A Two-Pulse Cellular Stimulation Test Elucidates ...Article A Two-Pulse Cellular Stimulation Test Elucidates Variability and Mechanisms in Signaling Pathways Madhuresh Sumit,1 Andreja

Article

A Two-Pulse Cellular Stimulation Test ElucidatesVariability and Mechanisms in Signaling Pathways

Madhuresh Sumit,1 Andreja Jovic,2 Richard R. Neubig,3 Shuichi Takayama,4,5,* and Jennifer J. Linderman4,6,*1Biophysics Graduate Program, University of Michigan, Ann Arbor, Michigan; 2Program in Molecular Pharmacology, Memorial Sloan-KetteringCancer Center, New York, New York; 3Department of Pharmacology and Toxicology, Michigan State University, East Lansing, Michigan;4Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan; 5Wallace H. Coulter Department of BiomedicalEngineering, Georgia Institute of Technology and Emory School of Medicine, Atlanta, Georgia; and 6Department of Chemical Engineering,University of Michigan, Ann Arbor, Michigan

ABSTRACT Mammalian cells respond in a variable manner when provided with physiological pulses of ligand, such as lowconcentrations of acetylcholine present for just tens of seconds or TNFa for just tens of minutes. For a two-pulse stimulation,some cells respond to both pulses, some do not respond, and yet others respond to only one or the other pulse. Are thesedifferent response patterns the result of the small number of ligands being able to only stochastically activate the pathway atrandom times or an output pattern from a deterministic algorithm responding differently to different stimulation intervals? Ifthe response is deterministic in nature, what parameters determine whether a response is generated or skipped? To answerthese questions, we developed a two-pulse test that utilizes different rest periods between stimulation pulses. This ‘‘rest-periodtest’’ revealed that cells skip responses predictably as the rest period is shortened. By combining these experimental results witha mathematical model of the pathway, we further obtained mechanistic insight into potential sources of response variability. Ouranalysis indicates that in both intracellular calcium and NFkB signaling, response variability is consistent with extrinsic noise(cell-to-cell variability in protein levels), a short-term memory of stimulation, and high Hill coefficient processes. Furthermore,these results support recent works that have emphasized the role of deterministic processes for explaining apparently stochasticcellular response variability and indicate that even weak stimulations likely guide mammalian cells to appropriate fates ratherthan leaving outcomes to chance. We envision that the rest-period test can be applied to other signaling pathways to extractmechanistic insight.

INTRODUCTION

Cellular response variability is evident when a population ofcells is exposed to two pulses of ligand: some cells respondonly to the first or to the second pulse, some respond to bothpulses, and some cells respond to neither pulse. Such vari-ability is important to consider given the multiple circum-stances under which cells are exposed to pulsatile orchanging ligand concentrations in physiology (1–5). Asdescribed in (5), all the examples show frequency- andrest-period-dependent outcome changes. Different biolog-ical processes such as neuronal growth or myocyte differen-tiation have been shown to be impacted by the frequency ofligand stimulation for the corresponding signaling path-ways. For example, pulsed stimulation of muscarinic recep-tors elicits nuclear translocation of a transcription factor,nuclear factor of activated T-lymphocytes (NFAT) (1). The

Submitted September 24, 2018, and accepted for publication January 18,

2019.

*Correspondence: [email protected] or [email protected]

Editor: Kevin Janes.

962 Biophysical Journal 116, 962–973, March 5, 2019

https://doi.org/10.1016/j.bpj.2019.01.022

� 2019 Biophysical Society.

frequency of stimulation determines whether NFAT4 orNFAT1 is translocated. Similarly, pulsed stimulation ofneurites with epidermal or nerve growth factors impactsgrowth and differentiation via extracellular-regulated kinasesignaling based on the frequency of stimulation (2). Inanother work, the frequency of transforming growth factorb pulses has been shown to impact the ability of myocytesto differentiate or not (3).

Noise in the signaling system is thought to influence thefidelity of the signaling under pulsatile stimulation (6).This noise can be either due to stochastic reactions afterexposure (intrinsic noise) or due to the preexisting heteroge-neity in cell state (extrinsic noise), and both can lead tocell-to-cell heterogeneity in the response. For intrinsicnoise, if the concentration of components is held constant,there would still have different outcomes from cell to cell.In contrast, with extrinsic noise, variation in componentconcentrations are the source of the variability from cellto cell. Small microorganisms, with volumes and proteinnumbers roughly three orders of magnitude smaller than

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Two-Pulse Test Elucidates Variability

that for the mammalian cells, display stochasticity inresponse to weak stimuli. Signaling variability in mamma-lian cells had also been generally considered to be due tostochastic processes. However, this has been debated morerecently because there are typically significantly larger vol-umes and numbers of protein molecules in mammalian cellsas well as experimental observations at single-cell levelswith deterministic explanations. For examples, cellularevents such as CDK2-dependent mitotic exit or TNFa-induced NFkB activation, which were earlier described asstochastic processes, have recently been shown to havedeterministic origins (7–9). Tools are needed to understandthe sources of and mechanisms behind this variability,which can lead to highly disparate cell fates.

Here, we describe a tractable, two-pulse experimental testand accompanying mathematical analysis. The ‘‘rest-periodtest’’ entails stimulating cells with two pulses of ligand,increasing the rest period between pulses, and observingthe effect on cellular responses. Because the rest periodbetween stimulation pulses is associated with signalingpathway recovery properties, our test provides a character-istic signature for a signaling process without measuringor inferring individual cell parameters. We used the rest-period test to gain mechanistic insight into cellular response.

Single HEK 293 cells stably expressing muscarinic M3

receptors, a G-protein-coupled receptor (GPCR), wereanalyzed using the rest-period test by exposing these cellsto two consecutive low-concentration pulses of anM3 agonistwithin a microfluidic device and monitoring the resultingintracellular calcium responses (10). Calcium responseswere quantified using live-cell imaging as described previ-ously (1). Building upon our previous mathematical modelof GPCR-induced calcium signaling (1,11,12), we addition-ally incorporated cell population heterogeneity (sometimesreferred to as extrinsic noise or biochemical variability).Using this approach, we found that cellular response vari-ability is in large part dictated by a high Hill coefficientstep, a short-term memory of stimulation, and variability inprotein levels between cells. Additionally, to illustrate broadapplicability of our findings beyond the M3 signalingpathway, we also analyzed published data on the TNFa-NFkB pathway (6,13,14), which operates at an entirelydifferent timescale (several minutes to hours) and foundthat highly variable cellular responses here are also consis-tent with similar deterministic processes and a heterogeneouscell population.

In both these signaling systems, we observed that as therest period between stimulation pulses was increased, cellseither responded to both pulses or responded to neitherpulse. This key observation demonstrates that even at lowlevels of stimulation, cells can be guided to their appropriatefate based on stimulation parameters, such as concentration,duration of stimulation, and rest period between successivestimulations, rather than through stochastic processes thatleave outcomes to chance. Our findings are supported by a

number of recent works that have used microfluidics or anal-ysis of single cells in a population (15–22). Our rest-periodtest and accompanying mathematical analysis is a comple-mentary approach, which provides unique insight intosignaling states and can be broadly applied for analysis ofother signaling systems.

MATERIALS AND METHODS

Materials

For microfluidic experiments on single cells, high-glucose Dulbecco’s

modified Eagle’s medium (DMEM) with phenol red, 0.05% trypsin,

10� HBSS (Hank’s Balanced Salt Solution; with Ca2þ, Mg2þ), HEPESbuffer (1 M), geneticin, and OPTIMEM were obtained from Gibco (Life

Technologies, Grand Island, NY), fetal bovine serum (FBS) was obtained

from Gemini Bioproduct (West Sacramento, CA), Lipofectamine 3000

was obtained from Invitrogen (Life Technologies, Carlsbad, CA),

D-glucose 10% (w/v) from Sigma (St. Louis, MO), carbachol (CCh)

from Calbiochem (EMD Biosciences, La Jolla, CA), and polydimethylsi-

loxane (PDMS) and curing agent from Dow Corning (Midland, MI). Imag-

ing media (1� HHBSS (pH 7.4)) was prepared as described by Palmer and

Tsien (23). CMV-R-GECO1 was a gift from Robert Campbell (plasmid no.

32444; Addgene, Watertown, MA) (24).

Methods

Cell culture

HEK 293 cells with stable transfection of human muscarinic acetylcholine

receptor M3 as described previously (25) were cultured in DMEMwith 10%

FBS and geneticin (400 mg/mL) in T-25 flasks. Transient transfection with

R-GECO1 plasmid was carried out using Lipofectamine 3000 following

prescribed protocol.

Microfluidic device

PDMS microfluidic devices for cell culture and pulsatile stimulation were

fabricated based on the computerized microfluidic cell culture system using

Braille display and is described in (10). The PDMS chips were filled with

laminin (100 mg/mL) and incubated overnight. Subsequently, the chips

were washed and incubated with DMEM/10% FBS under sterilized condi-

tions. HEK 293 cells transiently transfected with R-GECO1 were seeded in

the outlet channel of the device as described in Sumit et al. (1). The micro-

fluidic device was mounted on a custom-built setup and controlled by a

custom-written software to deliver periodic stimulation of CCh as described

in (10).

Time-lapse imaging and analysis

Cells in the microfluidic device were simultaneously stimulated with ligand

and imaged with a TE-2000 U Nikon microscope (Nikon, Tokyo, Japan)

using a 20� Fluor objective illuminated by a 100-W Hg lamp. Sequential

acquisition of R-GECO1 fluorescence was carried out every 3 s using

ET572/35 excitation filter and ET630/50 emission filter, respectively

(Chroma Technology, Rockingham, VT). The excitation and emission filters

were equipped in filter wheels controlled by a Lambda 10-3 shutter

controller (Sutter Instruments, Novato, CA). Regions of interest (ROIs)

within the cytoplasmic region were selected for single cells using MetaFluor

Software (Molecular Devices, Downingtown, PA) to determine the area

averaged intensity I(t) in cytoplasmic region (I(t)cyto). Calcium response

was measured by calculating the ratio I(t)cyto/I0. Here, I0 corresponds to

the basal R-GECO1 intensity in the cytoplasmic ROI. Background signal

was subtracted before the ROI intensity analysis in all the experiments by

choosing a region with no cells and assigning it as the background.

Biophysical Journal 116, 962–973, March 5, 2019 963

Sumit et al.

Calculating signal/noise ratio and intrinsic/extrinsic noise ratio

We adapted the method for experimental noise analysis provided in the sup-

porting material of a recent article (26). We first calculate the signal magni-

tude s2r (variance of average responses of n cells over all m input

concentrations) as follows:

s2r ¼ 1

m

Xmi¼ 1

1

m

Xmw¼ 1

1

nw

Xnwj¼ 1

rwj

!� 1

ni

Xnij¼ 1

rij

!!2

:

Here, r represents calcium peak responses from single cells; i (indexed

from 1 to m) represents input signals such as various concentrations of

CCh; j (indexed from 1 to nw) represents all the calcium peak response sig-

nals from a given input i; and j (indexed from 1 to ni) represents all the

calcium peak response signals from all them inputs. Different input concen-

trations are indexed as w ranging from 1 tom. Noise magnitude s2n is calcu-

lated as the average of the variances of ni responses to a single input level as

follows:

s2n ¼ 1

m

Xmi¼ 1

1

ni

Xnij¼ 1

1

ni

Xniw¼ 1

riw � rij

!2

:

The signal/noise ratio (SNR) is then defined as the ratio s2r=s

2n.

To calculate intrinsic/extrinsic noise ratio (IER), we used the portion of

calcium traces from step changes for which the intensity did not change

significantly. Intrinsic noise ðs2xÞwas estimated as the variance of the differ-

ences in R-GECO intensities between successive time points. Total noise

ðs2t Þ was calculated similar to the noise magnitude, s2n, but taking only

the static region of the calcium traces. Extrinsic noise is then calculated

as s2e ¼ s2t � s2x . The ratio s2i =s2e is IER.

Based on the noise analysis, we incorporated cell-to-cell variability in the

form of a uniform distribution of 520% in the model parameters, namely

the receptor, total G-protein, and the phospholipase-C (PLC) concentration.

The intrinsic noise (55%, normally distributed throughout the dynamic

data) was minimal and did not affect the calculation for ‘‘0’’ (nonrespond-

ing) and ‘‘1’’ (responding) cells.

Mathematical model and computational analysis

GPCR-calcium model with extrinsic noise. Previously, we developed a

mathematical model that links step/pulsatile ligand stimulation, receptor/

ligand binding, and calcium signaling and captures the characteristic fea-

tures of the microfluidic pulsatile experiments (1,11,12). The model

description, reactions, and parameter values are as detailed in our previous

work (1). Briefly, the ligand CCh binds to M3 muscarinic receptors, promot-

ing G-protein coupling. After the exchange of guanosine diphosphate

(GDP) for guanosine triphosphate on the a-subunit (Ga), Ga dissociates

from the receptor and binds to PLC, initiating downstream signaling. Gua-

nosine triphosphate on activated Ga is rapidly hydrolyzed to GDP, forming

inactive Ga-GDP. If Ga is bound to PLC, then this hydrolysis reforms inac-

tive PLC as well as inactive Ga. The ligand-receptor complex is reversibly

phosphorylated to form inactive L-R-P state. The inactive complex can be

dephosphorylated to reform the free receptor or can be internalized and

either degraded or recycled back to the surface via endosomal sorting.

Ga binding to PLC increases inositol triphosphate (IP3) production; IP3binds to the IP3 receptor on the endoplasmic reticulum (ER), triggering

the release of Ca2þ from ER into the cytosol. Cytosolic Ca2þ acts both to

stimulate and to inhibit its release from the ER through multiple pathways.

The oscillatory release of Ca2þ from the ER is achieved by the sarcoendo-

plasmic reticulum calcium transport ATPase pump, which pumps cytosolic

Ca2þ back into the ER. Ca2þ can also enter or leave the cell through the

plasma membrane. To incorporate extrinsic noise, the values for three major

nodes in the pathway, the receptor, G-protein, and PLC concentrations,

were chosen from a uniform distribution around the mean value so that

the SNR matches with the experimentally calculated value.


Computational analysis of response subpopulations

A system of ordinary differential equations was generated for the model and

solved in MATLAB (The MathWorks, Natick, MA) with the ode15s stiff

solver. Experimental data for more than 1000 cells under pulsatile stimula-

tion conditions for various concentrations (C¼ 10, 20, 40, and 80 nM) were

analyzed to determine SNR and IER following a method described in

Selimkhanov et al. (26). These quantities provided an estimate of plausible

range of extrinsic noise in our signaling system. Based on the noise analysis

of experimental data, the initial values for core signaling components (i.e.,

GPCR, G-protein, and PLC) were chosen from a 20% uniform distribution

around the mean value using Latin hypercube sampling (27). Thus, in silico

cell-to-cell variability was generated for three independent runs each con-

sisting 250 Latin hypercube sampling parameter sets.

Assignment of ‘‘0’’ and ‘‘1’’ binary responses

Analysis of the individual traces for peak finding and determining fraction

of subpopulations of (0,0), (0,1), (1,0), and (1,1) was done by writing script

files in MATLAB. Peak calcium responses from single cells for each of the

stimulation pulses were normalized with the basal cytoplasmic R-GECO1

intensity to calculate Ipeak/I0. Accounting for the variability in the peak in-

tensities from cell to cell, the following conditions were imposed to define

the binary responses: for a two-pulse stimulation, if both peaks were such

that Ipeak/I0 < 1.5 (defined as subthreshold peaks), it was counted as a

(0,0) response. For the rest of the cases, if the first peak was 0.3 times

the second peak, it was counted as (0,1) response and vice versa. The re-

maining peaks were assigned as (1,1) responses. For the simulation results,

the calcium concentration was normalized to match the R-GECO1 normal-

ized intensity (multiplied by 10), and the same algorithm was used to

determine the binary responses.

TNFa-NFkB deterministic model with extrinsic noise

We used the deterministic as well as the stochastic versions of the TNFa-

NFkB model from (6). Although both uniform and lognormal distributions

were applied to the model variables, results shown in the manuscript are

based on the uniform distribution. The lognormal distribution showed

similar trends (data not shown). No changes were made in the model equa-

tions. The parameter values used for the model analysis were taken from

(6). We performed sensitivity analysis of all the parameters used in the

model to determine the parameters sensitive to both first and second peak

in the in silico two-pulse experiment (Table S1). Subsequently, extrinsic

noise was incorporated in the deterministic model using a similar method

as described in the previous section by generating a distribution in sensitive

parameters limited within the same log scale. Similar to the GPCR-calcium

model, the model parameter values were drawn from a uniform distribution

for all the signaling components with nonzero initial concentrations. The

rest of the analysis was performed similar to that for the GPCR model.

Computational codes and data can be made available upon request.

RESULTS

Microfluidic two-pulse experiments reveal cellularcalcium response heterogeneity upon stimulationin a physiologically relevant concentrationregime

Wedesigned amicrofluidic experiment entailing cell stimula-tionwith two pulses of CCh, which binds and activates theM3

muscarinic receptor, eliciting an intracellular calcium signal(Fig. 1 a). The stimulation pulse can be characterized by itsconcentration (C), pulse duration (D), and the rest period be-tween two consecutive pulses (R). The concentration regimechosen (z5–10 nMCCh) was low enough to be insignificant

a b c

d

FIGURE 1 Microfluidic two-pulse experiments reveal cellular calcium response heterogeneity upon stimulation in a physiologically relevant concentration

regime. (a) Shown is the design of pulsatile stimulation experiments, in which two outcomes are possible for each stimulation (0 and 1), leading to four pos-

sibilities for two-pulse experiments. (b) The top panel shows time-montage images for two representative cells depicting a (0,1) response (top arrow) and a

(1,0) response (bottom arrow) under the two-pulse test with C¼ 7.5 nM,D¼ 16 s, and R¼ 120 s. The bottom panel shows a heat map of normalized R-GECO

intensity for single cells. Representative data for 20 single-cell responses out of>100 cells per condition are shown. (c) Representative single-cell data demon-

strate all four possible outcomes. (d) The subpopulation varies with stimulation parametersD and R; here R¼ 24 s is compared to R¼ 120 s for the indicatedD

values. Data represents three sets of two-pulse microfluidic experiments withz30 cells per set, with a total of>100 cells per condition. Error bars are standard

errors of the mean. Asterisks represent the p-value for unpaired t-test. *0.01 < p < 0.05, **0.01 < p < 0.001, and ***p < 0.001.


for receptor desensitization and sufficient to generate cellpopulations with a wide range of activation probability(11,12,28). We measured cytoplasmic calcium as our readoutfor hundreds ofHEK293 cells transiently transfectedwith theR-GECO1 calcium sensor (1). These cells were stimulatedwithin a microfluidic device that can deliver temporal rectan-gular pulses of ligand as described previously (1,10–12). Foreach pulse of ligand, a cellmay ormay not respondwith a cal-cium peak. A full or near-full peak response is designated asoutput ‘‘1’’ in the scheme,whereas no response or a subthresh-old peak is designated as output ‘‘0’’ (see Materials andMethods). Thus, for a two-pulse scheme, the four combinato-rial responses possible for any cell are no response to bothpulses (0,0), a calcium peak response only to the second stim-ulation pulse (0,1), a calcium peak response only to the firststimulation pulse (1,0), or calcium peak responses to bothstimulation pulses (1,1).

Although the experiment was conducted for a wide rangeof rest periods, results are shown only for the rest-periodregime for which the cells exhibited most of their responsevariability. Choosing an intermediate concentration in thetest regime (C ¼ 7.5 nM) and pulse duration that producesnonsaturating calcium responses (D ¼ 16 s), we observed

population heterogeneity in the calcium responses (Fig. 1b). The responses could be separated into the four aforemen-tioned outcomes (Fig. 1 c). Stimulation of cells withdifferent duration and rest period of pulses suggests thatthe subpopulation varies with varying stimulation parame-ters (Fig. 1 d). Increasing rest period, R, from 24 to 120 sresults in increased (0,0) or (1,1) subpopulation. Increasingpulse duration increases the (1,1) subpopulation and de-creases (0,0) subpopulation for the two rest-period regimestested. The existence of (1,1) and (0,0) responses is rela-tively easy to explain within a deterministic framework.However, the explanation for the simultaneous existenceof (0,1) and (1,0) responses using a deterministic mathemat-ical model has not been shown and often leads to the conclu-sion that the response outcomes have stochastic origins.

A mathematical model with deterministic reactionkinetics and extrinsic noise recreates cellularresponse variability

We previously reported a deterministic mathematical modelthat captures population-scale calcium response characteris-tics under both step increases and pulsatile stimulation with


d

a

Cell-to-cell variability

High Hill-coefficient pathway

b

Cytoplasmic calcium (µM)

In silico pulsed stimulation

Sing

le c

ells

(in

silic

o)

Time (s)

c

0 50 100 150 200

4

3

2

1

4

3

2

1

4

3

2

1

4

3

2

1

[0,0]

[0,1]

[1,0]

[1,1]

Cyt

opla

smic

ca

lciu

m (µ

M/1

0)

Time (s)

Sub-

)%( noitalupop

0 50 100 150 200

L R

LR* LRp

PLC* PLC

PIP2 IP3

Ca2+ (ER)

Ca2+(cyto)

Ca2+extracellularIP3R IP3R (i)

LRp_int

kL2kL1kgrk1

kgrk2

kg1

kg2kplc1

vplc vdeg

vserca

vinout vrel

kplc2

krec

kdegkint

`

G G*

FIGURE 2 Deterministic mathematical model with extrinsic noise in key components exhibits all four possible outcomes. (a) In the model schematic, the

ligand (L) binds to the receptor (R) to form a ligand-receptor (LR) complex, which initiates G-protein-mediated PLC activation and IP3 generation, ultimately

leading to the observed calcium responses. The shaded nodes indicate where extrinsic noise is introduced in the model. Phosphatidylinositol 4,5-bisphosphate

to IP3 pathway activated by PLC denotes a high Hill coefficient pathway. Model equations can be found in (1). (b) Shown is an in silico two-pulse stimulation

test with ligand (CCh) to generate representative single-cell traces by introducing cell-to-cell variability (biochemical noise) in the model (C ¼ 7.5 nM, D ¼16 s, and R ¼ 120 s). (c) Intracellular calcium concentrations for simulation data showing all the four possible outcomes similar to the experimental data are

shown. (d) Similar to the experimental results, the in silico subpopulation varies with varying stimulation parameters. Data represent three sets of two-pulse

in silico experiments with 250 cells per set. Error bars are standard errors of the mean.

Sumit et al.

ligand (1,11,12). To account for heterogeneity in responses atthe single-cell level, we additionally incorporated extrinsicnoise into our mathematical model. Note that we and others(29,30) use the term extrinsic noise to refer to cell populationheterogeneity in the levels of various molecules (e.g., mole-cules in signaling or metabolic pathways) that may have aninfluence on cell behavior. The origin of this heterogeneityis generally unknown but may be related to cell cycle, micro-environmental factors, previous signaling events, etc. Intro-ducing cell-to-cell variability in signaling response in acomputational model has been approached in differentways. Ideally, the parameter values should be drawn from aconcentration distribution established experimentally usingtechniques such as flow cytometry (20,31–35). However,most often, it is not practical to quantify distribution foreach signaling component in the pathway. An alternativeapproach developed by Selimkhanov et al. (26) uses an infor-mation theoretic approach to quantify intrinsic and extrinsicnoise in the output signaling response for several input levels(see supporting material of (26)), and this is the approach weused. Using this approach, extrinsic noise can be quantifiedand used to draw parameter values from a distribution.Thus, population heterogeneity was introduced in the modelby incorporating a uniform distribution in the concentrationof the signaling proteins in the model (Fig. 2 a). Briefly, hun-


dreds of single-cell calcium time traces were recorded for astep change in ligand concentration from C ¼ 0 nM toC ¼ 10, 20, 40, or 80 nM using our device. We then calcu-lated the SNR and IER for the CCh-induced calciumresponse, as described in Methods. Subsequently, the distri-butions of the concentration of signaling components wereset such that simulations matched the experimentallyobserved SNR. Using this updated model, we then generatedhundreds of in silico single-cell calcium traces under the two-pulse stimulation scheme (Fig. 2 b). These simulated tracesshow features similar to those observed in our microfluidicpulsatile stimulation experiments, and wewere able to obtainall four possible calcium response outcomes (Fig. 2 c).Similar to the experimental results, the in silico subpopula-tion also varies with varying stimulation parameters (Fig. 2d). Increasing R from 24 to 120 s results in increased (0,0)and (1,1) subpopulations. Increasing pulse duration increasesthe (1,1) subpopulation and decreases the (0,0) subpopula-tion for the two rest-period regimes tested. Similar resultswere obtained with a lognormal distribution of the signalingcomponents (Fig. S1). We also determined how individualcomponents in the signaling pathway influence the fate ofcells in terms of one of the four response outcomes. Althoughprotein expression variability in each of the signaling compo-nents affected the responses, an overall cumulative parameter

a

b

c d

e

FIGURE 3 Rest period determines subpopulation composition. (a and b) Microfluidic two-pulse test with widely separated rest periods (R¼ 24 s and R ¼120 s) shows that subpopulation composition changes with R in a predictable fashion for different pulse durations tested (D ¼ 8, 16, and 24 s; C ¼ 7.5 nM).

(a) The response denoted by the summation of (0,1) and (1,0) subpopulations decreases with increasing R for all the pulse durations tested. (b) The response

denoted by the summation of (0,0) and (1,1) subpopulations increases with increasing R. The scatter points show the corresponding model result for 250

simulation conditions from the distribution drawn on model parameters. (c) Response variability for extremely large rest periods (R ¼ 640 s) is shown.

(d) Response variability for extremely large stimulation concentrations (C ¼ 100 nM) is shown. (e) A simulation study showing the effect of rest period

on subpopulation composition in a two-pulse in silico experiment with GPCR-calcium model (C ¼ 10 nM; D ¼ 10 s) is shown. Experimental data

(bars) are presented as mean5 SDs for three sets of experiments, withz30 cells in each set, with a total of >90 cells for each condition. Modeling results

are shown for 250 in silico simulations with distribution drawn from model parameters. Asterisks represent the p-value for unpaired t-test. *0.01< p< 0.05,

**0.01 < p < 0.001, and ***p < 0.001.


Q (calculated by multiplying together the concentrations ofthe protein components in the pathway that vary from cellto cell) clearly distinguishes the four outcomes, indicatingthat the biochemical variability cumulatively may affect thedownstream cell fates (Fig. S2). Taken together, our deter-ministic mathematical model with added extrinsic noise cap-tures cellular response variability, which includes all fourpossible response outcomes under the two-pulse scheme.

Rest-period test reveals a deterministic basis forcellular response variability

The existence of all four possible calcium response out-comes for the two-pulse test (both in the model and in exper-iments) raises an interesting question: is the fraction of cellsresponding in each way related to the rest period R betweenthe pulses? If deterministic sources are primarily respon-sible for cellular response variability, increasing R shouldallow the two responses of the two-pulse test to uncouplefrom each other (i.e., increased R should result in less influ-ence of the first pulse on the second calcium response). In

other words, as R is increased, the fractions of cells fallinginto different subpopulations should change, with cells mov-ing into the (0,0) or the (1,1) subpopulations. However, ifstochastic sources are primarily responsible for cellularresponse variability, the responses to two stimulation pulsesare expected to be uncorrelated, and hence, the rest-periodchanges should not affect the response outcomes.

We tested this hypothesis with two widely separated restperiods (R ¼ 24 s and R ¼ 120 s), both in silico and withmicrofluidic experiments (Fig. 3). The concentration(C ¼ 7.5 nM) and durations of pulsed stimulation (D ¼8, 16, and 24 s) were carefully chosen based on previousdata (1,28) so that a wide range of response variabilitycould be observed. Furthermore, under these stimulationconditions, GPCR desensitization and gene- expression-induced feedback were minimal (1). Applying these stim-ulation conditions, we found that the summation of (0,1)and (1,0) responses decreases with increasing R (Fig. 3a) whereas the repeated response, denoted by the summa-tion of (0,0) and (1,1) responses, increases with increasingR (Fig. 3 b).


a

c

b

d

FIGURE 4 Deterministic NFkB signaling model also shows cellular response variability under low-concentration pulsatile stimulation, similar to the

GPCR-calcium signaling. (a) A schematic of the TNFa-NFkB signaling model is shown. Nuclear localization and transcriptional activity of NFkB upon stim-

ulation of TNF-receptor is regulated through negative feedbacks by A20 and IkBa at different levels of signaling. (b) Using sensitivity analysis to determine

parameters affecting the first and second peaks differentially and adding extrinsic noise to the parameters, the deterministic NFkB model can produce the four

subpopulation outcomes. Representative esponses from 20 out of n ¼ 250 simulated cells are shown. (c) Representative in silico single-cell traces of nuclear

NFkB from (b), showing all the four possible outcomes. (d) Rest-period test of NFkB signaling is shown. Experimental data from (13) was examined by calcu-

lating the percent of (0,1) and (1,0) responses and the rest of the subpopulation (0,0) and (1,1) responses at low TNFa stimulation (0.1 ng/mL). A shorter rest

period (R¼ 45 min;D¼ 45 min) and a longer rest period (R¼ 150 min;D¼ 30 min) were compared to find that the response variability decreases with longer

rest periods, similar to our experimental data for calcium response. The modified deterministic NFkB model also predicted similar results.

Sumit et al.

For extremely large rest periods, most of the cells re-sponded either as (0,0) or as (1,1) (Fig. 3 c). Similarly, forextremely large stimulation concentrations, most of the cellsresponded either as (0,0) or as (1,1) (Fig. 3 d). Our determin-istic model also suggests that the effect of R on each subpop-ulation in GPCR-calcium signaling is monotonic andpredictable for various pulse concentrations and durationsin the tested regime (Fig. 3 e; Fig. S3). When the rest-periodtest was extended to three pulses in the model, we observeda similar effect of rest-period (i.e., with increasing R, thesystem tends to either respond completely (1,1,1) or not atall (0,0,0)) (Fig. S3). Taken together, we find that longerrest periods reduce cellular response variability.

Rest-period test reveals a deterministic basis forcellular response variability in another signalingsystem: TNFa -NFkB signaling

Our model and experiments support a deterministic originfor the cellular response variability we observed in the


GPCR-calcium signaling pathway. Next, we asked whetherthe same might be true for a signaling pathway that signalsat a much longer timescale as compared with the intracel-lular calcium signaling described above. NFkB oscillationsare observed upon TNFa stimulation. The timescale ofTNFa-induced NFkB signaling is from several minutes tohours, unlike the GPCR-calcium system for which signalingis on the order of seconds to minutes. Briefly, nuclear local-ization and transcriptional activity of NFkB upon stimula-tion of the TNF-receptor is regulated through negativefeedbacks by A20 and IkBa at different levels of signaling.The activation of IKK-a is modeled as a high Hill coeffi-cient pathway (Fig. 4 a). Model equations and parameterscan be found in (6). Using microfluidic two-pulse stimula-tion of TNFa in 3T3 mouse fibroblasts and measuringnuclear localization of NFkB, Tay et al. (6) showed the ex-istence of cells with all four possible signaling outcomes(i.e., (0,0), (0,1), (1,0), and (1,1) responses). They suggestedthat the single-peak responses (i.e., (0,1) and (1,0)) were acombination of stochastic and deterministic effects and

FIGURE 5 Rest-period test can identify charac-

teristic difference between cellular response vari-

ability of deterministic and stochastic origins. (a)

Cellular response variability in the deterministic

GPCR-calcium model with extrinsic noise de-

creases with D and R. (b) Cellular response vari-

ability in the TNFa-NFkB deterministic model

with extrinsic noise decreases with D and R. (c)

The TNFa-NFkB stochastic model with no

extrinsic noise shows no significant effect of D or

R on response variability. To see this figure in

color, go online.


developed a hybrid model incorporating stochasticity atcertain nodes based on a previously existing deterministicmodel (4). We hypothesized that their deterministic modelalone may be able to generate all four possible signalingresponse outcomes upon incorporation of extrinsic noiseand performed a sensitivity analysis of the entire parameterset of their model to identify parameters that significantlyinfluence NFkB peak height (27). We limited explorationof the parameter space such that the parameters were ofthe same order of magnitude as reported in Tay et al. (6).Table S1 lists parameters significantly correlated with first-and second-peak responses (Fig. 4 a; Table S1). We gener-ated extrinsic noise by sampling from a uniform distributionof these parameters. Under the same stimulation conditionsused by Tay et al. (6), we found that this modification oftheir deterministic model that incorporates cell-to-cell vari-ability in the sensitive parameters exhibits all four responseoutcomes of the two-pulse experiment with subpopulationcompositions similar to the reported experimental values(Fig. 4, b and c). The effect of increasing rest period inthe NFkB model is similar to our GPCR model. Withincreasing R, the subpopulation (1,1) increases whereas(1,0) decreases, similar to the trends observed in theGPCR model. In contrast, the (0,0) response increaseswhereas (0,1) decreases with increasing R, similar to thetrend we observe in GPCR signaling, although these trendsare nonmonotonic around R �200 min (Fig. S4). The effectof increasing concentration and pulse duration in the NFkBmodel is also similar to our GPCR model (Fig. S5, a and b).We also applied the rest-period test to a recently reported

experimental data for pulsatile stimulation with low-con-centration TNFa (0.1 ng/mL) (13) (Fig. 4 d). We foundthat the ‘‘response variability,’’ denoted by the summationof (0,1) and (1,0) responses, is reduced at a longer restperiod (R ¼ 150 min) as compared to a shorter rest period(R ¼ 45 min), whereas the repeated responses (summationof (0,0) and (1,1) fractions) increase at longer R, similarto what we observe for the GPCR-calcium experiments.These computational and experimental findings suggestthat the cellular response variability in NFkB signaling isconsistent with a deterministic process.

Rest-period test can identify deterministic andstochastic origins

Analysis of our GPCR-calcium model showed that cellularresponse variability, such as quantified by the summation ofthe fractions constituted by (0,1) and (1,0) responses, de-creases with increase in D or R (Fig. 5 a). A similar responsewas observed when we decreased the concentration of stimu-lation ‘‘C’’ while keepingC�D the same (Fig. S6). Althoughit was known that the fractions of cells responding to a pair ofligand pulses are governed by concentrationC and stimulationduration D, we show that the role of rest period R is equallyimportant in determining the distribution of possible signalingresponse outcomes. We found similar trends for an NFkBdeterministic model, wherein a low D and R regime resultedin maximal cellular response variability (Fig. 5 b). Impor-tantly, the stochastic model reported in Tay et al. (6) did notexhibit any significant changes in response variability with


Sumit et al.

changes inR (Fig. 5 c). This difference in subpopulation shiftsbetween the stochastic and deterministic mechanisms iden-tifies our tractable, two-pulse rest-period test as a means todistinguish between the two mechanisms. The basis of thistest is that increasing R results in a reduction of responsevariability for deterministic mechanisms because cellular re-sponses tend toward (0,0) or (1,1) responses. In contrary, sto-chastic responses appear to remain unchanged.

A high Hill coefficient process and pathwayrecovery properties govern cellular responsevariability

The results above raise interesting questions about the inter-nal mechanism of the signaling pathway that leads to cellularresponse variability. We analyzed each signaling pathwaynode in our GPCR-calcium model for the two response sub-populations (0,0) and (1,1) to understand the potential differ-ences leading to the disparate signaling outcomes. Althoughthe two subpopulations differed slightly in the concentrationsof activated receptor complex, total G-protein, and activatedPLC, a much greater difference was seen with IP3 levels,leading to a seemingly bifurcated downstream response(Fig. 6 a). This difference is due to the high Hill coefficient(Hz2) at this point in the signaling pathway (Fig. S7).

We also tested the deterministic NFkB model byanalyzing the individual pathway nodes. Similar to ourGPCR model, we found that the bifurcation in signaling re-

FIGURE 6 Component-wise analysis of the GPCR model. (a) The two subpop

prime step that leads to amplification of the difference in responses. Basal PLC

response (a node of high Hill coefficient (Hz2)). (b) A model analysis of why

in the GPCR model is shown. The first light-gray pulsatile shape around t ¼ 0 is

with dotted and black lines underneath. All line plots are a mean of n ¼ 250 in


sponses is a result of a high Hill coefficient (Hz2) inthe signaling pathway, in this case in the generation ofactive IKK, a major component in TNFa-NFkB signaling(Fig. S8 a).

We investigated how the (1,0) and (0,1) subpopulationtransition to (0,0) and (1,1) responses with increasing R.Although transition from (1,0) to (1,1) responses withincreasing R is reported for both the signaling pathwaysand is attributed to the pathway recovery properties (4,12),the transition from (0,1) to (0,0) is less intuitive. So, usingthe model, we analyzed the transition from (0,1) to (0,0) re-sponses upon increase in R. Our analysis of this transitionentailed performing a component-wise analysis of theGPCR model using the rest-period test for three differentR values (120, 200, and 300 s) (Fig. 6 b). Our simulationdata show that for cases in which the cell does not respondto the first stimulation pulse ((0,0) and (0,1) cases), ashort-termmemory of the stimulation in the calcium concen-tration in the ER is created. This calcium gradually leaks outof the ER reservoir. An early second stimulation helps theER reach its threshold to release the calcium, and, hence,the cell responds, resulting in a (0,1) response; a delayed sec-ond stimulation does not have this advantage (28), resultingin a (0,0) response as R is increased. Similarly, we find thatin the TNFa-NFkBmodel, receptor activation creates a shortmemory of the stimulation through IKK kinase signaling.For shorter R, the active IKK kinase level increases moreupon a second stimulation compared to larger R, despite a

ulations (0,0) vs (1,1) suggest a high Hill coefficient reaction kinetics as the

activity brings about the major difference leading to either (0,0) or (1,1)

(0,1) calcium response translates into a (0,0) response upon increasing R

an overlap for all the three conditions, with the gray line on the top, along

silico simulations per condition.


lack of an NFkB response to the first stimulation. This in-crease in IKK kinase is amplified via a high Hill coefficientpathway downstream (Fig. S8 b), thus rendering cellularresponse variability sensitive to R. Although it is challengingto test experimentally, a high Hill coefficient pathway seemsto impart similar effects on signaling responses based on thetwo models analyzed in this work. Taken together, cellularresponse variability is altered by the length of the rest period(R) because of slow recovery of intermediate signalingprocesses.

DISCUSSION

Physiologically relevant weak stimulations, often low-con-centration pulsatile bursts of ligand, can lead to downstreamsignaling responses that are highly variable. A better under-standing of how stimulation parameters govern responsepatterns and overall response fidelity in a signaling systemis fundamental to biology (1,5,6,11,36). It will also be usefulin the analysis of pharmacological, in vitro culture, and syn-thetic biology applications.

There are three main conclusions from our work. First,within the stimulation regime in which cells exhibit signif-icant response variability, a two-pulse rest-period test is ableto distinguish whether the variability is likely driven bydeterministic or stochastic mechanisms. Second, responsevariability in GPCR-mediated calcium signaling and inTNFa-mediated NFkB nuclear localization is consistentwith a deterministic mechanism. The models suggest thatthe basis of such response variability is a short-term memoryof stimulation along with a high Hill coefficient pathwayand cell-to-cell variability in signaling protein expressionlevels. Third, although often ignored, looking at and ac-counting for the nonresponding population of cells, suchas the (0,0) response here, is essential to the understandingand analysis of single-cell data.

Our rest-period test provides a simple method forrevealing effects of stimulation parameters on cellular re-sponses. When applied to GPCR-induced calcium signaling,the test revealed that as the time between stimulation pulsesincreased, cells tended either to respond to every stimulationor did not respond at all. We envision that pulsatile stimula-tion parameters could thus be used as a means to preciselycontrol the percentage of fully responding and nonrespond-ing cells. This fascinating observation has implications onvarious facets of biology, providing a potential explanationfor how organisms are able to selectively control geneticallyhomogeneous groups of cells and yet guide them to partic-ular cell fates (15–17).

The combined experimental and computational approachdescribed in this article enabled extraction of mechanisticinsight for the intracellular calcium and NFkB pathway stud-ied. In particular, our analysis revealed that the bifurcation incellular responses described above could be attributed toextrinsic noise, a short-term memory of stimulation, and a

high Hill coefficient process operating within a deterministicprocess. Although the models studied in this work suggestbifurcation properties based on high Hill coefficient motifsin the pathways, in general, a motif or mechanism that pro-vides a strong bottleneck will likely provide similar bifurca-tion properties and influences over cell-to-cell variability.These results are in accord with previous studies that haveindicated that mammalian cellular signaling pathways,such as intracellular calcium and NFkB, are largely dictatedby deterministic mechanisms (4,11,13,19,37). Similar to ourapproach, these studies have applied pulsatile microfluidicsand computational analysis to reveal deterministic compo-nents of signaling responses. Other studies have combinedcomputational analysis with analysis of daughter cells (20)or contextual data making up a single cell’s microenviron-ment (8,9) and have shown that deterministic processeslargely dictate phenotypic cell-to-cell variability.

Most cell studies focus on high-ligand-concentrationstimulation to determine the minimal ‘‘reset’’ time asignaling system requires to recover between stimulationevents (4). Experimental metrics like peak amplitude ofcellular signals are often used to assess this reset time bymonitoring the amount of time needed between stimulationevents to produce responses of equal peak amplitudes. It isoften assumed that reset times that are assessed at high-ligand-concentration stimulation are sufficient for resettingthe signaling system upon exposure to low concentrations(6). However, our work provides new, to our knowledge, in-sights into how this assumption could be problematic andsuggests that low-concentration regimes, in which receptordesensitization does not dominate recovery time, shouldbe treated differently (i.e., the role of signal strength andpathway recovery properties must be considered). Rather,the positive and negative feedback mechanisms and highHill coefficient processes of the pathway play crucial rolesalong with cell-to-cell variability in determining thesignaling response. Recently, Yao et al. (38) have shownthat the variability in intracellular calcium signaling maybe a consequence of structured heterogeneity between cellsthat gives rise to distinct cellular states. Our results provide apossible explanation of how these cellular states may beachieved; it is not only based on cell-to-cell variability butalso depends on signaling pathway properties.

Many analyses of single-cell responses discard data fromnonresponding cells (the (0,0) case we describe above) anduse data only from responsive cells (12,39,40). In otherstudies, cells are stimulated at a very high concentrationof ligand to avoid this nonresponsive regime (4). Such ana-lyses can miss important aspects of signaling architectureand discount the role of cell-to-cell variability in governingthe population response. Our results suggest that nonres-ponding cells represent a legitimate cell subpopulationthat need to be factored into cellular response analyses.

An interesting feature of nonlinear dynamic systems isthat stochasticity can lead to enhanced signaling, such as


Sumit et al.

increased transcription relative to a linear system, in a pro-cess referred to as stochastic resonance (41). Mice fibro-blasts have been reported to exhibit stochastic resonancein NFkB expression upon weak, sawtooth-shaped TNFastimulation (41). We wondered whether the deterministicmechanism we find consistent with observed signalingshown above with the GPCR-calcium and TNFa-NFkBsystems could also produce ‘‘apparent’’ stochastic reso-nance. To test this, we performed simulations withsawtooth stimulation, similar to the stimulation strategyused in (41). Geometrical features can potentially influencethe stimulation parameters (C, D, and R). In case of squarewave pulses, the rest period does not change with anincrease or decrease in the ligand concentration(Fig. S9 a). In contrast, in case of sawtooth stimulation,a decrease in C is accompanied by a shortening in D andan increase in R. Thus, under conditions of weak stimula-tion, or lower C, there is a simultaneous increase in R, as inour rest-period test. Our work above suggests that it will beimportant to analyze all cells, including (0,0) or nonres-ponding cells, in these conditions. Indeed, we can producean ‘‘apparent’’ stochastic resonance effect using our deter-ministic model in a system with behavior previously attrib-uted to stochastic resonance (41) (Fig. S9 b).

CONCLUSIONS

In summary, our results suggest that the rest-period test canbe used to determine whether observed cellular responsevariability is consistent with a deterministic origin, as wefound to be the case for several mammalian signaling path-ways. Physiological, low-concentration pulsing of signalscan represent a deterministic strategy that allows thebody to guide distinct subsets of cells to their appropriatefate.

SUPPORTING MATERIAL

Supporting Text, nine figures, and one table are available at http://www.

biophysj.org/biophysj/supplemental/S0006-3495(19)30058-X.

AUTHOR CONTRIBUTIONS

M.S., A.J., J.J.L., and S.T. conceived and designed experiments. M.S. car-

ried out experiments, analyzed data, and wrote the article. A.J., R.R.N.,

J.J.L., and S.T. consulted on data analysis and edited the article.

ACKNOWLEDGMENTS

We thank Simeone Marino and Paul Wolberg for helping with sensitivity

analysis, Cordelia Ziraldo and Elsje Pienaar for valuable suggestions, and

Behirda Karaj for plasmid amplification.

This work was funded by National Institutes of Health grant GM096040.

A.J. was supported by a postdoctoral fellowship (125027-PF-13-284-01-

TBE) from the American Cancer Society.


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Biophysical Journal, Volume 116

Supplemental Information

A Two-Pulse Cellular Stimulation Test Elucidates Variability and Mech-

anisms in Signaling Pathways

Madhuresh Sumit, Andreja Jovic, Richard R. Neubig, Shuichi Takayama, and Jennifer J.Linderman

SUPPLEMENTARY FIGURES AND TABLES

Fig. S1

Fig. S1. Lognormal distribution of variables results in similar trends as that for uniform distribution. Experimental results (bar plots) and corresponding simulation results (scatter points) with lognormal distribution of variables [GPCR], [G-protein] and [PLC]. The standard deviation, xd = 20% was assumed based on the noise analysis of experimental data. The mean values of the variables were adjusted to account for asymmetry in distribution. Optimization with D = 16 s data resulted in μlognormal = 0.95* μuniform.

Fig. S2

Fig. S2. Distribution of parameters (components) in the model that distinguish the four responses. a-c. Box plots showing distribution of individual components in the GPCR model: total receptor [GPCR], total G-protein [GT] and total PLC [PLC]. The individual components may not be able to discern the four outcomes. d - e. A cumulative distribution of components, defined by Q (Q = [GPCR]*[G]*[PLC]) is able to discern the four outcomes. Data-set and statistical test method remain the same as above. Data information: In (a-e), data are presented as box plot for n = 750 in silico single cell time traces. ***: p < 0.001; n.s.: not significant, p > 0.05 (Student’s t-test).

Fig. S3

0 50 100 150 200 250

0

20

40

60

[CCh] = 10 nMD = 10 s

Su

b-p

op

ula

tio

n (

%)

Rest period (s)

[0,0,0] [0,0,1] [0,1,0] [1,0,0] [0,1,1] [1,0,1] [1,1,0] [1,1,1]

Fig. S3. A three-pulse extended test with the GPCR-calcium model. For three-pulse stimulation, there are eight possible outcomes as shown in the graph. Increasing rest period leads to either (0,0,0) response (black squares) or a (1,1,1) response (red circles).

Fig. S4

200 400 600 800 1000

0

20

40

60

80

100

Su

b-p

op

ula

tio

n (

%)

Rest period (min)

[0,0] [0,1] [1,0] [1,1]C = 0.1 ng TNF; D = 20 min

Fig. S4. Effect of rest period on subpopulation composition in a 2-pulse in silico experiment with TNFα-NFκB model. C = 0.1 ng/ml, D = 20 min. Similar to our GPCR-calcium model, this model also suggests that the sub-population composition changes with increasing R, and the apparent stochastic responses i.e., (0,1) and (1,0) vanish at sufficiently long rest period.

Fig. S5

Fig. S5. Effect of pulse duration on subpopulation composition in a two pulse in silico experiment. a. In GPCR-calcium model, increasing D increases the (1,1) sub-population (green lower triangles) and decreases the (0,0) sub-population (black squares). The other two responses increase and then decrease with increasing D. C = 5 nM, R = 120 s. Three sets of two-pulse in silico experiments with 250 cells/set were obtained to calculate the sub-populations. Error bars are standard deviations. b. Similar trends can be observed in a TNF-α NFκB signaling pathway that acts at an entirely different timescale. TNF input = 0.1 ng, R = 180 min. Data obtained from two-pulse in silico experiments with 1000 cells/set to calculate the distribution of sub-populations.

Fig. S6

Fig. S6. Cellular response variability in the deterministic GPCR-calcium model with extrinsic noise decreases with D and R. Similar to the results shown in Fig. 5a, when the model was tested for a different concentration (C = 5 nM), while keeping C*D the same, the cellular response variability (fraction of cells responding as either (0,1) or (1,0)) decreased with increase in ‘R’, thus validating the rest period test.

Fig. S7

Fig. S7. Effect of hill-coefficient on bifurcation of ‘0’ and ‘1’ responses amidst cell-to-cell variability. Hill coefficient for the reaction step involving IP3 generation from Phospholipase C was changed in the model. H = 0.5, 1 and 1.5 didn’t show significant bifurcation, while higher values (H ~2) showed significant bifurcation of IP3 and calcium response into ‘0’ and ‘1’. Red and black curves indicate curves with peaks greater than or less than the mean of all the peaks respectively.

Fig. S8

Fig. S8. Component-wise analysis of the NFkB model. a. Model analysis of the two sub-populations (0,0) vs (1,1) in NFkB model leading to similar conclusions as in the GPCR model (Fig. 4a). Basal IKK kinase activity brings about the major difference leading to either (0,0) or (1,1) response (also a node of high hill coefficient (h = 2)). b. Component- wise model analysis of why (0,1) NFkB response translates into a (0,0) response upon increasing R in the TNFa-NFkB model. Although a 0 or sub-threshold NFkB response occurs for some cells for the first stimulation and the cells appear to be not responding, the receptor activation does create a short memory of the stimulation at IKKK kinase level. For shorter R, the active IKKK Kinase level rises more than that for a longer R upon second stimulation, which in turn gets amplified via a high Hill coefficient pathway. The first blue pulsatile shape around t = 0 is actually all the three conditions overlapping, with blue line on the top.

Fig. S9

Fig. S9. Components that constitute cellular response variability. a. Schematic showing comparison between square wave pulse and saw-tooth pulse. b. A simulation of GPCR-calcium model under stimulation parameters C, D and R such that the stimulation properties are similar to the saw-tooth pattern (top panel). Three sets of stimulation parameters were chosen such that increase in C is accompanied by a proportional increase in D while keeping the time period (T = D+R) the same, thus mimicking saw-tooth. The heat-map shows 20 representative in silico simulations out of 100 per condition where non-responsive (0,0…) outcomes have been removed similar to (44).

Table S1

LHS-PRCC of TNF- NFkB deterministic model (Tay et al, 2010). + and – show positive and negative correlation of the parameter with the peak amplitude. The p-value of correlation is indicated by number of signs, i.e., ++++/----- : p < 10-12; +++/---- : p < 10-9; ++/--- : p < 10-6; ++/--- : p < 10-3; n.s.: not significant. Abbreviations remain the same as in the source code provided with Tay et al, 2010.

Model parameter Sensitivity to 1st peak Sensitivity to 2nd

peak NFKB ---- n.s. TNFR ++++ ++++ IKK n.s. n.s. A20 n.s. n.s. K1 ++++ ++ K2 +++ n.s. K3 ---- ---- K4 n.s. n.s. KA ++++ ++++

KA20 + n.s. KN ++++ ++++

KNN ++++ ++++ KI ---- ---- C1 ---- -- C3 + +++ C4 --- --- C5 ++++ +++ A1 n.s. n.s.

A20 n.s. n.s. A3 ++++ +

C1A ++ n.s. C5A n.s. n.s. C6A ---- n.s. KB ++++ +++ KF ---- ---

Text S1. Calculation of order of magnitude for number of ligand molecules interacting with single cells for single pulse stimulation under constant flow and diffusion limited cases

Case 1. Calculation of order of magnitude for ligand exposure during a single pulsed stimulation. Suppose the ligand concentration is x M. Let the cell volume be V m3. The total number of molecules in volume V is given by: # of molecules (static) = x*NA*V*1000 This will be the average number of molecules the cells would be exposed to for a static stimulation. Now, suppose we have a microfluidic flow of ligand exposure, wherein the fluid flow is v m/s. And the average characteristic length for cells is assume l m. Then, number of molecules exposed to cells per second is given by: # of molecules/s = x*NA*V*1000*l/v If the duration of stimulation is D s, then total number of agonist exposed per stimulation is: # of molecules per stimulation = D*x*NA*V*1000*l/v Parameters: Average cell-volume of HeLa cells/HEK cells is taken as 2000 um3. Therefore, V = 2000*10-18. Characteristic length for cells is taken as 20 μm. Hence, l = 20*10-6. Concentrations: x = 10*10-9 (for carbachol), x = 2*10-12 (for TNF-α). D = 10 s (for carbachol), D = 20 min = 20*60 s. NA: Avogadro number: ~ 1024. Using the above parameters, # of molecules per stimulation ~ 106 (for carbachol) # of molecules per stimulation ~ 105 (for TNF-α) We assume that during a continuous flow stimulation, the role of diffusion may be neglected. Case 2. Calculation for TNF-α when replenishment is hourly (not continuous), i.e., under diffusion limited condition (Stimulation method in Tay et al, 2010) Volume of the chamber = 35 nl; Concentration of TNF- α = 2 pM; Total number of molecules present in the chamber = 35*2* 10-21 * 1024 = ~ 104

Diffusion constant for TNF- α ~ 0.5 – 1.0 *10-6 cm2/s; Length scale to traverse = 0.3 mm (35nl chamber); Time scale to traverse diffusively ~ 450 s = 8 min (t ~ x2/2D) Therefore, a stimulation of ~ 20 min should be sufficient to allow TNF-α molecules in the same order of magnitude to be able to bind to the receptors, which is ~ 104. Note: V = 35*10-12 m3 implies that length scale for the microfluidic chamber can be estimated as ~ 3*10-4 m = 0.3 mm

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