ArticleMolecular Time Sharing through Dynamic Pulsing in
Single CellsGraphical AbstractTime
Molecular sharing Time-sharing
Time
σX
σD
σB σ
M
σW
σARNAP
Sigma factors compete for 
core RNAP
target
operons
??
RNAP
σA
σ1
σ2
σ3
σ5
σ4
0
2
40 600 20 80 100
Model: competition and pulsatility can generate time-sharing
Time (hours)
[R
N
A
P-
σ]
 ( 
μM
)
Timelapse
CFP
mCh
YFP
σA
Strain “Matrix”
σX
σD
σW
σM
σB
Dynamics and
Correlations
+ -
1
RNAP
Fr
ac
tio
n 
of
 
σ-
O
cc
up
ie
d 
 
RN
A
P
media
t t
… …
t
0
Fr
ac
tio
n 
of
 
σ-
O
cc
up
ie
d 
 
RN
A
PHighlightsd Alternative sigma factors activate in repetitive pulses under
constant conditions
d Time-lapse movies reveal positive and negative dynamic
correlations
d Sigma factors appear to compete with different strengths for
core RNAP
d Modeling shows competing pulsatile sigma factors can
dynamically "time share’’ RNAPPark et al., 2018, Cell Systems 6, 216–229
February 28, 2018 ª 2018 The Authors. Published by Elsevier In
https://doi.org/10.1016/j.cels.2018.01.011Authors
Jin Park, Marta Dies, Yihan Lin, ...,
Jordi Garcia-Ojalvo,
James C.W. Locke, Michael B. Elowitz
Correspondence
jordi.g.ojalvo@upf.edu (J.G.-O.),
james.locke@slcu.cam.ac.uk (J.C.W.L.),
melowitz@caltech.edu (M.B.E.)
In Brief
Cellular regulatory factors often compete
for limited amounts of core enzymes.
Sharing is typically assumed to involve
statically partitioning core enzyme
molecules. In contrast, using time-lapse
movies, we find that Bacillus subtilis
alternative sigma factors, which compete
for core RNA polymerase, activate
dynamically in stochastic, repetitive,
hour-long pulses. Using mathematical
modeling, we show how such pulsatile
competitive circuits can effectively time
share, or take turns using, core
polymerase under similar conditions.
Time-sharing represents an alternative
mode of resource sharing in cells.c.
Cell Systems
ArticleMolecular Time Sharing through Dynamic
Pulsing in Single Cells
Jin Park,1 Marta Dies,2,3,4 Yihan Lin,5 Sahand Hormoz,1 Stephanie E. Smith-Unna,6 Sofia Quinodoz,1
Marı´a Jesu´s Herna´ndez-Jime´nez,1 Jordi Garcia-Ojalvo,2,* James C.W. Locke,6,7,* and Michael B. Elowitz1,8,9,*
1Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA
2Department of Experimental andHealth Sciences, Universitat Pompeu Fabra, BarcelonaBiomedical Research Park, 08003Barcelona, Spain
3Department of Physics and Nuclear Engineering, Universitat Politecnica de Catalunya, 08222 Terrassa, Spain
4Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 18015, USA
5Center for Quantitative Biology, and Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies,
Peking University, Beijing 100871, China
6Sainsbury Laboratory, Cambridge University, Bateman Street, Cambridge CB2 1LR, UK
7Microsoft Research, Cambridge, UK
8Howard Hughes Medical Institute, California Institute of Technology, Pasadena, CA 91125, USA
9Lead Contact
*Correspondence: jordi.g.ojalvo@upf.edu (J.G.-O.), james.locke@slcu.cam.ac.uk (J.C.W.L.), melowitz@caltech.edu (M.B.E.)
https://doi.org/10.1016/j.cels.2018.01.011SUMMARY
In cells, specific regulators often compete for limited
amounts of a core enzymatic resource. It is typically
assumed that competition leads to partitioning of
core enzyme molecules among regulators at con-
stant levels. Alternatively, however, different regula-
tory species could time share, or take turns utilizing,
the core resource. Using quantitative time-lapse
microscopy, we analyzed sigma factor activity
dynamics, and their competition for RNA polymer-
ase, in individual Bacillus subtilis cells under energy
stress. Multiple alternative sigma factors were acti-
vated in 
1-hr pulses in stochastic and repetitive
fashion. Pairwise analysis revealed that two sigma
factors rarely pulse simultaneously and that some
pairs are anti-correlated, indicating that RNAP utili-
zation alternates among different sigma factors.
Mathematical modeling revealed how stochastic
time-sharing dynamics can emerge from pulse-
generating sigma factor regulatory circuits actively
competing for RNAP. Time sharing provides a
mechanism for cells to dynamically control the
distribution of cell states within a population. Since
core molecular components are limiting in many
other systems, time sharing may represent a general
mode of regulation.
INTRODUCTION
Many core cellular components are shared among distinct regu-
latory factors or substrates in the cell. For example, the protea-
some is shared by multiple substrate proteins, the ribosome by
multiple mRNA species, and core RNA polymerase (RNAP) by
multiple sigma factors in bacteria (Figures 1A and 1B). When
the shared core component is present in limited supply, sharing216 Cell Systems 6, 216–229, February 28, 2018 ª 2018 The Authors
This is an open access article under the CC BY-NC-ND license (http://gives rise to competition between regulatory factors. At steady
state, it is generally assumed that each substrate or factor uti-
lizes an approximately constant fraction of core component mol-
ecules. However, certain regulatory systems may operate more
dynamically, and far from a steady state. This opens up the pos-
sibility that sharing could occur in time. In such a time-sharing
system, the core component would effectively take turns, inter-
acting predominantly with only one or a few of its many potential
partner species at any given time (Figure 1C). Despite the famil-
iarity of time-sharing strategies in engineered systems such as
computers and communication networks, it is unknownwhether,
or how, time sharing could occur in cells.
In bacteria, alternative sigma factors function as subunits of
the RNAP holoenzyme, directing it to specific sets of target pro-
moters (Boylan et al., 1993; Helmann, 2002, 2016; Paget, 2015;
Price et al., 2001) (Figure 1A). Inmany contexts, alternative sigma
factors actively compete for limiting amounts of RNAP (Ganguly
and Chatterji, 2012; Grigorova et al., 2006; Hicks and Grossman,
1996; Maeda et al., 2000). In addition to competition, alternative
sigma factors are typically controlled through a multi-stage
regulatory system with feedback. In these systems, sigma fac-
tors are negatively regulated through cognate anti-sigma fac-
tors, which can (Cao et al., 2003; Estacio et al., 1998) prevent
their association with core RNAP. These anti-sigma factors can
in turn be inhibited by specific inputs or stresses to enable sigma
factor activation (Gruber and Gross, 2003). Finally, sigma factors
typically activate their own operons, which often contain the
genes for both the sigma factor and its anti-sigma factor,
creating interlocking positive and negative feedback loops
(Cao et al., 2002, 2003; Estacio et al., 1998; Huang et al., 1999;
Kalman et al., 1990; Yoshimura et al., 2004).
As a result of this regulatory structure, sigma factors can
exhibit complex dynamics, even under constant environmental
conditions. For example, the alternative sigma factor sB in
Bacillus subtilis is activated in a sustained series of stochastic
pulses in response to energy stress (Locke et al., 2011; Narula
et al., 2016). These pulses represent events in which many
sB molecules simultaneously become active, associate with
core RNAP to initiate transcription of target genes, and then. Published by Elsevier Inc.
creativecommons.org/licenses/by-nc-nd/4.0/).
A
+σ
σ
RNAP
RNAP
B C
σA
σB σL σD
σY σXσW
σM
E
D
 0 2.5 5 7.5
0
30
60
Time (hours)
Pr
om
ot
er
A
ct
iv
ity
 (a
.u
.)
Pr
om
ot
er
A
ct
iv
ity
 (a
.u
.)
σB
0
60
120
σD
0
75
150
σL
0
50
100
σM
0
40
80
σX
0
20
40
σY
0
65
130
σW
0
40
80
σA
natural regulon
reporter
Timet1 t2 t3
Sharing
σX
σL
σD
σB σY
σM
σW
σA
Molecular sharing
Time-sharing
Time (hours)Time (hours) Time (hours)
Time (hours) Time (hours)Time (hours) Time (hours)
0 2.5 5 7.5 0 2.5 5 7.5  0 2.5 5 7.5
 0 2.5 5 7.5 0 2.5 5 7.5 0 2.5 5 7.5  0 2.5 5 7.5
2 μm 2 μm 2 μm 2 μm
2 μm 2 μm 2 μm 2 μm
(legend on next page)
Cell Systems 6, 216–229, February 28, 2018 217
deactivate. However, sB is only 1 of 17 alternative sigma factors
inB. subtilis (Gruber andGross, 2003) (Table S1). It has remained
unclear whether pulsing is specific to sB or occurs across the
broader set of alternative sigma factors, whether multiple sigma
factors pulse under the same conditions, and howpulsing relates
to competition for core RNAP. Given that the concentration of
each sigma factor species may change with time and that they
compete with varying affinities for limiting amounts of core
RNAP, describing and understanding the dynamics that may
arise in a system expressing multiple sigma factors is non-trivial.
Here, we analyze the dynamics of multiple alternative sigma
factors in B. subtilis cells under energy stress conditions at the
level of individual cells. In addition to sB, we find that multiple
other alternative sigma factors, including sD, sM, sW, and sX,
also activate in repetitive pulses. Based on these observations,
we explore the idea that RNAP could be shared more dynami-
cally in time. We illustrate the principles of pure biochemical
time sharing using mathematical models, and then ask which
aspects of the alternative sigma factor dynamics observed
in vivo may be explained by dynamic competition for RNAP, of
which pure time sharing is a special case. Finally, we discuss
how time sharing can, in principle, provide a mechanism for
dynamically controlling the distribution of cell states or pheno-
types within a population.
RESULTS
Understanding the dynamics of multiple sigma factors interact-
ing with one another through competition for core RNAP requires
the ability to visualize their activity over time in individual cells. To
achieve this, we constructed a set of reporter strains, each con-
taining a yellow fluorescent protein gene specifically activated
by one of the B. subtilis alternative sigma factors not involved
in sporulation (Figure 1A; Table S1). Fluorescent reporters
were chromosomally integrated at the sacA locus (see STAR
Methods), and specifically responded to their corresponding
sigma factors (Figure S1A). We analyzed these strains in a mini-
mal medium containing 40 mg/mL mycophenolic acid (MPA), a
drug that reduces cellular ATP levels and stimulates a broad
energy stress response (Zhang and Haldenwang, 2005) (Fig-
ure S1B). Visualizing fluorescent protein levels in single cells re-
vealed markedly heterogeneous activation of seven alternative
sigma factors in these conditions (Figure 1D). In contrast, the
housekeeping sigma factor sA, which has higher affinity for
core RNAP and lacks an anti-sigma factor (Rollenhagen et al.,Figure 1. Multiple Alternative Sigma Factors Pulse under Energy Stres
(A) Alternative sigma factors bind core RNAP to activate target genes, including e
here (right target).
(B) Multiple distinct alternative sigma factor species (colored shapes) share c
core RNAP.
(C) In principle, sigma factor species could share core RNAP by partitioning, w
(molecular sharing, top). Alternatively, they could share RNAP in time, with one
followed by a different sigma factor or factors for another period of time, and so on
(D) Fluorescent reporter expression in growing microcolonies shows heterogene
neous activation of sA (bottom right) under energy stress conditions.
(E) Time-lapse analysis reveals stochastic pulsing of alternative sigma factors in i
derived from analysis of corresponding fluorescent reporter genes in three differ
fluorescent protein production, approximating instantaneous sigma factor activity
time. See also Figures S1 and S2.
218 Cell Systems 6, 216–229, February 28, 20182003), was activated in a more homogeneous manner, suggest-
ing that this type of heterogeneous activation was not general to
all sigma factors (Figures 1D, S1C, and S1D).
While the distributions of total fluorescent protein expressed
from alternative sigma factor promoters exhibited skewed distri-
butions with extended tails (Figure S1C), similar to those previ-
ously observed under conditions of pulsatile activation of sB
(Locke et al., 2011), this cumulative readout can obscure dy-
namics on timescales faster than the cell cycle. Therefore, we
computed for each cell the approximate instantaneous rate of
fluorescent protein production from its corresponding target
promoter, and corrected for photobleaching and dilution due
to cell growth (Dunlop, 2014; Young et al., 2011) (see STAR
Methods). This instantaneous activity should reflect the rate at
which free sigma factor (not sequestered by its cognate anti-
sigma factor) can associate with available core RNAP and initiate
transcription at target promoters (Locke and Elowitz, 2009). It
therefore depends on sigma factor protein levels, anti-sigma fac-
tor levels, and the availability of core RNAP.
For these experiments, we seeded cells on pads of low-melt
agarose in minimal media with 40 mg/mL MPA, and used quanti-
tative time-lapse fluorescence imaging to analyze individual cells
within growing microcolonies. This analysis revealed that the
seven alternative sigma factors mentioned above were activated
in a pulsatile fashion (Figures 1E and S1D; Movie S1). Pulses ap-
peared to be generated stochastically, as no significant correla-
tions were observed in sister cell pairs (Figure S2A), or between a
parent cell and its two daughters (Figure S2B). Widespread sto-
chastic pulsing of this type was not specific to MPA-induced
stress, as stationary phase conditioned media also caused
pulsing of many sigma factors (Figure S3A). Also, this pulsing
did not require sB, a factor previously shown to pulse (Fig-
ure S3B) (Locke et al., 2011).
We next sought to characterize the pulse dynamics more pre-
cisely. Because pulses occur much less than once per cell cycle,
this required analysis over many generations. Exponential accu-
mulation of cells on agarose pads limits the number of genera-
tions that can be analyzed, and leads to non-stationary environ-
mental conditions. To circumvent these issues, we turned to the
mother machine, a microfluidic device that enables analysis of a
single cell over tens or hundreds of cell division events (Taheri-
Araghi et al., 2015; Wang et al., 2010) (Figure 2A; Movie S2).
More specifically, we used a mother machine variant optimized
for B. subtilis that features a shallow side channel beside the
main growth trenches to enhance diffusion of media over longs
ndogenous targets (left target) and the engineered fluorescent reporters used
ore RNAP (gray). The ‘‘housekeeping’’ sigma factor sA (white) also utilizes
ith each sigma factor species utilizing some constant fraction of total RNAP
or more sigma factors occupying a large fraction of RNAP for some period,
(time sharing, bottom). Only three distinct species are shown here for simplicity.
ous activation of seven alternative sigma factors, as indicated, and homoge-
ndividual cell lineages. Here, each plot shows sigma factor activity time traces
ent cell lineages (different line shades). For each plot, the y axis shows rate of
. Note that the housekeeping sigma factor sA shows much less variability over
media
A B
C E FD
0 1 2 3 4
Relative Pulse
Amplitude
0
0.4
0.8
1.2
N
um
be
r o
f p
ul
se
s
(n
or
m
al
iz
ed
)
-2 -1 0 1 2
Time (hours)
0
0.2
0.4
0.6
0.8
1
Re
la
tiv
e 
Pr
om
ot
er
 
A
ct
iv
ity
0
0.2
0.4
0.6
0.8
D
ur
at
io
n 
(F
W
H
M
, h
ou
rs
)
0
100
200
0
20
40
0
40
80
0
20
40
0 20 40 60 80 1000
80
80
Time (hours)
Pr
om
ot
er
 A
ct
iv
ity
 (a
.u
.)
σB
σM
σW
σX
σD
Mother machine
σB
σM
σW
σX
σD
σB σMσW σX σD
σW
2 μm
0
0.04
0.08
0.12
Fr
eq
ue
nc
y 
(1
/h
ou
r)
σB σMσW σX σD
σB
σM
σW
σX
σD
160
0
40
σA
Figure 2. Five Alternative Sigma Factors Exhibit Pulsatile Dynamics over Extended Timescales in the Mother Machine
(A) Themother machine microfluidic device enables long-term analysis of a single cell maintained at the end of a channel for multiple cell generations (schematic,
top, and image of cells in device, bottom).
(B) Analysis of individual cell lineages show pulsatile dynamics of five alternative sigma factors as well as the constitutively active sigma factor sA for over 100 hr.
Traces represent rates of fluorescent protein expression from target promoters for each sigma factor (promoter activity). Cell cycles are indicated by alternating
gray and white vertical bands. Note that activity values in these conditions are not directly comparable with those in Figure 1E.
(C) Mean pulse dynamics for each alternative sigma factor species. For each sigma factor, n R 320 pulses were detected, aligned around their peaks, and
averaged. Error bars are SEM.
(D) Distribution of normalized pulse amplitudes for the indicated sigma factors.
(E) Mean pulse durations, quantified as full-width at half maximum (FWHM) for each of the alternative sigma factors. Error bars are SEM.
(F) Pulse frequencies for the indicated sigma factors. Error bars are SEM.
See also Figure S3.distance to reach cells at the end of each trench (Norman et al.,
2013). In the mother machine, we grew each reporter strain in
minimal media containing 40 mg/mL MPA. Analysis of reporter
dynamics revealed qualitatively similar dynamics as those
observed on agarose pads, with five alternative sigma factors
exhibiting pulsatile behavior (Figure 2B), with similar distributions
of pulse shapes (Figures 2C and 2D), with typical durations on
the order of 1 hr (Figure 2E), and varying frequencies (Figure 2F) .
The mean pulse showed an increase in activity relative to base-
line activity of at least 5-fold for each sigma factor. sY and sL
were not active under these conditions, possibly due to the
more chemostatic conditions in the device and the consequent
prevention of buildup of secreted components. Therefore, they
were not considered further in these experiments.To understand how pulsing affects the mode of sharing core
RNAP, we constructed a mathematical model where sigma fac-
tor pulsing is driven by key regulatory features common to many
alternative sigma factor systems (see STAR Methods). These
features include two feedback loops, based on transcriptional
autoregulation and inhibition by a co-expressed anti-sigma fac-
tor, as well as activation by an input. For simplicity, we represent
this activation process as a molecular ligand that inactivates the
anti-sigma factor (Figures 3A and S4A), although, in principle, it
can be any process with double-negative logic that inactivates
the anti-sigma in a concentration-dependent manner. This feed-
back structure occurs in all five alternative sigma factors exam-
ined in the mother machine, but has only been characterized in
the context of sB (Locke et al., 2011). As such, the model isCell Systems 6, 216–229, February 28, 2018 219
Eσ
A
anti-σ
input
(ligand)
RNAP
RNAP
σσ
RNAP
σA
σ1
σ2
σ3
σ5
σ4
A
C
D
B
F G H
Time (hours)
0
0.5
1
1.5
2
2.5
al
te
rn
at
iv
e 
σ 
 p
ro
m
ot
er
 a
ct
iv
ity
 (σ
-R
N
A
P 
co
m
pl
ex
 c
on
ce
nt
ra
tio
n,
 μ
M
)
0
2
4
6
8
10
12
σ
A
 prom
oter activity
( σ
A
-RN
A
P com
plex concentration, μM
)
0
1
2
total ligand
0
0.3
0.6
free anti-sigma
0
0.5
1
1.5 sigma-RNAP
0 2 4 6 8 10
Time (hours)
Co
nc
en
tr
at
io
n 
(μ
M
)
1 2 3 4 5
Number of simultaneously
active alternative sigma factors
σ1 activity at peak of σ1 or σ2
0
0.2
0.4
0.6
0.8
1
Fr
ac
tio
n 
of
 p
ul
se
s
σ2
 a
ct
iv
ity
 a
t 
pe
ak
 o
f σ
1  o
r σ
2
σ2
TimeP
ro
m
ot
er
 A
ct
iv
ity
(s
ch
em
at
ic
)
σ1
 P
ro
m
ot
er
A
ct
iv
ity
 (s
ch
em
at
ic
)
σ1
40 60500 2010 30 70 80 90 100
σ2 Promoter
Activity
3.0
3.5
0 1 2 3
0
0.5
1
1.5
2
2.5
-20 -10 0 10 20
-0.2
-0.15
-0.1
-0.05
0
0.05
Lag (hours)
Cr
os
s-
co
rr
el
at
io
n
RNAP limiting
RNAP non-limiting
Figure 3. A Mathematical Model Shows Time Sharing in Alternative Sigma Factor Dynamics
(A) Schematic of model of a single pulsatile alternative sigma factor species. The sigma factor autoregulates its own operon, which contains genes for the sigma
factor and its cognate anti-sigma factor. An input, taken to be a small-molecule ligand (black dot), induces pulses by reducing the inhibitory activity of the anti-
sigma factor.
(B) The simple sigma factor model can generate a pulsatile response to a sudden increase in ligand. Model parameters are in given in the STAR Methods (set A).
(C) Multiple alternative sigma factor circuits identical to the one in (A), along with a constitutive sigma factor representing sA, operating in the same cell, are
coupled through sharing of core RNA polymerase (gray arrows).
(legend continued on next page)
220 Cell Systems 6, 216–229, February 28, 2018
not intended to be a precise representation of any specific sigma
factor system, but rather to explore the behaviors that such
systems could generate when they are coupled through compe-
tition for RNAP. In particular, anti-sigma factors utilize diverse
mechanisms for activation, and the ligand does not directly
represent a specific molecular component. In contrast to other
work modeling the control of sigma factor activities at steady
state (Grigorova et al., 2006; Mauri and Klumpp, 2014; Narula
et al., 2016), we focused on dynamic pulsatile behaviors.
We identified physiologically reasonable parameters (STAR
Methods) that lead to pulsatile dynamics similar to those
observed experimentally for an individual sigma factor (Fig-
ure 3B). In this regime, pulses are initiated through a stochastic
burst of ligand production. These bursts are assumed to be
cell intrinsic based on the lack of correlation in pulsing between
sister cells (Figure S2A; STAR Methods). The ligand pulse can
suddenly reduce the activity of its cognate anti-sigma factor
and thereby de-inhibit the corresponding sigma factor. Autore-
gulation of the sigma factor operon initially amplifies the pulse
by upregulating expression of the sigma factor itself. Finally,
the pulse eventually terminates itself through increased expres-
sion of the anti-sigma factor, which is part of the sigma operon
(Figures 3B and S4B). These results show that the simple
sigma/anti-sigma operon architecture is capable of generating
pulsatile dynamics under physiologically reasonable conditions.
To explore howmultiple pulsatile sigma factor species interact
dynamically under conditions of limiting RNAP, we expanded the
model to include five identical, but orthogonal, pulsatile sigma
factor systems (Figure 3C). In addition, to represent the constitu-
tive, non-pulsatile sA (Figure 1E), we incorporated an additional
sigma factor species with no anti-sigma factor. All sigma factors
were coupled to one another exclusively through competition for
limiting amounts of shared core RNAP (STAR Methods). Such
competition has been established in previous work (Ganguly
and Chatterji, 2012; Grigorova et al., 2006; Hicks and Grossman,
1996; Maeda et al., 2000), and is further supported by experi-
ments in which ectopic expression of sB repressed sW and sD
activity under these conditions (Figures S5A, S5B, and S5C).
The model generated pulsatile dynamics for each of the alter-
native sigma factors, and an approximately constant activity for
sA, consistent with experiments (Figures 3D and S5D). In this
regime, more than 80% of core RNAP not bound to sA was
occupied by one alternative sigma (Figure 3E). Furthermore,
the sigma factors actively excluded one another, suppressing
simultaneous pulses of multiple sigma factors (Figures 3F and
3G), and generating an overall anti-correlation in their activity
when RNAP was limiting, but not when it was in excess (Fig-
ure 3H). We suggest that the regime, which does not depend(D) The multi-sigma factor model produces pulsatile dynamics of each alternativ
(black, right y axis).
(E) Histogram showing the mean fraction of sigma factors active during pulses in
factors are active (exceeding a threshold value of 0.2 mM) simultaneously.
(F) Quantifying the co-occurrence of pulses of distinct sigma factors (schematic
(vertical dashed lines, upper panel). Sigma factor activities at each of these poin
(G) Pulse amplitudes for all detected simulated pulses, plotted as in the lower pa
activities.
(H) Cross-correlation functions between the activities of two alternative sigma fact
not when it is in excess (gray). See also Figures S4 and S5.on the use of symmetric parameter sets for the alternative sigma
factors (Figure S8C), represents perfect time sharing.
The anti-correlations, characteristic of perfect time sharing,
arise because each sigma factor pulse reduces the amount of
core RNAP available for other sigma factors over a typical pulse
duration (
1 hr). Subsequent termination of the pulse causes the
sigma factor to relinquish core RNAP, allowing other sigma fac-
tors to initiate pulses (Figures S4B and S5D). While the overall
rate of pulsing in this parameter regime is controlled by the
rate of underlying stochastic inputs, represented in the model
by ligand species, these ligands are uncorrelated with one
another. The exclusion of simultaneous pulsing results from
coupling between sigma factor species, which can arise only
from competition for core RNAP. These modeling results show
that time sharing dynamics can emerge from the combination
of pulsatile activation dynamics from individual sigma factor
operons and coupling through competition for core RNAP.
These simulations provoke the experimental question of what
dynamic relationships occur among the pulsatile sigma factors
within the same cell. To address this issue, we constructed a
535 ‘‘matrix’’ of strains (15 strains in total, i.e., the upper half ma-
trix plus the diagonal), each containing a cyan fluorescent protein
(CFP) reporter for one sigma factor, and a yellow fluorescent
protein (YFP) reporter for a second sigma factor (Figure 4A).
The matrix also included ‘‘diagonal’’ strains containing two
distinguishable fluorescent reporters for the same sigma factor
to establish the upper limit of possible correlation (Elowitz
et al., 2002). Finally, all strains contained a third fluorescent
protein (mCherry) reporter for sA activity (see STAR Methods).
Using the mother machine, we recorded movies of individual
cells from each of these 15 strains (Figure 4B; Movie S3), flowing
minimal media containing 40 mg/mL MPA at a constant rate into
the microfluidic device. We then quantified instantaneous pro-
moter activities for all reporter pairs over time in each individual
cell lineage (Figure 4C).
To understand the dynamic relationships between each pair
of sigma factors, we computed the cross-correlation function
of each pair of CFP and YFP fluorescence traces. As expected,
strains with two reporters for the same alternative sigma factor
showed strong positive correlations (Figure 5A). By contrast,
four of the ten off-diagonal strains showed negative correlation
between two different sigma factors, as predicted by the model
(Figures 5A and 5B). These negative correlations occur despite
the many factors expected to positively correlate the signals,
including extrinsic fluctuations in cell growth rate and global
gene expression parameters (e.g., transcription and transla-
tion efficiencies) (Bar-Even et al., 2006; Elowitz et al., 2002; New-
man et al., 2006; Paulsson, 2004; Volfson et al., 2006), and thee sigma factor (colored traces, left y axis), but more constant dynamics for sA
the dynamics shown in (D). Most of the time, only one or two alternative sigma
). A pulse detection algorithm recognizes pulses in either of two sigma factors
ts can then be plotted relative to one another, as illustrated in the lower panel.
nel of (F). The constraint of total RNAP limits the sum of the two sigma factor
ors show anti-correlation between when RNA polymerase is limiting (black) but
Cell Systems 6, 216–229, February 28, 2018 221
CA
0
20
40
60
80
0
50
100
0 20 40 60 80 100
Time (hours)
0
10
20
30
40
0
50
100
CF
P 
Pr
om
ot
er
 A
ct
iv
ity
 (a
.u
.) YFP Prom
oter A
ctivity (a.u.)
σWσW
σDσX
CFP
mCh
YFP
σA
B
Time (15 min interval
between successive columns)
σW
σB
2 μm
grow
th
100
200
0
20
40
60
0
σBσW
Figure 4. A Matrix of Multi-reporter Strains Enables Analysis of Dynamic Correlations between Different Alternative Sigma Factors
(A) A matrix of strains was constructed, each of which contains a chromosomally integrated CFP reporter for one sigma factor (colored boxes) and a chro-
mosomally integrated YFP reporter for another (second set of colored boxes), along with mCherry under the control of sA (schematic).
(B) Filmstrip from a mother machine movie, showing a single lane at 15 min intervals. PB-CFP is shown in red, overlaid with PW-YFP in the green channel (see
Movie S3). Anti-correlations between the sigma factors are apparent from the lack of cells showing similar intensities in green and red channels (i.e., the lack of
yellow cells).
(C) Example traces showing the activity dynamics of different pairs of alternative sigma factors, including strains with two reporters for the same sigma factor
(top), and other pairs (lower two panels). See also Figure S6.co-activation of multiple sigma factors by overlapping stresses,
including MPA (Locke et al., 2011; Zhang and Haldenwang,
2005). The same negative correlations also appeared when
using a ‘‘pulse-triggered averaging’’ analysis approach that spe-
cifically focuses on pulses within these time traces (Lin et al.,
2015) (Figure S6). Of the remaining six pairs, five showed positive
correlations that were significant, although substantially weaker
than those observed for diagonal strains (Figure 5A). These will
be discussed in detail below. Finally, one sigma factor pair
showed no strong correlation in either direction. It is interesting
that, while the positively correlated pairs exhibited more
simultaneous pulses than expected if the two sigma factors
were independent, simultaneous pulses were still rare even for
the positively correlated pairs. This can be seen by plotting co-
occurrences of pulses for all sigma factor pairs (Figure 5C).
Perfect time sharing, as demonstrated by the model (Fig-
ure 3H), is predicated on exclusively negative pairwise correla-
tions between sigma factors and results in pulses where one
alternative sigma factor is exclusively active (Figure 3E). In vivo,
however, the appearance of positive and negative pairwise
correlations between sigma factors is consistent with partial
time sharing under these conditions, but also indicates a more
complex and asymmetrical dynamical structure. This can be
seen in the correlation graph (Figure 5B), where no two sigma222 Cell Systems 6, 216–229, February 28, 2018factors share the same pattern of correlations with other sigma
factors (Segre` et al., 2005). Even sB and sD, which show similar
(although not identical) interactions with the other sigma factors,
are anti-correlated with one another. We next asked whether
the complex dynamical correlations observed here could be
explained by competition for RNAP, or whether they require
more specific regulatory interactions.
To address this question, we constructed a minimal, analyti-
cally solvable model of sigma factors competing for a common
pool of core RNAP, dispensingwith the regulatory features incor-
porated in the computational model discussed above (Fig-
ure 5D). We solved this model for an arbitrary number of sigma
factors under the simplifying assumption of small equilibrium
fluctuations (see STARMethods) We obtained analytical expres-
sions for the cross-correlation functions between all sigma factor
pairs in terms of the binding/unbinding rates of the sigma factors
to core RNAP and their abundances.
These results show that competitive binding interactions alone
are sufficient to generate complex correlation graphs with mix-
tures of positive and negative correlations (see STAR Methods).
For example, in the case of three sigma factors, it is possible for
two of the sigma factors, s1 and s2, to exhibit positive correla-
tions with each other, and negative correlations with s3 (Figures
5E and S7A). This occurs when s3 has slower binding and
Figure 5. Dynamic Correlations between Sigma Factors in the Same Cell
(A) Fifteen double-reporter strains for pairs of alternative sigma factors (including ‘‘diagonal’’ strains with two reporters for the same sigma factor) were monitored
in themothermachine. The corresponding time traces were analyzed by cross-correlation analysis. The resultingmatrix of cross-correlations shows both positive
(green), negative (red), and one approximately neutral correlation (blue). Each plot displays the mean cross-correlation (solid line) and the SE of the mean
(shading). The diagonal strains do not show perfect correlation due to noise, and provide an upper limit on the possible strength of positive correlations.
(legend continued on next page)
Cell Systems 6, 216–229, February 28, 2018 223
unbinding rates to core RNAP compared with those of the other
two. In this regime, the fraction of core RNAP bound by s3 fluc-
tuates at a timescale longer than that of the other two sigma fac-
tors. At shorter timescales, s1 and s2 are both more likely to be
found bound to core RNAP when the fraction of bound s3 is
lower than its steady-state value, resulting in a positive correla-
tion between s1 and s2 (Figure 5F).
Similarly, it was possible to generate complex patterns of
dynamical correlations among five sigma factors under certain
parameter regimes in the simple model (Figure 5G). The analyt-
ical minimal model thus demonstrates that complex correlation
patterns, including positive correlations between certain pairs
of sigma factors, can arise from competitive interactions alone,
even without more specific regulatory interactions (although
these could also exist in the biological system). Most critically,
these results show that complex correlation patterns can arise
from asymmetries in the parameters governing sigma factors’
interaction with core RNAP.
To determine whether sigma factors exhibit such asymmetric
relationships with core RNAP in vivo, we constructed a 7 3 7
deletion ‘‘matrix’’ of strains. Sigma factor deletions enable anal-
ysis of competitive interactions without potential overexpression
artifacts. Each strain in thematrix was deleted for one sigma fac-
tor and contained a YFP fluorescent reporter for another sigma
factor. This matrix contained all five pulsatile strains whose
correlations were analyzed in the mother machine, as well as
sY and sL. All strains also contained a constitutive fluorescent
protein (mCherry) to assist in cell segmentation. For each strain
in the matrix, we grew cells in liquid minimal media containing
40 mg/mL MPA, and quantified sigma factor activity by acquiring
static fluorescence microscopy snapshots and quantitatively
analyzing single-cell expression levels (see ‘‘Sample Preparation
for Liquid Culture Snapshots and Agarose Pad Movies,’’ STAR
Methods).
If most interactions between sigma factors result from compe-
tition for core RNAP, then regardless of which sigma factor is
deleted, removing one sigma factor should cause similar relative
effects on the remaining sigma factors. By contrast, if interac-
tions are dominated by more specific regulatory interactions,
the deletion matrix would be expected to show very different
effects for each sigma factor deletion. Analysis of the deletion
matrix revealed that deletion of six of the seven sigma factors
predominantly increased sW activity, with smaller effects on(B) Diagram compactly summarizing the pattern of correlations revealed in (A),
correlations, respectively.
(C) Scatterplots of pulse amplitudes for the sigma factor pairs shown in (A) (cf. Fig
(STAR Methods).
(D) Positive correlations can arise from competitive interactions in aminimal mode
competing for binding to a limited pool of core RNAP. (Dii) Themodel assumes equ
abundance (ci), and its binding (ki) and unbinding (li) rates to core RNAP.
(E) Cross-correlation functions of the bound fractions of all pairs of sigma fact
factors 1 and 2 exhibit positive correlations over sufficiently large timescales (or,
(F) Simulated traces of binding fluctuations of the three sigma factors for the same
timescale than sigma factors 1 and 2. Over these timescales, the other two sigm
each other. In contrast, over shorter timescales (inset) the bound fraction of sigma
(G) Next, we extended the analytical model to six sigma factors (five observed
correlation matrix (among the five observed sigma factors) that exhibited a comple
is shown here (see Figure S7D for the optimal choice of parameters). Despite its sim
positive and negative correlations. See also Figures S6 and S7.
224 Cell Systems 6, 216–229, February 28, 2018other sigma factors (Figures 6A, S8A, and S8B). This result sug-
gests that competition plays a major role in determining sigma
factor activity. There was one exception to this pattern: deletion
of sigD increased activity of all sigma factors except sW and sX.
In addition, the sigD deletion, unlike the others, strongly affected
cell size, suggesting additional pleiotropic effects (Figure S8A).
Together, these results suggest that competition is asymmetric,
with sW and sD being more and less susceptible, respectively,
to competition than other sigma factors. Deletion of sD also
appeared to cause a broader set of effects on cell physiology
compared with other sigma factors.
We next asked whether the asymmetric competition observed
in the deletion matrix could explain the complex mixture of
experimental pairwise correlations between sigma factors. To
answer this question, we used insights from the deletion matrix
(Figure 6A), and the simplified model of competitive interactions
(Figures 5D–5G and S7), to create a hierarchy of sigma factor
‘‘strengths’’ in the model. First, we increased the upregulated
production rate of one sigma factor (labeled s5) by a factor of
1.4, making it more dominant in competitive interactions, analo-
gous to sD. Second, we reduced the affinity of a different sigma
factor (s3) for core RNAP, making it more susceptible to compe-
tition, like sW. Third, for the remaining sigma factors, we used
two intermediate strengths, with one sigma factor possessing
a higher affinity to core RNAP than the other two (see model
parameters, set B, in STAR Methods). As in the simpler case
described in Figure 3, time sharing dominates, with prevalent
negative correlations between alternative sigmas (Figure 6B)
and 
85% of pulses occurring in isolation; in only 15% of the
pulses, two (or more) sigma factors were active simultaneously
(Figure 6C).
In this model, the hierarchy of sigma factor strengths qualita-
tively recapitulated most of the experimentally observed asym-
metric interactions. ‘‘Deletion’’ ofmost sigma factors in themodel
predominantly increased activity of s3, the sW-like sigma factor,
while deletion of s5, the sD-like sigma factor, increased all other
sigma factor activities (Figure 6D). Furthermore, the resulting
pattern of positive and negative pairwise correlations in the
model (Figure 6B) also resembled that observed experimentally
(Figure 5A).s5 exhibited negative correlationswith all other sigma
factors. This result matched most experimental observations.
The exception was the sD -sX pair, which exhibited positive
correlations in the experiments. sD and sX also deviated fromalso using green, red, and blue to represent positive, negative, and neutral
ure 3F). Each dot represents an event in which one or both sigma factors pulse
l of sigma factor-RNAP interactions. (Di) A minimal model of three sigma factors
ilibrium binding/unbinding and uses three parameters for each sigma factor: its
ors calculated directly from the spectral densities. Bound fractions of sigma
equivalently, sufficiently low frequencies in the spectral densities).
parameter values. The bound fraction of sigma factor 3 fluctuates on a longer
a factors are anti-correlated with sigma factor 3 but positively correlated with
factors 1 and 2 are negatively correlated as expected from competitive binding.
and one unobserved) and searched for parameters that resulted in a 5 3 5
x mixture of positive and negative correlations. The resulting correlation matrix
plicity, competitive interactions are sufficient to generate a complex pattern of
00.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Fold Change
ΔsigB
ΔsigD
ΔsigL
ΔsigM
ΔsigW
ΔsigX
ΔsigY
σB σM σW σX σD σL σY
A B
Co
rr
el
at
io
n
σ1 σ2 σ3 σ5σ4
σ
1
σ
2
σ
3
σ
5
σ
4
Experiment Model
-0.5 0 0.5
Lag (hours)
0
0.5
1
-0.5 0 0.5
-0.4
-0.2
0
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0.4
-0.5 0 0.5
-0.4
-0.2
0
0.2
0.4
-0.5 0 0.5
-0.4
-0.2
0
0.2
0.4
-0.5 0 0.5
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0
0.2
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Lag (hours)
0
0.5
1
Co
rr
el
at
io
n
-0.5 0 0.5
-0.1
0
0.1
-0.5 0 0.5
-0.1
0
0.1
-0.5 0 0.5
-0.4
-0.2
0
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Lag (hours)
0
0.5
1
Co
rr
el
at
io
n
-0.5 0 0.5
-0.1
0
0.1
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0
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Lag (hours)
0
0.5
1
Co
rr
el
at
io
n
-0.5 0 0.5
-0.4
-0.2
0
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Lag (hours)
0
0.5
1
Co
rr
el
at
io
n
Model
Fr
ac
tio
n 
of
 p
ul
se
s
Number of simultaneously
active alternative sigma factors
1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
C
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Fold Change
Δsig1
Δsig2
Δsig3
Δsig4
Δsig5
σ1 σ4 σ5σ2 σ3
ModelD
Figure 6. Diversity in Sigma Factor Competition and Correlation
(A) To systematically analyze competition between sigma factors, we constructed a deletion matrix. Each strain in the matrix is genetically deleted for one sigma
factor (rows), and contains a chromosomally integrated fluorescent reporter for another sigma factor (columns). Cells were grown inminimal media with 40 mg/mL
MPA. Mean reporter expression was measured by fluorescence microscopy. Each element in the matrix shows the fold change in sigma factor activity upon
deletion of another sigma factor relative to wild-type. For instance, the DsigB,PW-yfp strain (row 1, column 3) exhibited
1.4-fold more fluorescent signal relative
to the PW-yfp reporter strain without deletion. The elements along the ‘‘diagonal’’ of the deletion matrix reflect negative controls on the sigma factors reporter
strains’ specificity. Asymmetric interactions are evident from the increased fold change along the DsigD row and the sW column.
(B) Simulated cross-correlations for asymmetric parameters inspired by the results in (A); see (D), and parameter set B in STARMethods. Amixture of positive and
negative cross-correlations can arise from asymmetric competition for core RNAP. Each trace is the average of 81 cross-correlation functions, calculated from
28,000 simulated cell cycles.
(C) Histogram showing the distribution of the number of sigma factors simultaneously active during pulses in the dynamics displayed in Figure S8C (parameter set
B in STAR Methods). Pulse detection threshold was as in Figure 3E, except for s3, which used a threshold of 0.1 mM.
(D) The asymmetric sigma factor model recapitulates the broad features of the experimental deletion matrix. The deletion matrix was simulated in the model
(parameter set B in STARMethods) by removing each alternative sigma factor one at a time, and then simulating the rest of the sigma factors. Each simulation was
run for 28,000 cell cycles. Deletion of s5 increases the activity of all other sigma factors. s3 is most sensitive to deletion of any other sigma factor. See also
Figure S8.expectation in the experimental deletion matrix, where sigD
deletion caused a decrease, rather than an increase, in sX activ-
ity (Figure 6A). These results suggest that there could be a more
complex and specific regulatory interaction between these two
sigma factors. In the model, s3 generally behaved like sW with
respect to its correlations with other sigma factors. It correlated
negatively with s5, and positively with the weaker sigma factors
s2 and s4, which we identify with sX and sM. These simple pa-
rameters did not capture all dynamic interactions. For instance,
sB showed positive and neutral, rather than negative, interac-
tions with sM and sX, respectively. Nevertheless, taken together,
our results demonstrate that sigma factor competition, in the
absence of additional regulation, can generate patterns of mixedpairwise correlations, broadly similar to those observed experi-
mentally. Moreover, this work suggests that, although it is not
perfect, many alternative sigmas may operate in regimes where
time sharing contributes to the promoter activity dynamics
observed.
DISCUSSION
Here we have analyzed the dynamics of sigma factor activity
and competition in B. subtilis under energy stress. Despite
the steady-state nature of the environmental conditions, we
find that many sigma factors activate not at constant levels,
but rather through repetitive pulsing (Figures 1 and 2). TheseCell Systems 6, 216–229, February 28, 2018 225
2σ  activity
σ3 activity
σ1 activity
state of an 
individual cell
2σ  activity
σ3 activity
σ1 activity
Molecular sharing Time-sharing
σ1+σ2+σ3≈const
A
σ1 active σ2 active σ3 active
B
CD
Selection
Time
Timeσ
2 activity
σ3 activity
σ1 activity
σ 2 activity
σ3 activity
σ1 activity
Condition 1 Condition 2
Distribution
switching 
on cell-cycle 
timescale
Figure 7. Time Sharing Could Control the Distribution of Cell States in a Population
(A) Two distinct modes of sigma factor sharing (schematic). Competition for core polymerase restricts mean sigma factor activities to a subspace indicated by
gray triangle, onwhich the sumof sigma factor activities is constant. Inmolecular sharing, each sigma factor would be active at a constant, intermediate level, with
all cells (yellow dots) in similar states. In time sharing, cells predominantly occupy the vertices and edges of the allowed subspace (yellow dots, right triangle), and
switch dynamically among these states through pulsing. They are therefore distributed over a broader variety of expression states at any given time. We consider
a hypothetical symmetric three sigma factor system for conceptual illustration.
(B) Because the duration of pulses is comparable with the cell-cycle duration, cells tend to switch states from one cell cycle to the next (schematic). Here, colors
indicate activity levels of each of three sigmas, following the scheme in (A).
(C) A schematic population of time-sharing cells. As in (B), colors indicate activities of three sigma factors. Due to stochasticity of sigma factor pulses, under these
assumptions, the distribution of cell states can recover within one cell cycle from a perturbation to the cell state distribution (e.g., selection for the red
state, arrow).
(D) In the time-sharing system, dynamic switching among states enables changes to the environment to rapidly shift the population from one distribution to
another (left and right spaces, schematic).dynamics expand previously published observations of sB puls-
ing (Locke et al., 2011) to a much broader set of sigma factors,
and suggest that pulsing is a general mode of sigma factor acti-
vation. Based on analogy with sB regulation, pulsatile activity
likely results from the interaction of a positive feedback loop
on sigma factor expression and a negative feedback loop medi-
ated by the corresponding anti-sigma factor. A model based on
this generic architecture, in which sigma factors compete for
limiting RNAP, demonstrates that competition can distribute
pulsatile sigma factor activities in time, reducing their temporal
overlap and resulting in negative correlations between their
activities, among more complex dynamics.
An ideal time-sharing system allows cells to focus the limited
resource of core RNAP on a few alternative sigma factor regu-
lons at a time, rather than spreading it across all sigma factor
regulons at lower, constant levels (Figure 1C). These dynamics
have a strong effect on the distribution of sigma factor activity
states within a population. For example, consider three hypo-
thetical alternative sigma factors. Without pulsatile dynamics
(molecular sharing), all cells would exhibit relatively similar
phenotypic states, with intermediate activities of each sigma fac-
tor, constrained by the total amount of core RNAP (Figure 7A, left
simplex). By contrast, time sharing causes sigma factor activities
to mainly occupy the edges and vertices of the allowed state-
space (Figure 7A, right simplex), and to dynamically transition226 Cell Systems 6, 216–229, February 28, 2018from one such state to another in a stochastic fashion. In the
time-sharing regime, inputs to the system could effectively regu-
late the fraction of time that cells spend in various sigma factor
activation states by controlling the relative frequency of pulses
of different sigma factors. In addition, because the pulse dura-
tions observed here, of 
1 hr, are comparable with the duration
of the cell cycle in these conditions, time sharing could cause
successive cell cycles to be dominated by different sigma factor
programs and corresponding phenotypes (Figure 7B). In this
way, cells could control the distribution of activity states in the
population, and regenerate the entire distribution of states after
a perturbation (Figures 7C and 7D).
The question remains whether the pulsatile dynamics
observed at the level of alternative sigma promoters have pheno-
typic consequences. For phenotypic time sharing to occur, two
conditions must be satisfied. First, anti-correlations observed
with fluorescent protein reporters should reflect corresponding
anti-correlations between phenotypes. Because the fluorescent
reporter proteins used here are stable, their concentrations
should be proportional to those of stable endogenous sigma fac-
tor target proteins, and thus the dynamic reporter correlations
measured here likely reflect correlations among endogenous
genes. Unstable target proteins could increase the magnitude
of correlations by reducing time averaging. Second, individual
sigma factor pulses must generate sufficient amounts of target
gene products to affect cellular functions. Future work should
address the propagation of pulses to specific phenotypes.
The dynamics observed here deviate from perfect time
sharing in several ways. First, sigma factor activities are not
exclusively pulsatile, as some basal activity is observed be-
tween pulses (Figure 2B). Second, competition appears to be
asymmetric (Figure 6A). Third, the sigma factors exhibit a com-
plex mixture of positive and negative correlations, rather than
uniform negative correlations (Figure 5A). Modeling revealed
how such mixed correlations can arise from asymmetric
competition, particularly when sigma factors differ in the relative
timescales of their interactions with RNAP (Figure S7). Higher-
dimensional measurements of more than two alternative sigma
factors at a time will be necessary to fully understand these
complex dynamics.
While pulses are a strong feature here, sigma factor dynamics
in general vary between systems and contexts. For example, the
transition from exponential phase to stationary phase in Escher-
ichia coli (Gruber and Gross, 2003), and the developmental pro-
gram of sporulation in B. subtilis (Fimlaid and Shen, 2015), both
involve, in different ways, sequentially ordered replacement of
one sigma factor by another. In addition, the same sigma factor
can activate with repetitive pulsing or adaptive dynamics in
different contexts, as has been shown for sB (Cabeen et al.,
2017; Young et al., 2013). Our observations are not incompatible
with previously analyzed modes of activation, but rather enlarge
the spectrum of dynamical modes implemented by sigma factor
systems.STAR+METHODS
Detailed methods are provided in the online version of this paper
and include the following:
d KEY RESOURCES TABLE
d CONTACT FOR REAGENT AND RESOURCE SHARING
d EXPERIMENTAL MODEL AND SUBJECT DETAILSB Bacillus subtilis Strains
d METHOD DETAILS
B Plasmid Construction
B Target Promoters for Sigma Factors
B Microscopy
B Sample Preparation for Liquid Culture Snapshots and
Agarose Pad Movies
B Sample Preparation for Stationary-Phase (Conditioned
Medium) Experiments
B Sample Preparation for Mother Machine Experiments
B Mathematical Model of s Factor Pulsing and Compe-
tition
B Model Parameters
B Analytical Minimal Model of Competing Sigma Factors
B Extension to an Arbitrary Number of Sigma Factors
B Example: Three Sigma Factors
d QUANTIFICATION AND STATISTICAL ANALYSIS
B Image Analysis for Liquid Culture Snapshots
B Image Analysis for Agarose Pad Movies
B Image Analysis for Mother Machine Movies
B Promoter Activity Calculation
B Pulse Identification for Agarose Pad MoviesB Pulse Identification for Mother Machine Movies and
Pulse Characteristic Calculations
B Cross Correlation Functions, Pulse Triggered Aver-
aging, and Pulse Amplitude Scatter Plots
B Deletion Matrix Experiments
d DATA AND SOFTWARE AVAILABILITY
d ADDITIONAL RESOURCES
SUPPLEMENTAL INFORMATION
Supplemental Information includes eight figures, one table, and three movies
and can be found with this article online at https://doi.org/10.1016/j.cels.2018.
01.011.
ACKNOWLEDGMENTS
We would like to thank Matt Cabeen, Richard Losick, Nathan Lord, Johan
Paulsson, and Suckjoon Jun for discussions and experimental training on
the mother machine. We also thank members of the Elowitz lab for comments
and feedback on the manuscript. This work was supported by NIH grants R01
GM079771B and R01 HD075605A (to M.B.E.), T32 GM07616 (to J.P.), and
NIHGMS K99BM118910 (to S.H.). The content is solely the responsibility of
the authors and does not necessarily represent the official views of the NIH.
It was also supported by National Science Foundation grant 1547056 and
the Institute for Collaborative Biotechnologies through grant W911NF-09-
0001 (KK9150) from the U.S. Army Research Office. The content of the infor-
mation does not necessarily reflect the position or the policy of the govern-
ment, and no official endorsement should be inferred. J.G.-O. and M.D.
were supported by the Spanish Ministry of Economy and Competitiveness
(MINECO) and FEDER (project FIS2015-66503-C3-1-P), the ICREA Academia
program, and the Maria de Maeztu Program for Units of Excellence in R&D
(MINECO, project MDM-2014-0370). Work in the Locke laboratory was sup-
ported by the European Research Council under the European Union’s Sev-
enth Framework Program (FP/2007-2013)/ERC Grant Agreement 338060, a
fellowship from the Gatsby Foundation (GAT3272/GLC), and an award from
the Human Frontier Science Program (CDA00068/2012).
AUTHOR CONTRIBUTIONS
Conceptualization, J.P., M.D., J.G.-O., J.C.W.L., and M.B.E.; Methodology,
J.P., M.D., J.G.-O., J.C.W.L., and M.B.E.; Software, J.P., M.D., Y.L., S.H.,
S.E.S.-U., S.Q., J.G.-O., J.C.W.L., and M.B.E.; Validation, J.P., M.D.,
M.J.H.-J, J.G.-O., J.C.W.L., and M.B.E.; Formal Analysis, J.P., M.D., Y.L.,
J.G.-O., J.C.W.L., and M.B.E.; Investigation, all authors; Writing, J.P., M.D.,
S.H., J.G.-O., J.C.W.L., and M.B.E.; Visualization, J.P., M.D., Y.L., S.H.,
J.G.-O., J.C.W.L., and M.B.E.; Funding Acquisition, J.P., M.D., J.G.-O.,
J.C.W.L., and M.B.E.
DECLARATION OF INTERESTS
The authors declare no competing interests.
Received: March 7, 2017
Revised: September 4, 2017
Accepted: January 10, 2018
Published: February 14, 2018
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STAR+METHODSKEY RESOURCES TABLEREAGENT or RESOURCE SOURCE IDENTIFIER
Bacterial and Virus Strains
PY79 BGSC 1A747 PY79
PY79; ppsB::PtrpE-mCherry PhleoR (Locke et al., 2011) JP1
JP1;ytvA::NeoR This paper JP2
JP2;sacA::PB-yfp CmR This paper JP3
JP2;sacA::PM-yfp CmR This paper JP4
JP2;sacA::PW-yfp CmR This paper JP5
JP2;sacA::PX-yfp CmR This paper JP6
JP2;sacA::PD-yfp CmR This paper JP7
JP2;sacA::PL-yfp CmR This paper JP8
JP2;sacA::PY-yfp CmR This paper JP9
JP2;sacA::PA-yfp CmR This paper JP10
JP3;rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP11
JP4; sigM::TetR This paper, (Luo and Helmann, 2009) JP12
JP4; sigW::ErmR This paper, (Luo and Helmann, 2009) JP13
JP6;sigX::SpectR This paper, (Cao and Helmann, 2002) JP14
sigD::TetR (Helmann et al., 1988; Steinmetz
and Richter, 1994)
JP15
JP7; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP16
JP1; sacA::PL-yfp CmR This paper, (Wiegeshoff et al., 2006) JP17
JP17;sigL::KanR This paper JP18
JP1; sacA::PY-yfp CmR This paper JP19
JP19;sigY::KanR This paper, (Cao et al., 2003) JP20
JP3;amyE::PB-3Xcfp SpectR This paper JP21
JP3;amyE::PM-3Xcfp SpectR This paper JP22
JP3;amyE::PW-3Xcfp SpectR This paper JP23
JP3;amyE::PX-3Xcfp SpectR This paper JP24
JP3;amyE::PD-3Xcfp SpectR This paper JP25
JP4;amyE::PB-3Xcfp SpectR This paper JP26
JP4;amyE::PM-3Xcfp SpectR This paper JP27
JP4;amyE::PW-3Xcfp SpectR This paper JP28
JP4;amyE::PX-3Xcfp SpectR This paper JP29
JP4;amyE::PD-3Xcfp SpectR This paper JP30
JP5;amyE::PB-3Xcfp SpectR This paper JP31
JP5;amyE::PM-3Xcfp SpectR This paper JP32
JP5;amyE::PW-3Xcfp SpectR This paper JP33
JP5;amyE::PX-3Xcfp SpectR This paper JP34
JP5;amyE::PD-3Xcfp SpectR This paper JP35
JP6;amyE::PB-3Xcfp SpectR This paper JP36
JP6;amyE::PM-3Xcfp SpectR This paper JP37
JP6;amyE::PW-3Xcfp SpectR This paper JP38
JP6;amyE::PX-3Xcfp SpectR This paper JP39
JP6;amyE::PD-3Xcfp SpectR This paper JP40
JP7;amyE::PB-3Xcfp SpectR This paper JP41
(Continued on next page)
e1 Cell Systems 6, 216–229.e1–e15, February 28, 2018
Continued
REAGENT or RESOURCE SOURCE IDENTIFIER
JP7;amyE::PM-3Xcfp SpectR This paper JP42
JP7;amyE::PW-3Xcfp SpectR This paper JP43
JP7;amyE::PX-3Xcfp SpectR This paper JP44
JP7;amyE::PD-3Xcfp SpectR This paper JP45
JJB213; rsbU-rsbX::TetR This paper JP46
JP1 ; rsbU-rsbX::TetR This paper JP47
JP47; amyE::Phyperspank-sigB SpectR This paper JP48
JP48; pyrD::PB-cfp KanR This paper JP49
JP49; sacA::PW-yfp CmR This paper JP50
JP49; sacA::PD-yfp CmR This paper JP51
JP50; hag::ErmR This paper, (Koo et al., 2017) JP52
JP51; hag::ErmR This paper, (Koo et al., 2017) JP53
JP21;hagTErmR This paper, (Koo et al., 2017) JP54
JP26;hagTErmR This paper, (Koo et al., 2017) JP55
JP31;hagTErmR This paper, (Koo et al., 2017) JP56
JP36;hagTErmR This paper, (Koo et al., 2017) JP57
JP41;hagTErmR This paper, (Koo et al., 2017) JP58
JP27;hagTErmR This paper, (Koo et al., 2017) JP59
JP32;hagTErmR This paper, (Koo et al., 2017) JP60
JP37;hagTErmR This paper, (Koo et al., 2017) JP61
JP42;hagTErmR This paper, (Koo et al., 2017) JP62
JP33;hagTErmR This paper, (Koo et al., 2017) JP63
JP38;hagTErmR This paper, (Koo et al., 2017) JP64
JP43;hagTErmR This paper, (Koo et al., 2017) JP65
JP39;hagTErmR This paper, (Koo et al., 2017) JP66
JP44;hagTErmR This paper, (Koo et al., 2017) JP67
JP45;hagTErmR This paper, (Koo et al., 2017) JP68
JP2; amyE::Phyperspank-yfp SpectR This paper JP69
JP69; hag::ErmR This paper, (Koo et al., 2017) JP70
JP3; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP71
JP4; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP72
JP5; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP73
JP6; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP74
JP7; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP75
JP8; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP76
JP9; rsbU-rsbX::TetR This paper, (Locke et al., 2011) JP77
JP3; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP78
JP4; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP79
JP5; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP80
JP6; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP81
JP7; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP82
JP8; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP83
JP9; sigD::TetR This paper, (Helmann et al.,1988;
Steinmetz and Richter, 1994)
JP84
(Continued on next page)
Cell Systems 6, 216–229.e1–e15, February 28, 2018 e2
Continued
REAGENT or RESOURCE SOURCE IDENTIFIER
JP3; sigL::KanR This paper, (Wiegeshoff et al., 2006) JP85
JP4; sigL::KanR This paper, (Wiegeshoff et al., 2006) JP86
JP5;sigL::KanR This paper, (Wiegeshoff et al., 2006) JP87
JP6;sigL::KanR This paper, (Wiegeshoff et al., 2006) JP88
JP7;sigL::KanR This paper, (Wiegeshoff et al., 2006) JP89
JP8;sigL::KanR This paper, (Wiegeshoff et al., 2006) JP90
JP9;sigL::KanR This paper, (Wiegeshoff et al., 2006) JP91
JP3;sigM::TetR This paper, (Luo and Helmann, 2009) JP92
JP4;sigM::TetR This paper, (Luo and Helmann, 2009) JP93
JP5;sigM::TetR This paper, (Luo and Helmann, 2009) JP94
JP6;sigM::TetR This paper, (Luo and Helmann, 2009) JP95
JP7;sigM::TetR This paper, (Luo and Helmann, 2009) JP96
JP8;sigM::TetR This paper, (Luo and Helmann, 2009) JP97
JP9;sigM::TetR This paper, (Luo and Helmann, 2009) JP98
JP4; sigW::ErmR This paper, (Luo and Helmann, 2009) JP99
JP4; sigW::ErmR This paper, (Luo and Helmann, 2009) JP100
JP5; sigW::ErmR This paper, (Luo and Helmann, 2009) JP101
JP6; sigW::ErmR This paper, (Luo and Helmann, 2009) JP102
JP7; sigW::ErmR This paper, (Luo and Helmann, 2009) JP103
JP8; sigW::ErmR This paper, (Luo and Helmann, 2009) JP104
JP9; sigW::ErmR This paper, (Luo and Helmann, 2009) JP105
JP3;sigX::SpectR This paper, (Cao and Helmann, 2002) JP106
JP4;sigX::SpectR This paper, (Cao and Helmann, 2002) JP107
JP5;sigX::SpectR This paper, (Cao and Helmann, 2002) JP108
JP6;sigX::SpectR This paper, (Cao and Helmann, 2002) JP109
JP7;sigX::SpectR This paper, (Cao and Helmann, 2002) JP110
JP8;sigX::SpectR This paper, (Cao and Helmann, 2002) JP111
JP9;sigX::SpectR This paper, (Cao and Helmann, 2002) JP112
JP3;sigY::KanR This paper, (Cao et al., 2003) JP113
JP4;sigY::KanR This paper, (Cao et al., 2003) JP114
JP5;sigY::KanR This paper, (Cao et al., 2003) JP115
JP6;sigY::KanR This paper, (Cao et al., 2003) JP116
JP7;sigY::KanR This paper, (Cao et al., 2003) JP117
JP8;sigY::KanR This paper, (Cao et al., 2003) JP118
JP9;sigY::KanR This paper, (Cao et al., 2003) JP119
JP7; hagTErmR This paper, (Koo et al., 2017) JP120
Chemicals, Peptides, and Recombinant Proteins
Mycophenolic Acid MP Biomedicals Cat #194172
Recombinant DNA
Plasmid ECE174, sacA::P?-yfp CmR , where ? can
be SigB,D,L,M,W,X,Y target site
This paper, (Locke et al., 2011) Plasmid #1 (see STAR Methods)
Plasmid pDL30, amyE::P?-3Xcfp SpectR,
where ? can be sigB,D,M,W,X, target site
This paper Plasmid #2 (see STAR Methods)
Plasmid pDR-111, amyE::Phyperspank-sigB SpectR This paper Plasmid #3 (see STAR Methods)
Plasmid ECE171, pyrD::PB-cfp kanR This paper Plasmid #4 (see STAR Methods)
Plasmid pDR-111, amyE::Phyperspank-yfp SpectR This paper Plasmid #5 (see STAR Methods)
Software and Algorithms
Custom MATLAB Algorithms for Image Analysis This paper, (Locke et al., 2011)
e3 Cell Systems 6, 216–229.e1–e15, February 28, 2018
CONTACT FOR REAGENT AND RESOURCE SHARING
Further information and requests for resources and reagents should be directed to andwill be fulfilled by the LeadContact, Michael B.
Elowitz, at melowitz@caltech.edu.
EXPERIMENTAL MODEL AND SUBJECT DETAILS
This section details the sample preparation for experiments as well as the mathematical model, as well as a reference table for which
strains werve to generate specific figures.Table of Figures and Associated Strains
Figure Strains
1 JP3...JP10
2 JP54, JP59, JP63, JP66, JP68, JP70
3 n/a
4 JP56, JP63, JP67
5 JP54...JP68
6 JP71...JP119
7 n/a
S1 JP3...JP10, JP71, JP82, JP90, JP93, JP101, JP109, JP119
S2 A,B,C JP3...JP9
S2 D JP73
S3A,B JP54, JP59, JP63, JP66, JP68, JP70
S3C JP7, JP120
S4 JP52, JP53
S5 n/a
S6 JP54...JP68
S7 n/a
S8 JP3, JP71, JP78, JP85, JP92, JP99, JP106, JP113Bacillus subtilis Strains
All strains were constructed in the PY79 genetic background, and the list of strains used is given in the Key Resources Table. Many
strains and genomic DNA were kind gifts of C.W. Price (see references), and many sigma factor deletion strains were kind gifts from
John Helmann. Several strains were obtained from the Bacillus Genetic Stock Center (BGSC), and their strain codes are noted in the
Key Resources Table.
In this table, in the column labeled ‘‘Source,’’ the term ‘‘This paper’’ indicates that this strain was constructed by the authors. Addi-
tional citations in the ‘‘Source’’ column reflect genetic material (or information) that was utilized to construct the strain. Genetic de-
letionsweremade by replacing genes of interest with a selectionmarker, typically by transforming genomic DNA alreading containing
such marker into the relevant strain, and then selecting with the appropriate antibiotic.
Antibiotic resistancewas switchedusing apreviouslydescribedantibiotic switching vector system (Steinmetz andRichter, 1994).De-
letionsweremade by replacing genes of interest with a selectionmarker via a linear DNA fragment homologous to the region of interest.
METHOD DETAILS
Plasmid Construction
All plasmids were cloned using E.coli strain DH5a and a combination of standard molecular cloning techniques and non-ligase
dependent cloning using Clontech In-Fusion Advantage PCR Cloning kits. Plasmid constructs were integrated into B. subtilis
chromosomal regions via double crossover using standard techniques. The following list provides a description of each plasmid
constructed, with details on integration position/cassette and selection marker given at the beginning. Note that all plasmids below
replicate in E. coli but not in B. subtilis.
Plasmid list:
1) ppsB::PtrpE-mCherry Erm
R - This plasmid was used to provide uniform expression of mCherry from a sA-dependent promoter,
enabling automatic image segmentation (cell identification) in time-lapse movie analysis. A minimal sA promoter from the trpE
gene was cloned into a vector with ppsB homology regions (Locke et al., 2011). The original integration vector was a giftCell Systems 6, 216–229.e1–e15, February 28, 2018 e4
e5fromA. Eldar (Eldar et al., 2009). For some strains, the selectionmarker was subsequently changed, inB. subtilis, to eitherKanR
or PhleoR.
2) sacA::P?-yfp Cm
R - Target promoters of each alternative sigma factor, (B, D, L, M, W, X, Y, A) were cloned into the EcoRI/
BamHI sites of AEC127 (Eldar et al., 2009). For sA, a minimal sA promoter was used from the trpE gene(Locke et al., 2011).
Target promoter sequences for alternative sigmas are described below.
3) amyE::P?-3Xcfp Spect
R. Target promoters of each alternative sigma factor (B, D, L, M, W, X, Y), were cloned into the EcoRI/
Nhe1 sites of plasmid amyE::3XCFP SpectR (Locke et al., 2011). This plasmid, based on pDL30, contains 3 tandem copies
of cfp, each with its own RBS. Target promoter sequences are described below.
4) amyE::Phyperspank-sigB Spect
R - The coding region of sigB, along with a 5’ transcriptional terminator, was cloned downstream
of the Phyperspank IPTG-inducible promoter in plasmid pDR-111 (gift of D. Rudner, Harvard).
5) pyrD::PB-cfp kan
R. Target promoter of sB, followed by the CFP fluorescent protein gene, was cloned into the EcoRI/BseRI site
of the ECE171 plasmid (Middleton and Hofmeister, 2004).Target Promoters for Sigma Factors
Below is a list of the target promoters used to report on each sigma factor’s activity. Each sequence below contains a binding site for
the corresponding sigma factor. These sequences were cloned upstream of a standard cassette containing an RBS followed by the
yfp reporter gene. Note restriction enzyme sites are not included in the displayed sequences.
1) sB : Sequence was chosen from the sB binding site upstream of the rsbV gene (Boylan et al., 1993; Kalman et al., 1990).5’-GTT
TCTTGGAGCGTCCTGATCTGCAGAAGCTCATTGAGGAACATATGTGTTCCTCTGCGCAGGAAATGGTCAAAAACATTTATGA
CAGCCTCCTCAAATTGCAGGATTTTCAGCTTCACGATGATTTTACGTTAATTGTTTTGCGGAGAAAGGTTTAACGTCTGTCAG
ACGAGGGTATAAAGCAACTAGTGATTTGAAGGAAAATTTG- 3’
2) sD: Sequence was chosen from the sD binding site upstream of the flgB gene (Estacio et al., 1998).5’ – TTTTGCATTTTTCTTCA
AAAAGTTTCAAAAATGCCGAAAAGAAAGGAGAAAAAACAGAAATTCTG –3’
3) sL: Sequencewas chosen from thesL binding site upstreamof the ptb gene (Debarbouille et al., 1999).5’- AATATGGCCTTGCA
AATGAAGGCATGCAATAATTTGCAGAATAAACGCAAACATCTGCACGAATGTTTCGGTATACCTGGTATGACAGCACCCTTA
AGAGCTGGCATGGAACTTGCATAATAAAAGGCGGAG – 3’
4) sM: Sequence was chosen from the sM binding site upstream of the sigM gene (Horsburgh and Moir, 1999).5’ – TTTGCATGTA
ATGTGCAACTTTAAACCTTTCTTATGCGTGTATAACATAGAGG-3’
5) sW: Sequence was chosen from the sW binding site upstream of the ydbS gene (Cao et al., 2002).5’ – TTAAGAATGAAACC
TTTCTGTAAAAGAGACGTATAAATAACGACGAAAAAAAG – 3’
6) sX: Sequence was chosen from the sX binding site upstream of the sigX gene (Huang et al., 1997).5’ – TTGTAATGTAACTTTTC
AAGCTATTCATACGACAAAAAAGTGAACGGAGGG – 3’
7) sY: Sequence was chosen from the sY binding site upstream of the sigY gene (Cao et al., 2003).5’ – GAATTGTAAAAAAGATGA
ACGCTTTTGAATCCGGTGTCGTCTCATAAGGCAGAAAAACA – 3’
These promoters were first cloned into the appropriate plasmid (see section Plasmid Construction), and next, these plasmids
were transformed into appropriate B. subtilis strains (see Key Resources Table). This transformation step resulted in an expression
chromosomally integrated at a target locus.
Microscopy
All data were acquired using a CoolSnap HQ2 camera attached to a Nikon inverted TI-E microscope, equipped with the Nikon Perfect
Focus System (PFS) hardware autofocus module. Molecular Devices commercial software (Metamorph 7.5.6.0) controlled micro-
scope, camera, motorized stage (ASI instruments), and epifluorescent and brightfield shutters (Sutter Instruments). For experiments
in liquid culture and agarose pads, epi-illumination was provided by a 300 W Xenon light source (LamdbaLS, Sutter instruments)
connected via a liquid light guide into the illuminator of the scope.Betweendays, relative lamp intensity levelsweremonitoredby taking
an imageof fluorescent beads andmeasuring theirmean intensity. Exposure timeswere then adjusted to keepper exposure light levels
constantbetweenexperiments. For experiments in themothermachine, epi-illuminationwasprovidedbyasolid statewhite light source
(Lumencor SOLA, Lumencor SOLA). Phase contrast illumination was provided by a halogen bulb to allow verification of cell focus and
cell shape.Temperaturecontrolwasachievedusinganenclosedmicroscopechamber (Nikon) attached toa temperature sensitiveheat
exchanger set to 37 C.All experiments usedaPhase100xPlanApo (NA1.4) objective.Chromafilter sets usedwere as follows: #41027
(mCherry), #41028 (YFP), and #31044v2 (CFP). The interval between consecutive imaging was 15 minutes.
Sample Preparation for Liquid Culture Snapshots and Agarose Pad Movies
Unless otherwise noted, cells were grown in Spizizen’s minimal media, or SMM (Spizizen, 1958), which uses 0.5% glucose as the
carbon source. Mycophenolic acid (MPA) was dissolved in DMSO and diluted 1,000 fold into working concentrations in liquid and
pad conditions. IPTG was dissolved in H2O and diluted 1,000 fold into working concentrations. Concentrations of 0.1% DMSO
were not found to affect cell growth or sB activity.Cell Systems 6, 216–229.e1–e15, February 28, 2018
Samples were prepared following a time-lapse microscopy protocol described previously (Young et al., 2011). A stab from a
glycerol stock was inoculated into SMM, placed into a 30 C shaking incubator, and grown overnight. Cells were then diluted
back to a final concentration of 0.01 OD600 in a total volume of 2 ml of SMM. Cells were then grown in a 37
C shaker for 3 hours.
For liquid culture experiments, MPA (MP Biomedicals cat #194172) was then added to the culture to a final concentration
for 40 mg/ml. Cells were returned the 37 C shaker for 3 hours, after which 2 ml of culture was spotted onto an agarose pad. Agarose
pads were constructed of 1.5% low melt agarose solution in PBS, and then imaged, as described in the ‘Microscopy’ section.
For time-lapse movies, cells were spotted on solidified 1.5% low melt agarose in SMM pads. MPA was also added to the pads to
final concentration of 40 mg/ml. These prepared pads were then enclosed in coverglass bottom dishes (Wilco #HBSt-5040), sealed
with parafilm or grease to prevent evaporation, and then imaged.
Sample Preparation for Stationary-Phase (Conditioned Medium) Experiments
Conditioned medium was prepared growing PY79 wild-type B. subtilis strain in 2 ml of LB at 37 C for 4.5h. Then, this culture was
diluted in 23ml of fresh LB and was grown at 37 C for 17.5h. After this, cells were removed by centrifugation (at 5,000 rpm for 10min)
and the supernatant was sterilized by filtration (using 0.2 mm pore-size filters) and stored at80 C. This conditioned media protocol
was defined previously (Espinar et al., 2013).
Cells were grown from glycerol stocks in LB until OD600 1.5-3.5, then diluted back into LB (1:10) in PBS to an OD600 of 0.05. This
culture was grown at 37 C for a minimum of 4 hours and a maximum of 7, when cells were diluted to an OD600 of 0.8-0.1 with condi-
tioned medium (1:45) in PBS for imaging. 1.5% low melting agarose pads were prepared with conditioned medium (1:45) in PBS.
Cells were allowed to equilibrate for 2-3 hours before initiating time-lapse imaging.
Sample Preparation for Mother Machine Experiments
Wafer Construction
Silicon wafers were constructed using photolithography by Shivakumar Bhaskaran at the Searle CleanRoomManager at the Univer-
sity of Chicago. The CAD file for the design was a kind gift from Richard Losick and Johan Paulsson (Norman et al., 2013).
Chip Construction
Mother machine chips were constructed by first mixing Sylgard 184 (Dow Corning) Parts A and B in ratios of 10 to 1 by weight,
respectively. Both parts were thoroughly mixed together, and then degassed in a vacuum chamber (Welch 256413-01) for 1 hr or
until there was no visual sign of bubbles. The PDMSmixture was poured onto a wafer that had been placed into a ‘boat’ of aluminum
foil, then baked at 65 C overnight. The solidified PDMS was then carefully peeled off the wafer, cut with a scalpel to isolate the
device, and fluidic inlets and outlets were created with with a 0.5 mm diameter hole punch (World Precision Instruments).
Chip Bonding to Coverslip
Glass coverslips (#1.5Gold Seal 3416) were cleaned by sonicating in an Isopropanol Bath for 30minutes, then sonicating in deionized
water 3 times for 30 min. The microfluidic chips were cleaned simply by applying and removing Scotch tape multiple times. Chips
were bonded using a plasma cleaner (Autoglow) with an attached O2 tank, at 50 W for 6 seconds, and was performed at the Micro
Nano Fabrication Laboratory at Caltech. The chip-coverslip complex was then baked at 85 C overnight. Importantly, we found
using O2 with the plasma cleaner strengthened the bond between the glass coverslip and PDMS chip.
Cell Preparation and Cell Loading onto Chip
Cells were grown from glycerol stocks in SMM at 30 C overnight. Cells were diluted to 0.01 OD600 in the morning, and then grown
for 3 hours at 37 C. MPA was then added to a final concentration of 40 mg/ml, and then the culture was grown at 37 C for another
6 hours. Cells were then pipetted into the chip inlet by utilizing gel loading tips (Molecular BioProducts 2155). To ensure cell entry into
the narrow side channels of the chip, the entire coverslip and chip assembly was placed into a custom adapter (Norman et al., 2013),
and then spun in a tabletop microcentrifuge (Eppendorf 5424R) for 10 min at 3,000 rcf.
Fluidic Inlet and Outlet
Fluid flow was driven by a syringe pump (NE-1600, syringepumps.com), which can drive up to six 10-ml syringes (BD 309604) in
parallel. Unless otherwise noted, we used a flow rate of 1.5 ml/min. We used Tygon tubing (Saint Gobain AAD04103) for all tubing
purposes. A blunt end needle (McMaster-Carr 75165A681) interfaced between the syringe and the tubing, and the same blunt
end needle (with luer lock tip removed) interfaced between the tubing and the chip.
Media Driven by the Syringe
Unless noted otherwise, the media used in the mother machine was SMM, supplemented with 40 mg/ml MPA and 100 mg/ml BSA
(Sigma A7906).
The exception was the competition assay in themother machine. Syringes were initially loaded with themedia as described above,
namely SMM + 40 mg/ml MPA + 100 mg/ml BSA. But in the middle of acquisition, the syringes were switched to new syringes that
contained the same media, excepted supplemented with additional 1 mM IPTG.
Mother Machine Microscopy
The coverslip/chip apparatus with attached fluidic inputs and outputs was fixed to the microscope stage insert (I-3014, ASI Imaging)
using lab tape, and then imaged as described in the Microscopy section.
Competition Assay in the Mother Machine
Cells were loaded into the mother machine as described above.Cell Systems 6, 216–229.e1–e15, February 28, 2018 e6
Mathematical Model of s Factor Pulsing and Competition
We constructed a model to simulate the activity of five identical, alternative sigma factor pathways, plus a housekeeping sigma fac-
tor, all interacting only through their association with shared RNA polymerase core (R). The main features of the model are:
d Transcriptional autoregulation. Each sigma factor comprises an operon containing the s factor (Si, where i = 1, 2,. 5) and its
cognate anti-s factor (Ai). This operon is activated by its own s factor. A sixth s factor with no anti-s is considered, representing
the housekeeping factor sA.
d Inhibition by a co-expressed anti-s factor. The s factor binding to its cognate anti-s prevents it from associating with RNAP.
d Limiting levels of RNAP resulting in competitive binding between s factors.
d A ligand that sequesters its cognate anti-s. A common feature among extra-cytoplasmic (ECF) sigma factors is that in most
cases the anti-s is a transmembrane protein that only releases its cognate sigma factor when it receives a certain input
from the extracellular environment (Helmann, 2002). Hence, we implemented in the model a ligand (Li) responsible for seques-
tration of its cognate anti-s, to allow for the release of the corresponding s factor. As shown below, we assume Poisson distrib-
uted steps in Li, which trigger sigma factor activation pulses.
This minimal structure is sufficient to generate pulses in the s$RNAP complex concentration in response to pulsatile ligand
fluctuations. Even though the ligand fluctuations are uncorrelated among sigmas, RNAP competition leads to anticorrelations in
s$RNAP complex concentration that enable the alternative sigma factors to time-share core RNAP (Figure 3H).
An additional equation (Equation S2, below) simulates sA, the main - or housekeeping - s factor. Its structure resembles that of the
alternative s factors, but without an anti-s factor or corresponding ligand. The removal of the anti-s factor results in a non-pulsatile
and constitutive sA$RNAP concentration.
The transcription terms for s factors and anti-s factors are assumed to be linear, as are all degradation terms. The positive tran-
scriptional regulation is modeled with Michaelis-Menten kinetics. sA is assumed to be expressed at higher levels than the alternative
s factors. Negative regulation occurs through sequestration, with linear rates for complex association and dissociation. Importantly,
the sigma-RNAP complex produces more anti-sigma factor than sigma factor, a feature consistent with experimental measurements
(Li et al., 2014). This relative advantage in anti-sigma production allows anti-sigma levels to overcome sigma factor activation and
terminate the pulse. The ligand pulses were uncorrelated in time and exponentially distributed in magnitude. This was motivated
by previous observations (Friedman et al., 2006; Raj et al., 2006; Taniguchi et al., 2010) that cellular protein concentrations follow
a gamma distributed Ornstein-Uhlenbeck (GOU) process (Locke et al., 2011). This implementation allows for independent manipu-
lation ofmean ligand pulse size and pulse frequency. To optimize computational efficiency, ordinary (not stochastic) differential equa-
tions were solved between the stochastic ligand bursts in the discretized stochastic GOU process.
The following ODEs describing the dynamics for each species and their complexes were solved numerically in MATLAB using a
variable step BDFmethod (http://www.mathworks.co.uk/help/matlab/ref/ode15s.html). Parameters can be found in the table below.
The MATLAB codes for the model simulation and analysis are available upon request.
Alternative s Factors (Si)
transcription + positive auto-regulation + complex dissociation + complex association + degradationd½Si
dt
=as + bs½RSi + krs½RSi + ksa½SAi  krs+ ½R½Si  ksa+ ½Si½Ai  ds½Si (Equation S1)
Housekeeping s Factor (SA)
transcription + positive auto-regulation + degradationd½SA
dt
=asA + bsA½RSA + krsA½RSA  krsA+ ½R½SA  dsA½SA (Equation S2)
Anti-s Factors (Ai)
transcription + up-regulation + complex dissociation – complex association – degradationd½Ai
dt
=aa + ba½RSi + ksa½SAi + kal½ALi  ksa+ ½Si½Ai  kal + ½Ai½Li  da½Ai (Equation S3)e7 Cell Systems 6, 216–229.e1–e15, February 28, 2018
RNA Polymerase,s Factor Complex (RS)
complex association – complex dissociation – degradationd½RSi
dt
= krs+ ½R½Si  krs½RSi  drs½RSi (Equation S4)
RNA Polymerase,sA Complex (RSA)
complex association – complex dissociation – degradationd½RSA
dt
= krsA+ ½R½SA  krsA½RSA  drsA½RSA (Equation S5)
Anti-s Factor,s Factor Complex (SA)
complex association – complex dissociation – degradationd½SAi
dt
= ksa+ ½Si½Ai  ksa½SAi  dsa½SAi (Equation S6)
Ligand (L)
complex dissociation – complex association – degradationd½Li
dt
= kal½ALi  kal + ½Ai½Li  dl½Li (Equation S7)
Anti-s Factor,Ligand Complex (AL)
complex association – complex dissociation – degradationd½ALi
dt
= kal + ½Ai½Li  kal½ALi  dal½ALi (Equation S8)
The free amount of RNAP is given by the conservation law
½R=Rtot X
i
½RSi (Equation S9)
where the sum runs over all sigma factors, including the housekeeping sigma factor.
Finally, in order to randomly trigger pulses of sigma factor activation, the dynamics of the ligands are modified by adding
the random quantity 30 (exponentially distributed and uncorrelated between sigma factor species) at random times T0 (uniformly
distributed) throughout the simulation.
LðtÞ/LðtÞ+ 30LðtÞ (Equation S10)
The ligand bursts triggering the sigma factor pulses could in principle have an origin external or internal to the cells. An external
perturbation would result in adjacent cells pulsing together. The fact that we did not observe sister cells pulsing together on agarose
pads (Figure S2A) argues against an external origin for pulsing. Similarly, a cell experiencing a large enough internal ligand perturba-
tion would pulse, but its daughter cells would also inherit this pulse-inducing molecule, meaning they would pulse as well. Thus,
under these conditions a pulse in the parent cell increases the probability of pulsing in the daughter cells, something not observed
experimentally (Figure S2B).
Based on these considerations, we implemented a different type of internal perturbation, in which it is the sharp change in the
concentration of the ligand that is critical for pulse generation. Here, a sharp rise in ligand concentration sequesters the anti-sigma
factor, which in turn frees up its cognate sigma factor to bind RNAP (Figure S4B). The sigma-RNAP complex creates more sigmaCell Systems 6, 216–229.e1–e15, February 28, 2018 e8
factors via positive autoregulation, which sustains the pulse even when the ligand is no longer present. In other words, the ligand itself
is not strictly necessary once the chain of events is initiated. In this scenario, we do not expect a parent cell’s pulse to increase the
chances of its daughters pulsing, consistent with observations.
Model Parameters
Given the current limitations in what is known about the regulation of alternative sigma factors, we lack sufficient information to
construct a biochemically detailed model without introducing many unverified assumptions and unknown parameters. Therefore,
the goal of the model is not to represent the complete complexity of the system, but rather to show that under a minimal set of as-
sumptions that incorporate features common to many sigma factors, dynamics like those observed experimentally could occur. We
selected biologically reasonable values for model parameters, shown in the table below. In particular, the decay rate of all species is
assumed to correspond to the cell division time, here considered to be 1 hour (that is, we assume dilution dominates degradation for
protein removal). The ligand burst sizes and total RNAP concentration are chosen to correspond to abundances on the order of 104
molecules per cell. The relative expression rates (both basal and regulated) of the anti-sigma factors with respect to their correspond-
ing cognate sigma are chosen on the order of 1.5, based on previous work (Li et al., 2014) showing that anti-sigma factors can be
produced at higher rates than sigma factors. Finally, the sigma factor-RNAP dissociation constant is assumed to be 10-fold lower
for the housekeeping sigma factor than for the alternative sigma factors, following existing literature (Sharma and Chatterji, 2010).Reaction Parameter Description Reactant(s)
Value Value
Set A Set B
Basal transcription as Basal rate alternative s factor 1.5 nM/min 1.5 nM/min
asA Basal rate housekeeping s factor s
A 180 nM/min 180 nM/min
aa Basal rate anti-s factor 2.3 nM/min 2.25 nM/min
Up-regulation bs Transcription rate alternative s factor 0.06 min
-1 0.06, 0.06, 0.06, 0.06, 0.084 min-1
bsA Transcription rate s
A 6310-4 min-1 6310-4 min-1
ba Transcription rate anti-s factor 0.09 min
-1 0.09 min-1
Association krs+ Binding rate RNAP, s factor 0.03 nM
-1 min-1 0.03, 0.0091, 0.003, 0.0091,
0.03 nM-1 min-1
krsA+ Binding rate RNAP, s
A 0.3 nM-1 min-1 0.3 nM-1 min-1
ksa+ Binding rate s factor, anti-s factor 0.024 nM
-1 min-1 0.024, 0.001716, 0.024,
0.0024, 0.024 nM-1 min-1
kal+ Binding rate anti-s factor, ligand 0.018 nM
-1 min-1 0.018 nM-1 min-1
Dissociation krs- Unbinding rate RNAP,s factor complex 0.3 min
-1 0.3, 0.99, 3, 0.99, 0.3 min-1
krsA- Unbinding rate RNAP,s
A factor complex 0.3 min-1 0.3 min-1
ksa- Unbinding rate s factor,anti-s factor complex 0.06 min
-1 0.06 min-1
kal- Unbinding rate anti-s factor,ligand complex 0.03 min
-1 0.03 min-1
Degradation ds Degradation rate alternative s factor 0.0167 min
-1 0.0167 min-1
dsA Degradation rate housekeeping sA factor 0.0167 min
-1 0.0167 min-1
da Degradation rate anti-s factor 0.0167 min
-1 0.0167 min-1
drs Degradation rate RNAP,s factor complex 0.0167 min
-1 0.0167 min-1
drsA Degradation rate RNAP,s
A complex 0.0167 min-1 0.0167 min-1
dsa Degradation rate s factor,anti-s factor complex 0.0167 min
-1 0.0167 min-1
dal Degradation rate anti-s factor,ligand complex 0.0167 min
-1 0.0167 min-1
dl Degradation rate ligand 0.0167 min
-1 0.0167 min-1
Total RNAP Rtot Concentration RNAP 12.6 mM 12.6 mM
Burst size 30 Concentration ligand 10 mM 10 mM
Burst frequency T0 Rate ligand 3.33310
-3min-1 3.33310-3min-1Analytical Minimal Model of Competing Sigma Factors
Here we introduce a minimal model of an arbitrary number sigma factors competing for binding to a common pool of core RNAP,
dispensing with the regulatory features of the sigma factors captured in themore detailed computational model (main text). We derive
the analytical form of the cross-correlation function of the steady-state fluctuations in the bound fractions of the sigma factors, in
terms of the microscopic parameters of the model (abundances of the molecular species and their binding/unbinding rates). For
the case of three or more sigma factors we show that, counter-intuitively, under some parameter regimes it is possible for certain
pairs of sigma factors to exhibit positive correlations in their fluctuations.e9 Cell Systems 6, 216–229.e1–e15, February 28, 2018
First, we write down the rate equations for the dynamics of binding and unbinding of two species with a common factor (the core
RNAP). The following notation will be used:
s1: total concentration of sigma factor 1 (bound or unbound).
s2: total concentration of sigma factor 2 (bound or unbound).
p: total concentration of the core RNAP (bound or unbound).
n1: fraction of core RNAPmolecules that are bound by sigma factor 1. Note that the concentration of bound sigma 1 is simply n1p.
n2: fraction of core RNAP molecules that are bound by sigma factor 2.
We also define:
c1: ratio of abundance of total core RNAP to total sigma factor 1, p/s1.
c2: ratio of abundance of total core RNAP to total sigma factor 2, p/s2.
The key attribute of the binding and unbinding equations is the competition between the two sigma factors. Namely, if a core RNAP
molecule is bound by sigma factor 1 then it is not available for binding with sigma factor 2, and vice-versa.
The equation takes the form,
p
dn1
dt
= f1ðs1  pn1Þpð1 n1  n2Þ  l1pn1 (Equation S11)
This equation can be simplified by dividing both sides by p and redefining the forward rate constant as k1 = f1s1.
dn1
dt
= k1ð1 c1n1Þð1 n1  n2Þ  l1n1 (Equation S12)
The binding/unbinding dynamics of sigma factor 2 can be described by a similar equation. Taken together, we have a coupled set
of ODEs for the fraction of core RNAP bound by each type of sigma factor:
dn1
dt
= k1ð1 c1n1Þð1 n1  n2Þ  l1n1
dn2
dt
= k2ð1 c2n2Þð1 n1  n2Þ  l2n2
(Equation S13)
To find the steady-state values of the fractional occupation of core RNAP by each sigma factor, we set the left-hand side of the
above equations to zero and solve for n1 and n2:
k1ð1 c1n1Þð1 n1  n2Þ  l1n1 = 0
k2ð1 c2n2Þð1 n1  n2Þ  l2n2 = 0 (Equation S14)
n1 and n2 depend on the values of the parameters ki, li and ci, with i = 1,2.
To introduce fluctuations in the above equations, we consider small thermal fluctuations that result in changes in the rate constants
ki/ki + dk and li/li + dli. We then compute the resulting fluctuations in the occupation fractions around the steady-state values
ni/ni + dni. Assuming that the fluctuations are small, we can expand the above equations to first order in dki, dli and dni, which
leads to
ddn1
dt
= ½  k1c1ð1 n1  n2Þ  k1ð1 c1n1Þ  l1dn1 + ½  k1ð1 c1n1Þdn2 + ½ð1 c1n1Þð1 n1  n2Þdk1  n1dl1 (Equation S15)
A similar equation can be written for the fluctuations in the core RNAP occupation fraction of sigma factor 2, dn2. For brevity, only
equations for sigma factor 1 are shown.
Assuming that binding and unbinding fluctuations occur at equilibrium, the forward and reverse rates are related through the free
energy change of the reaction,
k1
l1
= exp

F1
kBT

; (Equation S16)
where kBT is the Boltzmann constant multiplied by the temperature of the system. The change in free energy of binding can also
fluctuate from thermal kicks F1/F1 + dF1. Assuming small fluctuations, linearizing the above equation gives the relationship between
fluctuations of the rate constants and fluctuations in the change in free energy of the reaction.
dk1
k1
 dl1
l1
=
dF1
kBT
(Equation S17)
Inserting Equation S17 into Equation S15 and simplifying gives
ddn1
dt
= ½  k1c1ð1 2n1  n2Þ  k1  l1dn1 + ½  k1ð1 c1n1Þdn2 + n1l1 dF1
kBT
(Equation S18)Cell Systems 6, 216–229.e1–e15, February 28, 2018 e10
Finally, to get rid of the time-derivative on the left-hand side, we consider the fluctuations in the frequency domain, defining
d~n1ðuÞ=
Z N
0
dn1ðtÞeiutdt. Taking the Fourier transfer of both sides of the above equation gives,
iud~n1ðuÞ= ½  k1c1ð1 2n1  n2Þ  k1  l1d~n1ðuÞ+ ½  k1ð1 c1n1Þd~n2ðuÞ+ n1l1 dF1
kBT
(Equation S19)
The two coupled equations for fluctuations in the bound fractions of sigma factors 1 and 2 can be succinctly represented in
matrix form.

d ~F1
d ~F2

= kBT
2
6664
iu+ k1c1ð1 2n1  n2Þ+ k1 + l1
n1l1
1
1 n1  n2
1
1 n1  n2
iu+ k2c2ð1 n1  2n2Þ+ k2 + l2
n2l2
3
7775

d~n1
d~n2

(Equation S20)
We can present the above equation in a more compact form by introducing the matrix L.
d~F=Ld~n (Equation S21)
Equation S21 relates fluctuations in core RNAP occupation fraction dn to fluctuations in the free energy dF. This is a linear
response relation, with the free energy playing the role of the driving force (Bialek and Setayeshgar, 2005; Hormoz,
2013). From this relationship, we can calculate the power-spectrum of fluctuations in n by using the fluctuation dissipation
theorem, which relates the rate of decay of correlations to the response function (Bialek and Setayeshgar, 2005; Hormoz,
2013; Kubo, 1966)
SðuÞ= 2kBT
u
J

L1

(Equation S22)
J denotes the imaginary part of the inverse of matrix L. From S we can compute the covariance matrix,

dniðtÞdnjðt + tÞ
	
=
Z N
N
du
2p
SijðuÞeiut: (Equation S23)
The left-hand side of the above equation is the quantity measured in the experiments, namely, the cross-correlation of fluctuations
in the fraction of bound sigma factors. The right-hand side is an analytical expression in terms of the parameters of the model
(Equation S13) and the abundance (ci) and binding and unbinding rate constants (ki and li) of each sigma factor.
Extension to an Arbitrary Number of Sigma Factors
We now extend the above results for two sigma factors to an arbitrary number N of sigma factors simultaneously competing for
binding to the same pool of core RNAP. As before, the dynamics of sigma factor i is described by three relevant parameters:
its abundance ci (with respect to total core RNAP concentration), and its binding and unbinding rate constants to core RNAP,
ki and li respectively.
In analogy with Equation S13, the rate of change of the fraction of core RNAP bound by sigma factor i is given by,
dni
dt
= kið1 ciniÞ
 
1
XN
j =1
nj
!
 lini (Equation S24)
where 1PNj = 1nj is the total fraction of unbound core RNAP.
Similarly, Equation S18 can also be easily generalized to the case of N sigma factors.
ddni
dt
=
"
 kici
 
1 ni 
XN
j = 1
nj
!
 k1  l1
#
dni + ½  kið1 ciniÞ
 XN
ksi
dnk
!
+ nili
dFi
kBT
(Equation S25)
where the
P
ksi
denotes summation of k for all values of 1 toN except for i. ni is the steady-state of the bound fraction of sigma factor i,
and satisfies the equation
kið1 ciniÞ
 
1
XN
j =1
nj
!
 lini = 0 (Equation S26)
Equation S21, which relates the fluctuations in bound fraction of core RNAP to fluctuations of the binding energy of each sigma
factor, still holds in matrix form. For N sigma factors, the matrix L takes the form,e11 Cell Systems 6, 216–229.e1–e15, February 28, 2018
2
666666666666666664
iu+ k1c1


1 n1 
XN
j = 1
nj

+ k1 + l1
n1l1
.
1
1
XN
j = 1
nj
.
«
1
1
XN
j = 1
nj
1
iu+ kici


1 ni 
XN
j = 1
nj

+ ki + li
ni li
« 1
3
777777777777777775
(Equation S27)
Note that all the off-diagonal entries of the matrix are equal to 1=ð1PNj = 1njÞ.
Finally, the spectral density of the fluctuations can be calculated as before using the fluctuation-dissipation theorem.
SðuÞ= 2kBT
u
J

L1

(Equation S28)
Cross-correlation functions can be obtained by taking the Fourier transform of S,

dniðtÞdnjðt + tÞ
	
=
Z N
N
du
2p
SijðuÞeiut (Equation S29)
Nothing in the above derivation precludes the possibility of a mixture of positive and negative correlations for certain parameter
regimes. Next, we demonstrate how positive correlations between certain pairs of sigma factors can emerge in the case of three
sigma factors.
Example: Three Sigma Factors
Consider three sigma factors competing for binding to the same pool of core RNAP (Figure 5D), with the following parameter values:
ki = li = 50 for i = 1,2, k3 = l3 = 1, c1 = c2 = c3 = 1. These parameters imply that the abundances of the three sigma factors are equal.
However, the binding and unbinding rates of the first two sigma factors to RNAP are faster than that of sigma factor 3. Therefore, the
fraction of core RNAP bound by sigma factor 3 fluctuates at a time scale longer than that of the other two sigma factors.
To obtain analytical expressions for the correlation functions, we used Equation S22 to calculate S12(u), S13(u), and S23(u) for the
above parameters (Figure S7A). As expected, S13(u) is the same as S23(u), and both functions are negative, indicating that fluctua-
tions of the bound fraction of sigma factor 3 are negatively correlated with those of the other two sigma factors. This is not surprising,
since competition for binding implies that if a larger fraction of core RNAP is bound by sigma factor 3, then a smaller fraction ought to
be bound by sigma factors 1 and 2, resulting in negative correlations. However, the power spectrum of the correlation function be-
tween sigma factors 1 and 2 is positive for low frequencies. This implies that fluctuations of bound fractions of sigma factors 1 and 2
can be positively correlated over sufficiently long time scales.
To better understand the resulting correlations, we used Equation S23 to convert the calculated spectral densities to cross-cor-
relation functions, Cij(t) = hdni(t)dnj(t+t)i, by taking their inverse Fourier transforms (Figure 5E). As expected, for all lag times t the
cross-correlation function between sigma factor 3 and the other two sigma factors is negative. However, fluctuations between sigma
factors 1 and 2 are positively correlated for sufficiently large lag times t.
We now ask what is the physical origin of the positive correlations between sigma factors 1 and 2. These two sigma factors 1 and 2
follow the dynamics of the slower sigma factor 3. For example, if the fraction of bound sigma factor 3 fluctuates below its steady state
value then sigma factors 1 and 2 are both more likely to be found bound to core RNAP. Hence, fluctuations in the bound fraction of
sigma factors 1 and 2 are expected to be positively correlated over the time scales set by the binding/unbinding rates of sigma
factor 3. Conversely, in the shorter time scale set by the binding/unbinding rates of sigma factors 1 and 2, the fraction of core
RNAP bound to sigma factor 3 can be considered a constant. Over these times scales, sigma factors 1 and 2 compete for the
remaining available core RNAP through exclusionary binding, and are therefore anti-correlated.
Finally, to validate the finding of positive and negative correlations at different time-scales, we directly simulated the equations of
the simplemodel forN sigma factors, Equation S24, as stochastic differential equations (implemented inMatlab). An example trace is
shown in Figure 5F. The bound fraction of sigma factors 1 and 2 are anti-correlated with that of sigma factor 3 but positively correlated
with each other. For instance, an increase in the bound fraction of sigma factor 3 results in a decrease in the bound fractions of both
sigma factors 1 and 2, resulting in positive correlations. Over shorter time scales, however, fluctuations in the bound fraction of sigma
factors 1 and 2 are anti-correlated (inset in Figure 5F) as expected from competitive interactions. Critically, any readout of the bound
fractions of the sigma factors that integrates over the shorter time scales (for example a fluorescent reporter) will only reveal the
positive correlations at the longer time scales. Taken together, these results show that positive correlations between some pairs
of sigma factors can arise from competitive binding interactions alone in some parameter regimes.Cell Systems 6, 216–229.e1–e15, February 28, 2018 e12
QUANTIFICATION AND STATISTICAL ANALYSIS
Image Analysis for Liquid Culture Snapshots
Quantitative image analysis of microscopy images was performed in MATLAB as described previously (Rosenfeld et al., 2005).
Briefly, constitutive mCherry fluorescence was used as a segmentation channel, and cell edges were detected using a Laplacian
of Gaussian filter. The segmentation masks identified with mCherry were then used to extract cell fluorescence values from other
channels.
Image Analysis for Agarose Pad Movies
Quantitativemovie analysis used custom image analysis code, the Schnitzcells software written inMATLAB, as described in previous
work (Young et al., 2011). Briefly, cells were segmented on the constitutive mCherry using edge detection with a Laplacian of
Gaussian filter. Cell masks were then manually corrected, tracked, and then the cell tracks were further manually corrected, all using
Schnitzcells.
Image Analysis for Mother Machine Movies
Each microscope image contained multiple subchannels (lanes in the mother machine). We used customMATLAB code to automat-
ically identify subchannels, and crop them out into new image files. This was important not only to follow cells in individual subchan-
nels, but to reduce the computational load of segmentation (described below).
Cell segmentation was accomplished using the Trainable Weka Segmentation plugin in Fiji, and was automated using a custom
Beanshell script inside Fiji. We were careful to train the plugin to accurately separate adjacent cells. Cell tracking of the mother
cell was done in MATLAB, where for every frame we took the mother cell at the ‘end’ of the channel. This tracking method produced
accurate tracks except in cases of cell death or flickering segmentation, where a cell very dim in mCherry could be segmented in one
frame but not the next, leading to a tracking error. To correct tracking errors, we used a customMATLAB interactive system, based on
one used previously (Lin et al., 2015). By manually searching for errors in cell length, we manually marked problematic tracks to be
excluded from further analysis. Finally, extraction of cell fluorescence and other cell properties such as cell length were done in
MATLAB.
Promoter Activity Calculation
Single-cell promoter activity was computed using previously reportedmethods (Locke et al., 2011), for both agarose pad andmother
machine movies. Briefly, we are interested in finding the instantaneous rate of fluorescent protein production in individual cells. We
calculate this quantity from timelapse microscopy by taking a time derivative of the fluorescent protein level in the cell. Consider a
timelapse movie of a single growing B. subtilis cell expressing yfp. For the moment, let us ignore cell division, so we are simply
considering the cell as it elongates along its major axis. We denote the total fluorescence of the cell T(t), the yfp promoter activity
(i.e. production rate) P(t), and the combined rate of YFP photobleaching and degradation, g. T(t) and P(t) are functions of time.
The rate of YFP degradation rate is typically negligible. These variables are related to each other as follows:
T
0 ðtÞ=PðtÞ  gTðtÞ (Equation S30)
Here, the prime notation indicates a time derivative, and computing P(t) evidently requires measurement of the time derivative T’(t).
Although we could try to differentiate T(t) from microscopy data, this can be sensitive to cell segmentation errors. As an alternative,
we can replace T(t) with T(t) = M(t)V(t), where M(t) is the mean fluorescence of the cell, and V(t) is the cell volume. In addition, since
B. subtilis grows lengthwise, we replace V(t) with V(t) = cL(t), where c is a constant and L(t) is the measured cell length at time t. The
value c should be approximately equivalent to the cell’s cross-sectional area, but wewill omit c in further calculations, since it will only
change the final values by a constant factor, and fluorescence units are arbitrary to begin with. After substituting these 2 relationships
into the above equation for T’(t), we can solve for P(t):
T
0 ðtÞ=PðtÞ  gTðtÞðMðtÞVðtÞÞ0 =PðtÞ  gMðtÞVðtÞM
0 ðtÞVðtÞ+MðtÞV 0 ðtÞ=PðtÞ  gMðtÞVðtÞM
0 ðtÞLðtÞ+MðtÞL0 ðtÞ=PðtÞ  gMðtÞLðtÞe13 Cell Systems 6, 216–229.e1–e15, February 28, 2018
PðtÞ=M0 ðtÞLðtÞ+MðtÞL0 ðtÞ+gMðtÞLðtÞPromoter activityh
PðtÞ
LðtÞ =M
0 ðtÞ+MðtÞL
0 ðtÞ
LðtÞ +gMðtÞ (Equation S31)
This final equation enables us to calculate the promoter activity, or sigma activity, defined as PðtÞLðtÞ, or the production rate per
unit length of the cell. Sigma activity can be interpreted as the approximate protein production rate per chromosomal equivalent,
allowing comparison of protein production through all points in the cell cycle. To compute time derivatives, the measured values
of M(t) and L(t) were first smoothed to reduce noise (MATLAB smooth function with Lowess algorithm). For g, we used a value of
0.05 as described previously (Locke et al., 2011).
Pulse Identification for Agarose Pad Movies
To automatically identify pulses from the promoter activity traces, we used custom MATLAB software (Locke et al., 2011). The code
first identified local maxima (peaks) in the traces of promoter activity vs. time. A point in the trace was deemed a peak if its height was
the largest within a window of 7 frames (frames were separated by time intervals of 10-15 min depending on the movie). In other
words, a peak at time tkmust have height greater than all heights at times tk-3 through tk+3. For peaks near the start or end of the trace,
the window size was decreased as necessary, e.g. a peak at timepoint t3 was compared against t0-t6.
To suppress peaks arising from random fluctuations, the code utilized 2 additional parameters: 1) amplitude and 2) amplitude rela-
tive to baseline. The amplitude was defined as the height of the peak minus the average height of the 2 flanking minima surrounding
the peak. The amplitude relative to baseline was defined as the height of the peak divided by the average height of the 2 flanking
minima. The code rejected potential peaks whose amplitude is below the defined threshold of 7.5 arbitrary units (a.u.). The code
also rejected peaks whose amplitude relative to baseline was less than 0.5 a.u. These two thresholds were chosen to avoid peak
detection in timelapse data from a non-pulsatile Phyperspank-yfp strain induced with IPTG, where the IPTG level was such that the
average activity of the Phyperspank-yfp was equal to that of the PB-yfp strain at 40 mg/ml MPA. Note the Phyperspank-yfp strain in movies
shows only small fluctuations that are qualitatively distinct from the large pulses from the alternative sigma factor reporter strains. The
results of automatic pulse detection were checked against raw data and the promoter activity traces and showed good agreement
with manual identification of pulses.
Pulse Identification for Mother Machine Movies and Pulse Characteristic Calculations
Pulses were identified from promoter activity traces using MATLAB’s findpeaks function, where the minpeakdistance option was set
to 5 to prevent double-counting peaks, and the minpeakheight option was set to 1.7 standard deviations above the mean activity to
suppress detection of small fluctuations. Pulse identification showed good agreement with manual inspection of pulses.
Pulse characteristics were also foundwithMATLAB’s findpeaks function, which outputs the peak widths and peak amplitudes. The
average pulse shape (Figure 2C) was found by taking each pulse, subtracting its baseline, and then dividing by the amplitude. The
baseline was calculated by subtracting the pulse’s maximum value from the amplitude output by findpeaks. Data was pooled across
multiple matrix strains carrying the same fluorescent reporter for any given sigma factor, resulting in at least 320 pulses per sigma
factor. The normalized pulse amplitude distributions (Figure 2D) were normalized by the distribution mode.
Cross Correlation Functions, Pulse Triggered Averaging, and Pulse Amplitude Scatter Plots
All figure panels for the cross correlation functions (Figure 5A), pulse triggered averages (Figure S6) and amplitude scatter plots
(Figure 5C) were calculated from the same underlying dataset, namely from the matrix strains grown in the mother machine. For
each matrix strain, we obtained at least 73 single cell traces, each of which was > 
30 cell cycles in length.
Cross correlation functions (ccf) were calculated using MATLAB’s xcov function, with the ‘unbiased’ option, and were performed
onmean fluorescence (not on promoter activity traces). To correct for long-term changes in sigma factor activity, themean time trace
was first subtracted from each trace. The cross-correlation function (ccf) for each trace was calculated separately, and the resulting
set of ccf’s was averaged for Figure 5A. Each average ccf was calculated from at least 73 single cell traces.
The pulse triggered average plots (Figure S6) were also calculated from mean fluorescence traces. Each mean fluorescence time
trace was first standardized by subtracting the mean trace and then dividing by the standard deviation. Peaks were computationally
identified for one sigma factor (the ‘trigger’), and for each peak a timewindow in the other sigma factor (the ‘plotted’ sigma factor) was
extracted. The time window was centered at the peak in the ‘triggered’ sigma. All such extracted time windows were averaged and
then plotted. Thus, the same data set was used to generate multiple plots. For example, row 1, column 5 and row 5, column 1 were
generated from the same underlying dataset: the PB-cfp, PD-yfp strain. Each trace is the average of at least 75 peaks, and the shaded
error bars are s.e.m..
The scatter plots in Figure 5C were based on promoter activity traces from the matrix of reporter strains, analyzed in the mother
machine (Figure 4). Pulses were identified using MATLAB’s findpeaks function, retaining only peaks above the mean promoter
activity. Each point in the scatter represents a timepoint in which findpeaks identified a peak in either theCFP or YFP promoter activity
traces (or both).Cell Systems 6, 216–229.e1–e15, February 28, 2018 e14
Deletion Matrix Experiments
Deletion matrix strains were inoculated into Spizizen’s minimal media, and grown overnight in 30 C shaker. In the morning, strains
were diluted back to OD600 of 0.01, and grown for 2 hours at 37
C. This cycle was repeated two more times. After the final back-
dilution to OD600 of 0.01, strains were grown until the OD600 reached 
0.1, which took about 3 hours. MPA was then added to
the media to a final concentration of 40 mg/ml. Strains were then grown for an additional 3 hours at 37 C. Next, cells were transferred
to 1.5% Agarose Pads, and imaged with fluorescence microscopy. Details of agarose pad preparation and microscopy were as
described in section ‘Sample Preparation for Liquid Culture Snapshots and Agarose Pad Movies’ and section ‘Image Analysis for
Liquid Culture Snapshots’.
DATA AND SOFTWARE AVAILABILITY
All data and software used in this manuscript are available upon request, for contact information see section ‘Contact for Reagent
and Resource Sharing’.
ADDITIONAL RESOURCES
All relevant information, software, and data are provided in previous sections.e15 Cell Systems 6, 216–229.e1–e15, February 28, 2018