, G2, and M phases
(Eward et al., 2004). To distinguish cells in S phase from those in G2 (Robertson
et al., 2000; Whitfield et al., 2002), we labeled histone H4 mRNA (see Figure S3).
Table S1 lists all sequences of oligonucleotide probes.
We imaged the cells with a Nikon Ti-E equipped with appropriate filter sets.
We took a series of optical z sections, each 0.2–0.35 microns high, that
spanned the vertical extent of the cell.
Image Analysis and Quantification
We manually identified cell boundaries and counted and localized RNA spots
using custom software written in MATLAB (Raj and Tyagi, 2010; Raj et al.,
2008). We estimate the technical error in our RNA count determination to be
at most 15%.
To compute the volume of a cell, we used the 3D positions of a highly abundant mRNA found by RNA FISH to define the outline of the cell, applying corrections for bias in volume estimation. The volume computation did not
depend on the number of spots identified nor on the choice of mRNA (Figure S1). We limited ourselves to the cytoplasmic volume by removing a vertical
cylinder corresponding to the nuclear outline.
We identified transcription sites through intron/exon probe colocalization.
We manually annotated transcription sites by visually inspecting images of
intron and exon probes to determine instances of colocalized signal and
computationally determined their intensity.
RNA Degradation
We measured UBC and IER2 mRNA degradation by inhibiting transcription for
4 hr by applying actinomycin D at 1 ug/ml. We interpreted the data using
models of volume-dependent or -independent degradation.
LMNA siRNA Knockdown
We incubated primary fibroblast cells with an siRNA targeting LMNA for 72 hr,
verifying protein knockdown via western blot.
Heterokaryon Formation
We created heterokaryons by pelleting cultures of primary fibroblast cells
and WM983b-GFP-NLS cells and resuspending in PEG for 2 min. We
added media over the course of 5 min to allow cells to fuse, and then we
plated the cells onto two-well chambered coverglasses (Lab-Tek) and fixed
the cells after 12 hr.
Fractionation and RNA Polymerase II Western Blot
We performed cell fractionation and blotting as described in (Bhatt et al., 2012)
and based on (Wuarin and Schibler, 1994) with modifications.
Triptolide
We degraded RNA polymerase II in primary fibroblast cells by incubating cells
in 100 nM triptolide for 1 hr and then fixed cells in methanol.
Repli-seq Analysis
We accessed Repli-seq data from Hansen et al. (2010) using the UW Repli-seq
track on the UCSC Genome Browser.
Bulk RNA Sequencing
We sequenced total RNA from primary fibroblast cells. We used the NEB Next
Ultimate Library Preparation Kit for Illumina and the Ribo-Zero Magnetic Gold
Kit. We used 50 b single-end reads and sequenced each of two replicates at a
depth of 10–15 M reads. We aligned reads to hg19 using STAR’s included
annotation. We quantified reads per gene using HTSeq and a RefSeq hg19
12 Molecular Cell 58, 1–14, April 16, 2015 ª2015 Elsevier Inc.
annotation. We calculated FPKM for each gene using R. All sequencing data
are available at GEO accession number GSE66053.
Single-Cell RNA Sequencing
We prepared 96 cells for RNA sequencing on a Fluidigm C1 Single-Cell Auto
Prep System using a large-size chip. We added ERCC (External RNA Controls
Consortium) RNA controls, Mix 1 (Ambion 4456740) at a concentration of
1:10,000 before loading and prepared cDNA libraries as per the Fluidigm instructions. We obtained 75b paired-end reads to a depth of 1–2 M reads per sample.
We quantified reads per gene using HTSeq and a RefSeq hg19 annotation and
transformed the data to obtain an estimate of molecule count per cell. All
sequencing data are available at GEO accession number GSE66053.
C. elegans Growth and Imaging
We grew N2 (wild-type) and CB502 (sma-2 mutant) C. elegans at 20 C under
standard conditions. We performed RNA FISH and analyzed the data as previously described (Raj et al., 2008), determining the volume of each analyzed
region computationally.
ACCESSION NUMBERS
The GEO accession number for the single-cell RNA sequencing (primary fibroblast cell line) and the bulk RNA sequencing (primary fibroblast and lung cancer cell lines) data reported in this paper is GSE66053.
SUPPLEMENTAL INFORMATION
Supplemental Information includes Supplemental Experimental Procedures,
seven figures, and one table and can be found with this article online at
http://dx.doi.org/10.1016/j.molcel.2015.03.005.
ACKNOWLEDGMENTS
We thank members of the Raj lab for many helpful suggestions. We thank
Jeff Carey for suggesting the LMNA knockdown experiment and Sydney
Shaffer for the WM983b-GFP-NLS cell line. We thank Jan Skotheim for useful
discussions about mechanism and John I. Murray for pointing out that the
simple trans factor model would lead to overtranscription in early S phase.
We thank Hyun Youk and Uschi Symmons for a careful reading of the manuscript. We thank the Herlyn lab for providing the WM983b cell line. A.R. acknowledges support from an NSF CAREER award, NIH New Innovator Award
1DP2OD008514, and a Burroughs Wellcome Fund Career Award at the Scientific Interface. G.P.N. is a Howard Hughes Medical Institute Fellow of the Life
Sciences Research Foundation (http://www.lsrf.org). A.M. was supported by
Long-Term Postdoctoral Fellowships of the Human Frontier Science Program
(LT000314/2013-L) and EMBO (ALTF858-2012). L.S.C. acknowledges support
from an NIH grant (NHGRI R01HG007173), a Damon Runyon Cancer Research
Foundation Frey Award, and a Burroughs Wellcome Fund Career Award at the
Scientific Interface.
Received: September 22, 2014
Revised: January 16, 2015
Accepted: March 4, 2015
Published: April 9, 2015
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Molecular Cell
Supplemental Information
Single Mammalian Cells Compensate for Differences
in Cellular Volume and DNA Copy Number through
Independent Global Transcriptional Mechanisms
Olivia Padovan-Merhar, Gautham P. Nair, Andrew G. Biaesch, Andreas Mayer, Steven
Scarfone, Shawn W. Foley, Angela R. Wu, L. Stirling Churchman, Abhyudai Singh, and
Arjun Raj
D
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Cytoplasmic RNA concentration
(cycling) (count/pL)
10
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Volume calculated from
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Volume calculated from
GAPDH (pL)
1.00
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V
expression (Quiescent)
●
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0
Cytoplasmic RNA concentration
(quiescent) (count/pL)
●
Live
Fixed
Permeabilized
Volume calculated from
EEF2 (pL)
Single cells
C
E
Cell height (µm)
B
4000
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Volume calulated from half
GAPDH molecules (pL)
A
Cell area (µm2)
Supplemental Figure 1
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Figure S1, related to Figure 1.
A and B. We monitored primary fibroblast cells on the microscope throughout the process of fixation. We took measurements of the same cells live, after
fixing in 4% formaldehyde for 10 minutes, and after permeabilizing in ethanol for 30 minutes.
A. We measured the areas of the cells through brightfield images.
B. We measured the height of the cells by coating the cells with fluorescent beads. These measurements indicate that the cells remain roughly the same
size throughout the fixation and permeabilization process.
C. To demonstrate the robustness of the volume calculation algorithm, we calculated volume for the same cells using all the GAPDH mRNA spot coordinates as detected by RNA FISH, or using only half of the points, chosen randomly. Both methods result in approximately the same volume, suggesting
that the number of points we use is sufficient to calculate the volume accurately.
D. We calculated volume using a different gene, EEF2. On average, EEF2 has an abundance that is less than half that of GAPDH (mean EEF2 = 1079
mRNA/cell, mean GAPDH = 2673 mRNA/cell). Volume calculated using EEF2 is systematically lower than that calculated using GAPDH, but the values
are similar.Black lines in C, D indicate a fit with intercept = 0 and slope = 1.
E. mRNA concentration is similar in cycling and quiescent cells. We calculated the average mRNA concentration for 17 genes in both the cycling and
quiescent state in human foreskin fibroblast cells. Each data point represents one gene. Each gene had a minimum of 2 biological replicates, with at least
thirty cells per replicate. Line has intercept 0 and slope 1. Error bars represent standard error.
F,G. We compared volume-dependent and -independent abundance for cycling and quiescent cells. Both volume-independent and volume-dependent
expression are lower in quiescent cells. All error bars represent confidence intervals of the slope or intercept of the fit, normalized to the scale of the plot.
In C and D, we omitted error bars that extended below zero. Each gene had a minimum of two biological replicates, with at least 30 cells per replicate.
We omitted highly variable genes with intercept terms less than zero.
Supplemental Figure 2
ACTA2
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●● ●
●●
●
●●
●
●
●●●
●
●●●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●●
●
●
●
● ● ●●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●●
●●
●
●●●
●
●●
● ●●
● ●
●●● ●
●
●
Volume (picoliters)
●
rRNA Intensity (a.u.)
● ●●● ●
●
●●
● ● ●
●
●●
●
●
●
● ●
●●
●
●
●
●●
●●
●
●
●●●
●
●
●
●
●
●●●
●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●●
●
LMNA
400
300
200
100
0
●
30
20
10
0
80
60
40
20
0
●
●
●
●●
● ●● ●
●
●
● ● ●
● ●
● ●●●● ●●
●●
● ● ● ●● ●
● ●●
●
●●●
● ● ●
●
GAA
15
10
5
0
20
15
10
5
0
●
●
200
150
100
50
0
●
100
50
0
BABAM1
40
30
20
10
0
●
USF2
●
●
●●
●●
●●
● ●● ●
●
●●
●
●
●●
●
●●●●●●
●●● ● ●
● ●●
●●
●
●
●
●
●●●
●
●
●
●
●● ● ●
●●●● ● ● ●
0.0
2.5
5.0
7.5
60
40
20
0
MYC
●
SUPT5H
●●
●
●
Volume (picoliters)
ACTN4
600
400
200
0
●
●●
●●●
●
●
●● ●
●●●
●
●
●
●●●● ●●
●●
●●
●
●
● ●●
●
●
●
● ●●
●
●●
●
●
● ●
●
●
●
●
●
●
●
● ●
●
● ●
●
●
●
●
●
●●
●●●
●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●
● ●●
●●●
●
●●
●● ●● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●●
●●●●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
● ●●●
●
●●
●● ● ●
●
●
●●
●●
●
●
●●
●
200
100
0
●
●
●
●●
●
●●
●●●
●
●
●
●●
● ●
●●
●
● ●●
●●
●●●
●● ●
●●●
● ● ●
●●
●●●●
●
●
●
●●●●
●● ●
●
●●
● ● ●●
●
●
RBM3
●
150
100
50
0
●
● ●
●
●●● ●●
●
●
●●●● ●
●
●
●
●●
●
●●
●● ●
●●
●
●
●
●
●
●
●● ●
●●●
●●
●
●
●●
●
●●
●
●
●●
●
●●
IER2
●
●
●●
LUM
●
●
●
● ●●● ●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●● ●
●●
●
●
●
●●
●●
●
●
●
●●
●●
●●●●
●
●
●
●●●
400
300
200
100
0
●
●
●
●
●
●● ●● ●●●
●
●
●
●●
●
●●●●●
●●●●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
ICAM1
80
60
40
20
0
● ●●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●●
●●
●
●●
●● ●
●●●
●● ●●●
●
●
●●
●● ● ●●
●
●
●●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●●
●
●
● ●
●●
●
●
●
900
600
300
0
1200
800
400
0
●
●
●● ●● ●
● ●●●
●●●
●●
●
●
●
●●
●●●●
●
●
●
●●
●●
●
●
●
●
●●●●
●
●
●●●●
●
●
●
●
●●●
●
0.0
2.5
5.0
7.5
● ●●●
● ●
● ●
● ●●●●
●●
●● ●
● ●
●●
● ●●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●●●
●
●
●●
●●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
● ●●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
KDM5A
15
10
5
0
GAS6
●
FTL
10000
7500
5000
2500
0
●
●
● ●
● ●
●●
●
●●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
● ●
●●
●
●
●
●
ZNF444
400
300
200
100
0
●
● ●●
● ●●
●
● ●
●
●
● ●
●●
●
●
●
● ●●
● ●●●
●
●
●
●
●●
●
●
●●●●
●
●
●
●●●●
● ●
SLC1A5
●
●
40
30
20
10
0
●
●
●
●●
LMNA
1000
500
0
●
●
● ●●
●
●
● ● ●
●
●●●●●
●
●
●●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●●●●
●
●●
●
●
●●
●
●●
●●
ACTA2
●
●●
● ●
●●
●●
●●
●●
●
●●
●
●●
●
●
●
●●●
●●●
●●●
●
●
●
●
●
●● ●
●
●
●
●●
● ●
●
●
●
●
●
●●
●
●
●●●
0.0
2.5
5.0
7.5
mRNA Concentration (count/pL)
800
600
400
200
0
200
100
0
EEF2
3000
2000
1000
0
●
●
● ●
●
●
●
●●●
●
●
● ●
●●
●●
●●
●●
●
● ●●
GAPDH
RND3
0.0
2.5
5.0
7.5
B
DNMT1
●
●●
● ●
●●●
●
●● ●●● ● ● ●
●
●
●
●● ●
●●
●
●
●
●●
●●● ●●
●●
●
●
●●
●
●
● ●●● ●
●
●
●● ● ●
●●
●● ●
● ●
●
● ●
●
●
●●●●
●●
●●
●
●
●● ●●
●●●
●
●
●
●
●
●
●
●●●
●
●
● ●
●
●● ●●
●
●
●
USF2
●
● ● ●
●
●
●●● ●●
●
●●
●
●●
●
●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●●
●●●
●
●
●●
●
●
●●●●●
●
●
● ●●
BABAM1
KDM5B
80
60
40
20
0
1500
1000
500
0
●●
●●●
●
●
●
●●
●
●
●●●●● ●
●
●
●
●
●
●
●●
●●
●
●
●●●
●
●●●
●●●
● ●
●
150
100
50
0
8000
6000
4000
2000
0
●
● ●●
●●
●
●
●
●
●●●
●
●● ● ● ●
● ●● ●
●●
●
●
●●
●
●
●
●●
●
●
● ●●
●●
●
●
●
●
● ●
●
●
●
●
●
RBM3
400
200
0
125
100
75
50
25
0
●
●
●
●
●
●
●
●
●
● ● ●
●
●
● ●
●
●●●
●●
●
●●
●●
●
●●●●
●●
●
●●
●
●●
●●● ●
●
●●●
●
●
●
●●
●●
●
●
●
50
40
30
20
10
0
●
●● ● ●
●
●
●
●
●●
●●●
● ●●
● ● ● ●
●
●
●
●●● ●
●●
●
●●
●●
●
●●
●
●
●
●
●
●●
●
●
50
40
30
20
10
0
ACTN4
1500
1000
500
0
●
2000
1500
1000
500
0
2.0e+09
1.5e+09
●
●
●
●
1.0e+09
●
●
● ●
●
● ●●
●
●●
● ●
●
●
●
●
●●
●
●
●
5.0e+08
●
0.0e+00
0
1
2
3
4
Volume (picoliters)
D
rRNA ITS Intensity (a.u.)
A
●
●
●
7.5e+07
●
●
●
5.0e+07
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
2.5e+07
●
0.0e+00
0
1
2
3
4
Volume (picoliters)
Figure S2, related to Figure 1.
A, B. mRNA count (A) and concentration (B) measurements for all genes in cycling fibroblast cells. Each data point is an individual single cell measurement. In count plots, red line indicates best linear fit to the data. In concentration plots, red line indicates mean mRNA concentration. Each data set is a
combination of at least two biological replicates.
C. We measured ribosomal RNA by quantifying total fluorescence intensity in the cytoplasm from an rRNA FISH probe in cycling fibroblast cells.
D. We measured the rRNA ITS (the rRNA “intron”) by quantifying total fluorescence intensity in the nucleus from an ITS RNA FISH probe.
rRNA and the rRNA ITS both scale with volume to some degree, suggesting that the production of ribosomal RNA scales with volume. We have shown
that mRNA scales with volume, so a similar scaling of rRNA is not inconsistent with the production of protein to scale with volume as well. The data shown
for rRNA is one of three biological replicates.
Supplemental Figure 3
A
B
G1
G2
●
0.4
S
Fraction of cells
G1
G2
1000
●
●
500
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0
●
●
●
● ●
●
●
●
●
●●
●
●
● ●● ● ●
●●
● ●●
●
●
●
● ●
0
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
● ●
●●●
● ●●
●●● ●
●
●
100
●
●
●
●
●
200
300
Cyclin mRNA
●
0.0
2.5
5.0
7.5
Volume (picoliters)
●
●
●
●
●
●
●
●
●
●
●
● ●
● ●
● ● ●●
●
●
●
●
●
●●
●
●
●
● ●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
● ●
●
●
●● ● ●
●
●
●●
●●
●
●
● ●
●●
●
● ●●
●
●
●● ●
●● ●
● ●● ● ●
●
●●
● ●● ● ● ●●● ● ●●
● ●●
●
●
● ● ●
●
●
●
●
●● ●
●● ●
●
●●
● ●
● ●●● ●● ● ●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●●
● ●
●
●
●
● ●●
●
●
● ●●●●●
●● ●
●
● ●●●
● ●●
●●● ● ●●
●
●
●
●● ●●●●
●
●
●
●●
●●
● ● ●●
● ● ●●●
● ●●
●
● ●
● ●● ●●●
● ● ●●
●
●● ●
●●
●●● ●
●
●
●●●● ● ●●●
●
●●●●●●●●
●●
●●
●
● ●
●●●● ●●
●●
●●
● ●
●●
●●●●●
●●●●●
●
●
●
●●
●●
●● ● ● ●●●
●
●
●● ●● ●● ● ● ●
●●
●● ●
●
●
●
●
●●
●
●●●
●
●●
●●●
●●
●●
● ●
●●●
●●
●
●
●●
● ●
●●●
●
●
●
● ●●
●
●
●● ●
● ●●
●
●
●● ●
●●●
●●
●●●●●
●
●●
●●
●
● ● ●●
●
●●
●
●
●
● ● ●
●
●
●●
●
●●
●
●
●
●
●● ●
●●
●
● ●
●
●
● ●●● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●●
●
●
● ●●●●
●
● ●
●
●
●
●●
●
●
●
● ●●
●
●
●●
●
●●
●
●
●●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●●●●
●
●
●●
●
●
●
●
● ●●●
●
●●
●
●●
●●
●●
●●
●
●
●●
●
●●
●
●
●●●●●●
● ●
●
●
●
●●
●●
●●●
●
●
●
●
●
●
●
●●
●●
●●
●●
●
●
● ● ●●
●
●
●
●●
●●
●
●
●
●●●
●
●
●
●●
●
●
●●
●
●● ●
●
●●●● ●
●
●●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●●● ●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
● ●● ● ●●
●
●
●●●
●●
●
●
●● ●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
● ●●●
●
●
●●
●
● ●●
●
●
●
● ●●● ● ●●● ●● ●
●
●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●● ● ●●
●
● ●● ●
●
●
●
●
●●
●●
●
● ●●● ●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●● ●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●
● ● ● ● ●●● ● ●●
●
●
●
●
●
●
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Histone mRNA
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5.0
7.5
Cellular volume (picoliters)
100 200 300 400 500 600
Nuclear Area (µm2)
Figure S3, related to Figures 1, 5, 6.
A. We simultaneously measured CCNA2 and HIST1H4E mRNA by RNA FISH to precisely determine cell cycle position. Each data point is a single cell
measurement. CCNA2 is highly expressed in S and G2, but not G1. HIST1H4E is highly expressed only in S phase. Cells with low CCNA2 and
HIST1H4E are in G1 (cutoff = 20 CCNA2 mRNA), cells with mid-range CCNA2 and high HIST1H4E are in S, and cells with high CCNA2 and low
HIST1H4E are in G2 (cutoff = 230 CCNA2 mRNA). We determined thresholds for all samples using this method. Data shown are from one of four biological replicates.
B. Volume distributions in G1 and G2. We determine cell cycle position using CCNA2. We note that G2 cells are larger than G1 cells, but only 10% larger
on average, possibly due to non-linearities in growth over the course of the cell cycle. n = 841 cells in G1, 191 cells in G2.
C. Nuclear area vs. cytoplasmic volume. We measure cytoplasmic volume using our standard method. We measure nuclear area using the DAPI stain.
We note that we only measure nuclear area and not volume.
D. Density plot of nuclear area across cell cycle stages. While nuclear area generally scales with cytoplasmic volume, there is considerable spread in
the data (R2 = 0.358). n = 1866 cells.
Supplemental Figure 4
B
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POLR2A RNA
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2000
Volume (picoliters)
D
2.0
UBC mRNA
Mean number of transcription
sites per cell
●
C
UBC
Mean number of transcription
sites per cell
A
Triptolide Concentration
E
EEF2
MYC
MYC
2.0
1.5
1.0
0.5
0.0
Control 100nM
Triptolide Concentration
UBC
TUSC3
G1
GM
12878
S
G2
WS
G1
K562
S
G2
WS
G1
HeLa
S
G2
WS
G1
HepG2 S
G2
WS
G1
HUVEC S
G2
WS
Figure S4, related to Figures 5 and 6.
A. Quantification of RNA Polymerase II mRNA (quantified by RNA FISH) vs. cytoplasmic volume in A549 cells. Data shown is from a single biological
replicate.
B,C.We treated primary fibroblast cells with 100nM triptolide (100nM) or simply replaced the media on cells (Control) and fixed in methanol after one
hour. For genes UBC and MYC, we identified active transcription sites through intron/exon colocalization and quantified the number of active transcription
sites per cell with and without triptolide. Bars represent mean of cells, error bars are SEM. The data shown here is from two replicates, for a total of 282
cells for UBC and 257 cells for MYC. For both genes, the change in frequency between conditions is small compared to the change in intensity (Fig. 5).
D. UBC mRNA in a CRL2097 cell. RNA FISH probe in white, DAPI stain in purple. White arrows indicate transcription sites. We detect transcription sites
through intron/exon colocalization by RNA FISH. This cell is in G2 and has four transcription sites, demonstrating that all gene copies are transcriptionally
competent after replication.
E. Tracks from UCSC genome browser displaying UW Repli-Seq data in GM12878 (lymphoblastoid), K562 (chronic myelogenous leukemia), HeLa
(cervical cancer), HepG2 (liver carcinoma), and HUVEC (human umbilical vein endothelial) cell lines. The track displays data for different points in the
cell cycle: G1, S1 (early S phase), S2 (middle-early S phase), S3 (middle-late S phase), S4 (late S phase), and G2. WS represents a wavelet-smoothed
transform of the six other tracks. This data was generated by sequencing newly-replicated DNA in each point in the cell cycle. Darkness of track
corresponds to read density. Each track shown corresponds to entire length of each gene. Data is shown for early replicating genes EEF2, MYC, UBC,
and a late replicating gene, TUSC3.
Supplemental Figure 5
B
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CV2 RNA Concentration
Nm
C
0.75
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ICAM1
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MYC
RND3
Volume-corrected
Noise Measure
2.5
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V
TBCB mRNA Concentration
A
0.25
ZNF444
USF2
UBC
TBCB
SUPT5H
SLC1A5
RBM3
PABPC1
LMNA
KDM5B
KDM5A
IER2
GAS6
GAPDH
GAA
FTL
EEF2
DNMT1
BABAM1
ACTN4
0.00
Figure S5, related to Figure 7.
A. TBCB mRNA concentration vs. volume. These data are the same as in (Fig. 7A), but each is normalized by volume. Histogram indicates distribution
of mRNA concentration. Gray line indicates average concentration. Data are from a combination of two biological replicates.
B. We compared volume-corrected noise measure and mRNA half-life. We obtained half-life values from Tani et al., Genome Res. (2012). We find that
volume-corrected noise measure does not depend strongly on half-life. Each data point represents one gene. For each gene, we have at least two biological replicates with at least 30 cells per replicate. Error bars represent 95% confidence intervals, calculated by bootstrapping.
C. mRNA CV, concentration CV, and volume-adjusted CV for cycling primary fibroblast cells. Inset shows genes that exhibit higher cell-to-cell variability
in RNA, and had values too high for main axes. Generally, mRNA CV is highest, followed by concentration CV and volume-adjusted CV. Error bars
represent 95% confidence intervals by bootstrapping.
Supplemental Figure 6
A
B
1e+06
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C
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D
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y = 1.07x-532
●
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0.50
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Normalized Genomic/ERCC
FPKM ratio
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Figure S6, related to Figure 7.
A. Mean FPKM and known concentrations for each of the ERCC reference transcripts. Each point represents a single ERCC transcript and is an average
over all 96 samples. Below 10 FPKM, we begin to see significant dropouts, and therefore choose and FPKM of 10 as our cutoff for “reliable” measurements. All other data in the manuscript is taken from genes having greater than 10 FPKM.
B. Mean count as measured by RNA FISH vs. mean FPKM from single-cell RNA sequencing. Each point represents a single gene and is an average
over 44 single cells for single-cell sequencing, and an average over at least two biological replicates with at least 30 cells apiece for RNA FISH. These
data suggest that an FPKM of 1 corresponds to approximately 23.2 transcripts per cell, as measured by RNA FISH in our cells, although the relationship
between RNA FISH counts and FPKM scales nonlinearly (FPKM ~ (FISH)1.7, see Methods). We used this fitted relationship between RNA FISH count
and FPKM to transform FPKM into transcript counts. Error bars represent SEM.
C. Comparison of “total RNA” distributions from single-cell sequencing and RNA FISH. Data represent a collection of total RNA measurements from
single cells. We assume that total GAPDH mRNA counts by RNA FISH are proportional to total RNA. For sequencing data, we use the ratio of reads
mapped to genomic loci to reads mapped to ERCCs as a proxy for total RNA. We scaled this ratio to have the same mean as the distribution of total RNA
by RNA FISH. After scaling, the distributions are similar, suggesting that our method for measuring total RNA via the ratio of genomic to ERCC transcripts
is sound.
D. Mapping between total RNA count (here, total GAPDH mRNA in single cells) and volume, as measured by RNA FISH. Each point represents a single
cell. We use this mapping to convert total RNA from sequencing experiments to actual volume. The red line is the best fit, as computed by principle
components analysis.
3e+05
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2e+05
1e+05
0e+00
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200000
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"Good” cells
Eliminated cells
150000
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100000
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50000
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30
60
90
120
Genomic/ERCC count ratio ("volume")
E
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D
10.0
1.0
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0.1
FPKM CV2
(single-cell RNA sequencing)
●
Count CV2
(single-cell RNA sequencing)
B
4e+05
Summed ERCC counts
A
GAPDH FPKM * count ratio ("count")
Supplemental Figure 7
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r = 0.5898
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F
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Count CV2 (RNA FISH)
0e+00 1e+06 2e+06 3e+06
Summed genomic counts
10.0
1.0
10.0
Count CV2 (RNA FISH)
G
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ACTA2
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1
2
3
Log 10 (mean FPKM)
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Log 10 (Transformed Nm)
Mean mRNA (A549)
●
10.0
1000
10
●
Volume-corrected noise measure
(A549)
ACTA2
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1
0
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Cutoff for high Nm genes
Cutoff for low Nm genes
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4
1
2
3
Log 10 (mean FPKM)
4
Figure S7, related to Figure 7.
A. “Count” vs. “volume” for GAPDH from single-cell sequencing data. We define “volume” as the ratio between genomic reads and ERCC reads for each
cell. This quantity is more representative of total RNA, which we know to be roughly proportional to volume, although the relationship is not exactly
proportional due to volume-independent transcription (see main text Figure 1). We observed two clearly distinct classes of cells, those with a volume
range that matches what we see by imaging and RNA FISH and those that have very low volumes. For unknown reasons, these cells ended up with a
considerably higher ratio of ERCC reads than genomic reads, and we eliminated them from our subsequent analyses.
B. ERCC counts vs. genomic counts for the cells that we kept and those we eliminated.
C. Correspondence between CV2 of RNA FISH counts and CV2 of inferred counts from single-cell sequencing (transforming FPKM as in Supplemental
Figure 6 and Methods). Each data point represents a single gene.
D. Same as C, except using CV2 of FPKM from single-cell sequencing instead. Correlation is slightly higher than in C.
For C and D, error bars represent 95% confidence intervals, calculated by bootstrapping.
E. Average mRNA counts in cycling primary fibroblasts and A549 cells, calculated using RNA FISH. Gray line indicates a 1:1 correspondence. Error bars
represent standard error of the mean.
F. Volume-corrected noise measure in cycling primary fibroblast and A549 cells, calculated using RNA FISH. Gray line indicates a 1:1 correspondence.
Nm calculated by bootstrapping; error bars represent 95% confidence interval. Data in E and F for each gene is a combination of at least two biological
replicates, with at least 30 cells per replicate.
G. FPKM measurements from bulk RNA-sequencing in primary fibroblast and A549 cells. Each point represents one gene. We classified genes as
“ubiquitously expressed” if they had >5 FPKM in both cell types and differed by less than a factor of 2 in FPKM across the two cell types. We considered
genes “fibroblast specific” if they had >5 FPKM in fibroblasts and their FPKM was greater than five times higher in fibroblasts that A549 cells.
H. Single-cell RNA-sequencing data in primary fibroblast cells. Each point represents one gene. We used the method described in Supplemental Figure
6 and Methods to calculate Nm for each gene. We observe that higher abundance genes typically have lower Nm values. Red line indicates best fit line.
I. The same data as in H, but transformed to remove the abundance dependence from Nm. Red line here is transformed fit line from H. We use this
transformed data to select abundance-matched “low” and “high Nm” genes using a cutoff of Nm=0.5 and Nm=-0.5, respectively. We selected 307 high
Nm genes and 257 low Nm genes. Note that these high Nm genes actually have a higher mean abundance (FPKM=196.5) than the low Nm genes
(FPKM=55.4), thus showing that the observed differences in noise levels are not due to the overall increase in noise in genes of low abundance.
Supplemental Experimental Procedures
Cell culture:
We grew primary human foreskin fibroblast cells (CCD-1079Sk, ATCC CRL-2097™) and A549
cells (human lung carcinoma, A549, ATCC CCL-185™) in Dulbecco’s Modified Eagle Medium
(DMEM) supplemented with 10% FBS and 50U/mL penicillin and streptomycin (Pen/Strep). To
create quiescent cells, we grew primary fibroblast cells in DMEM with Pen/Strep, without FBS
for seven days. We cultured WM983b-GFP-NLS cells (WM983b is a human melanoma from the
lab of Meenhard Herlyn) in Tu2% media (78% MCDB media, 20% Leibovitz’s L-15 media, 2%
FBS, and 1.68 mM CaCl2). The WM983b-GFP-NLS contains EGFP fused to a NLS driven by a
cytomegalovirus promoter that we stably transfected into the parental cell line. Before imaging,
we plated cells on two-well Lab-Tek chambered coverglasses.
RNA fluorescence in situ hybridization and imaging:
We performed single molecule RNA FISH on the samples as described previously (Femino et
al., 1998; Raj and Tyagi, 2010; Raj et al., 2008). Briefly, we fixed the cells in formaldehyde or
methanol, performed RNA FISH using the specified pools of oligonucleotides, then washed and
stained nuclei with DAPI. We fixed most cells in this study using formaldehyde, but used
methanol for the experiments involving transcription site quantification because it resulted in
more accurate transcription site detection. We stained the actin cytoskeleton with PhalloidinAlexa 488 (Life Technologies) to detect cell boundaries.
We typically co-stained with sets of probes targeting many different mRNA. Typically, we used
exon probes labeled in Alexa 594, introns with Cy3, Cyclin A2 with Atto 647N (which labels cells
in S, G2 and M phase (Eward et al., 2004)) and GAPDH with Atto 700. To distinguish cells in S
phase from G2 (Robertson et al., 2000; Whitfield et al., 2002), we labeled Histone H4 mRNA
with Atto 647N and Cyclin A2 mRNA with Atto 700 (see Supplemental Fig. 3). Supplemental
data file 1 lists all sequences of oligonucleotide probes.
We imaged the cells with a Nikon Ti-E equipped with appropriate filter sets. We took a series of
optical z-sections, each 0.2-0.35 microns high, that spanned the vertical extent of the cell.
Image analysis and quantification:
We manually identified cell boundaries and counted and localized RNA spots using custom
software written in MATLAB (Raj and Tyagi, 2010; Raj et al., 2008). We estimate the technical
error in our RNA count determination to be at most 15%.
To compute the volume of a cell, we detected the 3D positions of a highly abundant mRNA by
RNA FISH. We selected only the points that defined the outer boundary of the cell by examining
each point and its neighbors within a 4µm radius. We kept only the points that had a higher zposition than their neighbors (signifying the top of the cell) or points that had no neighbors within
180 degrees (signifying the side of the cell). Once we had the points, we interpolated the points
to identify a smooth representation of the cell surface. We repeated this in both an upward and
downward direction to identify the top and bottom of the cell. We calculated the volume of the
cell by summing the heights between the top and bottom.
Calculating the volume in this manner will always result in an underestimation of the actual
volume. To correct for this bias, we first computed the outline of the cell as described above. We
then dilated this hull, filled it with the same number of randomly distributed points, and then
repeated the algorithm on this new set of points. If this volume matched that computed with the
actual spots in the cell, we then computed the volume by integrating between the top and
bottom boundaries of the dilated hull.
We used GAPDH mRNA as the primary mRNA for our volume determinations, but the volume
computation did not depend on the number of spots identified nor on the choice of volume-filling
gene (Supplemental Fig. 1). We limited ourselves to the cytoplasmic volume by removing a
vertical cylinder corresponding to the nuclear outline. This procedure does exclude the
cytoplasmic volume above and below the nucleus, but that region only comprised a very small
proportion of the total cytoplasmic volume.
We identified transcription sites through intron/exon probe colocalization. We manually
annotated transcription sites by visually inspecting images of intron and exon probes to
determine instances of colocalized signal. To determine spot intensity, we identified the z-plane
of maximum intensity in a 0.375µm-square region around the manually selected spot. We
defined the intensity as the difference between this maximum value and a background value.
For the background value, we used the median intensity in a 3.75µm-square annular region
around the maximum intensity point. Note that transcription site intensity need not necessarily
linearly relate to transcriptional burst size (Senecal et al., 2014).
RNA degradation:
We measured RNA degradation by inhibiting transcription for four hours by applying
actinomycin D at 1ug/ml. We measured degradation of UBC and IER2 mRNA because they
exhibited a strong correlation with volume while having a half-life short enough to enable us to
observe substantial degradation within four hours of actinomycin D treatment while avoiding
non-specific effects at longer times.
We used a model to determine whether degradation was volume-dependent (degradation ~ 1/V)
or volume-independent (degradation ~ constant). We first fit the untreated mRNA vs. volume
data with a line having zero intercept. If degradation is volume-independent, we expect the
treated cells to also be well-fit by a line having zero intercept, where the slope is determined by
the untreated fit and an exponential decay term:
!!" (!) = !! !! !!" ,
where !!" is the mRNA count after 4 hours of treatment, !! is the slope of the untreated data
(! = 0), ! is the decay constant (degradation rate), and ! is the treatment time. Note that here !
is the only fit parameter and is independent of volume.
If degradation is volume-dependent, the equation becomes:
!!" (!) = !! !! !!"/! .
Here, !/! is the decay constant (degradation rate), but ! itself is independent of volume and is
the fit parameter.
The line and curve described by these equations are the fits to the raw data, and the decay
constants ! and !/! are the fits we show to the calculated decay constants that we show in Fig.
3A-B.
We calculated the actual decay constant (Fig. 3A-B) for each cell measured at the 4 hour
timepoint assuming exponential decay:
!!" (!) = !!" (!)! !!" ,
where we approximate !!" = !! !, and ! could in principle be either volume-dependent or independent.
LMNA siRNA knockdown:
We used an siRNA targeting LMNA (Cat. #: AM16708, ID: 40502) at 30nM and a “scramble”
control siRNA (Cat. #: AM4611) at 30nM. We incubated primary fibroblast cells with the siRNA
for 72 hours. We verified protein knockdown via Western blot, using the SC-20680 (rabbit)
antibody and a goat-anti-rabbit 680 RD secondary (Licor 926-68071).
Heterokaryon formation:
We created heterokaryons by separately culturing primary fibroblast cells and WM983b-GFPNLS cells. Once the plates were 70-90% confluent, we trypsinized the cells, resuspended them
in DMEM Complete media, and combined half of each plate of cells in a 15ml tube. We pelleted
the cells and resuspended in PEG for 2 minutes. We added media over the course of five
minutes to allow cells to fuse, then plated the cells onto two-well chambered coverglasses (LabTek) and fixed the cells after 12 hours.
We identified heterokaryons as cells with two nuclei that expressed both GFP (WM983b-GFPNLS only) and GAS6 mRNA (primary fibroblast) by RNA FISH. We eliminated all homokaryons
from our analyses.
Fractionation and RNA polymerase II Western blot:
We performed cell fractionation as described in (Bhatt et al., 2012) and based on (Wuarin and
Schibler, 1994) with modifications. We conducted all subsequent steps on ice or at 4°C and in
the presence of 25 µM α-amanitin (Sigma, A2263) and Protease inhibitors cOmplete (Roche,
11873580001) according to manufacturer’s instructions. We pre-chilled all buffers on ice before
use. We grew primary fibroblast cells to a confluency of 90%. We removed media and washed
plates twice with 1x PBS before scraping cells into 1x PBS. We collected cells by centrifuging at
500 g for 10 min. We gently resuspended the cell pellet corresponding to 1x107 cells in 200 µl
cytoplasmic lysis buffer (0.15% NP-40, 10 mM Tris-HCl pH 7.0, 150 mM NaCl). We incubated
the cell lysate for 5 min on ice, layered it onto 500 µl sucrose buffer (10 mM Tris-HCl pH 7.0,
150 mM NaCl, 25% sucrose) and centrifuged at 16,000 g for 10 min. We carefully removed the
supernatant (600 µl) corresponding to the cytoplasmic fraction. We gently resuspended the
nuclei pellet in 400 µl nuclei wash buffer (0.1% Triton-X-100, 1 mM EDTA, in 1x PBS) and
centrifuged it at 1,500 g for 1 min. We removed the supernatant and gently resuspended the
pellet in 200 µl glycerol buffer (20 mM Tris-HCl pH 8.0, 75 mM NaCl, 0.5 mM EDTA, 50%
glycerol, 0.85 mM DTT). Next, we added 200 µl nuclei lysis buffer (1% NP-40, 20 mM Hepes pH
7.5, 300 mM NaCl, 1M Urea, 0.2 mM EDTA, 1 mM DTT), vortexed, incubated on ice for 2 min
and centrifuged at 18,500 g for 2 min. We carefully removed the supernatant corresponding to
the nucleoplasmic fraction (350 µl) and added 250 µl 1x PBS/Protease inhibitors cOmplete to
adjust the volume for Western blot experiments (described below). We resuspended the
chromatin pellet in 600 µl chromatin resuspension solution (25 µM α-amanitin, Protease
inhibitors cOmplete, in 1x PBS).
We monitored the success of cell fractionation by Western blot analyses. For Western blot
analyses, we probed membranes with the following primary antibodies: Pol II (F-12, Santa Cruz
Biotechnology; directed against the N-terminal region of Rpb1), Pol II Ser2-P (3E10, Active
Motif), Pol II Ser5-P (3E8, Active Motif), Histone 2B (FL-126, Santa Cruz Biotechnology), U1
snRNP70 (C-18, Santa Cruz Biotechnology) and GAPDH (6C5, Applied Biosystems). Next, we
probed membranes with Cy5- and Alexa Fluor 647-conjugated secondary antibodies (Cy5 goat
anti-mouse, A10524; Cy5 goat anti-rabbit, A10523; Cy5 goat anti-rat, A10525; Alexa Fluor 647
rabbit anti-goat, A21446; Life Technologies), and scanned using a Typhoon 9400 scanner (GE
Healthcare). We quantified fluorescent signals with ImageJ 1.47v software.
Triptolide:
We degraded RNA polymerase II in primary fibroblast cells by incubating cells in 100nM
triptolide for one hour, then fixed cells in methanol (control cells remained untreated).
Cell size verification:
To check that fixation did not alter cell size, we monitored the size of cells through the fixation
and permeabilization process by fixing cells while on the microscope stage. We monitored cell
area by taking images in brightfield, and we monitored cell height by coating the cells with
fluorescent beads and imaging them in a series of optical z-sections. We took images of the
same cells after 10 minutes of fixing in 4% formaldehyde and after 30 minutes of
permeabilization in ethanol. We calculated cell area by segmenting the cells as usual, and we
determined height by identifying the plane of the bottom of the cell and the plane of the top of
the cell (the last plane where beads remain motionless) and subtracting the two values.
Quantification of cell-to-cell variability:
We developed a phenomenological metric for cell-to-cell variability that takes into account both
volume-correlated and volume-independent contributions to mRNA numbers per cell (see
supplemental note for derivation and further information). We also used a model of
transcriptional bursting with volume-dependent transcription that enabled us to quantify
transcriptional parameters from population distributions of mRNA counts and volumes.
Repli-seq analysis:
We accessed Repli-seq data from Hansen et al. 2010 (Hansen et al., 2010) using the UW Repliseq track on the UCSC Genome Browser.
Bulk RNA Sequencing:
We sequenced total RNA from primary fibroblast cells. We used the NEB Next Ultimate Library
Preparation Kit for Illumina and the Ribo-Zero Magnetic Gold Kit. We used 50b single-end reads
and sequenced each of two replicates at a depth of 10-15M reads. We aligned reads to hg19
using STAR’s included annotation. We quantified reads per gene using HTSeq and a RefSeq
hg19 annotation. We calculated FPKM for each gene using R. All sequencing data is available
at GEO accession number GSE66053.
Single-cell RNA Sequencing:
We isolated 96 single cells, lysed, and performed first- and second-strand synthesis on a
Fluidigm C1 Single-Cell Auto Prep System using a large size chip. We spiked in ERCC
(External RNA Controls Consortium) RNA controls, Mix 1 (Ambion 4456740) at a concentration
of 1:10,000 before adding the cells to the C1. We prepared cDNA libraries using the Nextera XT
DNA Sample Preparation Kit (Illumina, PN FC-131-1096) and used 96 paired barcodes from the
Nextera XT DNA Sample Preparation Index Kit (96 Indices, 385 Samples) (Illumina, PN FC131-1002) following the abbreviated Fluidigm protocol for the Nextera XT kit. We sequenced the
samples on a NextSeq 500 using 75b paired-end reads to a depth of ~1-2M reads per sample.
To quantify sequencing data, we aligned reads to hg19 (using STAR’s included annotation) and
the ERCC reference transcripts. We quantified reads per gene using HTSeq and a RefSeq hg19
annotation. All sequencing data is available at GEO accession number GSE66053.
Single-cell RNA Sequencing Calibration and Analysis:
We independently calculated ERCC and genomic FPKM for each sample, normalizing to the
total number of reads mapped to ERCC loci or genomic loci, respectively. All FPKM data shown
for endogenous genes is this genomic FPKM. For each cell, we considered the ratio of total
genomic reads to total ERCC reads to be proportional to the total starting amount of mRNA in
that cell.
We sequenced 96 wells total, of which 5 were “control” wells that contained no cells and 14
were wells containing fixed cells. We excluded these 19 cells from the analysis. Further, we
excluded 12 cells that had fewer than 1 million total reads, and 21 cells that had a
genomic/ERCC read ratio of less than 30. We performed all further analyses on the 44
remaining cells.
Transform read ratio to volume: We assumed that the ratio of genomic/ERCC reads for each
sample was proportional to the total mRNA in each cell. We also assumed that, for our RNA
FISH measurements, total GAPDH mRNA counts were proportional to the total amount of
mRNA in each cell. The distributions for total mRNA obtained in this manner were similar
between RNA FISH and single-cell RNA sequencing, but had different means. We therefore
normalized the sequencing data to have the same mean as the RNA FISH distribution. From
our RNA FISH dataset, we have many co-measurements of GAPDH mRNA (total mRNA) and
volume from which we establish a transformation equation between total mRNA and volume.
We obtained this transformation equation using PCA, or orthogonal regression. Using this
equation, we transformed total mRNA obtained through sequencing into actual volume in
picoliters.
Transform FPKM to molecule count: FPKM is more a measure of mRNA concentration than
mRNA count, as it is normalized to total reads. To get a measure more similar to mRNA count,
for each cell, we multiplied each gene’s FPKM by the genomic/ERCC count ratio (“volume”) of
the cell. For each gene in our RNA FISH dataset, we fit the log of the seq “counts” and the log of
the actual counts from RNA FISH by orthogonal regression. We then used this transform to
convert the FPKM of all genes to their RNA FISH count equivalent. Note that, because we fit in
log space, the transform between FPKM and count is nonlinear, and actually scales as
approximately FPKM ~ (RNA FISH)1.7.
Once we had our single-cell sequencing data in terms of RNA FISH count and volume in
picoliters, we calculated Nm as described for RNA FISH. We performed all of our sequencing
analysis in R.
C. elegans growth and imaging:
We grew N2 (wild type) and CB502 (sma-2 mutant) C. elegans on NGM agar plates with OP50
lawns, kept at 20º C. Every 2-3 days, we transferred a small portion of each strain to new plates
to prevent overgrowth.
We released the worms off of the plates using phosphate buffered saline (PBS) solution, then
fixed with 4% formaldehyde for 45 minutes. We permeabilized and stored the worms in 70%
ethanol. We performed the RNA FISH protocol, then mounted the sample between a slide and
coverglass before imaging.
We manually identified head and gonad boundaries and counted and localized RNA spots using
custom software written in MATLAB.
To compute the volume of each worm segment, we multiplied the area of the segment by the
height of the segment (thus approximating the segment as a prism). We determined the height
by taking the vertical difference between the highest and lowest RNA spots’ positions, as
determined by our software. We determined the number of cells in each segment through
manually counting the DAPI-stained nuclei.
We obtained data from multiple segments. When combining the data (number of mRNA spots
per volume or per nucleus), we weighted each segment by its volume.
Model of di↵usible trans factor for volume:DNA ratio sensing
Here, we outline a fairly generic model for how a di↵usible trans factor may transmit information
on the ratio of volume to DNA to lead to increased transcription in larger cells irrespective of DNA
content. The primary assumptions are that the factor is predominantly localized to the nucleus, the
factor is required for mRNA transcription, and the cellular concentration of the factor is roughly
constant irrespective of cellular volume (i.e., the total amount of factor is proportional to cellular
volume). RNA polymerase II holoenzyme satisfies these conditions, although we do not claim that
RNA polymerase II is the factor.
The model assumes binding of the factor to the DNA, and that only bound factor can result in
productive transcription. The goal of the model is to provide a basis for the empirical finding that
larger cells have increased transcription from the same absolute number of DNA molecules. Our
model encompasses two broad categories of mechanism that would lead to a perfectly linear scaling
of transcription with cytoplasmic volume: (1) The factor is sequestered entirely in the nucleus, and
so if the nucleus doesn’t change with cellular volume, the concentration of the factor in the nucleus
will be proportional to the total amount of factor. Thus, the factor will be proportionally more
bound to the DNA in a larger cell than a smaller cell, producing more transcription. (2) The factor
is a purely “limiting” factor in the sense that it has a very high affinity for DNA and the number of
binding sites exceeds the amount of factor. In this situation, essentially all available factor will be
bound to the DNA, and so for each gene, there would be proportionally more transcription in larger
cells because more factor would be bound to DNA. These mechanisms are not necessarily mutually
exclusive. The model incorporates affinity and nuclear volume as parameters, and so encompasses
both of these potential mechanisms.
Briefly, the conclusion we derive from our model is that both scenarios pose viable mechanisms
for scaling transcription with cellular volume. That said, we overall mildly favor scenario 1. Our
data show that nuclear volume increases somewhat with nuclear size, which the model predicts
should lead to a slight decrease in transcription in larger cells, and thus a higher concentration of
mRNA in smaller cells, which is precisely what we observe. Moreover, there is a rough quantitative
agreement between the degree of increased nuclear volume and the higher concentration of mRNA
in smaller cells. Definitively proving that the cell follows scenario 1 of our model will require further
experiments.
We begin with a few definitions. We use quantities within brackets to denote concentration
(molecules per volume) and quantities without brackets to denote number of molecules per cell.
For instance, factorfree is the number of free molecules of the factor, while [factorfree ] is the number of
free molecules per unit volume. factorDNA denotes the number of factor molecules instantaneously
bound to DNA, factortotal is the total amount of factor in the cell/nucleus, and DNA is the number of
binding sites on the DNA for the factor in the nucleus. KDNA is the binding affinity of the factor for
a particular gene. The cellular volume is given by V , and the nuclear volume by Vnuclear . Thus, given
our assumption of proportionality, we define pfactor to be a constant such that factortotal = pfactor V .
The total factor is given by
factortotal = factorfree + factorDNA ,
(1)
Dividing by the nuclear volume, we arrive at a relationship between concentrations:
[factortotal ] = [factorfree ] + [factorDNA ] .
(2)
The binding affinity is defined via mass action as
KDNA =
[factorfree ] [DNA]
.
[factorDNA ]
(3)
and may be di↵erent for di↵erent genes owing to promoters having di↵erent numbers of binding
sites for the factor or di↵erent binding affinities.
Thus, the total concentration of the machinery bound to DNA is
[factorDNA ] =
([factorDNA ]
[factortotal ]) [DNA]
.
KDNA
(4)
Solving for [factorDNA ], we find:
[factorDNA ] =
[factortotal ] [DNA]
.
KDNA + [DNA]
(5)
In the limiting case where KDNA = 0, we expect all of the factor to be bound to DNA, and in
that case, we find [factorDNA ] = [factortotal ], as expected.
Relating concentrations to volumes yields
[factortotal ] =
pfactor V
,
Vnucleus
(6)
where pfactor is the proportionality constant defined earlier. Similarly,
[DNA] =
DNA
.
Vnucleus
(7)
Hence,
[factorDNA ] =
V
DNA
pfactor Vnucleus
Vnucleus
KDNA +
DNA
Vnucleus
.
(8)
Simplifying,
[factorDNA ] =
✓
1
Vnucleus
◆
pfactor · V · DNA
.
KDNA · Vnucleus + DNA
(9)
Because [factorDNA ] = factorDNA /Vnucleus , we can solve for the total amount of transcriptional
machinery bound to DNA:
factorDNA =
pfactor · V · DNA
.
KDNA · Vnucleus + DNA
(10)
In the limiting case KDNA = 0 here, we find that factorDNA is directly proportional to volume,
and equal to the total amount of factor in the nucleus irrespective of nuclear volume. However,
in the case where KDNA is not zero, then the volume of the nucleus will result in deviations from
perfect scaling of transcription with cellular volume. Intuitively, if the volume of the nucleus
increases somewhat in larger cells, then the concentration of the factor and the DNA will decrease
and hence the amount of factor bound to DNA will be somewhat less than it would be otherwise.
In that case, larger cells would have somewhat less transcription than would be expected in the case
of perfect scaling of transcription with cellular volume, which fits with our experimentally observed
volume-independent transcript abundance (i.e., decreased mRNA concentration in larger cells).
We also observed that nuclear volume is somewhat greater in larger cells. Thus, it was possible,
at least qualitatively, that the increase in nuclear volume could explain the apparent decrease in
mRNA concentration in larger cells. We thus wanted to check whether there is a quantitative
agreement between our observed relationship between nuclear volume and cytoplasmic volume and
the increased mRNA concentration in smaller cells, which would establish the plausibility of such
a model.
As mentioned, our measurements show that nuclear area and cellular volume positively correlate.
Approximating nuclear volume by raising nuclear area to the 3/2 power, we find a linear relationship
between nuclear “volume” and cellular volume (Vnucleus / a + bV ), with y-intercept a = 2169
femtoliters (95% C.I. = (1923, 2381)), and slope b = 0.9354 (95% C.I. = (0.8313, 1.042)). It is
important to note that the while the relationship is well-fit by a line, the line does not pass through
zero, and so nuclear volume is not directly proportional to total cellular volume. Using this linear
relationship, we can express the total amount of factor bound to DNA as a function of cellular
volume:
pfactor · V
⌘
factorDNA (V ) = ⇣
,
(11)
a
˜ + ˜bV + 1
DNA
DNA
where a
˜ = KDNA
· a and ˜b = KDNA
· b. The ratio a/b (= a
˜/˜b) has units of volume, and is geometrically
equivalent to the x-intercept of the line of best fit between nuclear volume and cellular volume.
We now wanted to check whether the volume-independent transcription we observed in our
mRNA-volume plots would quantitatively agree with this model. Because the factor is required
for transcription and only transcribes when bound to DNA, then each gene essentially grabs a
fixed proportion of the amount of factor bound to DNA. (This fraction will depend on the specific
regulation of the gene.) So the total transcription of a gene will be proportional to factorDNA . Thus,
lumping together this proportionality constant along with mRNA production and degradation and
other associated constants into a constant c, the relationship between RNA and volume is given
by:
RNA(V ) = c · factorDNA (V ) .
(12)
We should be able to fit our RNA vs. volume data using the above equation to obtain estimates
for a
˜ and ˜b, in particular their ratio, which is directly comparable to the ratio a/b.
We did so for three genes and found fitting parameters:
a
˜ (fL)
95% C.I. (˜
a) (fL)
˜b
95% C.I. (˜b)
a
˜/˜b (fL)
95% C.I. (˜
a/˜b) (fL)
U BC
1.578
(0.8524, 2.461)
1.936⇥10 4
(-7.617⇥10 5 , 4.595⇥10
7044
(-62743, 111200)
4)
ZN F 444
95.68
(70.23, 127.9)
0.01495
(0.004163, 0.02394)
6446
(2988, 28110)
EEF 2
0.2747
(-0.1518, 0.5630)
0.0003658
(0.0002680, 0.0005879)
744.4
(-253.5, 2064)
For the fit of nuclear area to volume, we find the ratio a/b = 2329 femtoliters, with a 95%
confidence interval of (1844, 2851). We note that the ratios a
˜/˜b for all of our genes are of that
same order of magnitude, albeit with large error. This result suggests that the above equation
for factorDNA (V ) may be the equation governing the production of mRNA in cells. This model
provides an explanation that is quantitatively consistent with our data for why smaller cells exhibit
proportionally slightly more transcription than larger cells—nuclei in small cells are slightly smaller
than those in large cells, increasing the concentration of factorDNA (V ), and therefore increasing
transcription.
Our results are consistent with RNA polymerase II holoenzyme being the factor. RNA polymerase II is required for transcription, transcribes when bound to DNA, and is almost exclusively
localized to the nucleus. Also, most reports indicate that most RNA polymerase II in the nucleus
is not specifically bound to DNA. Based on that fact, one would expect that increased nuclear size
should lead to slight under-transcription, as we observed. Our analysis shows that this relationship is quantitatively plausible. Further studies will be required to rigorously establish that RNA
polymerase II holoenzyme is the factor that connects volume/DNA ratio to transcription.
Note, however, that in many situations such as in early embryogenesis, nuclear size does change
dramatically as a function of cellular volume. In these situations, the mechanism we describe would
face a challenge because the concentration of RNA polymerase II holoenzyme in the cell’s nucleus
would remain the same after division (and the associated decrease in cellular volume), leading to
over-transcription. The limiting factor model (scenario 2, with KDNA very small) would not su↵er
from these issues. It is possible that some intermediate scenario is at play in early embryogenesis.
Another problem with these models is the potential for runaway positive feedback, in which a
random increase in the factor would lead to more production of the factor, thus leading to runaway
transcription. For this reason, we expect that the cell maintains strong control of factor levels
to avoid these issues. Ultimately, a complete understanding of factor dynamics will likely require
adding growth to models of transcriptional homeostasis.
Computing volume-corrected noise measure from single-cell mRNA
and volume measurements
We define volume-corrected noise measure as the cell-to-cell expression variability in mRNA levels
that cannot be accounted for by cell-to-cell di↵erences in volume. Throughout the section, we
2 .
denote the variance of a random variable X by X
Let m and V be random variables denoting single-cell mRNA level and volume, respectively. The
expected number of mRNA transcripts in a cell given its volume V is assumed to increase linearly
with V , i.e.,
hm|V i = a + bV =) hmi = a + bhV i,
(13)
where h.i represents the expected value, and a, b are gene-specific constants (volume-independent
and volume-correlated transcript abundance, respectively). From (13), the covariance between m
and V is given by
Cov(m, V ) = hmV i
hmihV i = h(a + bV )V i
(a + bhV i)hV i = b
2
V.
(14)
The extent of cell-to-cell variability in mRNA counts that can be accounted for by volume is
2
hm|V i
=
2
a+bV
= b2
2
V,
(15)
which using (14) can be written
2
hm|V i
= bCov(m, V ).
(16)
Volume-corrected noise measure N m defined as
N m :=
2
m
2
hm|V i
hmi2
(17)
is obtained as follows using (16)
N m = CVm2
bCov(m, V )
= CVm2
hmi2
S
Cov(m, V )
,
hmihV i
(18)
where CVm2 represents the total variability in mRNA levels measured by its Coefficient of Variation
(CV ) squared and
S=
bhV i
bhV i
=
.
hmi
a + bhV i
(19)
Noise measure in a two-state promoter model
Consider two alleles, where each allele transitions independently between active and inactive states
with rates kon and kof f . We assume that the transcription rate from the active state increases
linearly with cell volume V . We first compute CVm2 (mRNA coefficient of variation squared) for
the case where transcription is independent of volume, and then extend it to the volume dependent
case.
Transcription rate independent of volume
Let the transcription rate from active state be km . Then, the steady-state first and second-order
moment of the mRNA level m is given by
hmi =
2Gon km
m
, hm2 i = hmi +
m (1
2(Gon
Gon )hmi2
+ hmi2 ,
m + kon )
(20)
where
Gon =
kon
kon + kof f
(21)
is the fraction of time an allele is in the active state, and m is the mRNA degradation rate. Note
that the factor two in (20) arises due to the presence of two alleles. This results in
CVm2 :=
hm2 i hmi2
1
Gon )
m (1
=
+
.
hmi2
hmi 2(Gon m + kon )
(22)
Transcription rate dependent on volume
We assume km = a + bV , where volume V is a random variable with mean hV i and variance
Based on (20),
hm|V i =
2Gon (a + bV )
m
, hm2 |V i = hm|V i +
Gon )hm|V i2
+ hm|V i2 .
2(Gon m + kon )
m (1
2
V.
(23)
Unconditioning on the volume we obtain
hmi =
2Gon (a + bhV i)
(24a)
m
hm2 i = hmi +
⌦
Gon ) hm|V i
2(Gon m + kon )
m (1
Using (23)
⌦
hm|V i
2
↵
=
*✓
2Gon (a + bV )
m
◆2 +
↵
2
⌦
↵
+ hm|V i2 .
= hmi2 (1 + S 2 CVV2 ),
(24b)
(25)
where the mean mRNA count hmi is given by (24a), S is given by (19) and CVV2 is the volume
CV 2 . Substituting (25) in (24b)
hm2 i =
m (1
Gon )hmi2 (1 + S 2 CVV2 )
+ hmi2 (1 + S 2 CVV2 ) + hmi.
2(Gon m + kon )
(26)
Above equation yields
CVm2 :=
hm2 i hmi2
1
=
+
2
hmi
hmi
Gon )(1 + S 2 CVV2 )
+ S 2 CVV2 .
2(Gon m + kon )
m (1
(27)
As expected, (27) reduces to (22) when CVV2 = 0. In (27), the first term represent Poissonian noise
in mRNA level due to random-birth death of individual mRNA molecules. The second term is the
noise contribution from stochastic promoter switching. Variation in mRNA levels due to cell-to-cell
di↵erences in cell volume is represented by the last term. Removing the last term, we obtain the
noise measure as
Nm =
Gon )(1 + S 2 CVV2 )
.
2(Gon m + kon )
m (1
1
+
hmi
(28)
Estimating promoter transition rates between active and inactive
states
Noise measures obtained from single-cell mRNA count and volume measurements are used to
estimate promoter transition rates kon and kof f using (28). To correct for measurement noise,
we take into account a 15% error in mRNA counting. From (21) and (28)
Gon =
kon
kon + kof f
Nm =
1
+
hmi
(29a)
Gon )(1 + S 2 CVV2 )
2
+ CVcount
,
2(Gon m + kon )
m (1
(29b)
Average promoter dwell-time (30) obtained from the noise measure (Eq. (29)) or the total mRNA
expression variability (Eq. (31)). mRNA half-lives and dwell times are reported in hours.
Gene
Gon
CVm2
N m/CVm2
ACTN4
GAPDH
EEF2
FTL
ICAM1
ACTA2
LUM
SUPTH5
0.65
0.65
0.75
0.3
0.05
0.2
0.15
0.3
0.14
0.23
0.18
0.58
0.8
1.18
0.7
0.12
0.4
0.17
0.17
0.32
0.8
0.9
0.75
0.58
mRNA
half-life
13
24
16
24
6.5
3
24
10
Ton , Tof f
from N m
6.1, 3.3
4.9, 2.6
3.2, 1.1
6.3, 14.6
0.5, 9.7
5.1, 20.3
7.8, 44.3
0.45, 1.1
Ton , Tof f
from CVm2
40.5, 21.8
331, 178
1443.6, 481.2
45.4, 105.9
0.8, 15.4
7.9, 31.6
12.7, 72.5
1.4, 3.3
2
where CVcount
= 0.152 = 0.0225 represents the mRNA counting error. In the above equations,
quantities N m, S (defined in (19)), CVV2 (volume CV 2 ), hmi, Gon are computed from data for a
given gene. Using mRNA half-life information from literature, rates kon and kof f can be estimated
by solving (29). The average promoter dwell time in the active and inactive state is given by
Ton =
1
kof f
, Tof f =
1
,
kon
(30)
respectively, and reported in Table I under the column “Ton , Tof f from N m”. Since there may
be other unaccounted sources of noise in gene expression, these dwell time estimates should be
considered an upper bound on their actual values.
We contrast the above estimates to the scenario where all the mRNA expression variability is
assumed to arises from transcriptional bursting. From (22), kon and kof f in that case would be
estimated by solving
kon
kon + kof f
1
Gon )
m (1
2
=
+
+ CVcount
.
hmi 2(Gon m + kon )
Gon =
CVm2
(31a)
(31b)
Since CVm2 > N m, dwell times obtained from (31) (see “Ton , Tof f from CVm2 ” in Table I) are
significantly larger than those obtained from (29). For example, using the GAPDH noise measure,
we estimate Ton = 4.9 hours. However, if one ignores the contribution of cell volume in driving
intercellular variation in GAPDH mRNA, the mean dwell time in the active state is obtained to be
13 14 days (331 hours) from (31).