1521-0111/88/3/604–616$25.00 http://dx.doi.org/10.1124/mol.115.100057MOLECULAR PHARMACOLOGY Mol Pharmacol 88:604–616, September 2015Copyright ª 2015 by The American Society for Pharmacology and Experimental Therapeutics

MINIREVIEW—EXPLORING THE BIOLOGY OF GPCRS: FROM IN VITRO TO IN VIVO

G Protein–Coupled Receptor Signaling Networks froma Systems Perspective

S. Roth, B. N. Kholodenko, M. J. Smit, and F. J. BruggemanSystems Bioinformatics (S.R., F.J.B.) and Amsterdam Institute for Molecules, Medicines & Systems, VU University, Amsterdam,The Netherlands (M.J.S.); and Systems Biology Ireland, University College Dublin, Dublin, Ireland (B.N.K.)

Received May 18, 2015; accepted July 10, 2015

ABSTRACTThe signal-transduction network of a mammalian cell integra-tes internal and external cues to initiate adaptive responses.Among the cell-surface receptors are the G protein–coupledreceptors (GPCRs), which have remarkable signal-integratingcapabilities. Binding of extracellular signals stabilizesintracellular-domain conformations that selectively activateintracellular proteins. Hereby, multiple signaling routes are ac-tivated simultaneously to degrees that are signal-combinationdependent. Systems-biology studies indicate that signalingnetworks have emergent processing capabilities that gofar beyond those of single proteins. Such networks are

spatiotemporally organized and capable of gradual, oscillatory,all-or-none, and subpopulation-generating responses. Protein-protein interactions, generating feedback and feedforwardcircuitry, are generally required for these spatiotemporal phe-nomena. Understanding of information processing by signalingnetworks therefore requires network theories in addition tobiochemical and biophysical concepts. Here we review some ofthe key signaling systems behaviors that have been discoveredrecurrently across signaling networks. We emphasize the role ofGPCRs, so far underappreciated receptors in systems-biologyresearch.

IntroductionWe are far from a complete molecular understanding of how

a single mammalian cell makes its decisions, given extracel-lular and intracellular signals. We do not yet have the capa-bilities to determine the complete connection topology of itssignaling networks [although we are moving toward this goal(Oda et al., 2005; Hyduke and Palsson, 2010)], how it adapts intime, and how the kinetic properties and interaction partners ofthe signaling proteins shape network responses. Such in-formation is required for truly predictive medicine that isexpected to rely heavily on mathematical models (Aldridgeet al., 2006; Kholodenko, 2006; Du and Elemento, 2015).Great strides have, however, been made in identifying key

principles of cellular signaling, at the level of single proteinsand protein networks, including spatiotemporal aspects(Dehmelt and Bastiaens, 2010; Kholodenko et al., 2010).These efforts promise to lead to a set of standardized, quanti-tative approaches for mapping and exploring the dynamicsignaling capabilities of protein networks. That such an ap-proach can be a great success is indicated by current molecular

and cellular biology. Generic protein concepts, such as, forinstance, cooperativity, allostery, and catalysis, have led toa standardized nomenclature and design of experiments thatgreatly accelerates molecular biology approaches. The sub-sequent combination of molecular concepts with networkconcepts by systems biology is similarly powerful. For metab-olism, this already had great consequences. All metaboliccapabilities of a cell can now be computed with metabolicnetworkmodels (Bordbar et al., 2014). Cell biology and systemsbiology are together aiming at reaching a similar status for thesignaling network of a cell, requiring the merger of networkconcepts with the biochemistry of signaling proteins (Oda et al.,2005; Hyduke and Palsson, 2010). This is for many reasons,however, a much harder problem.The calculation of the metabolic capabilities of a cell re-

quires only the knowledge of the stoichiometry of the metabolicreactions encoded on the cell’s genome, not their kinetics. Thisis not so for the signaling capabilities of a cell, which do requirethe kinetics of the proteins, especially because signaling is sucha dynamic phenomenon. Kinetic assays with signaling proteinsare however notoriously hard. Whereas kinetic constants formetabolic enzymes can be determined in cell-free extract, thisis not feasible for many signaling proteins, in particular forthose that are active in protein complexes and the cellularmembrane.

S.R. and F.J.B. are funded by the Marie Curie Initial Training NetworkMultifaceted CaSR, FP7-264663. F.J.B. is also funded by NWO-VIDI projectNo. 864-11-011.

dx.doi.org/10.1124/mol.115.100057.

ABBREVIATIONS: GAP, GTPase-activating protein; GEF, guanine exchange factor; GPCR, G protein–coupled receptor; GRK, G protein receptorkinase; MAPK, mitogen-activated protein kinase.

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Why G Protein–Coupled Receptors Are SoAttractive for Systems Biology

From a biophysics and systems biology perspective,G protein–coupled receptors (GPCRs) are particularly attrac-tive. They can attain different conformations that coexist ina thermodynamic equilibrium, which shifts under the influ-ence of signal binding (Venkatakrishnan et al., 2013). Agonistbinding will induce a conformational change of the receptorthat activates intracellular signaling, whereas inverse ago-nists inhibit basal signaling and force the receptor in aninactive state. Allosteric modulators, which bind to allostericsites of the GPCR, promote conformational changes thatcan alter orthosteric ligand affinity and/or efficacy, or mayselectively activate a specific signaling pathway. It was longthought that GPCRs exclusively signal via G proteins.However, GPCRs can also signal via G protein–independentsignaling pathways that involve, for example, G protein

receptor kinases (GRKs) and b-arrestins or GPCR interactingproteins that activate (unexplored) G protein–independentsignaling pathways. Intriguingly, different ligands that bindto the same GPCR protein are able to induce distinct down-stream signaling pathways. These biased ligands selectivelystabilize only a subset of receptor conformations, thus pref-erentially modulating certain signaling pathways.Classic approaches for equilibrium-binding models of cooper-

ative proteins immediately apply to GPCRs (De Lean et al., 1980;Iyengar et al., 1980; Black and Leff, 1983; Hall, 2000; Changeux,2013; Roth and Bruggeman, 2014) and can account for signalintegration by receptors—so called "combinatorial ligand-bias."This is in contrast to, for instance, receptor tyrosine kinases thatrequire phosphorylations, a kinetic nonequilibrium process, foractivation and conformation transitions. The activation ofG proteins by GPCRs and their inactivation by GTPases, leadingto steady-state activation of G proteins, can be understood to agreat extent in terms of existing principles of covalent-modification

Fig. 1. Overview of receptor and network modules that areinvolved in cellular decision making and that are discussedin this minireview. Dimerization kinetics and ligand biasare biophysical aspects of GPCRs. The kinetics of G proteinactivation cycles and of covalent-modification cascades to-gether determine the sensitivity properties of signaling net-works, whereas feedbacks induce dynamic phenomena suchas robustness, oscillations, and bistability.

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cycles (Goldbeter and Koshland, 1981; Koshland et al., 1982;Blüthgen et al., 2006). Likewise, biochemical equilibrium-modelsof competitive binding describe the competition of immediatedownstream proteins, such as G proteins, GRKs, and b-arrestins,for receptor conformations.The conceptual and quantitative framework for under-

standing GPCRs and G protein activation is therefore largelyin existence, shifting the challenges more to the experimentaland data analysis side. Yet, systems biology has focused muchmore on receptor tyrosine kinases–induced cellular signaling(the RAF-MEK-ERK axis) than on GPCR-activated networks.In this review, we aim to introduce the GPCR researchers to

several systems biology findings about signaling networks. Thisreview is organized in a pragmatic manner (Fig. 1); we start byreviewing some of the basic biophysics aspects of GPCRs,followed by the kinetics of G protein activation cycles, and finallywe discuss several of the dynamic phenomena emerging insignaling networks that have been found with systems biologyapproaches. Throughout this review we placed informativetables, in which we explain a finding in quantitative systemsbiologic or biophysical terms, using mathematical models. Wehope that this review sparks further interest in systems biologystudies of the principles of GPCR signaling networks.

Quantification of the Membrane ProcessesIn systems biology, emphasis is put on quantitative stud-

ies (Aldridge et al., 2006). In the case of GPCRs, this concerns

quantification of their kinetics and abundance. Quantificationis, for instance, required for understanding the signalingoutcome of competition of multiple GPCRs for the same pool ofG proteins (Heitzler et al., 2012). This requires knowledge ofratios of receptor abundances and conformation-dependentG protein affinities. The expectation is that the kinetic con-stants of a GPCR will be constant across cell types, as longas isoenzymes or covalently modified variants do not occur,although their abundances (expression level) can greatly vary.In addition, monomer mobility and oligomerization affinities ofGPCRs are key factors, because they determine the activefraction of receptors.Advanced techniques have been developed for the de-

termination of receptor mobility and dimerization properties.In particular, tracking of single receptor molecules at thesurface of intact cells has proven very informative (Lohseet al., 2014). Receptors are expressed at several hundred toseveral thousands of copies per cell. They are surprisinglymobile with often localization-independent diffusivities (Hernet al., 2010; Lohse et al., 2012). The oligomerization kineticsfor several members of distinct GPCR families has beendetermined as well (Fig. 2) (Hern et al., 2010; Kasai et al.,2011; Kasai and Kusumi, 2014). In Table 1, we discuss thequantitative aspects of measured dimerization kinetics. Weemphasize that at this stage it is not at all clear whetherdimeric receptor complexes are always the active species.

Receptor Activation and Conformation SelectionThe advantage of receptor dimerization, and, in general, of

oligomerization, is that the signal affinity can be bettermodulated, via allosteric interactions, and the signal sensitivitycan be greatly increased, via cooperativity (Changeux, 2013). Aninfluential view is that the functional, signaling states of thereceptor correspond to specific receptor conformations, in partic-ular of their intracellular domain to which downstream signal-ing proteins bind. The presence of extracellular ligands istransduced to the intracellular domain by "conformationselection": the precise combination of ligands bound to theextracellular domain stabilizes particular conformations of theintracellular domain. Whether this involves stabilization ofmultiple conformations of a single GPCR in particular fractions,leading to a "G protein code" that is ligand specific, or of a singleconformation is unclear and presumably evenGPCR dependent.These ideas are in flux at the moment, with the

introduction of powerful structural methods. Structuralstudies provide evidence for conformation selection and

Fig. 2. Receptor dimerization kinetics. Kasai et al. (2011) determinedthat 41% of the receptors exist as transient dimers, and 59% as monomers.To emphasize the rapid dynamics—on a subseconds time scale—we calcu-lated the transient response of the dimer and monomer concentrationsupon small perturbations in their equilibrium concentrations, given thekinetic parameters measured by Kasai et al. (2011).

TABLE 1Membrane diffusion and the time scales of complex-formation equilibria of receptors

GPCRs are very dynamic (Fig. 2); they continuously diffuse through the plasma membrane and dimers (or oligomers) are continuously forming andfalling apart. To simplify the analysis, we consider only dimerization. Dynamic dimerization equilibria exist that are characterized by a constant,rapidly fluctuating monomer and dimer fraction. Kasai et al. (2011) recently quantified the monomer-dimer equilibrium of the N-formyl peptidereceptor (FPR), a GPCR. They found that:

2 m⇌kþ

k2m2;  kþ ¼ 1:085� 1023

�copiescell

s�21

;  k2 ¼ 11s2 1;  KD ¼ k2

kþ¼ 10138

copiescell

;

indicating that the dimer, denoted by m2, life-time is about 0.1 seconds (1/k2): 10 dimers fall apart every second. The total number of receptormonomers per cell,mT, was 6000. At thermodynamic equilibrium, when KD =m2/m2, and given mT =m + 2m2, the equilibrium concentrations of themonomer and the dimer become m = 3534 copies/cell and m2 = 1233 copies/cell: less than 50% of the monomers exist as dimers. The lifetime ofa monomer equals 0.4 seconds (=kfm

2/mT)21. The diffusion coefficient of a monomer in the membrane sets the upper limit of the association rate

constant (Shoup and Szabo, 1982) to 3 � 1023 cell/copies (Lauffenburger and Linderman, 1993). The k+ of FPR is very close to this limit. Givena realistic diffusion coefficient (D) of 0.1 mm2/s for a GPCR (Hern et al., 2010), the average distance that a GPCR travels in a membrane in onesecond equals

ffiffiffiffiffiffiffiffi4Dt

p= 0.6 mm.

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conformation-dependent activation of downstream signalingproteins (Bokoch et al., 2010). Kinetic information is pro-viding additional support for this mechanism (Marcaggi et al.,2009; Hlavackova et al., 2012; Preininger et al., 2013; Lohseet al., 2014).It is not a new concept in biochemistry that cooperative

proteins can accommodate alternative conformations withdifferent activities. Theories on cooperative proteins, re-viewed by Changeux (2013), have been describing suchbehavior already for a long time, early on mostly for metabolicenzymes and transcription factors. Allostery and cooperativ-ity are key signaling features of GPCRs that make themversatile signal integrators.An emerging view is that conformation selection by combi-

nations of bound ligands and conformation-specific G proteinactivation underlies ligand bias of GPCRs. This behavior can beaccounted for by extended models of cooperative proteins (Rothand Bruggeman, 2014). In Table 2 we present an example ofsuch a model. Cooperative proteins are generally comprised ofmultiple subunits with allosteric interactions between ligand

binding sites. Those properties play an important role in phar-macological applications, where conformation selection is usedas a drug design objective for altering ligand bias (Milligan andSmith, 2007; Keov et al., 2011).Ligands can induce shifts in the conformation equilibrium

of a GPCR, influencing its activation of intracellular G pro-teins and b-arrestins (Kahsai et al., 2011) (see Figs. 1 and 3).Using spectroscopy methods, Rahmeh et al. (2012) were ableto show that distinct conformations of the V2 argininevasopressin receptor were induced in response to different(biased) ligands. The resulting ligand-biased signaling, orfunctional selectivity, is now viewedmore often as an intrinsicproperty of the receptor-ligand complex, which can be un-derstood from the thermodynamics associated with stabiliza-tion of particular receptor conformations (Violin et al., 2014).Approaches for quantification of biasing effects was recentlyreviewed (Kenakin, 2014). During quantification of ligandbias, it is important to discern receptor biases from othersources, such as the signaling network (Kenakin andChristopoulos, 2013).

TABLE 2Conformation equilibria of a GPCR and their shifts upon ligand binding

We consider a receptor homodimer. Each monomer has an extracellular domain, with two ligand binding sites. A homodimer has a singleintracellular G protein–binding domain. The homodimer is in an “off ” state when its subunits are both in their “T” (tensed) conformation. When thesubunits are in the “R” (relaxed) conformation, the receptor can activate G proteins in an intracellular domain-state–specific manner. We considertwo G proteins, “1” and “2”, that are activated by the receptor in the R state if its intracellular binding domain is in the matching “1” or “2”conformation. This is a minimal mechanism of conformation selection by ligand combinations and conformation-dependent G protein activation.The fraction of active, ligand-saturated receptor with its intracellular domain in state “1” is (rT denotes the total receptor concentration) (Roth andBruggeman, 2014):

r1s4rT

¼

s2

aK2R;1

!2

ðzR;1 þ ℓRzR;2Þ2 þ LðzT;1 þ ℓTzT;2Þ2;  zi; j ¼ 1þ 2

sKi; j

þ s2

aK2i; j; (1)

it depends on the ligand concentration s, the conformation-dependent affinity of the subunits for the ligand KR,1, the allosteric factor a, theintracellular-domain conformation equilibrium constants ℓR and ℓT and, finally, on the receptor equilibrium constant L. The power "2" indicated inred signifies the additional sensitivity of the receptor due to the fact that it is a dimer, the dimer makes the active fraction dependent on s raised tothe power 4 (rather than 2). When positive allostery is really potent and the receptor its affinity for the ligand is independent of its intracellulardomain conformation then,

r1s4rT ¼

s2

aK2R

!2

1þ s2

aK2R

!ð1þ ℓRÞ

!2

þ L

1þ s2

aK2T

!ð1þ ℓTÞ

!2: (2)

This equation gives a sigmoidal dependency of the active receptor fraction on the ligand concentration. The Hill coefficient of this equation

equals 2∂ ln r1s4∂ ln s

at s = s0.5 when r1s4 = rT /2. This model displays all the features associated with ligand bias (Fig. 3) (Roth and Bruggeman, 2014).

Ligand affinity, maximal response, and signal sensitivity are all dependent on the precise combination of ligands bound to the extracellular bindingdomain, in agreement with experiments.

Fig. 3. Illustration of ligand bias and ultrasensitivity. (A) Two different signaling outputs are plotted against each other in a "bias plot." In sucha plot, identical signaling responses lead to a straight line with slope 1 (solid line). Biased signaling responses cause a deviation from this linearrelation and are represented by the curved, dashed lines. (B) Ultrasensitivity is represented as a sigmoidal dose-response curve (solid line), whereasa hyperbolic curve, characteristic for a hyperbolic "Michaelis-Menten" response is not ultrasensitive (dashed line).

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In addition to classic, extracellular signals, peptides,pepducins, and nanobodies that bind the receptor intracellu-larly can also affect the coupling GPCR to signaling molecules(Quoyer et al., 2013; Staus et al., 2014; reviewed in Shukla,2014). This indicates that the intracellular state can alsomodulate biased signaling. Scaffolding proteins, or othermolecules that influence the receptor, may therefore primethe receptor from the inside for specific extracellular signals oralter intracellular signaling. A dynamic model of G proteinactivation (Kinzer-Ursem and Linderman, 2007), which incor-porates measured biochemical parameters, indicates the im-portance of cell-specific parameters, such as receptor anddownstream protein expression ratios, and kinetic constants,for instance for GTP hydrolysis and ligand-binding affinities,forGprotein activationdynamics (Kinzer-UrsemandLinderman,2007). Similarly, a model of the M1 muscarinic receptorsignaling, involving ligand-binding constants, receptor–G pro-tein interactions, and Ga-PLC interactions gave rise to ligand-response relationships in close agreement with experiments(Falkenburger et al., 2010). The GPCR field has advanced toa stage where enough kinetic information is available to quan-titatively explain the dynamic responses of G protein activationto extra- and intracellular stimuli. Such an approach is particu-larly relevant when mutant and wild-type receptors arecompared with respect to their signaling properties.

G Protein Activation and Inactivation CyclesUpon binding of a GDP-bound G protein to an active con-

formation of a GPCR, the G protein can become activatedin this complex via a guanine exchange event; this ki-netic activity presumably resides on the GPCR (Oldham and

Hamm, 2008). The activating conformation change of theGPCR causes it to have guanine exchange factor (GEF) activ-ity. Upon activation, the G protein can dissociate from thecomplex and activate downstream signaling until it is in-activated by its GTPase activity, which is usually enhanced byGTPase-activating proteins (GAPs). The G protein thereforecycles between active and inactive states. The fraction ofactive G protein is determined by the balance between GEFand GAP activities (Oldham and Hamm, 2008). In Table 3 weshow some of the basic aspects of such processes.Covalent-modification cycles, e.g., formed by a kinase and

phosphatase pair, can display zero-order ultrasensitivity withrespect to signals (Fig. 3) (Goldbeter and Koshland, 1981;Blüthgen et al., 2006; Ferrell and Ha, 2014a). A GPCRactivation/inactivation cycle can in principle show the samebehavior—although it is not strictly a covalent-modificationcycle—with respect to signals acting on the GPCR.In case of ultrasensitivity, a large fractional change in the

GGTP concentration occurs upon a small fractional change inthe concentration of the ligand that binds to the receptor.Accordingly, the dose-response curve of [GGTP] as functionof the signal concentration is switch-like (e.g., with a Hillcoefficient exceeding 4). Switch-like, zero-order, ultrasensi-tive behavior occurs when both the GEF and the GAPenzymes are saturated with their substrates—½GGDP�≫KGEF

Mand ½GGTP�≫KGAP

M —such that they operate in their zero-orderregimen (KM denotes the Michaelis-Menten constant of theenzyme) (Table 3). Trunnell et al. (2011) present an experi-mental illustration of ultrasensitivity.Turcotte et al. (2008) developed a kineticmodel of a G protein

covalent-modification cycle and found ultrasensitivity in thecalculated dose-response curves. Ultrasensitive responses have

TABLE 3G protein activation and sensitivity of its GTP-bound state ([GGTP]) to GPCR ligands

A GPCR acts as a guanine exchange factor (GEF) for G proteins. The resulting exchange of GDP by GTP leads to the activation of the G protein;whereas a GAP hydrolyses this GTP,

RA þGGDP⇌RAGGDP→RAGGTP⇌RA þGGTP (3)GAPþGGTP⇌GAPGGTP→GAPGGDP⇌GAPþGGDP (4)

Here RA denotes the active conformation of the receptor. Using an equilibrium-binding model, these reactions lead to the following enzyme kineticequation for the GEF and GAP activities:

yGEFðGGDP;GGTPÞ ¼ kGEFRAGGDP

KGEFGDP

1þ GGDP

KGEFGDP

þ GGTP

KGEFGTP

(5)

yGAPðGGDP;GGTPÞ ¼ kGEFGAPT

GGTP

KGAPGTP

1þGGDP

KGAPGDP

þGGTP

KGAPGTP

: (6)

The sensitivities of the steady-state signaling output, the steady-state concentration of activated G protein, GGTP, with respect to a change in theconcentration of the GEF reaction catalyst, the active conformation of the receptor (RA) equals (Kholodenko et al., 1997),

∂ lnGGTP

∂ lnRA [ rGGTP

RA 51

½GGTP �½GGDP �e

yGEFGGDP 2 eyGEF

GGTP 1 eyGAPGGTP 2

½GGTP �½GGDP �e

yGAPGGDP

(7)

The e coefficients are generalized kinetic orders [or elasticity coefficients (Kholodenko et al., 1997)] of the reactions: eyGAPGGDP 5

∂ ln yGAP

∂ lnGGDP. When they are

close to zero, the enzyme operates in its zero-order regimen (y} ½substrate�0) and zero-order ultrasensitivity occurs (Blüthgen et al., 2006). This is

most noticeable when we assume both enzyme rates insensitive to their product concentrations; then∂ lnGGTP

∂ lnRA [ rGGTP

RA 51

½GGTP �½GGDP �e

yGEFGGDP 1 eyGAP

GGTP

, which is

much greater than 1 when the e coefficients are close to 0. The sensitivity of [GGTP] to a ligand of the GPCR, RGGTP

S ¼ d lnGGTP

d lnS , can be decomposed into(Kholodenko et al., 1997):

s →rR

AS RA →

rGGTP

RA GGTP;  RGGTP

RA ¼ rGGTP

RA rRA

S : (8)In a dose-response curve of log[GGTP] as function of log S, the slope, which is the sensitivity, equals the product of the receptor sensitivity, rR

A

S , andthe G protein sensitivity, rG

GTP

RA . Therefore, "sensitivity amplification" (Goldbeter and Koshland, 1981; Koshland et al., 1982; Kholodenko et al., 1997)occurs when both r values exceed 1.

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found experimentally with PIP3 activation (Karunarathneet al., 2013). In a combined experimental and modeling study,Karunarathne et al. (2013) demonstrated that PIP3 concen-trations are ultrasensitive with respect to GPCR activation.The phosphorylation of GPCRs by GRKs and the associated

dephosphorylation events can also lead to G protein ultra-sensitivity. GRKs have a broad influence on GPCR signaling(Jiménez-Sainz et al., 2006). Systems biology studies on GRK-regulated GPCR activity (Vayttaden et al., 2010; Heitzleret al., 2012) indicate the versatility GRK regulation and areexamples of the insightful combinations of experiments andmodeling.

Signal Transduction Cascades of BiochemicalReaction Cycles: Sensitivity Amplification

Downstream of GPCRs and their direct activation targets,such as G proteins and arrestins, signals that are initiatedat the cell surface are transduced via cascades of covalent-modification cycli, among other processes. The best un-derstood cascade of covalent-modification cycles is themitogen-activated protein kinase (MAPK) cascade, involvingthree covalent-modification processes in sequence (Morrison,2012). GPCRs activate the ERK, c-Jun N-terminal kinase,and p38 MAPK cascades using spatially and temporallydistinct pathways that are dependent on either G proteins orb-arrestins (DeWire et al., 2007). Direct MAPK activation viaGa is transient, b-arrestin independent, and can involve PKCactivity (Goldsmith and Dhanasekaran, 2007). The otherpathway leading to MAPK activation is triggered by the re-cruitment of b-arrestins as scaffolding molecules (Lefkowitzand Shenoy, 2005; Goldsmith and Dhanasekaran, 2007). Forb-arrestin–mediated ERK signaling, b-arrestins scaffold allthree MAPK cascade kinases, Raf, MEK, and ERK (DeFeaet al., 2000). Because b-arrestins interact with components ofthe clathrin-mediated endocytic pathway, GPCRs bound tob-arrestins are targeted to clathrin-coated pits. For differentGPCRs, b-arrestins either rapidly dissociate and receptorsrecycle to the plasma membrane, or GPCR-b-arrestin com-plexes stay together on the surface of endocytic vesicles. Ineither case, b-arrestin scaffolds mediate activation of multiplesignaling proteins (such as the tyrosine kinase Src and MAPKcascades), thereby displaying a novel role of signal trans-ducers in addition to their classic function of GPCR signalingattenuation (Kholodenko, 2002). Strikingly, only ERK mole-cules that are stimulated via G protein–dependent pathways

translocate into the nucleus, leading to transcriptional acti-vation and DNA synthesis, whereas active ERK moleculesgenerated via b-arrestins accumulated on endosomal vesiclesare entirely retained in the cytoplasm (Ahn et al., 2004). Notonly are the MAPK cascades that are activated via G proteinsor b-arrestins spatially separated, but their temporal activa-tion profiles are also remarkably different. In human embry-onic kidney-293 cells, G protein–dependent ERK1/2 activationis transient, rapidly reaching a peak at about 2 minutes anddescending to low levels after about 10 minutes after stimu-lation, whereas activation via b-arrestins is sustained until atleast 90 minutes (Ahn et al., 2004). Different spatiotemporalpatterns of ERK stimulation via G proteins or b-arrestinsentail distinct functional outcomes at the level of downstreamERK substrates. A decrease in G protein–dependent ERKstimulation due to increased expression of b-arrestins in-hibits ERK-mediated phosphorylation of transcription factors,such as ELK-1, whereas b-arrestin–mediated ERK signaling

TABLE 4Sensitivity of networks to signals: cascades, feedback, and feedforward networks

In a signaling cascade, the net sensitivity of the output D with respect to the input A at steady state equals the product of the sensitivities along thecascade (Kholodenko et al., 1997; Bruggeman et al., 2002), with A-to-D as concentrations of signaling proteins,

A→rBA B→

rCB C→rDC D;  RD

A ¼ rDC rCBr

BA (9)

All these local sensitivities, each denoted by an "r", can be obtained from steady-state dose-response curves. When D feedbacks onto A, regardless ofwhether this is a positive or negative interaction, we obtain:

FRDA ¼ RD

A12 r A

DRDA; (10)

with rAD as the feedback strength, it is,0 in case of negative feedback and .0 in case of positive feedback. The effect of negative feedback is that thesensitivity of the output D with respect to the input signal A is reduced. These equations lose their meaning when the feedback destabilizes thesystem. In the case of positive feedback, stability is guaranteed as long as the denominator remains positive. The positive feedback sensitizesthe cascade for the signal when FRD

A .RDA . When rADR

DA ¼ 1, the sensitivity becomes infinite and all-or-none response occurs associated with

"bistability," which is a known response of signaling cascades. When feedbacks destabilize the system oscillations or bistability can occur asdiscussed in the main text.

Fig. 4. Sensitivity amplification by a signal transduction cascade.A covalent modification cascade (left) can amplify the signal sensitiv-ity (right). The signaling response becomes steeper along the signalingcascade.

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induces cell motility phenotype, which is associated with therearrangement of cytoskeleton, membrane ruffling, and che-motaxis caused by prolonged activation and retention of activeERK in the cytoplasm.The same principle of b-arrestin scaffolding leads to GPCR-

induced NFkB signaling (Sun and Lin, 2008), a signalingcascade that is also controlled by a series of posttranslationalmodifications. The MAPK system has been studied exten-sively and several interesting signaling features have beenfound, such as oscillations, drug robustness, and ultrasensi-tivity (Ferrell and Machleder, 1998; Shankaran and Wiley,2010; Sturm et al., 2010a; Fritsche-Guenther et al., 2011).One finding is that the outputs of cascades of covalent

modification cycli can display a sensitivity to cascade inputsignals that exceeds the sensitivity of any of its elementalcycli (Goldbeter and Koshland, 1981; Huang and Ferrell,1996; Kholodenko et al., 1997; Ferrell and Machleder, 1998).For instance, the MAPK pathway of Xenopus oocytes wasfound to have aHill coefficient of 8, which is truly a switch-likeresponse (Ferrell and Machleder, 1998), and believed to bedue to "sensitivity amplification." Sensitivity amplificationcan be understood in terms of intuitive theory (Kholodenkoet al., 1997), an example of this is shown in Table 4, and withmathematical models based on enzyme kinetics (Huang andFerrell, 1996). How heightened sensitivity arises in cascadesfollows from basic principles of the enzyme kinetics of theassociated kinases and phosphatases (Blüthgen et al., 2006;Ferrell and Ha, 2014a). The cascade sensitivity equals theproduct of the sensitivities of the individual covalent-modification cycli in the cascade (Fig. 4; Table 4) (Kholodenkoet al., 1997; Bruggeman et al., 2002). The sensitivity of

a single covalent modification cyclus depends on the extent ofthe saturation of the kinases and phosphatases (Table 3).Activation of signaling proteins by double phoshorylation,

such as of MEK and ERK leading to MEKP2 and ERKP2, cancause to heightened sensitivity at the level of a single cascadeelement (Markevich et al., 2004). It has also been show to giverise to a more surprising phenomenon, called "bistability,"which is an all-or-none response of the output, e.g., of ERKP2,with respect to the input, e.g., MEKP2, with hysteresisproperties. Bistability is explained in Fig. 7 and has been foundin mathematical models for a number of signaling networks(Bhalla and Iyengar, 2001; Markevich et al., 2004; Qiao et al.,2007;Ravichandran et al., 2013). Bistability is also amechanismthat can lead to the formation of subpopulations in monoclonalcell cultures and it is for this reason associated with differen-tiation of stem cells (Laslo et al., 2006; Ferrell, 2012).Ultrasensitivity, sensitivity amplification, and bistability

(Ferrell and Ha, 2014a,b,c) are examples of network proper-ties that arise from the interactions between protein activitiesand cannot be attributed to single proteins. Because multipleproteins are required for these systems properties, in additionto precise values of kinetic parameters and expression levels,mathematical models are useful tools when studying them(Aldridge et al., 2006).

Negative Feedback in Signal TransductionCascades: Oscillations and Robustness to DrugsThe output of signaling networks, such as cascades, often

feedback to stimulate or inhibit the processing of the input(s)of the network (Volinsky and Kholodenko, 2013). Negative

Fig. 5. Robustness of the RAF-MEK-ERK cascade due to negative feedback. (A) A network diagram showing that phosphorylated ERK inhibits theactivation of RAF by negative feedback. (B) This feedback reduces signaling sensitivity (left panel, blue line). The inhibition of ERK phosphorylation bya MEK inhibitor [(A) indicated in red; (B) right panel, blue] is reduced by the negative feedback; it makes the cascade robust to perturbations (Fritsche-Guenther et al., 2011).

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feedback is a prerequisite for the emergence of oscillations.Feedback mechanisms arise from transcriptional regulation ofcascade compounds, their covalent modification, endocrineactions, or receptor initiation (Blüthgen et al., 2007). The studyof negative feedbacks has revealed their impact on signalingand appear to contribute to adaptation, robustness, andoscillations (Kholodenko, 2006) (Fig. 5). Oscillatory dynamics hasbeen found in a range of signaling networks, e.g., during NFkB,ERK, and intracellular-Ca21 signaling (Hoffmann et al., 2002;Nelson et al., 2004; Shankaran et al., 2009; Dupont et al., 2011),many of which are linked to GPCRs. GPCRs are also directlyregulated by negative feedback, for instance, via feedbackactivation of GRKs leading to inhibitory phosphorylation of aGPCR (Pitcher et al., 1999) or via othermechanisms (Ferguson,2007). An important example of negative feedback regulation ofGPCR-activated signaling is found in cAMP signaling, wheredownstream activation activates phosphodiesterases that re-duce cAMP levels (Sassone-Corsi, 2012).Calcium oscillations are linked to GPCR signaling. Feed-

back inhibition by calcium of the agonist-receptor complex,presumably through the calcium-sensitive receptor kinases,has shown that oscillations of intracellular calcium areinfluenced by activation of Ga (Fig. 6) (Kummer et al., 2000)and the internalization rate of bg subunits (Giri et al., 2014).Various mathematical models exist that focus on differentaspects of calcium oscillations (reviewed in Dupont et al.,2011). Cross-talk between Gai and Gas regulated signaling,investigated with a modeling approach by Siso-Nadal et al.(2009), suggests that both species can oscillate, likely pro-viding an additional layer of complexity that allows the cellto discriminate between different combinations of signals.Future studies with, for instance, G protein fluorescenceresonance energy transfer sensors should give more insightinto oscillations of G protein activation. It was also found thatgreen fluorescent protein–tagged ERK displayed oscillationsbetween cytosol and nucleus over a broad range of ligandconcentrations (Shankaran et al., 2009). Through modelingand experiments it was concluded that the negative feedbackfrom ERK onto upstream proteins underlies these oscillations,which are likely functional during development (Shankaranet al., 2009; Shankaran and Wiley, 2010). In NFkB signaling,a strong negative feedback of IkBa is leading to oscillations inNFkB (Hoffmann et al., 2002). Thus, the function of NFkB asa transcription factor might therefore depend on the character-istics of its oscillations, leading to dynamic control of geneexpression (Nelson et al., 2004). Direct involvement of negativefeedback of GPCRs in signaling oscillations has, as far as weknow, not yet been established.

Other than oscillations, robustness is another featureassociated with negative-feedback activity. The negativefeedback from ERK to upstream Raf in the MAPK pathwayresembles a negative feedback amplifier used in engineeringto design robust systems (Sturm et al., 2010b). The switch-like behavior of the RAF-MEK-ERK cascade, in the absence offeedback, is changed to a more gradual, linear response(illustrated in Fig. 5) by the feedback. The feedback causesrobustness of phosphorylated ERK against variations in thetotal ERK level, via expression regulation, in agreement withtheory and experiments (Fritsche-Guenther et al., 2011). Italso contributed to robustness to a MEK inhibitor duringmedical treatment (Sturm et al., 2010b; Fritsche-Guentheret al., 2011). For colorectal cancer cells, it was shown thatthe negative feedback in EGFR signaling led to cross-talkbetween ERK and AKT signaling; inhibition of ERK resultedin activation of AKT, via EGFR, and combined inhibition ofERK and EGFR inhibited Ras, ERK, and AKT (Sturm et al.,2010b; Klinger et al., 2013). These predictions were firstmade with a mathematical model before being validated witha xenograft model. All these studies indicate that targeting ofsignaling networks at a single protein, for example duringcancer treatments, can be insufficient and be overcome by thecell, due to compensatory feedback mechanisms. Likewise,

TABLE 5Drug insensitivity of signaling cascades due to negative feedback

The response equation of a signaling network with negative feedback (Kholodenko et al., 1997; Bruggeman et al., 2002),FRD

A ¼ RDA

12 r ADRD

A; (11)

was introduced in Table 4. When negative feedback occurs, the feedback term rAD is negative. When 2 rADRDA ≫ 1, which can occur when 2 rAD ≫ 1 or

RDA ≫1, the previous equation can be approximated by:

FRDA � 1

2 r AD: (12)

This equation represents the slope of the dose-response curve of log D as function of log A. This equation indicates that the response of the output Dof a cascade with negative feedback to a change in its input A only depends on the feedback strength, provided the above mentioned conditions aremet! This result has remarkable consequences. First, it shows how cells can make their responses to signals insensitive to undesired disturbancesthat happen in their own signaling networks and affect RD

A . Second, the medical consequence is that the effect of drugs, acting on the signalingcascade and changing RD

A , will not have a huge effect as long as 2 rADRDA ≫ 1; in particular in the case of strong negative feedback, when rAD ≫ 1

(Sturm et al., 2010a; Fritsche-Guenther et al., 2011).

Fig. 6. Oscillatory signaling dynamics can be induced by a negativefeedback (Kummer et al., 2000). (A) Oscillations of the concentrations ofsignaling molecules. (B) Detailed view of the cytosolic calcium oscillations.

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studies indicate that the absence of a feedback, e.g., by amutation in Raf, can sensitize cells to inhibitors (Sturm et al.,2010b; Fritsche-Guenther et al., 2011) (Table 5). Mathematicalmodels and network concepts are therefore providing newwaysfor studying signaling networks and predicting drug responses.

Positive Feedback in Signal TransductionCascades: From Gradual to All-or-None Bistable

ResponsesAlthough mild negative feedback makes cells robust and

strong negative feedback causes them to oscillate, positivefeedback increases signal sensitivities, amplifies these sensi-tivities, and can even lead to all-or-none, switch-like, binaryresponses (Kholodenko, 2006; Ferrell and Ha, 2014a,b,c).Thus, negative and positive feedback have very different func-tions in a signaling network.Positive feedback can cause networks to display bistability.

Bistability has three features: a switch-like response, a

history-dependent response (hysteresis) (Ferrell andHa, 2014a,c),and generation of cellular subpopulations (phenotypic diversifi-cation, cellular differentiation) (Ferrell, 2012; Ferrell and Ha,2014c) (see Fig. 7). Bistability has been documented for a largenumber of systems. Most examples are currently of microbialsystems, because the type of single-cell experiments required foridentification of bistability are still laborious formammalian cells.Bistability has, however, been shown in experiments of differen-tiating Xenopus oocytes (Ferrell and Machleder, 1998; Xiong andFerrell, 2003) during immune responses (Mariani et al., 2010),cellular differentiation (Chickarmane et al., 2006; Glauche et al.,2010), and the MAPK pathway (Ferrell and Machleder, 1998;Bhalla et al., 2002). A requirement for bistable behavior is thatthe signaling cascade displays sensitivity amplification along thefeedback loop (Table 4).Theoretical analyses suggest that bistability can also arise

in signaling networks via other mechanisms. For instance,double phosphorylation of signaling proteins, such as of MEKand ERK in MAPK cascade, can bring about bistability even

Fig. 7. Illustration of bistability. Positivefeedback in a system can cause it to becomebistable. A bistable system can be in oneout of two stable states, represented astwo valleys in a hilly surface. The state isrepresented in this analogy by the positionof the ball. A separating tipping point—a metastable state—exists that separatesthe two stable states. When the systemresides in the metastable state, fluctua-tions can cause the system to end up instable state 1 or 2. Parameter changes, e.g.,transcription rate, alter the shape of thesurface, such that the number of stablestates can vary from 1 to 2 to 1 (left).Depending on the direction of parameterchanges (from low to high or the reverse),the system switches between stable statesat different points. This phenomenon iscalled hysteresis.

TABLE 6Fold change detection by a molecular activation cascade

A simple model of a feedforward motif illustrates the principle of fold change detection (Goentoro et al., 2009). We consider a system with the signalS and two signaling proteins X and Y, their concentrations change according to:

ddt

x ¼ k1s2 k2x

ddt

y ¼ k3sx2 k4y:

(13)

S therefore "feeds forward," it directly activates X and Y and it activates Y indirectly via X. At steady state, when the concentration of the signal S

equals s, the concentration of X and Y are: xs ¼ k1sk2

and ys ¼ k2k3k1k4

. Note that a change in s does not affect ys, y therefore displays "exact adaptation";

the influence that s has on the synthesis rate of Y is compensated for by x. To show that this system is capable of fold-change detection, wenormalize the concentration with respect to their basal, steady-state levels at reference concentration s,

Fs ¼ �ss;Fx ¼ x

xs;Fy ¼ y

ys; (14)

with �s as the new value of s, applied when the system is at a steady state at the basal value, s, when x = xs and y = ys. The dynamics of the foldchanges in the concentration becomes:

ddt

Fx ¼ Fs 2Fx

k2k4

ddt

Fy ¼ Fs

Fx2Fy

(15)

with t = k2t. The fact that the concentration dynamics can be rewritten in terms of fold changes indicates that the basal steady-state concentrations,at which the change in s is applied, do not matter. The same fold change in s always gives the same fold change in x and y regardless of the basallevels xs and ys. The system therefore responds to fold changes rather than to absolute changes in concentrations. This system is therefore robust toundesired distorting changes in basal concentrations, because they do not affect signaling outcome as long as the outcome is considered normalizedto the basal concentrations.

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in the absence of feedback loops or cascade interactions(Markevich et al., 2004). Legewie et al. (2007) reported thatcomplex formation in signaling cascades, for instance viascaffolds, can cause bistability. One of the uses of mathemat-ical models is therefore to explore the capabilities of signalingnetworks and then design targeted experiments that eithervalidate or falsify model predictions.Applications of quantitative, single cell-based assays of sig-

naling dynamics, e.g., using fluorescence methods, will un-doubtedly lead to more cases of bistability and oscillations ofsignaling networks.With cell population-basedmethods thosebehaviors can generally not be observed.

Experimental Observations of Bistability andOscillations Require Single-Cell ApproachesThe complication of studying dynamic features of signaling

networks is that cell population studies are not alwaysreflective of the dynamic behavior of single cells. Becausecells do not generally function in exact synchrony, oscillationsmay not be visible at the level of a population of cells, onlyat the single-cell level. Likewise, subpopulations that ariseduring bistability are not visible from cell population studies.Single-cell studies, using, for instance, fluorescent protein-based methods, are therefore required to study dynamics ofsignaling circuits. For instance, studies of NFkB, intracellularCa21, and ERK oscillations and of bistability during signalingand cellular differentiation relied on fluorescent reporters(Hoffmann et al., 2002; Nelson et al., 2004; Sigal et al., 2006;Cohen-Saidon et al., 2009; Shankaran et al., 2009).Single-cell studies also indicate that isogenic cells, with the

same cultivation history, display fluctuations in the levelof signaling proteins, likely arising from stochastic eventsduring transcription and cell division (Sigal et al., 2006;Raj and van Oudenaarden, 2008; Cohen-Saidon et al., 2009;Spencer et al., 2009), which can be understood from basicbiophysics (Schwabe and Bruggeman, 2014). This phenome-non has been termed "noise" (Raj and van Oudenaarden,2008). Feedbacks in networks can both reduce and enhancenoise. A consequence of noise is that cells can vary in theirindividual responses to physiologic triggers (Yuan et al.,2011), including drugs (Spencer et al., 2009). Kempe et al.(2015) quantified the variability of transcript level in humancells and showed that transcript number variabilities betweencells derive from differences in cell volume and stochasticityat the level of transcription. Noise is not only an undesirablefeature of molecular systems that scrambles informationtransfer, it is functional as well. It is, for instance, intimatelylinked to bistability, giving rise to subpopulations duringcellular differentiation (Balázsi et al., 2011).

Fold-Change Detection by NetworksCompensates for Stochastic Fluctuations in

Protein LevelsBecause of inevitable fluctuations in molecular activi-

ties (Elf and Ehrenberg, 2003; Paulsson, 2004), cells exploitregulatory circuitry to reduce the harmful impacts of noise,occurring in signal transduction and transcription (Perkinsand Swain, 2009; Cheong et al., 2011). In this way, cellsincrease the reliability of information transfer in signaling

networks (Levchenko and Nemenman, 2014). Negativefeedback is an example of a noise-reduction mechanism(Bruggeman et al., 2009).Another mechanism for noise reduction is fold-change

detection (Table 6). Networks that detect fold changes havethe same dynamics upon the same fold change in the stimulus,regardless of its basal level (Goentoro et al., 2009); this isvisualized in Fig. 8. An (incoherent) feedforward loop in asignaling network gives rise to fold-change detection (Goentoroet al., 2009), as well as other network motifs (Shoval et al.,2010). Fold-change detection has been reported formammaliansignaling (Cohen-Saidon et al., 2009; Goentoro et al., 2009). Forinstance, Cohen-Saidon et al. (2009) studied the dynamics ofnuclear ERK2 upon EGF stimulation using a geneticallyencoded, yellow fluorescent protein–tagged ERK2 in singlecells. They found that ERK levels in the nucleus differedgreatly from cell to cell, but the fold changes of individualcells, upon EGF addition, was much more homogeneous. In

Fig. 8. A network with an incoherent feed-forward loop can give rise tofold-change detection. Two identical fold changes in the signal X, appliedat two different of basal levels, give rise to basal-level dependent dynamicsofY, whereas the dynamics of Z is basal state independent (the dashed andfull lines overlap). Z therefore detects fold changes in X.

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addition, the fold-changes returned to basal levels after atransient period, indicating exact adaptation. All these phe-nomena can be understood from a simple mathematical modelof an incoherent-feedforward loop network (Cohen-Saidonet al., 2009; Goentoro et al., 2009).Hart et al. (2013) studied the integration of two different

stimuli by fold-change–detecting systems, using mathemati-cal models. They used Monod-Wyman-Changeux–based mod-els of receptors associated with bacterial chemotaxis. Thesemodels are also applicable toGPCRs (Table 2), and it is thereforetempting to speculate that some GPCRs may have fold-change–detecting properties as well.These studies indicate that the operation of some signaling

systems should not be appreciated in terms of absolute con-centrations of signaling proteins, but rather in terms of foldchanges in concentrations of active signaling proteins. Againa system concept, originating from engineering in this case,proves a useful concept for the quantitative study of signalingnetworks.

Outlook: Appreciating How a GPCR Plays a Rolein the Decision-Making Machinery of a CellPresently, we understand the basic principles of how single

GPCRs integrate signals and activate intracellular proteins ina biased, signal combination-dependent manner. Combina-tion of new techniques, such as G protein fluorescence reso-nance energy transfer sensors, structural methods, andmutant screens, will undoubtedly give deeper insights intosingle GPCR functioning in the near future.Systems biology studies of signaling networks are in-

dicating that the signaling does not stop at the cell surfacereceptors, much of the cellular signaling capacities derivefrom those networks. Activation/inactivation cycles of pro-teins, signaling cascades, and interwoven feedback andfeedforward circuitry lead to counterintuitive, functionalsignaling dynamics that are best understood with mathemat-ical models and single-cell experiments. We therefore expectthat the next developments in the GPCR field will movetoward quantitative single-cell studies on the signalingconsequences of biased GPCR activation using mathematicalmodels for hypothesis generation and data integration. Suchstudies can elucidate the interplay between the receptors andthe signal transduction machineries of the cell; this knowl-edge is of great value for medical applications (as, e.g., pro-posed by Klinger et al., 2013).In this review, we gave a glimpse of results obtained by

systems biology of cellular signaling. We discussed variousnetwork motifs of signaling pathways that have been in-vestigated with respect to their potential effects on signaloutputs. For example, we illustrated how ultrasensitivityarises and can result from cascade sensitivity amplification.An important aspect was how feedbacks shape signaling func-tions in a cell, including oscillations and robustness. Weemphasize that many of these network-centered studies donot yet focus on GPCRs, although those proteins are often thenetwork inputs. Thus, we hope that future studies willinvestigate GPCR signaling with systems approaches.As more and more knowledge is gained about the cross-talk

between membrane receptors and their induced signalingpathways (Lowes et al., 2002), we are forced to envision

signaling not as separated pathways but as a network. A singlereceptormay then play only aminor role in setting the behaviorof the whole cell, rather it may be that signal integration bydifferent receptors and intracellular wiring of protein-proteininteractions is decisive. This view of signal transduction hasgreat potential for the design and application of new (multi-target) therapeutics. The approach to combine mathematicalmodels and to validate their predictions with experimentaldata will enable new insights into the mechanisms of signaltransduction and promises innovative clinical applications.

Authorship Contributions

Wrote or contributed to the writing of the manuscript: Roth,Kholodenko, Smit, Bruggeman.

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Address correspondence to: Prof. Dr. Frank J Bruggeman, SystemsBioinformatics, Amsterdam Institute for Molecules, Medicines & Systems,VU University, De Boelelaan 1087, NL-1081 HV, Amsterdam, The Nether-lands. E-mail: f.j.bruggeman@vu.nl or Prof. Dr. Martine Smit, MedicinalChemistry, Amsterdam Institute for Molecules, Medicines & Systems, VUUniversity, De Boelelaan 1083, NL-1081 HV, Amsterdam, The Netherlands.E-mail: mj.smit@vu.nl

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