Crosstalk and the evolution of specificity in two-component signaling

Significance

The global architectures of signaling networks in bacteria and eukaryotes are remarkably different: crosstalk between pathways is very common in eukaryotes but is very limited in bacteria. Bacteria use two-component signaling (TCS) to transduce information, relying on a single enzyme to act as both kinase and phosphatase for targets. We used mathematical models to show that introducing crosstalk in TCS always decreases system performance. This indicates that the large-scale differences between eukaryotic and bacterial networks likely derive from differences in the dynamics of the fundamental motifs from which the networks themselves are constructed. We further demonstrated that the pressure to avoid crosstalk has influenced the evolution of new TCS pairs, driving rapid sequence divergence in protein interaction interfaces immediately postduplication.

Abstract

Two-component signaling (TCS) serves as the dominant signaling modality in bacteria. A typical pathway includes a sensor histidine kinase (HK) that phosphorylates a response regulator (RR), modulating its activity in response to an incoming signal. Most HKs are bifunctional, acting as both kinase and phosphatase for their substrates. Unlike eukaryotic signaling networks, there is very little crosstalk between bacterial TCS pathways; indeed, adding crosstalk to a pathway can have disastrous consequences for cell fitness. It is currently unclear exactly what feature of TCS necessitates this degree of pathway isolation. In this work we used mathematical models to show that, in the case of bifunctional HKs, adding a competing substrate to a TCS pathway will always reduce response of that pathway to incoming signals. We found that the pressure to maintain cognate signaling is sufficient to explain the experimentally observed “kinetic preference” of HKs for their cognate RRs. These findings imply a barrier to the evolution of new HK–RR pairs, because crosstalk is unavoidable immediately after the duplication of an existing pathway. We characterized a set of “near-neutral” evolutionary trajectories that minimize the impact of crosstalk on the function of the parental pathway. These trajectories predicted that crosstalk interactions should be removed before new input/output functionalities evolve. Analysis of HK sequences in bacterial genomes provided evidence that the selective pressures on the HK–RR interface are different from those experienced by the input domain immediately after duplication. This work thus provides a unifying explanation for the evolution of specificity in TCS networks.

Two-component signaling (TCS) represents the primary signaling modality in bacteria (1). The prototypical TCS pathway includes a membrane-bound sensor histidine kinase (HK) that autophosphorylates upon receiving an input signal. The HK then binds and transfers its phosphoryl group to a response regulator (RR), which often functions directly as a transcription factor, regulating gene expression patterns in response to the signal (1, 2). Many HKs are bifunctional, acting as both the kinase and phosphatase for their RR; the ratio of kinase to phosphatase activity, and thus the phosphorylation state of the RR, is controlled by the input (1–8).

Signaling networks in eukaryotes display extensive “crosstalk,” with individual kinases acting on large numbers of targets: the kinase Cdk1, for instance, has hundreds of substrates in yeast (9–11). Bacterial TCS networks show a remarkably different topology: HKs usually act on a single target (12–17). Intensive experimental study over the past 10 years has revealed the biochemical and biophysical basis for this lack of promiscuity. In general, HKs demonstrate a strong “kinetic preference” for their cognate substrates, preferentially phosphorylating them on short timescales (7, 15, 16, 18–21). A relatively small number of residues in the protein–protein interaction interface between HKs and RRs is responsible for maintaining this specificity (14–16, 20–23). Recently, Capra et al. (23) demonstrated that making just two mutations in this interface could introduce an interaction between an HK (PhoR) and a noncognate RR (NtrX) in Escherichia coli. This exogenous interaction decreased phosphate 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 to TCS can reduce information transfer efficiency under certain conditions (24), but it remains unclear exactly why TCS pathways are constrained from evolving crosstalk.

One of the most common motifs in eukaryotic signaling networks is a pair of enzymes (e.g., a kinase and a phosphatase) acting on a shared substrate (Fig. 1A) (25, 26). Using mathematical models, we recently showed that adding multiple competing substrates to this type of Goldbeter–Koshland (GK) loop would tend to induce an ultrasensitive, switch-like behavior in the system, which could easily have positive phenotypic consequences for the cell (26–29). In the work described here, we performed a similar analysis, extending a well-studied and validated mathematical model of bifunctional HKs (Fig. 1B) to the case of multiple substrates (3, 4). We found that, because the HK acts both as the kinase and the phosphatase in these systems, the addition of competing interactions with multiple RRs always decreases the response of the cognate RR. This is consistent with the findings of Capra et al. (23), who showed that the phenotypic effects of their crosstalk mutant were not due to the misregulation of NtrX targets, but rather a direct result of decrease in phosphate starvation signaling.

Fig. 1.

TCS pathways vs. Goldbeter–Koshland Loops. (A) Diagram of a Goldbeter–Koshland loop. An input activates a kinase K, which phosphorylates the substrate. The phosphatase P is a separate enzyme that undoes this modification. (B) Diagram of a TCS pathway. An input causes the autophosphorylation of an HK, which transfers its phosphoryl group to the RR. The unphosphorylated HK also serves as the phosphatase. (C) The fraction of phosphorylated substrate S as a function of input concentration (on a log scale) 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 are shaded pink and green, respectively. Note that the addition of substrate makes the response more switch-like (25). (D) The fraction of phosphorylated response regulator RR as a function of input concentration for two total concentrations of RR ([RR]₀ = 100 nM, black, and [RR]₀ = 10 μM, red). As discussed in the text, HKs are always in the phosphatase regime, so the entire plot is shaded pink. Note that increasing total substrate concentration in this case reduces the response efficiency of the RR.

The pressure to maintain cognate signaling suggests the existence of a barrier in the evolution of new TCS pathways. New HK–RR pairs can arise from the duplication of existing HK–RR genes, which subsequently diverge into a new pathway (21, 30). There is unavoidable crosstalk immediately postduplication, which can attenuate the response to the original signal. Using our models, we characterized a set of “near-neutral” evolutionary trajectories that minimize the impact of the new pair on the signaling of the parent pathway. All of these trajectories involved insulating the two pathways from one another before establishing new input and output functionalities. To test this prediction, we separately aligned multiple HK and input domain sequences from fully sequenced bacterial genomes. Analysis of the K_A/K_S ratios of the most recently diverged domains revealed that the interaction interface of the HK is under strong positive selection immediately after duplication, likely owing to the pressure to insulate 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 input functionality by wholesale exchange of domains with other proteins in the genome (21, 30). Analysis of K_S values indicates that these swapping events generally occur only after the HK interfaces have had sufficient time to evolve interaction specificity. These findings suggest that the majority of HK–RR duplications follow the near-neutral evolutionary paths we predicted. Overall, our work indicates that the bifunctional nature of HKs has likely been a major driving force in the evolution of insulated topologies in bacterial signaling networks (21).

Results

Response to Changes in RR Concentration.

To understand the impact of crosstalk on signaling, it is helpful to consider the response of the system to changes in the concentration of a single substrate (26). As mentioned above, eukaryotic signaling networks 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 of this system over 30 years ago, finding that the response of the system at steady-state followed:

where S* ≡ [S*]/[S]₀ is the mole fraction of phosphorylated substrate, K_K ≡ K_M,K/[S]₀ and K_P ≡ K_M,P/[S]₀ are the Michaelis constants divided by the total concentration of substrate, and r ≡ k_cat,K[K]₀/k_cat,P[P]₀ is the ratio of the maximum velocities of the enzymes (25). Because protein concentrations (and thus the saturation 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 input molecule binds and activates the kinase, thus modulating r (SI Appendix). At unsaturating concentrations of substrate, substrate phosphorylation increases hyperbolically (Fig. 1C). At saturating concentrations, however, the system displays a switch-like behavior known as “0^th-order ultrasensitivity.” When r < 1, phosphatase activity dominates and the addition of substrate decreases S*; we call this the “phosphatase regime.” When r > 1, kinase activity dominates and the addition of substrate increases S*; this is the “kinase regime.” These two opposing trends lead to an increasingly ultrasensitive response as total substrate concentration increases (Fig. 1C) (25–29).

A major difference between eukaryotic GK loops and bacterial TCS is the fact that the HK often acts as both kinase and phosphatase for its substrate RR (Fig. 1B). Ten years ago, Batchelor and Goulian (3) developed an approximate analytical solution of a mathematical model of TCS signaling and demonstrated that the concentration of phosphorylated RR ([RR*]) was insensitive to changes in total RR concentration ([RR]₀). To study crosstalk in TCS, we constructed a model very similar to that of Batchelor and Goulian and other authors (see SI Appendix for the details of the model) (3, 4). We were able to obtain a complete analytical solution in this case and found that the steady-state response of the system follows:

where RR* ≡ [RR*]/[RR]₀ is the fraction of phosphorylated response regulator, K_K and K_P are as previously defined, and r ≡ k_cat,K/k_cat,P becomes a constant ratio between the catalytic rates of the kinase and phosphatase reactions. In this case, the dominant response parameters to changes in input are the new β and ε terms, which are dependent upon the autophosphorylation and autodephosphorylation rates of the HK and thus the input signal (see SI Appendix for derivation and details). We compared the predictions of this solution to previous experimental results by Batchelor and Goulian (3) in which the concentrations of the HK and RR were varied and found that Eq. 2 reproduces their data (SI Appendix).

As with the GK loop, we considered a case in which an explicit input molecule binds and activates the HK (Fig. 1B). Because bacterial TCS are well studied, experimental values are available for both total concentrations and kinetic parameters in this model (SI Appendix) (2, 3, 13, 32). Using those parameters for the purpose of display, we found a dramatic decrease in RR* when total RR concentration is high (Fig. 1D). Note that this is the fraction of phosphorylated RR; the total concentration of active RR molecules does not depend on [RR]₀ when the RR is at saturating concentrations, as previously noted (SI Appendix) (3). Thus, although the response of the system is robust to changes in total RR in this regime, it also becomes inefficient; that is, increasing the expression of the RR does not increase the response capacity of the system.

In the GK loop (Fig. 1 A and C), the separation of the kinase and phosphatase regimes depends upon the term (r – 1) in the denominator of Eq. 1, which is negative in the phosphatase regime and positive in the kinase regime. Eq. 2 contains a similar term, (rβ – β′), and this term is always negative. TCS loops are thus always in the phosphatase regime, and the general trend in Fig. 1D does not depend on specific values of kinetic parameters (SI Appendix). This behavior ultimately arises from the fact that both the kinase and phosphatase reactions produce unphosphorylated HK, which itself is a phosphatase, keeping the system in the phosphatase regime.

Competition in TCS.

To consider crosstalk in TCS, we added a single competing RR to the system diagrammed in Fig. 1B. We denote the cognate RR as RR₁, the noncognate interaction partner as RR₂, and define the ratio of their total concentrations to be R ≡ [RR₂]₀/[RR₁]₀. To account for the impact of crosstalk on RR₁ function, we also added explicit output molecules (O₁ binding phosphorylated RR₁ and O₂ binding phosphorylated RR₂) to the model. To study the responses of this system to a competing RR when the HK displays no kinetic preference for either substrate, we set the kinetic parameters of RR₂ to be the same as those for RR₁ (7, 15, 16, 18–21). We found that adding RR₂ at the same total concentration as the cognate substrate results in a decrease in output activity of the system, which we defined as the fraction of O₁ molecules bound by phosphorylated RR₁ (Fig. 2A). As the total concentration of RR₂ is increased, impact on RR₁ activity becomes even more significant. The situation is similar to that in Fig. 1D, but in this case the total concentration of RR₁ is constant, so both the fraction and concentration of phosphorylated RR₁ decreases, leading to a decrease in output activity. Our results thus indicate that the type of crosstalk introduced experimentally by Capra et al. (23) into bacterial cells would likely decrease the performance of the PhoR/PhoB signaling system, providing an explanation for the lower fitness of crosstalk mutants in phosphate-limiting conditions.

Fig. 2.

Effects of competition on TCS signaling. (A) Fraction of active output as a function of input concentration in response to competition between the cognate RR₁ and noncognate RR₂. The ratio R ≡ [RR₂]₀/[RR₁]₀ is varied as indicated. (B) Diagram of a TCS network with N HKs and N RRs. Each HK_i interacts with its cognate RR_i with K_D,C (black arrows) and with noncognate RR_j with K_D,NC (gray arrows). (C) Fraction of active output as a function of K_D ratio = K_D,C/K_D,NC in TCS networks of varying size N. The input concentration was set at a concentration that produces 50% phosphorylation for an isolated HK–RR pair. (D) Concentration of HK* (dashed lines) and RR* (solid lines) as a function of time for a cognate substrate and two noncognate substrates with K_D 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 are highlighted, 10 s (pink vertical line) and 1 h (orange vertical line).

Bacterial genomes can encode 5–200 HK–RR pairs, depending on the species in question (21). To consider the impact of crosstalk in such cases, we expanded the model to include N HKs and RRs (Fig. 2B). In this model each HK can interact with each RR; in principle, every pair in this case has an independent association affinity (i.e., K_D). To simplify the problem, we assigned every cognate pair in the system (HK_i-RR_i, e.g., HK₁ interacting with RR₁) the same affinity K_D,C, and every noncognate pair (HK_i-RR_j, i ≠ j, e.g., HK₁ interacting with RR₂) the same affinity K_D,NC (Fig. 2B). We fixed the cognate interaction to the value observed experimentally (K_D,C ≈ 1 μM) (32). We then varied the ratio between noncognate and cognate K_D’s (K_D ratio ≡ K_D,NC/K_D,C ) in networks of various sizes N and measured the output activity of RR₁ in response to the activation of HK₁ (Fig. 2C). We find that output activity is heavily attenuated for all systems when the noncognate K_D’s are relatively strong. However, when the noncognate K_D’s are weaker than the cognate’s by approximately three to four orders of magnitude, the activity of the single active pathway is essentially unaffected for N = 5 to N = 50.

To determine whether K_D ratios in this range provide “kinetic preferencing” similar to that observed by Skerker et al. (18), we replicated their in vitro experiment using our model. This involved mixing either a cognate or noncognate RR with a fully phosphorylated HK at equal concentrations. When the HK acts on a cognate substrate, the phosphorylation of the RR peaks at 10 s, and after 1 h both the HK and RR are completely dephosphorylated. In contrast, a noncognate substrate with a K_D ratio of either 10³ or 10⁴ exhibits no phosphorylation at 10 s but considerable response after 1 h (Fig. 2D), directly recapitulating the findings of Skerker et al. (18). A K_D ratio of ∼10⁴ also gives cognate catalytic efficiencies (k_cat/K_M) that are 10⁴ higher than noncognate efficiencies, consistent with other experimental findings (14). Our results thus indicate that the observed kinetic preference of HKs for their cognate substrates can be explained simply by the need to maintain cognate responses (Fig. 2C) in the presence of competing substrates, rather than an explicit pressure to prevent misregulation of noncognate targets (23).

Evolutionary Trajectories.

New TCS pathways can arise through the duplication and divergence of existing HK–RR pairs (21, 30). The duplication event itself produces two HK–RR pairs that are identical (Fig. 3A, steps 0 to 1). This effectively increases both the total concentration of the substrate and the concentration of the HK, both of which can decrease the response of the “parent” signaling pathway (Fig. 2 and SI Appendix). Because such decreases could strongly affect the fitness of cells in which the duplication occurs (23), the unavoidable crosstalk that occurs immediately postduplication could present a barrier to the evolution of new TC signaling pathways. Subsequent evolutionary events, such as the evolution of one duplicate RR that cannot activate the original output genes but still competes with the original RR for phosphorylation by the HKs, could easily exacerbate this problem (Fig. 2).

Fig. 3.

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

We thus determined whether there were any “evolutionary trajectories” that could minimize the effect of crosstalk on the parent signaling pathway. To do this, we developed a simple model of the evolution of HK–RR pairs postduplication. In this model, we defined two types of evolutionary steps: the removal of an interaction, meaning that the kinetic parameters of the interaction are set so weak that binding of the two molecules becomes very unlikely, and the addition of an interaction, meaning that the kinetic parameters for the binding of two molecules are made stronger. There are thus six specific events that can occur in our evolutionary trajectories: (A) removing the HK₂–RR₁ interaction, (B) removing the HK₁–RR₂ interaction, (C) adding the I₂–HK₂ interaction, (D) removing the I₁–HK₂ interaction, (E) removing the RR₂–O₁ interaction, and (F) adding the RR₂–O₂ interaction. This provides a model with 64 possible states, depending upon the existence of these six interactions, and 720 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. Each trajectory was then analyzed at each step for the activation of both outputs in the presence of either input. The neutrality of the trajectories was measured based upon a single criterion: having minimal impact on parental signaling, which we defined using the total concentration of active O₁ in the presence of saturating concentrations of I₁, summed across all of the “steps” in the trajectory.

We obtained 24 “near-neutral” trajectories that minimize impact on parental signaling equally well across all steps (Fig. 3B); the example trajectory in Fig. 3A is a member of that set. In all of these trajectories, the crosstalk interactions between the HKs and RRs are removed before HK₂ and RR₂ lose their capacity to interact with I₁ and O₁. This prevents inactive HK₂ from acting as a phosphatase for RR₁, and avoids reductions in O₁ activation owing to competition between RR₁ and RR₂ for phosphorylation by HK₁ (Fig. 2A). The red curves in Fig. 3B represent the four trajectories with the maximal total impact on parental signaling. These trajectories all exhibit the opposite order of events: in those cases, input/output functionality is always altered before the HK–RR crosstalk is removed.

Evidence for Near-Neutral Trajectories.

HK proteins generally contain a distinct “kinase” (K) domain, which interacts with the RR and is involved in the phosphotransfer reaction, as well as an “input” domain (I) that recognizes external signals and modulates HK function (Figs. 1B and 3C) (1, 16, 21, 30, 33). Our model predicts a pressure to eliminate crosstalk relatively early in the evolutionary trajectory of a given sequence pair, before changes occur in the input domain. In evolutionary terms, this pressure would manifest itself as set of amino acid changes in the HK–RR interaction interfaces of the duplicate pairs to insulate the two pathways from one another (14, 16, 20, 22, 23).

To test these predictions, we obtained the amino acid and DNA sequences of HKs from bacterial genomes in the Kyoto Encyclopedia of Genes and Genomes (KEGG) database (34). Using available Pfam annotations (35), we restricted our analysis to sequences that contain a PAS domain, because this is the most common and well-studied input domain for HK proteins (30, 33). We retained only those genomes where we could identify five or more such sequences, resulting in a total of 352 bacterial genomes. To identify putative recent duplication events, we performed multiple sequence alignments of the K domains from each genome separately and focused only on those pairs that were nearest neighbors in the phylogenetic trees obtained from those alignments.

Although duplication and divergence are common in the evolution of HKs, new pathways can also enter a lineage through horizontal gene transfer (HGT) (21, 30). To remove HGT pairs from our analysis, we followed the approach of Alm et al. (30) exactly, constructing a “phylogenetic profile” for each HK gene in our dataset based on its presence or absence across the phyolgentic tree of our bacterial genomes. Of the 2,243 closely related nearest-neighbor pairs we identified, 342 of them (∼15%) represented recent HGT events. We thus obtained a total of 1,901 pairs that represented bona fide duplication events, at least according to this analysis. Further details regarding the sequences we obtained and the HGT analysis can be found in Materials and Methods and SI Appendix.

We used this data to calculate the rate of synonymous substitutions (K_S) and the rate of nonsynonymous substitutions (K_A) for our sequences (36). The ratio of these two parameters, K_A/K_S, provides an estimate of the relative strength of selection on the coding sequence of the protein. A value of K_A/K_S >1 indicates positive selection for changes at the protein level, whereas a K_A/K_S <1 indicates “purifying” selection to maintain the sequence of the protein unchanged (36). We included the sequence of Spo0B in our K domain alignments, using the available cocrystal structure between Spo0B and Spo0F (its RR) to determine which residues in each HK sequence were likely to participate in this interface (16, 37). Using the alignment for each non-HGT pair, we calculated K_A and K_S values for the interfacial residues of the K domain and the noninterfacial residues of the K domain.

In Fig. 4A, we plot the value of K_A/K_S as a function of K_S (a rough estimator of time since duplication) for non-HGT sequence pairs based on all residues in either the K domain interface or the noninterface region. We found that the strength of selection on these subsets of residues was quite different: for one, the average K_A/K_S in the interfacial residues is higher overall (SI Appendix, Fig. S9, P = 4.73 × 10⁻⁹). We also found a strong power-law dependence of K_A/K_S on K_S for the interface, whereas noninterface residues showed a statistically distinct and much weaker dependence (P < 2 × 10⁻¹⁶, SI Appendix, section 5.3).

Fig. 4.

Sequence analysis. (A) The K_A/K_S values as a function of K_S 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 correspond to 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 to that in A, but for the interface and noninterface residues of RR proteins. (C) The K_S value for each HK domain pair is plotted against the K_S value for the corresponding PAS domains. Of the 1,300 points in this plot, 951 are above the diagonal (the black line, P < 2 × 10⁻¹⁶). (D) A plot of the distribution of substitution rates for all of the K domains in C (red) and just those K domains from very recent duplications (K_S <1) where the PAS domain is younger (the blue triangle in C corresponds to the points used to make the blue line). The number of amino acid substitutions in the interface positions (solid lines) is compared with the number obtained from random subsets of noninterface positions of the same size (dashed lines).

To test whether the size of the subset of residues considered might influence the calculation of K_A and K_S, we generated random subsets of noninterface residues with the same total number of residues as the interface. We also used the Spo0B structure to generate similar random subsets of noninterface surface residues, to control for the fact that surface residues (such as those on the HK/RR interface) might experience relaxed evolutionary pressures. In both cases, the trends were the same as those in Fig. 4A (SI Appendix, Figs. S6 and S7). Using a second available HK/RR structure to determine the interface residues [HK853/RR468 from Thermotoga maratima (7)] also gives similar results (SI Appendix, Fig. S8). Finally, the raw substitution rates (i.e., the total number of amino acid changes between two sequences) shows much higher values for interface positions compared with other positions in the sequence, regardless of whether these positions are on the surface or not (SI Appendix, Fig. S10). The difference in substitution rates can be readily seen in an example alignment for a recently diverged pair of K domains from the bacterium Halococcus turkmenicus (SI Appendix, Fig. S11). Using a similar analysis for RR proteins, we found essentially the same trends when comparing interface to noninterface residues for those proteins (Figs. 4B and SI Appendix, Figs. S8 and S9). Overall, these findings indicate that the interface residues of both the HK and RR proteins tend to diversify after duplication to prevent crosstalk, consistent with our predictions (Fig. 3).

We also considered the evolution of input functionality in HK proteins. In our alignments, we found only 67 cases out of the 2,243 nearest-neighbors in the K domain alignment where the PAS domains for those two proteins were also nearest neighbors in the PAS domain alignment for that genome. In other words, we found that PAS domains tend to display extensive domain swapping, where new input functionality evolves not through divergence of the ancestral input domain, but rather the replacement of the original function through wholesale introduction of the input domain from another, unrelated protein. This is consistent 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 K_A/K_S analysis similar to that in Fig. 4 A and B. Instead, we focused on understanding the timing of the domain-swapping event relative to the duplication of the HK gene. There are two possible scenarios in this case: in scenario A, an HK gene is duplicated and subsequently picks up a “new” PAS domain from some other protein in the genome. In scenario B, a protein with a PAS domain is duplicated, and later picks up a new K domain through domain swapping. Our model predicts that scenario A should be more common in HK evolution, because input changes should occur relatively 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 K_S of the K domain from that pair with the K_S of the closest PAS domain. Of the 1,300 cases for which we could obtain the relevant K_S values, 951 of them had a larger K_S value for the K domain than for the PAS domain (Fig. 4C, P < 2 × 10⁻¹⁶), as our model predicted. This statistical bias is present if we consider only those cases where the PAS domain that is swapped originates only from other HK proteins, or only from non-HK proteins (P < 2 × 10⁻¹⁶ in both cases, SI Appendix, Fig. S12). Even in cases of very recent duplications where scenario B seems more likely (i.e., the blue triangle in Fig. 4C, with K_S for both domains <1), we see significant pressure to mutate interface residues. In particular, the average number of substitutions in the interface for those sequence pairs is approximately eight, similar to that observed for all pairs in the dataset (Fig. 4D). The average substitution rate in this case is much larger than that observed for random noninterface subsets of the same size (P < 10⁻⁵, permutation test). This indicates a near-universal pressure to diversify the interface residues of newly evolved HK/RR pairs.

Discussion

The results described above indicate that the vast global differences in topology between eukaryotic and bacterial signaling networks are likely the result of differences in the atomic “motifs” from which the networks themselves are constructed. In particular, the kinase–phosphatase pairs that are typically found in eukaryotic networks become more ultrasensitive as they become more saturated, a behavior that allows these loops to couple the responses of multiple downstream targets in interesting and potentially adaptive ways (Fig. 1C) (25, 26). In contrast, the two-component architecture of bacterial signaling motifs makes them inherently less efficient as they become saturated, ultimately driving down total system response as competitive substrates are added (Fig. 1D). This behavior likely underlies the fitness cost of crosstalk observed in vivo, resulting in a natural evolutionary pressure to maintain isolated cognate signaling pathways (23). Indeed, our models indicate that a requirement to maintain cognate responses is sufficient to obtain the degree of kinetic preference that HKs show for their substrates (Fig. 2) (18).

Although our models indicate that crosstalk in TCS generally decreases response, this does not imply that such systems absolutely cannot tolerate the presence of more than one interaction partner. Indeed, there are known examples of HKs that act efficiently on more than one RR (e.g., the bacterial chemotaxis pathway) (38). Although introducing crosstalk does decrease response, the system can compensate by increasing the total expression level of that particular RR to maintain a particular concentration of active RR* (SI Appendix) (3). Of course, such an increase comes with its own fitness cost: the bacterium must invest more energy in protein synthesis to obtain the same level of signaling performance. In some cases, the phenotypic benefits of crosstalk may outweigh this cost, resulting in HKs with more than one target. As the number of targets increases, however, the cost of maintaining the response becomes larger (Fig. 2). This is likely the reason that even the few bifunctional HKs that have more than one target rarely act on more than two or three downstream RRs (34, 38). Monofunctional HKs, however, should act more like kinases in GK loops (Fig. 1), and so proteins like the chemotaxis kinases may experience a considerably relaxed constraint against evolving crosstalk.

The evolution of new signaling pathways in bacteria often involves the duplication and subsequent divergence of an existing TCS pair (Fig. 3A) (21). Our findings indicate that the impact of crosstalk on HK signaling likely shapes the evolutionary landscapes of these duplicate pairs. Specifically, the fitness costs of crosstalk generate significant evolutionary pressures that result in rapid diversification of the HK–RR interface, insulating the protein interactions and allowing the subsequent evolution of new input and output functionalities (Figs. 3 and 4). It is currently possible to engineer both HK and PAS domain sequences to introduce a wide variety of HK–RR and HK–I interactions. It would thus be straightforward to create a number of the intermediate evolutionary “states” considered by our model (e.g., Fig. 3A) and assess their relative fitness costs in vivo. One such case has already been investigated experimentally (23); the investigation of systems with related topologies would provide detailed tests of our predictions. The combination of these experimental efforts with more detailed phylogenetic analyses of recent duplication events (30) would ultimately result in a definitive characterization of the evolutionary trajectories of new TCS pathways.

The reliance of bacterial signaling systems on only two components results in signaling dynamics that cannot easily admit competitive interactions. Our work indicates that this inherent feature of TCS dynamics underlies a diverse array of observations, including kinetic preferencing (18), the evolution of protein interaction interfaces (Fig. 4) (14–16, 18–23), and the deleterious effects of crosstalk in vivo (23). The constraint against crosstalk may limit the types of information processing available to bacterial signaling networks, with more involved computations occurring at the level of the complex gene regulatory networks downstream of RRs (39, 40).

Materials and Methods

Our model of TCS dynamics, and the corresponding systems of ordinary differential equations (ODEs), is described in SI Appendix, section 1. We used the CVODE package from SUNDIALS (41) to numerically integrate the system of ODEs. Nucleic acid and amino acid sequences of HKs were obtained from the KEGG database (34), and domain boundaries were obtained from Pfam annotations (35). The amino acid sequences of the domains within each genome were aligned using CLUSTALW (42). The nucleic acid sequences were then mapped to the amino acid multiple sequence alignments. K_A and K_S values were obtained using the seqinR library in the R statistical computing platform (43). Further details on our simulations and analyses can be found in SI Appendix.