The organization TOL regulatory and metabolic circuit of P. putida mt-2 for biodegradation of m-xylene is shown in Figure 1. The two pathways/operons encoded in the self-transmissible plasmid pWW0 present in this strain are coordinately expressed in response to the aromatic compounds which can be used by this bacterium as a sole carbon source if no other more palatable growth substrate is available 15 . Degradation of m-xylene takes place through two series of biotransformations. First, the upper pathway encodes enzymes for the conversion of m-xylene into m-toluate (i.e. 3-methylbenzoate, 3 MBz), which are expressed from the Pu upon activation by the regulatory protein XylR in response to the aromatic substrate ( 22 ; Figure 1). Second, the meta (also called lower) pathway encodes activities for the ensuing metabolism of 3 MBz into intermediates of the TCA cycle. This second operon of the system is activated by another plasmid-encoded regulator, XylS. This factor has the ability to trigger transcription at the cognate promoter Pm either by itself (provided that there is enough concentration of the protein) or in combination with 3 MBz, in which case much lower levels of XylS are required to the same end 23 24 . Apart of these plasmid-encoded regulatory components, a number of host factors (such as σ⁷⁰, σ⁵⁴, σ³⁸, σ³², IHF and HU) and global regulators (Crc, PtsN, TurA, PprA, ppGpp; 25 ) mediate a fine tuning of the system to a large number of environmental signals. Under the same physiological conditions, these default connections to the growth status of the host remain unaffected and they can be basically ignored. In particular, the action of the Crc factor that inhibits XylR translation when cells grow in a rich medium 26 can be suppressed experimentally by culturing cells in a synthetic mineral medium devoid of amino acids and other repressive substrates 27 28 .

Figure 1 shows only the TOL-specific regulatory and metabolic constituents of the TOL system, around which the work presented below revolves. Furthermore, the mechanism for regulation of the two TF encoded in pWW0 is of special interest. xylR and xylS genes are divergently transcribed in a fashion that affords XylR to repress its own transcription (both in the presence or absence of m-xylene) as well as activating xylS expression in response to m-xylene 29 as shown in Figure 2a. This regulatory node makes the system ultimately dependent on changes in XylR levels or activity 27 30 . As described elsewhere 17 , known pair-wise interactions between such constituents can be faithfully recreated with Boolean formalisms to produce a logic circuit composed of a number of logic gates (Figure 2b). The resulting relational chart represents the minimal logic structure of the system (i.e. the logicome) as a single circuit with defined inputs and outputs (Figure 2c). On this basis, the corresponding ensemble of logic gates (Figure 2c) could then be formalized into a set of piecewise-linear (PL) differential equations. These portray approximate kinetic behaviors by describing the regulation of the synthesis and degradation of proteins and other molecular species by means of Boolean functions (see Methods section and 19 ).

As shown in Figure 1, the upper TOL pathway is expressed from the Pu promoter that is in turn activated by XylR bound to m-xylene 15 . As both the XylR protein and the inducer are necessary to trigger Pu expression, expression of the upper operon has an AND logic (Figure 2b) where both inputs are strictly necessary to generate an output (Figure 2c). In the case of xylS expression, its logic is the same as for the upper expression as this regulator is expressed from a promoter called Ps1 which also requires XylR bound to m-xylene for activity 29 31 . Unlike Pu, however, a second weak constitutive promoter (Ps2) originates a low amount of XylS protein 32 . For meta pathway expression, the logic operation performed by the Pm promoter (which controls transcription the meta operon) is not trivial -in fact it is remarkably puzzling. Pm can be turned on by either XylS bound to 3 MBz 33 or by overproduction of the same effector-free XylS due to activation of the Ps1 promoter by XylR 23 29 . In this way, Pm activation by XylS/3 MBz is represented by a AND gate which is in turn integrated in an OR gate, where the second input is XylS itself (Figure 2c). However, 3 MBz-dependent XylS activation is specified in the PL model as the result of upper and m-xylene (thus symbolizing the enzymatic degradation of m-xylene, see Methods section). This is a reasonable simplification 34 because enzymatic reactions are way faster than expression of the corresponding genes. Therefore, the process of 3 MBz production can be considered instantaneous in terms of time-scale once the enzymes are formed. Assuming such time-scale criteria helps to raise models that are easier to handle and avoid aberrant results likely to occur in qualitative modeling if different temporal hierarchies are mixed up. Another simplification involves XylR. This protein controls negatively its own expression and it is therefore represented by a single NOT gate (Figure 2c). However, since various experiments indicate that XylR auto-regulation allows a constant supply of protein levels 30 35 we formalized XylR expression in the model as a simple unregulated process. The resulting set of equations (Table 1) where instrumental for assembling the mini-logicome of Figure 2c, which was employed to inspect the behavior of the TOL network under a number of operational conditions.

In order to simulate the activation of the TOL network in response to m-xylene, equations 1-4 (see Table 1) where implemented in the Genetic Network Analyzer software (GNA; 21 ), as described in the Methods section. Also, m-xylene was placed as an input variable 21 , meaning that [i] no PL equation is specified in the model associated to this component, and [ii] its concentration is not allowed to change during the simulations. As a pre-requisite to perform model simulation, parameter inequalities (Table 1) where defined for all variables in the system as described previously 21 . This approach allows setting the thresholds of the interaction processes, a fundamental attribute when a component of the system has more than one target or synthesis rate (which is indeed the case in TOL).

A first simulation contemplated the TOL system in the presence of the input m-xylene or its absence. In either condition, a single steady-state was found in the transition graph generated (Figure 3). A state transition graph describes the qualitative dynamics of the network, indicating the possible states of the system (concentration levels of enzymes and regulators) and transitions between these states occurring under the influence of regulatory events. It should be noted that the states of a transition graph (annotated with an s letter followed by a number) do not signify time intervals but occurrence of consecutive conditions regardless of the time it takes to move from one state to the other. For instance, shift from s1 → s5 in Figure 3a happens before s5 → s6 but it says nothing on the time involved in each transition: numbers 1, 5 and 6 refer to the name of the state but not to any temporal scale. A steady state characteristically lacks a successive stage in the transition graph. If m-xylene is low, only XylR is high (i.e. above the threshold defined in Table 1), while XylS is at low level (i.e. below that necessary for activating Pm in the absence of 3 MBz, see Table 1) and the upper and meta levels/activities are zero (Figure 3a). When m-xylene is high, all elements are high at steady-state. Inspection of the transition graph (which represents the successive order of events) in m-xylene-high condition shows a progression of regulatory steps identical to the known activation itinerary of the TOL pathway i.e. both upper and XylS are expressed in response to XylR activation, followed then by activation of meta due both to 3 MBz formation and XylS hyperexpression (Figure 3b). This coarse equivalence between the non-perturbed Boolean model and the recognizable behavior of the system in vivo in response to m-xylene set a reference for inspecting in silico the inner network logic as explained below.

The chief control step for TOL expression relies on signal (toluene/m-xylene) sensing by XylR. As mentioned before, this regulator of the NtrC family targets two σ⁵⁴-dependent promoters, Pu and Ps1 (Figure 1). This network motif, where a master regulator controls multiple targets in response to a single signal is named single-input module (SIM, Figure 4a) and it is overrepresented in bacterial regulatory networks 2 . The basic property of a SIM motif is that by having different affinities for multiple targets, the master regulator can impose a temporal order of gene expression in response to the same signal 2 36 . This just in time gene expression device is often used for the control of genes encoding a complex machinery (e.g., the flagellum) where the components must be assembled in a given order 37 . In the case of the TOL system, the temporal order of Pu vs. Ps activation is foreseen to have considerable consequences for the system, because XylR-dependent XylS hyper-expression is transmitted downstream into the node controlling meta expression (Figure 1).

In order to examine the consequences of having XylR as the upstream regulator in the SIM_XylR motif we simulated the response Pu and Ps under various θ_XylR parameter values (Table 1). To this end we just varied the value of the θ_XylR parameter in equations for Pu and Ps. The same value for the two promoters means synchronization (i.e. XylR is equally capable to activate Pu and Ps; Figure 4b) whereas setting different θ_XylR parameters for each promoter results in a temporal order of activation (not shown). But what is the actual state of affairs in the TOL system in vivo? To answer this question we analyzed experimentally the activation kinetics of Pu and Ps. For this, we cloned these promoters upstream of a promoter-less luxCDABE operon placed in a low-copy broad-host range plasmid (Figure 4c). The resulting transcriptional fusions were introduced into a wild type P. putida mt-2 strain to faithfully monitor the dynamics of the TOL system. The system was induced with 3-methylbenzyl alcohol (3MBA) as a proxy of m-xylene. 3MBA is the first intermediate of the biodegradation route and it is equally able to trigger the TOL system 15 . Furthermore, its much higher solubility (in contrast to the volatile m-xylene) makes 3MBA more suitable for induction experiments in liquid media 38 . As shown in Figure 4d, both cloned promoters were efficiently induced upon 3MBA exposure. In order to quantify the response of Pu and Ps to 3MBA, overnight grown cells were diluted in fresh M9 medium supplemented with either 3MBA as the sole carbon source or with 3MBA plus succinate. The luminescent signals of the strains were quantified along the growth curve and normalized respect to the respective optical density at 600 nm. The very small offsetting between Pu and Ps observed in the medium with both succinate and 3MBA (Figure 4e) disappeared altogether in the culture where 3MB was employed as sole C-source (Figure 4f). The behavior of both promoters is thus virtually identical under the conditions tested (absolute values were also comparable, not shown). The lack of significant differences in the timing or overall kinetics of Pu and Ps activation indicated that the SIM_XylR motif of the TOL network operates in a synchronous way for triggering expression of the upper pathway and the xylS gene. Finally, we could observe that Pm activity reached its maximum activity with a noticeable delay in respect to Pu and Ps (Figure 4f), as anticipated with the results of the simulation of Figure 3b. This delay is expected because Pm functionality does require more steps (production of XylS, formation of 3 MBz) than the instant trigger of Pu and Ps by effector-activated XylR (XylRa).

The results above were very informative because -to the best of our knowledge- synchronous SIM motifs have not been reported before in genetic networks. The role of SIM_XylR for the TOL circuit dynamics is therefore likely to be crucial. If upper were expressed earlier than xylS, 3 MBz production would occur also earlier than maximal expression of meta (i.e. Pm activation by hyper-expressed XylSh would be delayed) and it would thus result in a transient accumulation of 3 MBz. In contrast, if xylS were activated before upper, expression of meta would start earlier and cells would have the degradation machinery for 3 MBz in place before the compound could actually materialize from m-xylene biodegradation. Interestingly, proteins TurA and PprA have been recently demonstrated to interfere with XylR binding to the Pu promoter but not to Ps 39 40 . Such interference, which is factually equivalent to decreasing the affinity of XylR for Pu, would favor the second scenario (i.e. meta expressed before 3 MBz appears), thereby suggesting that these proteins have a role to set a temporal order in activation of the TOL operons. Alas, the signals that trigger TurA and PprA activities are unknown 39 40 .

As mentioned above, expression of Pm/meta takes place through an uncommon process, in which the same regulator (XylS) operates either by itself at high concentrations or bound to 3 MBz, albeit at lower protein concentrations 24 . This is formalized by operatively considering 3 forms of the protein: inactive (XylSi), active by binding the inducer (XylSa) and active by hyperproduction (XylSh). This last protein form (which may not be a different protein species, but XylSi at high concentrations) causes what we call the XylSh loop, that links production of the meta pathway directly to the first input of the system m-xylene (Figure 5a). The logic of the circuit tells us that kinetics of this XylSh loop must intrinsically rule the timing of expression of the meta vs. the upper pathway, thereby accounting for the fine temporal tuning of Pm output. To clarify the significance of such a dual regulation of Pm by XylSa and XylSh we entered their absence/presence as variables of the TOL model. We implemented such in silico mutation by changing parameter inequalities for XylRa-dependent XylS expression and for the capability of high levels of XylS (i.e. XylSh) to activate Pm (see Table 1 and Methods section). These relatively small modifications were enough to inspect the behavior of the TOL network as shown in Figure 5b. The new parameter inequalities were implemented separately and the result of the simulations were compared to the wild-type network. The results shown in Figure 5c indicated that the expression levels of the meta pathway are lower in each separate TOL variant while the timing of Pm activation remains the same than the intact system.

The predictions above were tested with in vivo experiments in which we analyzed the induction kinetics of the Pm promoter using again the complete luxCDABE operon as reporter system. For this, a wild type strain of P. putida mt-2 harboring a plasmid with the Pm-luxCDABE fusion at stake was separately exposed to different inducers known to have distinct effects in the rest of the network. In one case, grown cells were exposed to m-xylene (formally equivalent to 3MBA employed before). This inducer not only does activate XylR (thereby triggering the XylSh loop) but it also makes m-xylene to be converted into 3 MBz through the action of the upper pathway, which leads to formation of XylSa (Figure 6a). In sum, m-xylene/3MBA originate both XylSh and XylSa. In a second case, the one inducer that was exogenously added was 3 MBz, which coverts XylS only into XylSa, i.e. the XylSh loop is not activated. Finally, Pm- luxCDABE cells were exposed to o-xylene. This is as good inducer of XylR as m-xylene, but it is not a substrate of the upper pathway 41 and thus cannot be converted into 3 MBz. This makes effector-less, overproduced XylSh the only possible activator of Pm. This simple choice of inducers causes a selective action of XylSa, XylSh or both on Pm, what faithfully mimics the effect of lacking each of these components of the circuit in the simulations above. Note that -given the volatile nature of m-xylene and o-xylene, we resorted to an in situ, non-disruptive method to record the response of the Pm-luxCDABE cells to these inducers. For this, the strains under examination were streaked in small sectors of M9-succinate plates and let grown overnight at 30°C. The plates with the patches of bacterial growth were then exposed to saturating vapors or m-xylene or o-xylene and the luminescent signals recorded every 30 min with a photon-counting device. To have a control that m-xylene and its non-metabolizable analogue o-xylene were equally able to trigger XylR activation under such experimental conditions, a Pu-luxCDABE fusion strain was subject to the same procedure as well.

As shown in Figure 6d, the expression profiles of Pu in response to both xylene species were virtually identical, as quantification of the signal intensities in both conditions gave nearly overlapping induction curves (Figure 6e). In contrast, the effect of each of these aromatics on the strain with the Pm-luxCDABE fusion was different, as o-xylene triggered a lower response than the metabolizable inducer. Quantification of signal intensities revealed that o-xylene-mediated Pm stimulation was ~20% of that brought about by m-xylene (Figure 7b). This figure reports the relative contribution of XylSh to Pm functioning but it does not tell us much about the XylSa-only counterpart. To tackle this, we examined the response of Pm to 3 MBz (i.e. caused only by XylSa) vs. the sum of XylSa and XylSh made happen by 3MBA. In this case, Pm-luxCDABE P. putida cells were inoculated in liquid M9/succinate medium, added with 1.0 mM 3 MBz or 1.0 mM 3MBA and the promoter activities monitored along the growth curve (see Methods). As shown in Figure 7c, maximal Pm induction by 3 MBz was ~25% of the expression level of the promoter in cells exposed to 3MBA, a percentage close to the same contribution of the XylSh-only loop.

The outcome of these in vivo experiments is that the Pm induction levels derived from each of the two forms of XylS are similar when acting separately but they become synergistic by >4-fold when working together (Figure 7d). This is mechanistically easy to explain, because overproduced XylSh can be converted to XylSa by exposure to 3 MBz. The XylSh loop thus ensures [i] that expression of the meta pathway is well underway before 3 MBz is formed through the action of the upper TOL pathway and [ii] that the lower route is boosted very significantly by 3 MBz. These in vivo results not only match the findings stemming from model simulations discussed above but also suggest that the rationale of the regulatory architecture of the TOL network is to maintain a good level of all products of the two operons at all times following exposure to m-xylene and thus avoid any transient accumulation of 3 MBz by first anticipating its production from m-xylene (the XylSh loop) and then by amplifying expression of the 3 MBz-degrading genes (i.e. the lower pathway) as soon as 3 MBz is formed. This regulatory device could have evolved to solve a metabolic conflict between the enzymatic modules encoded in the TOL plasmid and the indigenous metabolic network of the host, as argued below.

Formalization of each of the regulatory components of the TOL system (Figure 1) as binary logic gates and the assembly of the complete network as a digital circuit has been described before 17 . The streamlined scheme of Figure 2c was used as a guide to the formulation of equations for each of the regulatory and metabolic steps of the network. To this end, we adopted piecewise-linear (PL) differential equations 45 for describing the circuit dynamics as described 21 46 . The rationale of this approach is that production of metabolites in the model is determined by state equations, which define the metabolic reactions as the result of [i] the presence of substrates and [ii] the activation of a regulation function that encodes transcriptional and metabolic interactions. Under this scheme, a regulatory function accounts for the expression of a given gene and the production of the corresponding protein owing to the presence of an effector. Specific regulatory functions can thus be expressed as:

f i ( x j ) = k i * s + ( x j , Θ j )

This equation indicates that the synthesis of product i is a function of the presence of the effector j. In this equation, s+ is a step function, a Boolean operator that is set to a value 1 if the concentration of j (x_j ) is above a particular threshold (θ_j ), and to a value 0 if the concentration is below θ_j . The synthesis of i occurs at a rate determined by k_i only when x_j >θ_j , and does not take place if x_j <θ_j . In this case, j is an activator of the synthesis of i. By the same token, the effect of a repressor can be represented using a negative step function:

f i ( x j ) = k i * s - ( x j , Θ j )

which is set to a value 1 when x_j <θ_j , and to a value 0 when x_j >θ_j . On this basis, the production of a given component of the network as a result of the combined influence of different effectors can be written as, e.g.:

f i ( x j , x k ) = k i * [ s + ( x j , Θ j ) * s − ( x k , Θ k ) ]

where the appearance of product i is regulated by the activator j and the repressor k. Such a component i is synthesized only if j is present and k is absent. This is equivalent to a logic device (a logic gate) involving an AND/NOT operator (ANDN), taking j and k as inputs and producing i as output. In this way, it is possible to model all possible transcriptional and metabolic interactions in the system as logic constructs, determining the production of particular compounds as a function of the presence or absence of some of the others 47 . Furthermore, it is possible to set different thresholds for the concentration of a particular compound when it controls different synthesis rates at different concentrations. For instance, if effector j regulates the synthesis of A and B, we can set the constraint θ_j ¹ <θ_j ² , to indicate that synthesis of A is regulated by a lower concentration of j than the synthesis of B. These constraints are known as threshold inequalities 21 and are described below for the TOL system. Such threshold inequalities are related to the effective concentration of a given molecular species (e.g., a TF) above which it is able to have a regulatory effect on a target (e.g. promoter). In the case of TF-promoter pairs, inequalities are entered in the corresponding equations by means of a threshold value (θ_j ) which represents the relative affinity of the TF under consideration for one or more target promoters. The active concentration of each of the components is then determined by its production rate (expressed by k_i ), and its degradation rate (g_i * x_i ), which is a strictly positive function, proportional to the concentration of the compound. These simple expressions of positive and negative step functions were adopted for representing all possible regulatory interactions in the system. The resulting set of equations was then implemented with the GNA (Genetic Network Analyzer) software 21 . GNA models describe the evolution of the regulatory circuit by specifying qualitative constraints on the parameters of the system. This allows the model to be reliably run even if the actual threshold concentrations and the reaction rates at stake are not known. One set of constraints thus includes such threshold inequalities. A second type of constraints consists of the so-called focal inequalities that set the possible steady-state concentrations of the components in the system with respect to their threshold values, for instance:

z e r o < Θ i 1 < k i ∕ g i < Θ j 2 < m a x

This inequality indicates that when component i is produced at rate k_i and degraded with a rate constant g_i , so that its concentration converges towards the level k_i/g_i 45 , it exceeds the threshold θ_i ¹ , but not θ_i ² . This allows an estimate of the concentration of the components in reference to their threshold values, even in absence of quantitative information on the parameters of the system. The inequalities for the TOL model were set as shown in Table 1.

It is possible to follow the dynamics of the regulatory network by computing a temporal progression of so-called qualitative states, each consisting of the levels of the concentration variables with respect to their thresholds. In each qualitative state the trend of the concentration variables (increasing/decreasing/steady) determines the possible transitions to successor states. The resulting directed graph of qualitative states and transitions between qualitative states is called a state transition graph (for a more detailed description, see 21 46 . Note that the PL equations above and the associated transition graph describe the temporal order of signal propagation in the network when the first input signal is present and the system moves toward a steady state (where the concentrations of the components stop to change). The actual time interval during which the system remains in a state before reaching the next is not contained in these qualitative models. However, the representation reliably predicts the temporal ordering of states, and thus the consecutive changes in the levels of each of the components of the network.

Using the biological assumptions for known regulatory interactions (Figure 1) and the resulting logic operations (Figure 2c), we defined four PL equations describing XylR, XylS, upper and meta production (Table 1). The sole input for the system was m-xylene, which was defined as an input variable i.e. one having a constant concentration along the simulations, 21 . For implementation of in silico mutations, we changed threshold inequalities as follows. In one case Pm activation was simulated in the absence of the XylSh loop by setting the parameter θ² _XylSh to be higher than the maximal concentration reachable upon Ps activation (No XylS hyper-expression condition, Table 1). Similarly, simulation of the Pm activation event in a scenario lacking XylSa, we set the upper pathway not to produce enough concentrations of 3 MBz for creating XylSa (No XylSa condition, Table 1). Consideration of different threshold inequalities in the TOL model allowed us to simulate the specific conditions as discussed in the Results section.

The activity of the TOL promoters in response to inducers was examined with different procedures depending on the nature of the specific chemical tested. In case of soluble inducers (3MBA and 3 MBz), overnight grown P. putida cells harboring the reporter plasmid under examination were diluted 1:20 in fresh minimal media with the inducer of interest at a final concentration of 1 mM. 200 μl aliquots (with four replicates) of the thereby diluted cells were placed in 96-well Microplates (Optilux™, BD Falcon) and incubated in a Wallac Víctor II 1420 Multilabel Counter (Perkin Elmer) at 30°C, the optical density at 600 nm (OD₆₀₀) and the bioluminescence being recorded every 30 min. Promoter activity was quantified by normalizing bioluminescence in respect to cell density (i.e. bioluminescence/OD₆₀₀). For testing volatile inducers (m-xylene and o-xylene), single colonies of P. putida clones bearing the reporter plasmids indicated were patched on M9/citrate agar plates, grown overnight an exposed to saturating vapors of a 1 M inducer solution in DMSO. Non-disruptive monitoring of promoter output was carried out with a VersaDoc™ Imaging System (BioRad) and the results processed with the ImageJ software (http://rsbweb.nih.gov/ij

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