Our scenario is akin to the magnetic

furnace model proposed by Axford and

McKenzie (14–16) and to ideas invoking

reconnection of mesoscale loops (38, 39).

We adopt from the furnace model the idea

that reconnection plays a major role, as it will

release plasma, set free magnetic energy, and

produce Alfve

n waves. However, our model

of the nascent solar wind is intrinsically 3-D,

and the magnetic field geometry is derived

empirically. The plasma is accelerated in the

funnel above a critical height of 5 Mm but

originates below from the neighboring loops.

The initial heating of the solar wind plasma is

achieved in the side loops.

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Heliosphere,J.R.Jokipii,C.P.Sonett,M.S.Giampapa,

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40. The National Natural Science Foundation of China

supported C.-Y.T., C.Z., and L. Z. under projects with

the contract nos. 40336053, 40174045 and

40436015; J.-X.Wang, contract no. 10233050; and

L.-D.X., contract no. 40436015. The foundation

Major Project of National Basic Research supported

C.-Y.T., C.Z., L.-D.X., L. Z., and J.-X.W. under contract

no. G-200078405. C.-Y.T. is supported by the Beijing

Education Project XK100010404. The SUMER project

is financially supported by DLR, CNES, NASA, and the

ESA PRODEX program (Swiss contribution). SUMER,

EIT, and MDI are instruments on SOHO, an ESA and

NASA mission. We thank the teams of MDI and EIT

for providing the magnetic field data and the context

image.

Supporting Online Material

www.sciencemag.org/cgi/content/full/308/5721/519/

DC1

Materials and Methods

Fig. S1

References

6 January 2005; accepted 1 March 2005

10.1126/science.1109447

Causal Protein-Signaling

Networks Derived from

Multiparameter Single-Cell Data

Karen Sachs,

Omar Perez,

Dana Pe’er,

Douglas A. Lauffenburger,

. Garry P. Nolan

Machine learning was applied for the automated derivation of causal influ-

ences in cellular signaling networks. This derivation relied on the simultaneous

measurement of multiple phosphorylated protein and phospholipid components

in thousands of individual primary human immune system cells. Perturbing these

cells with molecular interventions drove the ordering of connections between

pathway components, wherein Bayesian network computational methods auto-

matically elucidated most of the traditionally reported signaling relationships

and predicted novel interpathway network causalities, which we verified ex-

perimentally. Reconstruction of network models from physiologically relevant

primary single cells might be applied to understanding native-state tissue signal-

ing biology, complex drug actions, and dysfunctional signaling in diseased cells.

Extracellular cues trigger a cascade of infor-

mation flow, in which signaling molecules

become chemically, physically, or location-

ally modified; gain new functional capabil-

ities; and affect subsequent molecules in the

cascade, culminating in a phenotypic cellular

response. Mapping of signaling pathways typ-

ically has involved intuitive inferences arising

from the aggregation of studies of individual

pathway components from diverse experimen-

tal systems. Although pathways are often con-

ceptualized as distinct entities responding to

specific triggers, it is now understood that in-

terpathway cross-talk and other properties of

networks reflect underlying complexities that

cannot be explained by the consideration of

individual pathways or model systems in isola-

tion. To properly understand normal cellular

responses and their potential disregulation in

disease, a global multivariate approach is re-

quired (1). Bayesian networks (2), a form of

graphical models, have been proffered as a

promising framework for modeling complex

systems such as cell signaling cascades, be-

cause they can represent probabilistic depen-

dence relationships among multiple interacting

components (3–5). Bayesian network models

illustrate the effects of pathway components on

each other (that is, the dependence of each

biomolecule in the pathway on other biomol-

ecules) in the form of an influence diagram.

These models can be automatically derived

from experimental data through a statistically

founded computational procedure termed net-

work inference. Although the relationships are

statistical in nature, they can sometimes be in-

terpreted as causal influence connections when

interventional data are used; for example, with

the use of kinase-specific inhibitors (6, 7).

There are several attractive properties of

Bayesian networks for the inference of sig-

naling pathways from biological data sets.

Bayesian networks can represent complex

stochastic nonlinear relationships among mul-

tiple interacting molecules, and their proba-

bilistic nature can accommodate noise that is

inherent to biologically derived data. They

can describe direct molecular interactions as

well as indirect influences that proceed through

additional unobserved components, a property

crucial for discovering previously unknown

effects and unknown components. Therefore,

very complex relationships that likely exist in

Biological Engineering Division, Massachusetts Insti-

tute of Technology (MIT), Cambridge, MA 02139, USA.

Stanford University School of Medicine, The Baxter

Laboratory of Genetic Pharmacology, Department of

Microbiology and Immunology, Stanford, CA 94305,

USA.

Harvard Medical School, Department of Genet-

ics, Boston, MA 02115, USA.

*These authors contributed equally to this work.

.To whom correspondence should be addressed.

E-mail: lauffen@mit.edu (D.A.L.); gnolan@stanford.edu

(G.P.N.)

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CORRECTED 19 AUGUST 2005; SEE LAST PAGE

signaling pathway architectures can be mod-

eled and discovered. The Bayesian network

inference algorithm constructs a graph dia-

gram in which nodes represent the measured

molecules, and arcs (drawn as lines between

nodes) represent statistically meaningful rela-

tions and dependencies between these mole-

cules. When inferring a Bayesian network

from experimental data, the network infer-

ence algorithm aims to discern a model that

closely predicts the observations made. The

algorithm approximates the most likely mod-

els by traversing the space of possibilities

via single-arc changes that improve the score.

There is a trade-off between simple models

and those that accurately capture the em-

pirical distribution observed in the data. The

employed Bayesian scoring metric captures

this trade-off; thus, a high-scoring model is a

both simple and accurate representation of

the data (8, 9). Bayesian networks have been

applied to gene expression data for the study

and discovery of genetic regulatory pathways

(4, 6, 10). However, because of the probabilis-

tic nature of the Bayesian modeling approach,

effective inference requires many observations

of the system. Thus, such studies have often

been limited by data sets of insufficient size;

for instance, those made up of measurements

based on averaged samples derived from heter-

ogeneous cell populations (a necessary limita-

tion when using lysates from large numbers

of cells) (5, 11).

In contrast to lysate-based methods, intra-

cellular multicolor flow cytometry (12, 13)

allows more quantitative simultaneous obser-

vations of multiple signaling molecules in

many thousands of individual cells. Hence, it

is an especially appropriate source of data for

Bayesian network modeling of signaling path-

ways; for instance, because it allows for simul-

taneous measurement of biological states in

more native contexts, as well as for large sam-

ple sets. Flow cytometry can be used to quan-

titatively measure a given protein_s expression

level and can also include measures of protein-

modification states such as phosphorylation

(13–15). Because each cell is treated as an

independent observation, flow cytometric data

provide a statistically large sample that could

enable Bayesian network inference to accu-

rately predict pathway structure (Fig. 1A). As

demonstrated in this article, interrogating sig-

naling networks in populations of single cells

provides a robust source of statistically power-

ful dependencies that can be used to automat-

ically infer signaling causality using Bayesian

network computation.

Modeling Bayesian networks with

multivariable individual-cell data. Fig. 1B

(panel a) presents a sample Bayesian network

representing four hypothetical biomolecules.

A directed arc from X to Y is interpreted as a

causal influence from X onto Y; in this case,

we say X is Y’s ‘‘parent’’ in the network. In

the case that X activates Y, where activation

can be read out by phosphorylation status, we

expect and observe correlation in levels of

phosphorylation as measured by flow cytom-

etry (simulated data in Fig. 1C, panel a). Criti-

cal to causal interpretation of Bayesian network

models is the inclusion of interventional cues

(whether activating or inhibiting) that directly

Fig. 1. Bayesian network modeling with single-cell data. (A) Schematic of Bayesian network in-

ference using multidimensional flow cytometry data. Nine different perturbation conditions were

applied to sets of individual cells (Table 1). A multiparameter flow cytometer simultaneously

recorded levels of 11 phosphoproteins and phospholipids in individual cells in each perturbation

data set (Table 2). This data conglomerate was subjected to Bayesian network analysis, which

extracts an influence diagram reflecting dependencies and causal relationships in the underlying

signaling network. (B) Bayesian networks for hypothetical proteins X, Y, Z, and W. (a) In this

model, X influences Y, which, in turn, influences both Z and W. (b) The same network as (a), except

that Y was not measured in the data set. (C) Simulated data that could reconstruct the influence

connections in (B) (this is a simplified demonstration of how Bayesian networks operate). Each dot

in the scatter plots represents the amount of two phosphorylated proteins in an individual cell. (a)

Scatter plot of simulated measurements of phosphorylated X and Y shows correlation. (b) Inter-

ventional data determine directionality of influence. X and Y are correlated under no manipulation

(blue dots). Inhibition of X affects Y (yellow dots) and inhibition of Y does not affect X (red dots).

Together, this indicates that X is consistent with being an upstream parent node. (c) Simulated

measurements of Y and Z. (d) A noisy but distinct correlation is observed between simulated mea-

surements of X and Z.

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perturb the states of the measured molecules

(Fig. 1C, panel b) and strengthen inference di-

rectionality. For instance, inhibition of mole-

cule X might lead to inhibition of both X and

Y, whereas inhibition of molecule Y leads only

to inhibition of Y. Thus, we would infer X to

be upstream of Y as shown in Fig. 1B, panel a.

Moreover, because flow cytometry can mea-

sure multiple molecules within each cell, it is

possible to identify complex causal influence

relationships involving multiple proteins. Con-

sider the signaling cascade from X onto Y onto

Z (Fig. 1B, panel a), where correlation exists

between the measured activities of each pair,

including between X and Z (Fig. 1C, panel d).

Bayesian network inference yields the most

concise model, automatically excluding arcs

basedondependenciesalready explained by the

model. Thus, despite the correlation between

them, the arc between X and Z is omitted,

because the X-Y and the Y-Z relationships

explain the X-Z correlation. Similarly, because

Z and W are both activated by their common

cause Y, we expect their activities to be cor-

related, but no arc appears between them be-

cause their respective arcs from Y mediate

this dependency. Finally, consider a scenario

in which molecule Y was not measured. The

statistical correlation between the observed

activities of X and Z does not depend on ob-

serving Y; therefore, their correlation would

still be detected. An indirect arc would be de-

tected from X onto Z (Fig. 1B, panel b).

Expanding this concept to a real data set,

we applied Bayesian network analysis to mul-

tivariate flow cytometry data. Data were col-

lected after a series of stimulatory cues and

inhibitory interventions (Table 1), with cell

reactions stopped at 15 min after stimulation

by fixation, to profile the effects of each con-

dition on the intracellular signaling networks

of human primary naı¨ve CD4

Tcells,down-

stream of CD3, CD28, and LFA-1 activation

(Fig. 2 shows a currently accepted consensus

network). We made flow cytometry mea-

surements of 11 phosphorylated proteins and

phospholipids [Raf phosphorylated at posi-

tion S259, mitogen-activated protein kinases

(MAPKs) Erk1 and Erk2 phosphorylated at

T202 and Y204, p38 MAPK phosphorylated

at T180 and Y182, Jnk phosphorylated at

T183 and Y185, AKT phosphorylated at S473,

Mek1 and Mek2 phosphorylated at S217 and

S221 (both isoforms of the protein are recog-

nized by the same antibody), phosphorylation

of protein kinase A (PKA) substrates [cAMP

response element–binding protein (CREB),

PKA, calcium/calmodulin-dependent protein

kinase II (CaMKII), caspase-10, and caspase-2]

containing a consensus phosphorylation motif,

phosphorylation of phospholipase C–g (PLC-g)

on Y783, phosphorylation of PKC on S660,

phosphatidylinositol 4,5-bisphosphate (PIP

and phosphatidylinositol 3,4,5-triphosphate

(PIP

)] (Table 2) (8, 16). Each independent

Table 1. Known biological effects of perturbations employed. The left-hand column lists the specific

reagents used in each perturbation condition, and the right-hand column classifies the reagent class into

either a general perturbation that overall stimulated the cell or a specific perturbation that acted on a

defined set of molecules. The conditions used in the study were as follows: (i) anti-CD3 þ anti-CD28, (ii)

anti-CD3/CD28 þ ICAM-2 (intercellular adhesion molecule–2), (iii) anti-CD3/CD28 þ U0126, (iv) anti-

CD3/CD28 þ AKT inhibitor, (v) anti-CD3/CD28 þ G06976, (vi) anti-CD3/CD28 þ psitectorigenin, (vii)

anti-CD3/CD28 þ LY294002, (viii) phorbol 12-myristate 13-acetate (PMA), and (ix) b2 cyclic adenosine

3¶,5¶-monophosphate (b2cAMP).

Reagent Reagent class

Anti-CD3/CD28 General perturbation: Activates T cells and induces proliferation and cytokine

production. Induced signaling through the T cell receptor (TCR), activated ZAP70,

Lck, PLC-g, Raf, Mek, Erk, and PKC. The TCR signaling converges on transcription

factors NFkB, NFAT, and AP-1 to initiate IL-2 transcription.

ICAM-2 General perturbation: Induces LFA-1 signaling and contributes to CD3/CD28

signaling that converges on AP-1 and NFAT transcriptional activity.

b2cAMP Specific perturbation: cAMP analog that activates PKA. PKA can regulate NFAT

activation and T cell commitment processes.

AKT inhibitor Specific perturbation: Binds inositol pleckstrin domain of AKT and blocks AKT

translocation to the membrane where normally AKT becomes phosphorylated and

active [median inhibitory concentration (IC

) 0 5 mM]. Inhibition of AKT and

phosphorylation of AKT substrates are needed to enhance cell survival.

U0126 Specific perturbation: Inhibits MEK1 (IC

0 72 nm) and MEK2 (IC

0 58 nm) in a

noncompetitive manner (ATP and Erk substrates). Inhibits activation of Erk,

arresting T cell proliferation and cytokine synthesis.

PMA Specific perturbation: PMA activates PKC and initiates some aspects of T cell

activation.

G06976 Specific perturbation: Inhibits PKC isozymes (IC

G 8 nM). Inhibits PKC and arrests

T cell activation.

Psitectorigenin Specific perturbation: Inhibits phosphoinositide hydrolysis. Inhibits PIP2 production

and disrupts phosphoinositol turnover.

LY294002 Specific perturbation: Phosphatidylinosital 3-kinase (PI3K inhibitor. Inhibits PI3K and

subsequent activation of AKT.

Fig. 2. Classic signaling network and points of intervention. This is a graphical illustration of the

conventionally accepted signaling molecule interactions, the events measured, and the points of

intervention by small-molecule inhibitors. Signaling nodes in color were measured directly. Signaling

nodes in gray were not measured, but are presented to place the signaling nodes that were measured

within contextual cellular pathways. The interventions classified as activators are colored green and

inhibitors are colored red. Intervention site of action is indicated in the figure. Arcs are used to

illustrate connections between signaling molecules; in some cases, the connections may be indirect

and may involve specific phosphorylation sites of the signaling molecules (see Table 3 for details of

these connections). This figure contains a synopsis of signaling in mammalian cells and is not

representative of all cell types, with inositol signaling corelationships being particularly complex.

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sample in this data set consists of quantita-

tive amounts of each of the 11 phosphorylated

molecules, simultaneously measured from sin-

gle cells [data sets are downloadable (8)]. For

purposes of illustration, examples of actual

fluorescence-activated cell sorter (FACS) data

plotted in prospective corelationship form are

shown in fig. S1. In most cases, this reflects the

activation state of the kinases monitored, or in

the cases of PIP

and PIP

, the levels of these

secondary messenger molecules in primary cells,

under the condition measured. Nine stimula-

tory or inhibitory interventional conditions were

used (Table 1) (8). The complete data sets were

analyzed with the Bayesian network structure

inference algorithm (6, 9, 17).

A high-accuracy human primary T cell

signaling causality map. The resulting de

novo causal network model was inferred

(Fig. 3A) with 17 high-confidence causal arcs

between various components. To evaluate the

validity of this model, we compared the mod-

el arcs (and absent potential arcs) with those

described in the literature. Arcs were catego-

rized as the following: (i) expected, for con-

nections well-established in the literature that

have been demonstrated under numerous con-

ditions in multiple model systems; (ii) reported,

for connections that are not well known, but

for which we were able to find at least one

literature citation; and (iii) missing, which indi-

cates an expected connection that our Bayesian

network analysis failed to find. Of the 17 arcs

in our model, 15 were expected, all 17 were

either expected or reported, and 3 were missed

(Fig. 3A and table S1) (8, 18–22). Table 3

enumerates the probable paths of influence

corresponding to model arcs determined by

surveying published reports.

Several of the known connections from

our model are direct enzyme-substrate rela-

tionships (Fig. 3B) (PKA to Raf, Raf to Mek,

Mek to Erk, and Plc-g to PIP

), and one has a

relationship of recruitment leading to phos-

phorylation (Plc-g to PIP

). In almost all cases,

the direction of causal influence was correctly

inferred (an exception was Plc-g to PIP

,in

which case the arc was inferred in the reverse

direction). All the influences are contained

within one global model; thus, the causal di-

rection of arcs is often compelled so that these

are consistent with other components in the

model. These global constraints allowed de-

tection of certain causal influences from mole-

cules that were not perturbed in our assay.

For instance, although Raf was not perturbed

in any of the measured conditions, the meth-

od correctly inferred a directed arc from Raf

to Mek, which was expected for the well-

characterized Raf-Mek-Erk signal transduc-

tion pathway. In some cases, the influence of

one molecule on another was mediated by in-

termediate molecules that were not measured

in the data set. In the results, these indirect

connections were detected as well (Fig. 3B,

panel b). For example, the influence of PKA

and PKC on the MAPKs p38 and Jnk likely

proceeded via their respective (unmeasured)

MAPK kinase kinases. Thus, unlike some

other approaches used to elucidate signaling

networks [for example, protein-protein inter-

action maps (23, 24)] that provide static bio-

chemical association maps with no causal

links, our Bayesian network method can de-

tect both direct and indirect causal connections

and therefore provide a more contextual pic-

ture of the signaling network.

Another feature demonstrated in our mod-

el is the ability to dismiss connections that

are already explained by other network arcs

(Fig. 3B, panel c). This is seen in the Raf-

Mek-Erk cascade. Erk, also known as p44/42,

is downstream of Raf and therefore dependent

on Raf, yet no arc appears from Raf to Erk,

because the connection from Raf to Mek and

the connection from Mek to Erk explain the

dependence of Erk on Raf. Thus, an indirect

arc should appear only when one or more

intermediate molecules is not present in the

data set, otherwise the connection will proceed

via this molecule. The intervening molecule

may also be a shared parent. For example,

the phosphorylation statuses of p38 and Jnk

are correlated (fig. S2), yet they are not di-

rectly connected, because their shared parents

(PKC and PKA) mediate the dependence be-

tween them. Although we cannot know wheth-

er an arc in our model represents a direct or

indirect influence, it is unlikely that our model

contains an indirect arc that is mediated by

any molecule observed in our measurements.

Correlation exists between most molecule

pairs in this data set [per Bonferroni corrected

P value (fig. S2)], which can occur with close-

ly connected pathways. Therefore, the relative

lack of arcs in our model (Fig. 3A) contrib-

uted greatly to the accuracy and interpret-

ability of the inferred model.

A more complex example is the influence

of PKC on Mek, which is known to be me-

diated by Raf (Fig. 3B, panel d). PKC is

known to affect Mek through two paths of

influence, each mediated by a different ac-

tive phosphorylated form of the protein Raf.

Although PKC phosphorylates Raf directly

at S499 and S497, this event is not detected

by our measurements, because we use only

an antibody specific to Raf phosphorylation

at S259 (Table 2) (16). Therefore, our algo-

rithm detects an indirect arc from PKC to

Mek that is mediated by the presumed un-

measured intermediate Raf phosphorylated

at S497 and S499 (18). The PKC-to-Raf arc

represents an indirect influence that proceeds

via an unmeasured molecule, presumed to be

Ras (19, 20). We discussed above the ability

of our approach to dismiss redundant arcs. In

this case, there are two paths leading from

PKC to Mek, because each path corresponds

to a separate means of influence from PKC

to Mek: one via Raf phosphorylated at S259

and the other through Raf phosphorylated at

S497 and S499. Thus, neither path is redun-

dant. This result demonstrates the distinction

that this analysis is sensitive to specific phos-

Fig. 3. Bayesian network inference

results. (A) Network inferred from

flow cytometry data represents ex-

pected outcomes. This network rep-

resents a model average from 500

high-scoring results. High-confidence

arcs, appearing in at least 85% of

the networks, are shown. For clarity,

the names of the molecules are used

to represent the measured phospho-

rylation sites (Table 2). (B) Inferred

network demonstrates several fea-

tures of Bayesian networks. (a) Arcs

in the network may correspond to

direct events or (b) indirect influ-

ences. (c) When intermediate mol-

ecules are measured in the data

set, indirect influences rarely appear as an additional arc. No additional

arc is added between Raf and Erk because the dependence between Raf

and Erk is dismissed by the connection between Raf and Mek, and be-

tween Mek and Erk (for instance, see Fig. 1C). (d) Connections in the

model contain phosphorylation site–specificity information. Because Raf

phosphorylation on S497 and S499 was not measured in our data set,

the connection between PKC and the measured Raf phosphorylation site

(S259) is indirect, likely proceeding via Ras. The connection between PKC

and the undetected Raf phosphorylation on S497 and S499 is seen as an

arc between PKC and Mek.

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phorylation sites on molecules and is capable

of detecting more than one route of influence

between molecules.

Three well-established influence connec-

tions do not appear in our model: PIP

PKC, PLC-g to PKC, and PIP

to Akt. Bayes-

ian networks are constrained to be acyclic,

so if the underlying network contains feedback

loops, we cannot necessarily expect to un-

cover all connections (fig. S3). Availability

of suitable temporal data could possibly per-

mit this limitation to be overcome using dy-

namic Bayesian networks (25, 26).

Experimental confirmation of predicted

network causality. Two influence connec-

tions in our model are not well established in

the literature: PKC on PKA and Erk on Akt.

To probe the validity of these proposed causal

influences, we searched for reports in the lit-

erature. Both connections have previously been

reported: the PKC-to-PKA connection in rat

ventricular myocytes and the Erk-to-Akt con-

nection in colon cancer cell lines (21, 22). An

important goal of our work was to test the abil-

ity of Bayesian network analysis of flow cytom-

etry data to correctly infer causal influences

from unperturbed molecules within a network.

For example, Erk was not directly acted on by

any activator or inhibitor in the sample sets,

yet Erk showed an influence connection to Akt.

Our model thus predicts that direct perturba-

tion of Erk would influence Akt (Fig. 4A).

On the other hand, although Erk and PKA are

correlated (fig. S2), the model predicts that

perturbation of Erk should not influence PKA.

As a test of these predictions (Fig. 3A),

we used small interfering RNA (siRNA) inhi-

bition of either Erk1 or Erk2, and the amounts

of S473-phosphorylated Akt and phosphoryl-

ated PKA were then measured. In accord with

the model predictions, Akt (P G 9.4  10

)

phosphorylation was reduced after siRNA

inhibition of Erk1 but the activity of PKA (P G

0.28) was not (Fig. 3, B and C). Akt phos-

phorylation was not affected by the inhibition

of Erk2. The connection between Erk1 and Akt

may be direct or indirect, involving mediatory

molecules yet to be understood, but the con-

nection is supported by both the model and

the validation experiment.

Enablers of accurate inference: network

interventions and sufficient numbers of

single cells. Three features distinguish our

data from the majority of currently attainable

biological data sets. First, we simultaneously

measured multiple protein states in individ-

ual cells, eliminating population-averaging

effects that could obscure interesting corre-

lations. Second, because the measurements

were on single cells, thousands of data points

were collected in each experiment. This feature

constitutes a tremendous asset for Bayesian

network modeling, because the large number

of observations allows for accurate assessment

of underlying probabilistic relationships, and

therefore allows for the extraction of complex

relationships from noisy data. Third, interven-

tional assays generated hundreds of individual

data points per intervention (because flow

cytometry measures single cells in popula-

tion), allowing for an increase in inferences of

causality. To evaluate the importance of these

features, we created the following variations

on our original data set: (i) an observation-only

data set (that is, without any interventional

data) of 1200 data points; (ii) a population-

averaged (that is, a simulated Western blot)

data set; and (iii) a truncated individual-cell

data set of size comparable to the simulated

Western blot data set (that is, the original data

set with most of the data randomly excluded

to reduce its size) (8).

Bayesian network inference was perform-

ed on each set of data. The network inferred

from 1200 observational data points included

only 10 arcs, all undirected, of which 8 were

expected or reported, and 10 arcs were missing

(fig. S4A). This result demonstrates that inter-

ventions are critical for effective inference,

particularly to establish directionality of the

connections (Fig. 1B). The truncated single-

cell data set (420 data points) shows a large

(11-arc) decline in accuracy, missing more

connections and reporting more unexplained

arcs than its larger (5400 data points) counter-

part (fig. S4B). This result emphasizes the

importance of sufficiently large data set size

in network inference. The network inferred

from averaged data (fig. S4C) shows a fur-

ther five-arc decline in accuracy relative to

that inferred from an equal number of single-

cell data points, emphasizing the importance

of single-cell data. The fact that population

averaging destroys some of the signals pre-

sent in the data may reflect the presence of

heterogeneous cellular subsets that are masked

by averaging techniques.

Discussion and summary. As shown, we

correctly reverse-engineered and rapidly in-

ferred the basic structure of a classically under-

stood signaling network that connects a number

of key phosphorylated proteins in human T cell

signaling, a map built by classical biochemistry

and genetic analysis over the past two decades.

The network was automatically constructed

with no a priori knowledge of pathway connec-

tivity. The application of Bayesian networks

to single-cell flow cytometry has distinct ad-

vantages, including an ability to measure events

in primary cells after in vivo interventions (thus

measuring context-specific signaling biology in

tissues), inference of directed arcs and causal-

Table 2. Nodes measured in pathway and

specificity antibodies used. The left-hand column

shows target molecules measured in this study

that were assayed using monoclonal antibody to

the target residues (site of phosphorylation or

phosphorylated product as described) (16).

Measured

molecule

Antibody

specificity

Raf Phosphorylation at S259

Erk1 and

Erk2

Phosphorylation at T202 and Y204

p38 Phosphorylation at T180 and Y182

Jnk Phosphorylation at T183 and Y185

AKT Phosphorylation at S473

Mek1 and

Mek2

Phosphorylation at S217 and S221

PKA

substrates

Detects proteins and peptides con-

taining a phospho-Ser/Thr res-

idue with arginine at the –3

position

PKC Detects phosphorylated PKC-a,-bI,

-bII, -d,-e,-h, and -q isoforms

only at C-terminal residue homol-

ogous to S660 of PKC-bII

PLC-g Phosphorylation at Y783

PIP

Detects PIP

PIP

Detects PIP

Table 3. Possible molecular pathways of influence represented by arcs in the model. Shown are the

possible pathways of influence inferred from the data, with the connection shown in Fig. 3A and the

unmeasured molecules (in bold) that might mediate indirect influences. E, expected; R, reported. See

main text for further discussion. Specific phosphorylation sites are included as subscripts. See table S1

for citations that support the inferences.

Connection Influence path Type Category

PKCYRaf PKCYRasYRaf

S259

Indirect E

PKCYMek PKCYRaf

S497/S499

YMek Indirect E

PKCYJnk PKCYYMKKsYJnk Indirect E

PKCYp38 PKCYYMKKsYp38 Indirect E

PKCYPKA PKCYcAMPYPKA Indirect R

PKAYRaf PKAYRaf

S259

Direct E

PKAYMek PKAYRaf

S621

YMek Indirect E

PKAYErk PKAYHePTPYErk Indirect E

PKAYJnk PKAYYMKKsYJnk Indirect E

PKAYp38 PKAYYMKKsYp38 Indirect E

RafYMek Direct phosphorylation Direct E

PKAYAkt PKAYCaMKKYAkt

T308

YAkt

S473

Indirect E

MekYErk Direct phosphorylation Direct E

Plc-gYPIP

Direct hydrolysis to IP3 Direct E

Plc-gYPIP

Recruitment leading to phosphorylation Reversed E

PIP

YPIP

Precursor-product E

ErkYAkt Direct or indirect R

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ity therein, and the ability to detect indirect as

well as direct connections. This latter point

is a powerful feature when the known list of

participating molecules may not be exhaus-

tive, and can be especially important when

networks are used to assess the effects of sys-

tem perturbations (as in a pharmaceutical con-

text). A limiting step in the experiment is the

availability of suitable reagents; currently, there

are about 80 antibodies to phosphorylated

molecules that are compatible with flow cytom-

etry, but this number is expected to rapidly

increase (27, 28).

Application of this approach to other sets

of molecules, cell types, disease states, and in-

terventions (for example, siRNA and dominant

negative screens, or pharmaceutical agents)

should enhance our understanding of signaling

networks, especially with respect to complex

nonlinear cross-talk between pathways. An-

other important experimental issue that this

approach can address is the differences among

specific primary cell types and cell subpopu-

lations. The traditional understanding of path-

way structures as collated from diverse model

cell types and organisms demonstrates the es-

sential congruity of basic signaling networks,

but does not easily reveal the subtle differ-

ences that exist in different primary cell sub-

types. It is now possible to appreciate pathway

intricacies in primary cell subsets, including

those with previously uncharacterized signal-

ing molecules. The application of this ap-

proach during biochemical interrogation of

cellular subset–specific signaling networks in

the course of a disease state or in the presence

of pharmaceutical agents can potentially pro-

vide important mechanistic information of clin-

ical relevance. For example, this method could

identify sets of signaling molecules that ex-

plain differences between responses to chemo-

therapy in patients with cancer (15).

Concerning the computational aspect, a

key advantage of Bayesian networks is that

they are relatively robust to the existence of

unobserved variables; for example, their abil-

ity to detect indirect influences via unmea-

sured molecules. At the forefront of Bayesian

network research is the development of meth-

ods to automatically infer the existence and

location of such hidden variables. Although

our results were restricted to 11 phosphomo-

lecular measurements per cell, the number of

simultaneous parameters measured by flow cy-

tometry is steadily growing (27, 28). As mea-

surement systems improve, and the ability to

readily and accurately measure greater num-

bers of internal signaling events increases,

additional opportunities to discover novel influ-

ences and pathway structures become possible.

One of the caveats in the use of Bayesian

networks for the elucidation of signaling path-

ways is that they are restricted to be acyclic,

whereas signaling pathways are known to

be rich in feedback loops. Indeed, our infer-

ence missed three classic arcs, most likely for

this reason. Given time series data, dynamic

Bayesian networks could potentially capture

these feedback loops. To measure the amounts

of internal phosphorylated proteins, the cells

must be fixed. Therefore, continuous, real-time,

simultaneous, multiparameter, single-cell time-

series data cannot be collected with the cur-

rent technology. Because Bayesian networks

belong to a more general class of probabilistic

graphical models, within the formalism of these

models it is possible to develop a model that

could handle feedback loops, given a series of

static time points using the current technology.

Although there is much to be developed

both computationally and experimentally, by

extending the concepts derived here it is clear

that simultaneous multivariate analysis of bio-

logical states in multiple discrete entities, such

as cells, offers a useful approach for rapidly

deriving signaling network hierarchies and

structures. Extension of this approach to bio-

logical systems involving multiple cell pop-

ulations, such as solid tissues and organs,

or whole-animal studies such as in whole-

body fluorescence imaging of phosphoryl-

ation states in staged Caenorhabditis elegans

or Drosophila larva, or thin-slice tissue sec-

tions from mammalian organs, could allow

automated construction of signaling network

influences not only within but also across cell

boundaries in an increasing number of phys-

iological contexts.

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Fig. 4. Validation of model prediction. (A) The model predicts that an intervention on Erk will

affect Akt, but not PKA. (B) To test the predicted relationships, Erk1 and Erk2 were inhibited using

siRNA in cells stimulated with antibody to CD3 (anti-CD3) and anti-CD28. (C) Amounts of Akt phos-

phorylation in transfected CD4

cells [enhanced green fluorescent protein (EGFPþ) cells] were as-

sessed, and amounts of phosphorylated PKA are included as a negative control. When Erk1expression is

inhibited, phosphorylated Akt is reduced to amounts similar to those in unstimulated cells, confirming

our prediction (P 0 0.000094). PKA is unaffected (P 0 0.28).

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29. The authors thank G. Church, N. Friedman, J. Albeck,

P. Jasper, L. Garwin, R. Tibshirani, T. Jaakkola, D. Gifford,

and D. Koller for helpful discussions or readings of the

manuscript and R. Balderas and BD-PharMingen Bio-

sciences for reagents. K.S. and D.A.L. were supported

by the National Intitute of General Medical Sciences

Center of Excellence in Complex Biomedical Systems

at MIT. O.D.P. was supported as a Bristol-Meyer Squibb

Irvington Fellow and a Dana Foundation human immu-

nology award. D.P. was supported by a PhRMA Center

of Excellence in Integration of Genomics and Infor-

matics grant, an NIH Center of Excellence in Genomic

Studies grant to G. Church, and an NSF Postdoctoral

Research Fellowship in Biological Informatics. G.P.N.

was supported in this work by NIH grants P01-AI39646

and AI35304, a grant from the Juvenile Diabetes Foun-

dation, and National Heart, Lung, and Blood Institute

Proteomics Center contract N01-HV-28183I.

Supporting Online Material

www.sciencemag.org/cgi/content/full/308/5721/523/

Materials and Methods

Figs. S1 to S4

Table S1

Data Sets S1 to S14

References

29 September 2004; accepted 19 January 2005

10.1126/science.1105809

Parallel and Serial Neural

Mechanisms for Visual Search

in Macaque Area V4

Narcisse P. Bichot,

Andrew F. Rossi,

2,3

Robert Desimone

1,4

To find a target object in a crowded scene, a face in a crowd for example, the

visual system might turn the neural representation of each object on and off

in a serial fashion, testing each representation against a template of the

target item. Alternatively, it might allow the processing of all objects in par-

allel but bias activity in favor of those neurons that represent critical fea-

tures of the target, until the target emerges from the background . To test

these possibilities, we recorded neurons in area V4 of monkeys freely scanning

a complex array to find a target defined by color, shape, or both. Throughout

the period of searching, neurons gave enhanced responses and synchronized

their activity in the gamma range whenever a preferred stimulus in their re-

ceptive field matched a feature of the target, as predicted by parallel models.

Neurons also gave enhanced responses to candidate targets that were se-

lected for saccades, or foveation, reflecting a serial component of visual search.

Thus, serial and parallel mechanisms o f response enhancement and neural

synchrony work together to identify objects in a scene.

In a crowded visual scene, we typically focus

our attention on behaviorally relevant stimuli.

When subjects know the location of a relevant

object, the brain mechanisms that guide their

spatial attention to the object largely overlap

with those for selecting the targets for eye

movements (1). The outcome of this selection

for attention or eye movements is to enhance

the responses of visual cortex neurons to the

relevant object, at the expense of distracters

(2–6). As a result, object recognition mecha-

nisms in the temporal cortex are typically con-

fronted with only a single relevant stimulus

at a time (7). However, in most common vi-

sual scenes, people rarely know the specific

location of the relevant object in advance—

instead, they must search for it, based on its

distinguishing features, such as color or shape,

which is commonly termed visual search. A

long-standing issue has been whether object

selection in visual search is also mediated by

neural mechanisms for spatial attention, which

scan the objects in the scene sequentially until

the target is identified (serial search), whether

or not eye movements are made. If so, then

visual attention could be broadly served by a

unitary mechanism, linked to the neural sys-

tems that control gaze. Alternatively, search

may be mediated by nonspatial attentional

mechanisms that are sensitive to features

such as color and shape and that bias visual

processing in favor of neurons that represent

the target features throughout the visual field,

all at once (parallel search) (7). Search could

also be mediated by hybrid mechanisms such

as guided search (8).

Previous studies of visual search (9–11)

and attention to stimuli with particular fea-

tures (12–14) in brain area V4 have found

that neuronal responses to attended target

stimuli were enhanced over time, but the studies

were not designed to test whether the targets

were B found[ by serial or parallel neural mech-

anisms. In one of these studies, monkeys did

not search for a specific feature but instead

searched for a singleton (i.e., popout) stimulus

in one of two feature dimensions (11). In an-

other study that used backgrounds of natural

scenes, the average neural activity throughout

the trial varied according to the searched-for

target features, but the authors could not rule

out that these effects were due to differences

in eye scan paths across the scene for differ-

ent targets rather than feature-selective effects

on neuronal responses (10).

We tested for parallel and serial attentional

mechanisms in area V4 in monkeys perform-

ing a search task with free gaze. We recorded

not only neuronal responses but also the syn-

chrony between neuronal responses and the

local field potential (LFP) (15, 16), because V4

neurons synchronize their activity when atten-

tion is directed to their receptive fields (RFs)

(17), similar to neurons in parietal cortex dur-

ing a memory-saccade task (18). Such syn-

chrony, especially in the gamma frequency

range, could potentially amplify their effect

on postsynaptic neurons, similar to increases

in firing rate (19). The monkeys freely scanned

multielement arrays composed of colored

shapes to find a target defined by color or

shape (20). During color feature search (Fig.

1A), the cue was a colored square, and the

monkey was rewarded for fixating the stim-

ulus in the array that matched the cue color.

During shape feature search (fig. S1), the cue

was a gray shape, and the monkeys were re-

warded for fixating the stimulus in the array

that matched the cue shape. When shape was

relevant, color was irrelevant, and vice versa.

We selected two colors and two shapes as cues

for each recording session, on the basis of ini-

tial recordings in which we determined a pre-

ferred (strong response) and nonpreferred (weak

response) color and shape for a given neuron.

Overall, monkeys performed similarly dur-

ing color and shape search, finding the target

on 86% and 91% of the trials, respectively.

Both tasks were demanding, taking an average

of 6.3 saccades to find the target out of 20

items (Fig. 1A and fig. S1) (21). In separate

behavioral studies in which we varied the num-

ber of display items, the monkeys took an aver-

age of 160 ms per item to find the target, again

indicating that the target did not Bpop out.[

Parallel selection during feature

search. The key element of parallel search

models is that the neural bias in favor of

stimuli containing features of the searched-for

target occurs throughout the visual field, and

throughout the time period of the search, long

before a target is identified. Thus, we reasoned

that the critical neurons to test for this bias

were not the neurons whose RF contained

the stimulus that was the target for a saccade

at a given moment. Rather, the critical neurons

Laboratory of Neuropsychology,

Laboratory of Brain

and Cognition, National Institute of Mental Health

(NIMH), National Institutes of Health, Bethesda, MD

20892, USA.

Department of Psychology, Vanderbilt

University, Nashville, TN 37203, USA.

McGovern In-

stitute for Brain Research at the Massachusetts In-

stitute of Technology, Cambridge, MA 02139, USA.

*To whom correspondence should be addressed.

E-mail: bichotn@mail.nih.gov

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www.sciencemag.org SCIENCE Erratum post date 19 AUGUST 2005

post date 19 August 2005

ERRATUM

C ORRECTIONS AND C LARIFICATIONS

RReeppoorrttss::

“Causal protein-signaling networks derived from multiparame-

ter single-cell data” by K. Sachs

et al.

(22 Apr. 2005, p. 523). The author

names in reference (

) were incorrect. The authors are I. M. Ong, J. D.

Glasner, D. Page. The URL for the supporting online material was incor-

rect; it should be www.sciencemag.org/cgi/content/full/308/5721/523/

DC1. There was also a reference missing in the last sentence of the last

paragraph on page 527 that continues on page 528. The new reference

(

) is P. O. Krutzik, G. P. Nolan,

Cytometry

5555

, 61 (2003). The acknowl-

edgments should now be reference (

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