Corrections

BIOPHYSICS AND COMPUTATIONAL BIOLOGYCorrection for “Crosstalk and the evolution of specificity in two-component signaling,” by Michael A. Rowland and Eric J. Deeds,which appeared in issue 15, April 15, 2014, of Proc Natl Acad SciUSA (111:5550–5555; first published March 31, 2014; 10.1073/pnas.1317178111).The authors note that ref. 4, “Huynh TN, Stewart V (2011)

Negative control in two-component signal transduction by trans-mitter phosphatase activity. Mol Microbiol 82(2):275–286.” shouldinstead appear as “Ray JC, Igoshin OA (2010) Adaptable func-tionality of transcriptional feedback in bacterial two-componentsystems. PLoS Comput Biol 6(2):e1000676.”

www.pnas.org/cgi/doi/10.1073/pnas.1408294111

PLANT BIOLOGYCorrection for “Differential processing of Arabidopsis ubiquitin-like Atg8 autophagy proteins by Atg4 cysteine proteases,” byJongchan Woo, Eunsook Park, and S. P. Dinesh-Kumar, whichappeared in issue 2, January 14, 2014, of Proc Natl Acad SciUSA (111:863–868; first published December 30, 2013; 10.1073/pnas.1318207111).The authors note that the following statement should be

added to the Acknowledgments: “National Science FoundationGrant NSF-IOS-1258135 funded to Dr. Georgia Drakakaki sup-ported Eunsook Park.”

www.pnas.org/cgi/doi/10.1073/pnas.1409947111

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Crosstalk and the evolution of specificity intwo-component signalingMichael A. Rowlanda and Eric J. Deedsa,b,1

aCenter for Bioinformatics and bDepartment of Molecular Biosciences, University of Kansas, Lawrence, KS 66047

Edited by Thomas J. Silhavy, Princeton University, Princeton, NJ, and approved March 7, 2014 (received for review September 11, 2013)

Two-component signaling (TCS) serves as the dominant signalingmodality in bacteria. A typical pathway includes a sensor histidinekinase (HK) that phosphorylates a response regulator (RR), mod-ulating its activity in response to an incoming signal. Most HKs arebifunctional, acting as both kinase and phosphatase for theirsubstrates. Unlike eukaryotic signaling networks, there is verylittle crosstalk between bacterial TCS pathways; indeed, addingcrosstalk to a pathway can have disastrous consequences for cellfitness. It is currently unclear exactly what feature of TCS neces-sitates this degree of pathway isolation. In this work we usedmathematical models to show that, in the case of bifunctional HKs,adding a competing substrate to a TCS pathway will alwaysreduce response of that pathway to incoming signals. We foundthat the pressure to maintain cognate signaling is sufficient toexplain the experimentally observed “kinetic preference” of HKsfor their cognate RRs. These findings imply a barrier to the evolutionof new HK–RR pairs, because crosstalk is unavoidable immediatelyafter the duplication of an existing pathway. We characterized a setof “near-neutral” evolutionary trajectories that minimize the im-pact of crosstalk on the function of the parental pathway. Thesetrajectories predicted that crosstalk interactions should be re-moved before new input/output functionalities evolve. Analysisof HK sequences in bacterial genomes provided evidence that theselective pressures on the HK–RR interface are different from thoseexperienced by the input domain immediately after duplication.This work thus provides a unifying explanation for the evolutionof specificity in TCS networks.

bacterial signaling | network evolution | signal specificity

Two-component signaling (TCS) represents the primary sig-naling modality in bacteria (1). The prototypical TCS path-

way includes a membrane-bound sensor histidine kinase (HK)that autophosphorylates upon receiving an input signal. The HKthen binds and transfers its phosphoryl group to a responseregulator (RR), which often functions directly as a transcriptionfactor, regulating gene expression patterns in response to thesignal (1, 2). Many HKs are bifunctional, acting as both the ki-nase and phosphatase for their RR; the ratio of kinase tophosphatase activity, and thus the phosphorylation state of theRR, is controlled by the input (1–8).Signaling networks in eukaryotes display extensive “crosstalk,”

with individual kinases acting on large numbers of targets: thekinase Cdk1, for instance, has hundreds of substrates in yeast (9–11). Bacterial TCS networks show a remarkably different to-pology: HKs usually act on a single target (12–17). Intensiveexperimental study over the past 10 years has revealed the bio-chemical and biophysical basis for this lack of promiscuity. Ingeneral, HKs demonstrate a strong “kinetic preference” for theircognate substrates, preferentially phosphorylating them on shorttimescales (7, 15, 16, 18–21). A relatively small number of resi-dues in the protein–protein interaction interface between HKsand RRs is responsible for maintaining this specificity (14–16,20–23). Recently, Capra et al. (23) demonstrated that makingjust two mutations in this interface could introduce an in-teraction between an HK (PhoR) and a noncognate RR (NtrX)in Escherichia coli. This exogenous interaction decreased phos-phate starvation signaling, leading to profound decreases in

growth rate and fitness in mutant cells grown under phosphate-limiting conditions. It has been shown that adding crosstalk toTCS can reduce information transfer efficiency under certainconditions (24), but it remains unclear exactly why TCS pathwaysare constrained from evolving crosstalk.One of the most common motifs in eukaryotic signaling net-

works is a pair of enzymes (e.g., a kinase and a phosphatase)acting on a shared substrate (Fig. 1A) (25, 26). Using mathe-matical models, we recently showed that adding multiple com-peting substrates to this type of Goldbeter–Koshland (GK) loopwould tend to induce an ultrasensitive, switch-like behavior inthe system, which could easily have positive phenotypic con-sequences for the cell (26–29). In the work described here, weperformed a similar analysis, extending a well-studied and vali-dated mathematical model of bifunctional HKs (Fig. 1B) to thecase of multiple substrates (3, 4). We found that, because the HKacts both as the kinase and the phosphatase in these systems, theaddition of competing interactions with multiple RRs alwaysdecreases the response of the cognate RR. This is consistent withthe findings of Capra et al. (23), who showed that the phenotypiceffects of their crosstalk mutant were not due to the mis-regulation of NtrX targets, but rather a direct result of decreasein phosphate starvation signaling.The pressure to maintain cognate signaling suggests the exis-

tence of a barrier in the evolution of new TCS pathways. NewHK–RR pairs can arise from the duplication of existing HK–RRgenes, which subsequently diverge into a new pathway (21, 30).There is unavoidable crosstalk immediately postduplication,which can attenuate the response to the original signal. Usingour models, we characterized a set of “near-neutral” evolution-ary trajectories that minimize the impact of the new pair on thesignaling of the parent pathway. All of these trajectories involvedinsulating the two pathways from one another before establishingnew input and output functionalities. To test this prediction, we

Significance

The global architectures of signaling networks in bacteria andeukaryotes are remarkably different: crosstalk between path-ways is very common in eukaryotes but is very limited in bac-teria. Bacteria use two-component signaling (TCS) to transduceinformation, relying on a single enzyme to act as both kinase andphosphatase for targets. We used mathematical models to showthat introducing crosstalk in TCS always decreases system per-formance. This indicates that the large-scale differences betweeneukaryotic and bacterial networks likely derive from differencesin the dynamics of the fundamental motifs from which the net-works themselves are constructed. We further demonstratedthat the pressure to avoid crosstalk has influenced the evolutionof new TCS pairs, driving rapid sequence divergence in proteininteraction interfaces immediately postduplication.

Author contributions: M.A.R. and E.J.D. designed research; M.A.R. performed research;M.A.R. and E.J.D. analyzed data; and M.A.R. and E.J.D. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: deeds@ku.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1317178111/-/DCSupplemental.

5550–5555 | PNAS | April 15, 2014 | vol. 111 | no. 15 www.pnas.org/cgi/doi/10.1073/pnas.1317178111

separately aligned multiple HK and input domain sequencesfrom fully sequenced bacterial genomes. Analysis of the KA/KSratios of the most recently diverged domains revealed that theinteraction interface of the HK is under strong positive selectionimmediately after duplication, likely owing to the pressure toinsulate interactions between the parent and duplicate pairs (7,15, 16, 18–21). Input domains in HKs often evolve through“domain swapping,” whereby a new pathway picks up inputfunctionality by wholesale exchange of domains with other pro-teins in the genome (21, 30). Analysis of KS values indicates thatthese swapping events generally occur only after the HK inter-faces have had sufficient time to evolve interaction specificity.These findings suggest that the majority of HK–RR duplicationsfollow the near-neutral evolutionary paths we predicted. Overall,our work indicates that the bifunctional nature of HKs has likelybeen a major driving force in the evolution of insulated topolo-gies in bacterial signaling networks (21).

ResultsResponse to Changes in RR Concentration. To understand the im-pact of crosstalk on signaling, it is helpful to consider the re-sponse of the system to changes in the concentration of a singlesubstrate (26). As mentioned above, eukaryotic signaling net-works are formed largely from a motif in which one enzyme(e.g., a kinase K) modifies a substrate and a second enzyme(e.g., a phosphatase P) removes the modification (Fig. 1A).Goldbeter and Koshland first characterized the behavior ofthis system over 30 years ago, finding that the response of thesystem at steady-state followed:

S p=ðr− 1Þ− ðKK + rKPÞ+

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiððr− 1Þ− ðKK + rKPÞÞ2 + 4ðr− 1ÞrKP

q

2ðr− 1Þ ;

[1]

where S* ≡ [S*]/[S]0 is the mole fraction of phosphorylated sub-strate, KK ≡ KM,K/[S]0 and KP ≡ KM,P/[S]0 are the Michaelisconstants divided by the total concentration of substrate, andr ≡ kcat,K[K]0/kcat,P[P]0 is the ratio of the maximum velocities ofthe enzymes (25). Because protein concentrations (and thus thesaturation parameters) remain constant over short timescales(31), r represents the dominant response parameter. In Fig. 1C,we considered a model of a GK loop in which an explicit inputmolecule binds and activates the kinase, thus modulating r (SIAppendix). At unsaturating concentrations of substrate, sub-strate phosphorylation increases hyperbolically (Fig. 1C). Atsaturating concentrations, however, the system displays a switch-like behavior known as “0th-order ultrasensitivity.” When r < 1,phosphatase activity dominates and the addition of substrate de-creases S*; we call this the “phosphatase regime.” When r > 1,kinase activity dominates and the addition of substrate increasesS*; this is the “kinase regime.” These two opposing trends lead toan increasingly ultrasensitive response as total substrate concen-tration increases (Fig. 1C) (25–29).A major difference between eukaryotic GK loops and bacte-

rial TCS is the fact that the HK often acts as both kinase andphosphatase for its substrate RR (Fig. 1B). Ten years ago,Batchelor and Goulian (3) developed an approximate analyticalsolution of a mathematical model of TCS signaling and dem-onstrated that the concentration of phosphorylated RR ([RR*])was insensitive to changes in total RR concentration ([RR]0). Tostudy crosstalk in TCS, we constructed a model very similar tothat of Batchelor and Goulian and other authors (see SI Ap-pendix for the details of the model) (3, 4). We were able to obtaina complete analytical solution in this case and found that thesteady-state response of the system follows:

RR p =

�rβ− β′

�−�e′KK + erKP

�+

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi��rβ− β′

�− ðe′KK + erKPÞ

�2+ 4

�rβ− β′

�erKP

q

2�rβ− β′

� ;

[2]

where RR* ≡ [RR*]/[RR]0 is the fraction of phosphorylated re-sponse regulator, KK and KP are as previously defined, and r ≡kcat,K/kcat,P becomes a constant ratio between the catalytic ratesof the kinase and phosphatase reactions. In this case, the dom-inant response parameters to changes in input are the new β and« terms, which are dependent upon the autophosphorylation andautodephosphorylation rates of the HK and thus the input signal(see SI Appendix for derivation and details). We compared thepredictions of this solution to previous experimental results byBatchelor and Goulian (3) in which the concentrations of theHK and RR were varied and found that Eq. 2 reproduces theirdata (SI Appendix).As with the GK loop, we considered a case in which an explicit

input molecule binds and activates the HK (Fig. 1B). Becausebacterial TCS are well studied, experimental values are availablefor both total concentrations and kinetic parameters in thismodel (SI Appendix) (2, 3, 13, 32). Using those parameters forthe purpose of display, we found a dramatic decrease in RR*when total RR concentration is high (Fig. 1D). Note that this isthe fraction of phosphorylated RR; the total concentration ofactive RR molecules does not depend on [RR]0 when the RR isat saturating concentrations, as previously noted (SI Appendix)(3). Thus, although the response of the system is robust tochanges in total RR in this regime, it also becomes inefficient;that is, increasing the expression of the RR does not increase theresponse capacity of the system.

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Fig. 1. TCS pathways vs. Goldbeter–Koshland Loops. (A) Diagram of aGoldbeter–Koshland loop. An input activates a kinase K, which phosphorylatesthe substrate. The phosphatase P is a separate enzyme that undoes thismodification. (B) Diagram of a TCS pathway. An input causes the autophos-phorylation of an HK, which transfers its phosphoryl group to the RR. Theunphosphorylated HK also serves as the phosphatase. (C) The fraction ofphosphorylated substrate S as a function of input concentration (on a logscale) for two total concentrations of S ([S]0 = 100 nM, black, and [S]0 = 10 μM,red). The phosphatase regime and kinase regime defined in the main text areshaded pink and green, respectively. Note that the addition of substratemakes the response more switch-like (25). (D) The fraction of phosphorylatedresponse regulator RR as a function of input concentration for two totalconcentrations of RR ([RR]0 = 100 nM, black, and [RR]0 = 10 μM, red). As dis-cussed in the text, HKs are always in the phosphatase regime, so the entire plotis shaded pink. Note that increasing total substrate concentration in this casereduces the response efficiency of the RR.

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In the GK loop (Fig. 1 A and C), the separation of the kinaseand phosphatase regimes depends upon the term (r – 1) in thedenominator of Eq. 1, which is negative in the phosphatase re-gime and positive in the kinase regime. Eq. 2 contains a similarterm, (rβ – β′), and this term is always negative. TCS loops arethus always in the phosphatase regime, and the general trend inFig. 1D does not depend on specific values of kinetic parameters(SI Appendix). This behavior ultimately arises from the fact thatboth the kinase and phosphatase reactions produce unphos-phorylated HK, which itself is a phosphatase, keeping the systemin the phosphatase regime.

Competition in TCS. To consider crosstalk in TCS, we addeda single competing RR to the system diagrammed in Fig. 1B. Wedenote the cognate RR as RR1, the noncognate interactionpartner as RR2, and define the ratio of their total concentrationsto be R ≡ [RR2]0/[RR1]0. To account for the impact of crosstalkon RR1 function, we also added explicit output molecules (O1binding phosphorylated RR1 and O2 binding phosphorylatedRR2) to the model. To study the responses of this system toa competing RR when the HK displays no kinetic preference foreither substrate, we set the kinetic parameters of RR2 to be thesame as those for RR1 (7, 15, 16, 18–21). We found that addingRR2 at the same total concentration as the cognate substrateresults in a decrease in output activity of the system, which wedefined as the fraction of O1 molecules bound by phosphorylatedRR1 (Fig. 2A). As the total concentration of RR2 is increased,impact on RR1 activity becomes even more significant. The sit-uation is similar to that in Fig. 1D, but in this case the totalconcentration of RR1 is constant, so both the fraction and con-centration of phosphorylated RR1 decreases, leading to a de-crease in output activity. Our results thus indicate that thetype of crosstalk introduced experimentally by Capra et al. (23)

into bacterial cells would likely decrease the performance ofthe PhoR/PhoB signaling system, providing an explanation forthe lower fitness of crosstalk mutants in phosphate-limitingconditions.Bacterial genomes can encode 5–200 HK–RR pairs, depend-

ing on the species in question (21). To consider the impact ofcrosstalk in such cases, we expanded the model to include NHKsand RRs (Fig. 2B). In this model each HK can interact with eachRR; in principle, every pair in this case has an independent as-sociation affinity (i.e., KD). To simplify the problem, we assignedevery cognate pair in the system (HKi-RRi, e.g., HK1 interactingwith RR1) the same affinity KD,C, and every noncognate pair(HKi-RRj, i ≠ j, e.g., HK1 interacting with RR2) the same affinityKD,NC (Fig. 2B). We fixed the cognate interaction to the valueobserved experimentally (KD,C ≈ 1 μM) (32). We then varied theratio between noncognate and cognate KD’s (KD ratio ≡ KD,NC/KD,C )in networks of various sizes N and measured the output activity ofRR1 in response to the activation of HK1 (Fig. 2C). We find thatoutput activity is heavily attenuated for all systems when the non-cognate KD’s are relatively strong. However, when the noncognateKD’s are weaker than the cognate’s by approximately three to fourorders of magnitude, the activity of the single active pathway isessentially unaffected for N = 5 to N = 50.To determine whether KD ratios in this range provide “kinetic

preferencing” similar to that observed by Skerker et al. (18), wereplicated their in vitro experiment using our model. This in-volved mixing either a cognate or noncognate RR with a fullyphosphorylated HK at equal concentrations. When the HK actson a cognate substrate, the phosphorylation of the RR peaksat 10 s, and after 1 h both the HK and RR are completelydephosphorylated. In contrast, a noncognate substrate with a KDratio of either 103 or 104 exhibits no phosphorylation at 10 sbut considerable response after 1 h (Fig. 2D), directly re-capitulating the findings of Skerker et al. (18). A KD ratio of ∼104also gives cognate catalytic efficiencies (kcat/KM) that are 104

higher than noncognate efficiencies, consistent with other ex-perimental findings (14). Our results thus indicate that the ob-served kinetic preference of HKs for their cognate substrates canbe explained simply by the need to maintain cognate responses(Fig. 2C) in the presence of competing substrates, rather thanan explicit pressure to prevent misregulation of noncognatetargets (23).

Evolutionary Trajectories. New TCS pathways can arise throughthe duplication and divergence of existing HK–RR pairs (21, 30).The duplication event itself produces two HK–RR pairs that areidentical (Fig. 3A, steps 0 to 1). This effectively increases boththe total concentration of the substrate and the concentration ofthe HK, both of which can decrease the response of the “parent”signaling pathway (Fig. 2 and SI Appendix). Because such de-creases could strongly affect the fitness of cells in which theduplication occurs (23), the unavoidable crosstalk that occursimmediately postduplication could present a barrier to the evo-lution of new TC signaling pathways. Subsequent evolutionaryevents, such as the evolution of one duplicate RR that cannotactivate the original output genes but still competes with theoriginal RR for phosphorylation by the HKs, could easily exac-erbate this problem (Fig. 2).We thus determined whether there were any “evolutionary

trajectories” that could minimize the effect of crosstalk on theparent signaling pathway. To do this, we developed a simplemodel of the evolution of HK–RR pairs postduplication. In thismodel, we defined two types of evolutionary steps: the removalof an interaction, meaning that the kinetic parameters of theinteraction are set so weak that binding of the two moleculesbecomes very unlikely, and the addition of an interaction,meaning that the kinetic parameters for the binding of twomolecules are made stronger. There are thus six specific eventsthat can occur in our evolutionary trajectories: (A) removing theHK2–RR1 interaction, (B) removing the HK1–RR2 interaction,(C) adding the I2–HK2 interaction, (D) removing the I1–HK2

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HK1 HK2 HKN

RR1 RR2 RRN

Fig. 2. Effects of competition on TCS signaling. (A) Fraction of active outputas a function of input concentration in response to competition between thecognate RR1 and noncognate RR2. The ratio R ≡ [RR2]0/[RR1]0 is varied asindicated. (B) Diagram of a TCS network with N HKs and N RRs. Each HKi

interacts with its cognate RRi with KD,C (black arrows) and with noncognateRRj with KD,NC (gray arrows). (C) Fraction of active output as a function of KD

ratio = KD,C/KD,NC in TCS networks of varying size N. The input concentrationwas set at a concentration that produces 50% phosphorylation for an iso-lated HK–RR pair. (D) Concentration of HK* (dashed lines) and RR* (solidlines) as a function of time for a cognate substrate and two noncognatesubstrates with KD ratios of 103 and 104. These models start with 2.5 μM HK*and 2.5 μM RR, exactly replicating the in vitro experiments of Skerker et al.(18). The two time points investigated experimentally in that work arehighlighted, 10 s (pink vertical line) and 1 h (orange vertical line).

5552 | www.pnas.org/cgi/doi/10.1073/pnas.1317178111 Rowland and Deeds

interaction, (E) removing the RR2–O1 interaction, and (F) addingthe RR2–O2 interaction. This provides a model with 64 possiblestates, depending upon the existence of these six interactions, and720 possible trajectories (e.g., A, B, C, D, E, F or E, A, D, F, C, B).An example of one such trajectory is diagrammed in Fig. 3A. Eachtrajectory was then analyzed at each step for the activation of bothoutputs in the presence of either input. The neutrality of the tra-jectories was measured based upon a single criterion: havingminimal impact on parental signaling, which we defined using thetotal concentration of active O1 in the presence of saturating con-centrations of I1, summed across all of the “steps” in the trajectory.We obtained 24 “near-neutral” trajectories that minimize im-

pact on parental signaling equally well across all steps (Fig. 3B);the example trajectory in Fig. 3A is a member of that set. In all ofthese trajectories, the crosstalk interactions between the HKsand RRs are removed before HK2 and RR2 lose their capacity tointeract with I1 and O1. This prevents inactive HK2 from actingas a phosphatase for RR1, and avoids reductions in O1 activationowing to competition between RR1 and RR2 for phosphorylationby HK1 (Fig. 2A). The red curves in Fig. 3B represent the fourtrajectories with the maximal total impact on parental signaling.These trajectories all exhibit the opposite order of events: in thosecases, input/output functionality is always altered before theHK–RR crosstalk is removed.

Evidence for Near-Neutral Trajectories. HK proteins generallycontain a distinct “kinase” (K) domain, which interacts withthe RR and is involved in the phosphotransfer reaction, aswell as an “input” domain (I) that recognizes external signalsand modulates HK function (Figs. 1B and 3C) (1, 16, 21, 30,33). Our model predicts a pressure to eliminate crosstalkrelatively early in the evolutionary trajectory of a given se-quence pair, before changes occur in the input domain. Inevolutionary terms, this pressure would manifest itself as setof amino acid changes in the HK–RR interaction interfaces ofthe duplicate pairs to insulate the two pathways from oneanother (14, 16, 20, 22, 23).To test these predictions, we obtained the amino acid and

DNA sequences of HKs from bacterial genomes in the KyotoEncyclopedia of Genes and Genomes (KEGG) database (34).Using available Pfam annotations (35), we restricted our anal-ysis to sequences that contain a PAS domain, because this is themost common and well-studied input domain for HK proteins(30, 33). We retained only those genomes where we couldidentify five or more such sequences, resulting in a total of 352bacterial genomes. To identify putative recent duplication events,we performed multiple sequence alignments of the K domainsfrom each genome separately and focused only on those pairsthat were nearest neighbors in the phylogenetic trees obtainedfrom those alignments.Although duplication and divergence are common in the

evolution of HKs, new pathways can also enter a lineage throughhorizontal gene transfer (HGT) (21, 30). To remove HGT pairsfrom our analysis, we followed the approach of Alm et al. (30)exactly, constructing a “phylogenetic profile” for each HK genein our dataset based on its presence or absence across thephyolgentic tree of our bacterial genomes. Of the 2,243 closelyrelated nearest-neighbor pairs we identified, 342 of them(∼15%) represented recent HGT events. We thus obtaineda total of 1,901 pairs that represented bona fide duplicationevents, at least according to this analysis. Further details re-garding the sequences we obtained and the HGT analysis can befound in Materials and Methods and SI Appendix.We used this data to calculate the rate of synonymous sub-

stitutions (KS) and the rate of nonsynonymous substitutions (KA)for our sequences (36). The ratio of these two parameters,KA/KS, provides an estimate of the relative strength of selectionon the coding sequence of the protein. A value of KA/KS >1indicates positive selection for changes at the protein level,whereas a KA/KS <1 indicates “purifying” selection to maintainthe sequence of the protein unchanged (36). We included thesequence of Spo0B in our K domain alignments, using theavailable cocrystal structure between Spo0B and Spo0F (its RR)to determine which residues in each HK sequence were likely toparticipate in this interface (16, 37). Using the alignment for eachnon-HGT pair, we calculated KA and KS values for the interfacialresidues of the K domain and the noninterfacial residues of theK domain.In Fig. 4A, we plot the value of KA/KS as a function of KS

(a rough estimator of time since duplication) for non-HGT se-quence pairs based on all residues in either the K domain in-terface or the noninterface region. We found that the strength ofselection on these subsets of residues was quite different: forone, the average KA/KS in the interfacial residues is higheroverall (SI Appendix, Fig. S9, P = 4.73 × 10−9). We also founda strong power-law dependence of KA/KS on KS for the interface,whereas noninterface residues showed a statistically distinctand much weaker dependence (P < 2 × 10−16, SI Appendix,section 5.3).To test whether the size of the subset of residues considered

might influence the calculation of KA and KS, we generatedrandom subsets of noninterface residues with the same totalnumber of residues as the interface. We also used the Spo0Bstructure to generate similar random subsets of noninterfacesurface residues, to control for the fact that surface residues(such as those on the HK/RR interface) might experience relaxed

B

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Fig. 3. Evolutionary trajectories. (A) An example of an evolutionary tra-jectory starting with a single TCS pathway in which the input I1 activatesHK1, HK1 phosphorylates RR1, and RR1 activates the output O1. The HK–RRpair is duplicated in the first step (step 0→ 1), introducing crosstalk. The newHK–RR pair is modified through a series of coarse-grained events. Each stepcorresponds to a discrete change in the interaction capabilities of the mol-ecules in question (events A–F described in the text). Any alternative or-dering of these events constitutes a unique evolutionary trajectory. (B)Fraction of active output O1 in response to saturating I1 at each evolutionarystep for the 24 trajectories that displayed the least impact on parental sig-naling (black) and the 4 trajectories that displayed the largest impact onparental signaling (red). Multiple trajectories can exhibit the same trends inparental signaling; hence, there are only a few visible curves. (C) Diagram ofan HK containing two domains: an input domain I (PAS domain) and thekinase domain K.

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evolutionary pressures. In both cases, the trends were the sameas those in Fig. 4A (SI Appendix, Figs. S6 and S7). Using a secondavailable HK/RR structure to determine the interface residues[HK853/RR468 from Thermotoga maratima (7)] also gives sim-ilar results (SI Appendix, Fig. S8). Finally, the raw substitutionrates (i.e., the total number of amino acid changes between twosequences) shows much higher values for interface positionscompared with other positions in the sequence, regardless ofwhether these positions are on the surface or not (SI Appendix,Fig. S10). The difference in substitution rates can be readily seenin an example alignment for a recently diverged pair of K do-mains from the bacterium Halococcus turkmenicus (SI Appendix,Fig. S11). Using a similar analysis for RR proteins, we foundessentially the same trends when comparing interface to non-interface residues for those proteins (Figs. 4B and SI Appendix,Figs. S8 and S9). Overall, these findings indicate that the inter-face residues of both the HK and RR proteins tend to diversifyafter duplication to prevent crosstalk, consistent with our predic-tions (Fig. 3).We also considered the evolution of input functionality in HK

proteins. In our alignments, we found only 67 cases out of the2,243 nearest-neighbors in the K domain alignment where thePAS domains for those two proteins were also nearest neighborsin the PAS domain alignment for that genome. In other words,we found that PAS domains tend to display extensive domainswapping, where new input functionality evolves not throughdivergence of the ancestral input domain, but rather the re-placement of the original function through wholesale introductionof the input domain from another, unrelated protein. This is con-sistent with earlier findings on PAS domain evolution in HKs (30).Because the evolution of input functionality is dominated by

domain swapping, we could not perform a robust KA/KS analysissimilar to that in Fig. 4 A and B. Instead, we focused on under-standing the timing of the domain-swapping event relative to the

duplication of the HK gene. There are two possible scenarios inthis case: in scenario A, an HK gene is duplicated and sub-sequently picks up a “new” PAS domain from some other pro-tein in the genome. In scenario B, a protein with a PAS domainis duplicated, and later picks up a new K domain through domainswapping. Our model predicts that scenario A should be morecommon in HK evolution, because input changes should occurrelatively later in the evolutionary trajectory (Fig. 3).To test this prediction, we took each of our domain-swapped

non-HGT HK pairs and compared the KS of the K domain fromthat pair with the KS of the closest PAS domain. Of the 1,300cases for which we could obtain the relevant KS values, 951 ofthem had a larger KS value for the K domain than for the PASdomain (Fig. 4C, P < 2 × 10−16), as our model predicted. Thisstatistical bias is present if we consider only those cases wherethe PAS domain that is swapped originates only from other HKproteins, or only from non-HK proteins (P < 2 × 10−16 in bothcases, SI Appendix, Fig. S12). Even in cases of very recentduplications where scenario B seems more likely (i.e., the bluetriangle in Fig. 4C, with KS for both domains <1), we see sig-nificant pressure to mutate interface residues. In particular, theaverage number of substitutions in the interface for those se-quence pairs is approximately eight, similar to that observed forall pairs in the dataset (Fig. 4D). The average substitution rate inthis case is much larger than that observed for random noninter-face subsets of the same size (P < 10−5, permutation test). Thisindicates a near-universal pressure to diversify the interface resi-dues of newly evolved HK/RR pairs.

DiscussionThe results described above indicate that the vast global differ-ences in topology between eukaryotic and bacterial signalingnetworks are likely the result of differences in the atomic“motifs” from which the networks themselves are constructed. Inparticular, the kinase–phosphatase pairs that are typically foundin eukaryotic networks become more ultrasensitive as they be-come more saturated, a behavior that allows these loops tocouple the responses of multiple downstream targets in in-teresting and potentially adaptive ways (Fig. 1C) (25, 26). Incontrast, the two-component architecture of bacterial signalingmotifs makes them inherently less efficient as they become sat-urated, ultimately driving down total system response as com-petitive substrates are added (Fig. 1D). This behavior likelyunderlies the fitness cost of crosstalk observed in vivo, resultingin a natural evolutionary pressure to maintain isolated cognatesignaling pathways (23). Indeed, our models indicate that a re-quirement to maintain cognate responses is sufficient to obtainthe degree of kinetic preference that HKs show for their sub-strates (Fig. 2) (18).Although our models indicate that crosstalk in TCS generally

decreases response, this does not imply that such systems abso-lutely cannot tolerate the presence of more than one interactionpartner. Indeed, there are known examples of HKs that act ef-ficiently on more than one RR (e.g., the bacterial chemotaxispathway) (38). Although introducing crosstalk does decreaseresponse, the system can compensate by increasing the totalexpression level of that particular RR to maintain a particularconcentration of active RR* (SI Appendix) (3). Of course, suchan increase comes with its own fitness cost: the bacterium mustinvest more energy in protein synthesis to obtain the same levelof signaling performance. In some cases, the phenotypic benefitsof crosstalk may outweigh this cost, resulting in HKs with morethan one target. As the number of targets increases, however, thecost of maintaining the response becomes larger (Fig. 2). This islikely the reason that even the few bifunctional HKs that havemore than one target rarely act on more than two or threedownstream RRs (34, 38). Monofunctional HKs, however, shouldact more like kinases in GK loops (Fig. 1), and so proteins like thechemotaxis kinases may experience a considerably relaxed con-straint against evolving crosstalk.

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Fig. 4. Sequence analysis. (A) The KA/KS values as a function of KS for non-HGT HK sequence pairs for both the K domain interface residues (green circles)and noninterface residues (orange circles). The black and red lines correspondto power-law regressions of the interface and noninterface data, respectively.(Inset) The same data and fits, plotted on a log-log scale. (B) A plot similar tothat in A, but for the interface and noninterface residues of RR proteins. (C)The KS value for each HK domain pair is plotted against the KS value for thecorresponding PAS domains. Of the 1,300 points in this plot, 951 are above thediagonal (the black line, P < 2 × 10−16). (D) A plot of the distribution of sub-stitution rates for all of the K domains in C (red) and just those K domains fromvery recent duplications (KS <1) where the PAS domain is younger (the bluetriangle in C corresponds to the points used to make the blue line). The numberof amino acid substitutions in the interface positions (solid lines) is comparedwith the number obtained from random subsets of noninterface positions ofthe same size (dashed lines).

5554 | www.pnas.org/cgi/doi/10.1073/pnas.1317178111 Rowland and Deeds

The evolution of new signaling pathways in bacteria ofteninvolves the duplication and subsequent divergence of an existingTCS pair (Fig. 3A) (21). Our findings indicate that the impact ofcrosstalk on HK signaling likely shapes the evolutionary land-scapes of these duplicate pairs. Specifically, the fitness costs ofcrosstalk generate significant evolutionary pressures that resultin rapid diversification of the HK–RR interface, insulating theprotein interactions and allowing the subsequent evolution ofnew input and output functionalities (Figs. 3 and 4). It is cur-rently possible to engineer both HK and PAS domain sequencesto introduce a wide variety of HK–RR and HK–I interactions.It would thus be straightforward to create a number of the in-termediate evolutionary “states” considered by our model (e.g.,Fig. 3A) and assess their relative fitness costs in vivo. One suchcase has already been investigated experimentally (23); theinvestigation of systems with related topologies would providedetailed tests of our predictions. The combination of theseexperimental efforts with more detailed phylogenetic analysesof recent duplication events (30) would ultimately result in adefinitive characterization of the evolutionary trajectories ofnew TCS pathways.The reliance of bacterial signaling systems on only two com-

ponents results in signaling dynamics that cannot easily admitcompetitive interactions. Our work indicates that this inherentfeature of TCS dynamics underlies a diverse array of observations,

including kinetic preferencing (18), the evolution of protein in-teraction interfaces (Fig. 4) (14–16, 18–23), and the deleteriouseffects of crosstalk in vivo (23). The constraint against crosstalkmay limit the types of information processing available to bac-terial signaling networks, with more involved computations oc-curring at the level of the complex gene regulatory networksdownstream of RRs (39, 40).

Materials and MethodsOur model of TCS dynamics, and the corresponding systems of ordinarydifferential equations (ODEs), is described in SI Appendix, section 1. We usedthe CVODE package from SUNDIALS (41) to numerically integrate the systemof ODEs. Nucleic acid and amino acid sequences of HKs were obtained fromthe KEGG database (34), and domain boundaries were obtained from Pfamannotations (35). The amino acid sequences of the domains within eachgenome were aligned using CLUSTALW (42). The nucleic acid sequenceswere then mapped to the amino acid multiple sequence alignments. KA andKS values were obtained using the seqinR library in the R statistical com-puting platform (43). Further details on our simulations and analyses can befound in SI Appendix.

ACKNOWLEDGMENTS. We thank Justin Blumenstiel, Tom Kolokotrones,Walter Fontana, and Michael Laub for many helpful discussions regardingthis work.

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