Deconvolution of gene expression noise into physical dynamics of upstream promoters

Abstract

Gene expression noise is not only the mere consequence of stochasticity, but also a signal that reflects the upstream physical dynamics of the cognate molecular machinery. Soil bacteria facing recalcitrant pollutants exploit noise of catabolic promoters to deploy beneficial phenotypes such as metabolic bet-hedging and/or division of biochemical labour. Although the role of upstream promoter-regulator interplay in the origin of this noise is little understood, its specifications are probably ciphered in flow cytometry data patterns. We studied Pm promoter activity of the environmental bacterium Pseudomonas putida and its cognate regulator XylS by following expression of Pm-gfp fusions in single cells. Using mathematical modelling and computational simulations, we determined the kinetic properties of the system and used them as a baseline code to interpret promoter activity in terms of upstream regulator dynamics. Transcriptional noise was predicted to depend on the intracellular physical distance between regulator source (where XylS is produced) and the target promoter. Experiments with engineered bacteria in which this distance is minimised or enlarged confirmed the predicted effects of source/target proximity on noise patterns. This approach allowed deconvolution of cytometry data into mechanistic information on gene expression flow. It also provided a basis for selecting programmable noise levels in synthetic regulatory circuits.

Introduction

Information processing inside bacterial cells in response to physicochemical stimuli requires regulatory cascades to propagate input/output signals effectively. This process typically involves several steps in which transcription factors (TF) interact with promoters to trigger gene expression responses. These interactions occur stochastically rather than deterministically^1–5, leading to specific and variable noisy signals. The customary view considers this effect the necessary result of random fluctuations of regulatory elements present in short supply in individual cells⁶. The dynamic properties of promoter activation have a determining influence on expression noise range and intensity^7–9.

Single-cell technologies^10–12 has helped to clarify various mechanisms behind noise generation. A major noise source in virtually every prokaryotic promoter is the so-called bursting effect^{13, 14}, a pulse-like activity that results largely from discontinuous topological changes in DNA caused by RNA polymerase progression through DNA^{15, 16}. Different in vivo noise generators can be measured by fluorescence distribution in single cells, which can be followed by cytometry¹⁷. Cell cytometry profiles bear embedded information on the mechanistic origin of the gene expression noise, but it remains unclear how these data can be retraced to the physical TF-promoter dynamics that produces this fluorescence distribution.

The Gram-negative soil bacterium Pseudomonas putida mt-2 provides an excellent model for responding to these questions. This microorganism can thrive in sites polluted with aromatic chemicals¹⁸ such as m-xylene (m-xyl), because of a complex metabolic and regulatory network encoded in its single-copy TOL plasmid pWW0¹⁹ (Figure 1A). The noise from each of the four promoters seems to be precisely controlled, giving rise to metabolic diversification²⁰. This allows a fraction of the cells in a population to explore new nutritional landscapes without risking communal collapse^{20, 21}.

Figure 1. Structure of the TOL network borne by plasmid pWW0of Pseudomonas putida mt-2 with Pm promoter as output.

A. As shown, m-xylene is first converted to 3-methylbenzoate (3MBz) through the action of the enzymes encoded by the upper TOL pathway; this compound is further processed by the activity of the lower, and the resulting intermediates are metabolised in the tricarboxylic acid (TCA) cycle. XylR and XylS are transcriptional regulators, whereas Pu, Pm, Ps and Pr are promoters. The master regulatory gene xylR controls expression of both the upper pathway and the second transcription factor, XylS, which is encoded in a location adjacent to the end of the lower operon.. This regulatory architecture has a decisive role in Pm activation dynamics, as the levels of its cognate activator (XylS) vary depending on the inducer. In one case, 3MBz activates those XylS molecules found in low numbers in the cell due to leaky Ps promoter expression. This results in the active form of the protein, termed XylS^a, which is able to bind and activate Pm. In the second case, m-xylene (m-xyl) causes both XylS overexpression (due to Ps activation by XylR) and intracellular production of metabolic 3MBz (due to Pu-driven activity of the upper pathway operon)… B. Abstracted Pm activation as an OR logic gate. Pm activity will be triggered by using either 3MBz or m-xyl as the inducer. C. m-xyl leads to a higher concentration of XylS^a (XylS overexpression and intracellular generation of 3MBz) than externally added 3MBz (use of only leaked XylS moecules). This difference is the key feature for decoding Pm output

The noise of the TOL network Pu and Ps promoters is explained by the small number of molecules of their regulatory protein XylR²²; however, that of Pm, which controls the lower operon of the TOL pathway in response to 3-methylbenzoate²³ (3MBz) is puzzling. This promoter can be activated by two separate mechanisms, [i] low intracellular concentration of its regulator, XylS, bound to its effector, 3MBz, or [ii] m-xyl-induced XylS overproduction with no 3MBz involvement (Figure 1A). When these conditions coincide (i.e., high XylS levels and presence of 3MBz), Pm activity is very high^{24, 25}. Therefore, Pm function is that of an OR logic gate (Figure 1B) where either input, 3MBz or m-xyl, can be used to trigger its activity. The puzzling feature of the Pm regulatory node is that the Pm noise pattern varies greatly depending on the induction mode. We analysed whether cell cytometry data for transcriptional Pm-gfp fusions could be decoded into information on the physical dynamics of promoter activation, including clues to XylS/Pm regulatory node spatial arrangement.

A combination of modelling and wet experiments shows these noise regimes can be changed by regulator numbers and the spatial arrangement of regulatory components. These predictions were validated in cells engineered to minimise the distance between the XylS source site and Pm location.

Results

Two distinct noise regimes define Pm output

The activity of the TOL plasmid promoter Pm (Figure 1) can be induced by exposing P. putida mt-2 to one of two inputs. The first input, 3MBz, activates the XylS molecules leaked from a non-active Ps promoter. The second, m-xyl, is converted metabolically inside cells by the upper TOL pathway enzymes to 3MBz. In addition, the latter scenario leads to XylS overproduction since m-xyl triggers the activity of the Ps promoter via the XylR regulator. Therefore, the input m-xyl leads to a higher concentration of activated XylS molecules (XylS^a) than 3MBz (Figure 1C). Although the Pm/XylS node of the TOL network is often abstracted as a binary switch with only ON/OFF states, the unique noisy nature of Pm output invalidates this view and highlights the role of signal variability²⁶.

The P. putida mt-2-Pm, strain derives from the natural P. putida mt-2 isolate bearing the TOL plasmid pWW0, but was engineered to bear a transcriptional Pm-gfp fusion in its chromosome (Table 1 and Fig. 2A). This strain has its sole XylS source in the pWW0-encoded gene, which is expressed through the TOL plasmid Ps promoter (see Figure 1 and Methods), and the XylS target, the encoded Pm-gfp, in the chromosome. Because of this arrangement, the DNA region that encodes and supplies XylS transcriptional regulators is not adjacent to the target promoter, from which it is physically separated in trans. Differences in Pm expression regimes depend on whether the XylS/Pm regulatory node is induced with m-xyl or 3MBz (Figure 2A), as shown by flow cytometry results of promoter activity (Figure 2B, C). Induction with m-xyl (XylS overproduction and intracellular 3MBz production) leads to a situation in which the output signal noise range allows a null overlap between ON (uninduced) and OFF (induced) states. In contrast, induction with exogenous 3MBz (low XylS) left the OFF state unaffected while producing an ON state in which the noise regime consisted of a broad, plateau-like distribution from the lowest to the highest intensity value. The output ON signals are patently different in both cases, suggesting that they originate in a different type of TF-promoter interplay beyond randomness. We measured the noise produced by leaky XylS expression (no Ps activity, Figure 2C) and that of the full XylS production (Ps activity, Figure 2B). The former scenario, while very noisy, does not depend of upstream nodes. The latter does depend on upstream nodes, but does not generate noisy patterns. Altogether, we can assume that upstream Pm nodes are not a source of noise in our setup. Therefore, we focus our study in Pm-gfp kinetics and TF-promoter dynamics.

Table I. Bacterial strains and plasmids used in this study.

Bacterial strain or plasmid	Relevant characteristics	Reference or source
Strains
Escherichia coli CC118□pir	Cloning host; Δ(ara-leu) araD ΔlacX174 galE galK phoA thiE1 rpsE rpoB(Rif) agrE(Am) recA1 λpir lysogen	(Herrero et al., 1990)76
HB101	Helper strain; F- λ- hsdS20(rB- mB-) recA13 leuB6(Am) araC14 Δ(gpt-proA)62 lacY1 galK2(Oc) xyl-5 mtl-1 thiE1 rpsL20(Smr) glnX44(AS)	(Boyer and Roulland-Dussoix, 1969)77
Pseudomonas putida
KT2440	Wild-type strain; mt2 derivative cured of the TOL plasmid pWW0	(Nelson et al., 2002; Bagdasarian et al., 1981)78,79
mt-2	Wild-type strain bearing pWW0 plasmid	(Worsey and Williams, 1975)80
mt-2-Pm	Gmr. P. putida KT2440 inserted in its genomic attTn7 with the hybrid mini-Tn7 delivered by plasmid pBG-Pm (Supplementary Figure S6)	This study
KT-BGS	Gmr. P. putida KT2440 inserted in its genomic attTn7 with the hybrid mini-Tn7 delivered by plasmid pBGS (Supplementary Figure S6)	This study
Plasmids
pRK600	Cmr. Helper plasmid used for conjugation; oriV ColE1, RK2(mob+ tra+)	(Kessler et al., 1994; Keen et al., 1988)67,81
pTnS-1	Apr, oriR6K, TnSABC+D (Tn7 transposase) operon	(Choi et al, 2005)82
pBG	Kmr, Gmr, oriR6K, mini-Tn7 delivery vector; Tn7L and TnR bracketting a mobile DNA segment for engineering standardised BCD2-msf GFP reporter fusions (Supplementary Figure S6)	(Zoebel et al., 2015)83
pBG-Pm	Kmr, Gmr, oriR6K. pBG inserted with Pm promoter and thus bearing a standardised Pm-gfp fusion	This study
pSEVA228	Kmr, oriRK2, xylS/Pm expression system	(Martínez-García et al., 2014)66
pBGS	Kmr, Gmr, oriR6K, pBG inserted with the xylS/Pm module of pSEVA228 and thus bearing the TF adjacent to the same standardised Pm-gfp fusion as in pBG-Pm	This study

Figure 2. Variable noise patterns depending on input signal in P. putida mt-2-Pm strain.

A. In these experiments, XylS molecules are produced by the TOL plasmid borne by the P. putida mt-2-Pm, whereas the target Pm-gfp reporter fusion is inserted in the chromosome (see Methods); that is, the source of the TF and its target promoter are non-adjacent and encoded in separate mono-copy replicons (i.e., TOL plasmid and chromosome). B. In cells alone or in the presence of m-xyl (m-xylene), the Pm promoter activity recorded (based on green fluorescent protein intensity) can be abstracted as a binary switch with a 0 or OFF state and a 1 or ON state. Flow cytometry results show this behaviour, where the noise range allows a null overlap between 0 and 1 (termed 1a to differentiate it from the following). C. Using 3MBz as the inducer again provokes switch-like behaviour in Pm, with 0/OFF and 1/ON states. As the cytometry results show, the noise range is much wider here, from maximum expression to the minimum (ON state thus called 1b).

Noise deconvolution and rate optimisation

The regulatory node formed by the pair XylS-Pm can be modelled according to the kinetic rates in Figure 3A. The regulator in its active form, XylS^a, binds Pm (k₁, molecules^-1hour^-1) to fire its activity and unbinds it (k_-1, hour^-1) back to the default silent state. When bound, mRNA molecules are transcribed (k₂, hour^-1) from the downstream gene, gfp, which produce proteins through translation (k₃, hour^-1). Even when the regulator is not bound, there is some leakage of basal Pm transcription (k₆, hour^-1). To complete the model, we included degradation rates for mRNA (k₄, hour^-1) and GFP (k₅, hour^-1).

Figure 3. Rate optimisation according to output-state fitness and binding sensitivity.

A. The Pm promoter studied here and the rates involved in the model. XylS^a in its active form is the activator of the inducible promoter. The Pm^a complex refers to the promoter with the bound regulator. Rates k₁ and k_-1 correspond to binding and unbinding events, respectively. Transcription, k₂, translation, k₃, degradation rates, k₄ and k₅; the basal transcription rate is represented by k₆. B. The two fitness parameters (conditions) used in the optimisation process to select values for the rates: wide-rage signal going from basal to full expression, and plateau-shaped distribution with roughly the same number of cells representing each value in between. C. Simulated signals under the same rate values but different TF numbers: 200 (3MBz case, up) and 3000 (m-xyl case, bottom) with flow cytometry signals shadowed for comparison. D. Several time-course simulations are shown in which the Pm promoter is exposed to three concentrations of its regulator, XylS^a: 10 (null induction, thus basal, yellow line), 200 (low induction, green line) and 3000 molecules (high induction, purple line). Centre; the graph corresponds to the rates established in Figure 3C, with k₁ = 0.004 and k_-1 = 1.5. Top, k₁ increased to 250%. Bottom, k₁ reduced to 40% its original value. Left, k_-1 at 250%. Right, k_-1 at 40%.

Our goal was to find those values for the rates that allow Pm to produce different noise regimes depending on the inducer used. To this end, we considered a training vector θ with the rates mainly responsible for Pm dynamics, defined as follows: θ = (k₁, k_-1, k₂, k₃, [XylS^a]), where [x] (molecules) denotes number of molecule x. Basal activity (k₆ = 15) and degradations (k₄ = 10, k₅ = 2) were specified within standard ranges for mathematical analysis^27–31 (see Methods). To identify the set of values that best simulated the experimental output, we defined two fitness parameters (f) based on the ON state produced by 3MBz (Figure 2C), wide-range signal (f₁) and plateau-like surface (f₂) (Figure 3B). An optimisation process (see Methods) yielded vector θ_f = (0.004, 1.5, 900, 80, 200). Strong expression kinetics (transcription + translation) are needed to produce high signal intensity (requirement for f₁), while low binding/unbinding rates guarantees affinity instability and thus helps generate the final plateau-shaped distribution (f₂). These values produce the broadest range signal possible while assuring flatness which resembles the ON state induced by 3MBz (Figure 2B). To test whether the noise regime observed in the ON state during m-xyl induction could be reproduced, we carried out stochastic simulations (see Methods) in which the number of XylS^a molecules was increased while vector θ_f rates were untouched; this concentration was fixed at [XylS^a] = 3000 molecules, which reproduced the m-xyl-induced ON state (simulations in Figure 3C). The balanced relationship of the two quantities, 200 and 3000,is based on qualitative observations³². Although some rates may have unusual values e.g. low binding, it is important to take into account that these are the output of the optimisation process. Therefore, they are information-rich from a mathematical standpoint since they indicate where the model needs further analysis. During the present study, more realistic rates^{33, 34} will be investigated (while maintaining system output) under more complex scenarios than mere time-based approaches.

We observed that Pm activity or its in-silico counterpart θ_f, is very specific; in other words, changes in certain rates can cause incorrect promoter function. As an example, the stability of the system at variable binding and unbinding rates is shown in Figure 3D. The vertically aligned graphs in the figure shared the value for k_-1, while that for k₁ was increased to 250% its original value (top graph) or decreased to 40% (bottom). The same ratios were applied to the changes in k_-1 in the horizontal simulations, for which k₁ was constant (left, right). When these key rates were altered, the ideal behaviour (centre, maximum differential variability of DV =11.7) was no longer maintained.

A stress analysis on the model tested its robustness to rate variation. GFP degradation rate (k₅) was gradually decreased from 2.0 to 0.7 to render the protein more stable; affinity rates (k₁ and k_-1) were increased (up to 0.64 and 24.0, respectively) to analyse different TF-to-promoter behaviour (Supplementary Text S1). In all cases an adjustment of XylS^a numbers for high and low induction (maintaining the 3000-to-200 ratio previously optimised) was sufficient to restore system function. Additionally, we performed a multi-agent simulation (Supplementary Figure S1) to include [i] XylS^a entry and degradation rates, [ii] molecule dilution upon cell division and [iii] extrinsic noise (see Methods). A decrease in the unbinding rate was enough to reproduce the noise patterns under this new scenario. That indicates that dilution is not a decisive source of noise. Moreover, both Ps and Pm double their copy number (from one to two) just before division, so potential effects due to dilution are mitigated by a synchronous increase/decrease in both regulators and promoters. Altogether, the above information, plus a more general simulation of the full TOL network (Supplementary Text S2) suggested that for a given possible set of rates, as θ_f, the model for Pm expression depends crucially on the number of TF molecules to produce the observed behaviour. We now analyse these considerations in detail.

System sensitivity to alterations in the number of transcription factor

Simulations of the Pm response to gradual changes in regulator numbers showed our estimated XylS^a figures for both ON states (200 and 3000 for 3MBz and m-xyl, respectively) were optimal for maximising differences between the two expression noise regimes (under θ_f). The simulated Pm transfer function indicated the signal range and mean value at a given XylS^a concentration (Figure 4A). Unlike other reported promoter transfer functions^35–37, by which transcriptional activity produces similar noise (error bars in graphs) regardless of regulator concentration, here the central section of the curve shows a wider noise profile than the remainder. Indeed, the noise ranges reach maximum and minimum levels at ~200 and 3000 XylS^a molecules, respectively. Such wider noise at intermediate induction has been observed^{38, 39} for gradients of one single input. However, the noise patterns of our system are controlled by two distinct inputs, yet one regulator, which makes it dynamically unique. The simulation in Figure 4B shows the system tested in continuous function in which the inducer is changed sequentially. Pm activity suggests a trinary (rather than binary) signal, with three states: one OFF and two ON, each state with a distinct shape that unequivocally recalls its input. There is thus a direct correlation between the time intervals of the bursting effect and the max-min distance (amplitude) of the resulting gene expression levels. Furthermore, such a signal could be of potential use for multi-valued genetic logic circuits beyond the mere binary (0/1) abstraction^{40, 41}.

Figure 4. Analysis of Pm activity noise relative to regulator dynamics.

Study of simulation sets in which regulator number is the only parameter changed. A. Pm transfer function, which measures the output level resulting from different input values. Whereas the average value (red line) shows no additional relevant information, the noise produced by the signal (blue error bars, which denote max-min signal values) displays distinct behaviour according to input numbers, with wider range at middle concentrations. B. Number of GFP molecules over time while input changes (3MBz, m-xyl or none). The three logic values of the signal (‘0’, ‘1a’ and ‘1b’ in Figure 2B, C) are wide-range noise (0-20 h and 40-60 h), small-range high-level noise (20-40 h, 60-80 h) and small-range low-level noise (80 h onwards). C. 24 h simulations at different XylS^a levels (from 0 to 3000 molecules) were used to measure 1) the cumulative pulse duration, which corresponds to the length of time that the Pm promoter is in the ON state (regulator bound to the DNA) and 2) signal amplitude, defined here as the the maximum difference (in molecules) between the highest and lowest values achieved during the simulation (measured in steady-state).

Two further analyses that link regulator dynamics with output noise are shown in Figure 4C. They must be interpreted in terms of the pulsing transcriptional bursts that frame the prokaryotic promoter activity. Two measurements, cumulative pulse duration and signal amplitude, were monitored in 24-h simulations of the system at several XylS^a numbers (Figure 4C). Cumulative pulse refers to the core of the bursting effect, the total time that Pm is in its active state when XylS^a is bound to it. Total XylS^a residence time on Pm increased with the number of regulator molecules, which indicated that the ON state produced during m-xyl induction corresponds to large numbers of XylS^a molecules. Signal amplitude, the difference between the highest and lowest output values of a single simulation run, decreased except in the interval in which the number of XylS^a molecules was in the range ∈ [0, ≃150], when the distance between the uppermost/lowermost signal increases. The cognate inflexion point can thus be explained as the number of XylS^a molecules that brings about the ON state during 3MBz induction. The fact that such inflection point occurs at low regulator levels (direct consequence of the rate values used) matches our intuition since the inducer 3MBz will activate the only XylS molecules leaked from a silent Ps promoter.

Influence of intracellular regulator-promoter proximity on transcriptional output

Based on these findings, we asked whether the low-noise regime produced by m-xyl induction would be generated if 3MBz were the only input. When we interrogated the model with this question, the answer was positive when and only when 3MBz co-occurs with large numbers (3000) of the regulator XylS^a. Although this condition would appear impossible to achieve since m-xyl, and not 3MBz, is needed to stimulate XylS^a production (see Figure 1), we must consider the possible spatial effects of XylS^a molecules. In the initial zero-dimensional model, it is assumed that each regulator is able to bind its target promoter at a given fixed rate (thus only time-based), as if it were a pure chemical reaction. When measuring living cells (as in Figure 2), one must consider that due to imperfect diffusion caused by molecular crowding and non-homogenous microviscosity^{42, 43}, not all regulators are equally effective in reaching and binding cognate target DNA sequences. A specific regulator will not interact with its promoter if they cannot meet, since its access to the target promoter will be limited by the ease of diffusion towards the physical Pm location.

To examine this possibility, we simulated protein trajectories^{33, 44, 45} inside a cell, following Brownian motion^{43, 46, 47}. Figures 5A and B record the trajectories of regulator molecules (XylS^a) being expressed from what we term the source region: the physical Ps promoter location from which xylS is expressed. Given the coupling of transcription/translation processes in prokaryotic gene expression^48–50, it is safe to assume that the TF protein is produced in close proximity to the Ps-xylS promoter gene pair (Figure 1). To trigger transcription, XylS^a must migrate to a physically separate target site where Pm is located; Figure 5A and B illustrate two possible scenarios, which diverge only in the number of proteins stemming from the source region. If regulator numbers are low, there are necessarily empty locations within the cell that XylS^a may not encounter easily. Should Pm be located in one such regulator-empty sector, a productive contact is physically impossible, which leads to an OFF promoter state.

Figure 5. Effects on promoter activity of its distance from regulator source.

A. Left: spatial distribution of simulated proteins following Brownian movement in a cell-like compartment with high protein occupancy. Each coloured line inside the cell represents a protein trajectory from its source (in the middle of the space; labelled S) to its final position at a given time. Density of trajectory positions in each section (longitudinal and transversal) is shown in side graphs. Right: final protein position and their distribution in side graphs. B. Left: simulated spatial trajectories (colour lines) under low protein occupancy. Desnsity of trajectory positions in each section (longitudinal and transversal) is shown in side graphs. Two zoom-in regions (source S and target T) with distinct trajectory points occupation are displayed in detailed. Right: stochastic simulations of Pm-gfp activity with k₁ = 0.5 and k_-1 = 50 under basal, 200 TFs (blue) and variable TFs (green) conditions. The latter reproduce the noise pattern of 3MBz induction with the new rates and spatial-based constraints.

When this situation is scaled up to several thousand bacteria, each individual target region could accommodate a different number of regulators ranging from all to none, leading to pronounced cell-to-cell variability. In contrast, when many regulatory proteins originate in the source region, there are few empty areas in the intracellular space and the variability range narrows. Protein distribution at any given time does not necessarily match trajectory distribution (Figure 5A), meaning that the trails of the regulators are more space-dependent than their spread. As a result, the apparent binding rate, k₁, in reality combines promoter-TF affinity proper (the ability of the two molecular partners to interact physically) with the probability that the regulator is located near the promoter (availability). In our initial time-based kinetic model, it was not possible to obtain both expression noises with usual parameter values, for instance, k₁=0.5 and k_-1=50. Using such parameters in a simulation with 200 TFs (corresponding to 3MBz induction) returned a unimodal distribution (Figure 5B, right) that was far from the noisy pattern observed experimentally (Figure 2C). The initial optimisation process returned a binding value of k₁ = 0.004, unrealistic yet necessary to reproduce the observations. That was because all TFs were available to bind at any time i.e. the number of XylS^a was fixed for a single simulation run. However, by taking a spatial-based approach, where the number of TFs was variable during the stochastic simulation, we restored system function even with k₁=0.5 and k_-1=50 (Figure 5B, right). To that end, the spatial Brownian-motion simulation updated the Gillespie algorithm with the number of TFs that crossed a specific target region at given time-points (see Methods). This generated a crucial fluctuation in the availability of TFs that could bind Pm. The source-target distance becomes then a decisive parameter.

Upon the inclusion of spatial dynamics in time-based kinetics, the distinction between the absolute number of TFs and the trajectory points becomes unavoidable. Since a given TF would bind/unbind more than once⁵¹, it seems coherent to talk about TF crossings in a particular region when referring to the availability parameter described above. That value would be obviously higher than the actual number of TF molecules present in the cell. In our study, we match time-based absolute TF numbers (Figure 3C) with spatial-based trajectory points (Figure 5B).

Physical proximity between Pm and XylS decreases transcriptional noise

In the experimental setting that showed the differences in Pm noise (Figure 2), the promoter and its regulator were placed at distant locations within the cell. This was done by placing the Ps promoter for xylS expression and the reporter Pm-gfp fusion in different replicons, the P. putida mt-2-Pm TOL plasmid and the chromosome, respectively (see Methods). A key interpretation of the simulations is that physical proximity between genomic sites bearing the Ps-xylS and Pm-gfp DNA segments would result in better Pm occupation at lower XylS concentrations, and thus in reduced GFP expression noise.

To test this prediction, we positioned the Ps-xylS and Pm-gfp sequences within the frame of a mini-Tn7 transposon vector (see Methods), which was delivered to the single attTn7 site of P. putida KT2440 (identical to P. putida mt-2 without the TOL plasmid) to generate a strain termed P. putida KT-BGS (Table 1). In these engineered bacteria, the two components of the regulatory device (Ps-xylS/Pm-gfp) were designed to be adjacent, in monocopy and at a fixed chromosomal site, with an artificially minimised distance between TF source and promoter target regions (Figure 6A).

Figure 6. Pm promoter activity influenced by its distance from regulator source.

A. Left: physically rearranged XylS/Pm regulatory node engineered in P. putida KT-BGS (Table 1) to maximise proximity between source (XylS production via Ps promoter) and target (Pm). Both promoters were inserted adjacent to each other into the chromosome of strain KT2440, from which the TOL plasmid was removed (see Methods). Right: flow cytometry results with P. putida KT-BGS cells. As predicted by the model, use of 3MBz as inducer with minimal distance between source and target (top, in green) gives results similar to use of m-xyl as inducer of the reference P. putida mt-2-Pm strain (Figure 2B). Bottom, 3MBz induction in P. putida mt-2-Pm cells, where the TF source and the target promoter are not adjacent. B. Quantitative PCR to measure mRNA molecules transcribed from xylS shows similar Ps promoter activity in both strains, uninduced or 3MBz-induced. C. Visualisation of the single-copy TOL plasmid (J. Kim) At division, the TOL plasmid replicates itself using its own machinery.

We then carried out flow cytometry measurements of 3MBz induction in the P. putida KT-BGS strain as for the reference P. putida mt-2-Pm strain (Figure 6A, top). For the sake of comparison, Figure 6A (bottom) reproduces the information for 3MBz-induced P. putida mt-2-Pm (from Figure 2C). The proximity of Ps-xylS to Pm-gfp in P. putida KT-BGS results in a 3MBz response that delivers a much narrower noise regime at high GFP intensity values. The fluorescent signals of 3MBz-induced P. putida KT-BGS (in which xylS expression is low but spatially proximal to Pm, Figure 6A) were indistinguishable from those of m-xyl-induced P. putida mt-2-Pm (in which XylS expression is high but distant from the Pm target promoter).

According to simulations, for the P. putida KT-BGS strain, Ps-xylS proximity to Pm-gfp yields a larger number of regulators in the local molecular environment of Pm, which are thus available for binding. The uninduced performance is null in both strains (Supplementary Figure S2) pointing out that XylS molecules alone do not trigger Pm activity. It has been reported that a high concentration of non-active XylS molecules would, in principle, induce Pm⁵². However, that scenario is not applicable to our study. Not even in KT-BGS where XylS molecules are more abundant in the proximity of Pm.

To ensure that the modifications in P. putida KT-BGS did not distort the physical structure of the bacteria⁵³, we compared the size and complexity of individual cells to those of the P. putida mt-2-Pm counterpart, in which Ps-xylS and Pm-gfp are separated. The two strains were virtually indistinguishable, with no important differences in physical quality (Supplementary Figure S3). We compared Ps promoter activity in mt-2-Pm and KT-BGS strains by quantitative PCR, which showed similar levels of XylS molecules in response to 3MBz, (Figure 6B); growth curves validated strain comparability (Supplementary Figure S4). Visualisation of the TOL plasmid (Figure 6C, see Methods) allowed us to confirm its single-copy nature, thus comparable to the single copy Ps insertion in the chromosome.

It has been recently suggested that molecular crowding effects inside bacteria lead to a non-homogenous intracellular space⁵⁴. This spatial heterogeneity adds complexity to the abstract cell compartment of Figure 5 and would cause an uneven diffusion of molecules. To analyse the simulation effects resulting from local environments with different diffusion specifications (see Methods), we included regions where the Brownian motion was slowed down (Supplementary Figure S5). The presence of low mobility regions facilitated TF accumulation and help regulator numbers increase in highly-condensed areas. This scenario matched the physical architecture of P. putida KT-BGS, in which the target region was inserted into the chromosome, presumably a crowded environment with restricted mobility.

The noise-dependence of promoter-to-regulator distance is likely to increase if the TF is very unstable, as appears to be the case for XylS⁵⁵. These data identify a function within the intricate architecture of the regulatory network that governs biodegradation of m-xylene in Pseudomonas. Future work on this line would focus on re-arranging network components across different genome locations and/or vary their copy number to establish universal spatial-dependent design rules. Moreover, it is worth studying in detail the complex motility of molecules inside crowded regions of the cell⁵⁶ in order to develop more accurate spatial predictions.

Discussion

Intracellular signals are transmitted according to specific dynamics of the components involved in their transfer. These communications are therefore endowed with precise information, whose decodification promises valuable insights into cellular kinetic and structural properties⁹. Signal variability, commonly referred to as gene expression noise^{4, 5}, constitutes the fingerprint of such transmission, and thus the target data to be interpreted. In the case documented here, the expression signals produced initially by the Pm promoter activity in P. putida^{19, 22, 23} lead to highly specific, stable noise patterns depending on the stimulus to which the cells were exposed.

Using mathematical modelling and computational analysis, we deconvoluted the flow cytometry data for each setting to describe the kinetics that could reproduce that behaviour. As a result, the kinetic values that fit the experimental observations highlight the importance of the bursting-specific rates, binding and unbinding^13–16, where each of these values influences the final promoter activity distinctly. We pinpointed how the dynamics of Pm-regulator interplay determines gene expression by including spatial effects, in particular protein distribution, within a cell. Our model, validated by the experiments shown above, indicates that the physical distance between the regulator source and the target promoter is translated into specific noise patterns that change radically depending on promoter-TF proximity. This is due to the fact that regulators, or rather their trajectories (Figure 5), are not distributed homogeneously⁵⁷ and TF are thus more likely to meet the promoters they regulate if located near the source⁵⁸. This concept was hypothesized by Ten Wolde to explain the frequent genomic association of TF and target promoters as an evolutionary remedy to an excess of noise^{59, 60}. In contrast, our analyses raise questions as to whether gene expression noise caused by a non-homogeneous intracellular matrix is an adaptive trait that endows regulatory networks with specific properties. We show that changing the spatial positioning of components, Pm noise patterns can be altered, which opens the opportunity to use one expression profile or another depending on needs. As one Pm activity regime is much more variable than the other, it might well have been co-opted evolutionarily to create phenotypic heterogeneity within a population to increase its metabolic or else fitness^{61, 62}. The other regime, full-expression and low variability could be used, for example for decreasing phenotypic diversity of a clonal population of productive cells⁶³.

Our data also offer a new challenge for engineering non-native regulatory circuits or, more generally, synthetic genetic implants in the genomic and biochemical chassis of a bacterial cell^{36, 41, 64}. Each gene sequence and each protein (including TF) might need a specific physical address in the spatial frame of a cell for optimal performance, a question that is rarely considered in contemporary synthetic biology and which deserves more attention. Finally, our results add a new perspective to the much-debated generality of transcription/translation coupling in prokaryotes^48–50, as the noise regime of promoters is certainly influenced by whether their cognate TF are generated near the genes that encode them or whether they must migrate to other cell sites.

Materials and Methods

Bacterial strains, growth conditions and genetic constructs

Bacterial strains and plasmids used are listed in Table 1. Escherichia coli cells were grown at 37ºC in LB medium and used as hosts for cloning procedures. Pseudomonas putida cells were incubated at 30ºC in M9 minimal medium supplemented with 2 mM MgSO₄ and 20 mM citrate as sole carbon source⁶⁵. When needed, gentamycin (Gm; 10 µg mL^-1), kanamycin (Km; 50 µg mL^-1), ampicillin (Ap; 150 µg mL^-1) and chloramphenicol (Cm; 30 µg mL^-1) were added to growth media. Reporter strain P. putida mt-2-Pm is the original TOL plasmid pWW0-containing P. putida mt-2, which was inserted in the single attTn7 site of its genome with a Pm-gfp transcriptional fusion. The Pm promoter sequence was amplified from plasmid pSEVA228⁶⁶ as a 122 base pair (bp) PacI/AvrII fragment with primers 5’TTAATTAAGGTTTGATAGGGATAAGTCC3’ and 5’CCTAGGT CTGTTGCATAAAGCCTAA3’, and cloned into the mini-Tn7 promoter-calibrating vector pBG (Zoebel et al., 2015). The organization of this vector (Supplementary Figure S6A) is such that inserting promoter-bearing PacI/AvrII originates a standardised translation/transcription fusion that minimises any effect of the non-translated 5’ end of the reporter transcript in the final GFP readout. Cloning the Pm promoter in pBG generated mini-Tn7 delivery vector pBG-Pm (Supplementary Figure S6B). This construct was then mobilised to pWW0-containing P. putida mt-2 strain by tetra-parental mating⁶⁷. Finally, Gm^R exconjugants were verified for insertion of the hybrid mini-Tn7 transposon (bearing the Pm-gfp fusion) in a specific orientation at the attTn7 site by amplifying the genomic region of interest with diagnostic PCR using primer pairs 5-Pput-glmS UP 5’AGTCAGAGTTACGGAATTGTAGG3’/3-Tn7L (5’ATTAGCTTACGACGCT ACACCC3’ and 5-PpuglmS DOWN 5’TTACGTGGCCGTGCTAAAGGG3’/3-Tn7R 5’CACAGCATAACTGGACTGATTTC3’. One of these clones yielding DNA products of 400 and 200 bp^{68, 69}, was designated as P. putida mt-2-Pm and used for the experiments discussed above. To obtain an entirely equivalent P. putida strain with a physically rearranged XylS/Pm regulatory node, a 1088 bp DNA segment containing the array of regulatory parts xylS ← Ps - Pm → was excised from plasmid pSEVA228⁶⁶ as a PacI/AvrII fragment and cloned in the corresponding sites of the pBG vector (Supplementary Figure S6C). The resulting construct (pBGS) was mobilised to the genome of the pWW0-less strain P. putida KT2440, and Gm^R exconjugants were tested for insertion of the mini-Tn7 transposon (with the Pm-gfp fusion adjacent to the xylS gene) in the same genomic site and orientation as before. One of these clones, termed P. putida KT-BGS, was chosen to test the effects of XylS/Pm proximity. This genetic strategy allowed a faithful comparison between the expression noise produced by the Pm-gfp fusion borne by either P. putida mt-2-Pm (Ps → xylS and Pm in non-adjacent, separate replicons) or P. putida KT-BGS (Ps → xylS and Pm in close genomic proximity).

Single cell analysis by flow cytometry

Single-cell experiments were performed with a Gallios (Beckam Coulter) flow cytometer. GFP was excited at 488 nm, and the fluorescence signal recovered with a 525(40) BP filter. Strains grown overnight were diluted 1/100 and allowed to grow at 30ºC in pre-filtered M9 citrate medium and incubated (3-4 h). After pre-incubation, cells in the late exponential phase (OD_600nm = 0.4) were treated with the inducer 3MBz (1 mM); cultures were incubated with aeration (30ºC). At 3 h post-induction, an aliquot of each sample was analysed by flow cytometry; 20,000 events were analysed for each sample.

RNA purification and real-time q-PCR

P. putida strains KT-BGS and mt-2-Pm were grown overnight (30ºC) in citrate-supplemented M9 with in aerated flasks. Cultures were diluted 1/100 in the same medium, alone or with 1 mM 3MBz and grown to exponential phase (OD₆₀₀ = 0.3-0.5). A 3 ml aliquot of each sample was treated with 300 µl ice-top solution (5% water-saturated phenol in ethanol) and centrifuged; pellets were frozen in liquid nitrogen and stored at -80ºC. RNA was extracted using the miRNeasy kit (Qiagen) with some modifications to optimise isolation of high quality RNA from P. putida. The quantity of total RNA was determined in a Nanovue Plus spectrophotometer (GE Healthcare Life Sciences), and RNA integrity analysed by agarose gel electrophoresis. The absence of DNA was confirmed using primers for rpoN (5’TCGACCCGGAGCTGGATA and 3’CGGCTCGAACTGCTGGAT) and xylS (5’CGAGTTGCTGGAGATTGTGT and 3’TCGTTAAATTGCCCTCAGTG). Real-time RT-PCR was performed using total RNA preparations from three independent cultures (three biological replicates). The process was monitored by q-PCR in an ABI pRISM 7900HT Fast RealTime PCR system (Applied Biosystems). To calculate the relative amount of xylS transcript, we used the ΔΔCt method⁷⁰, which is designed to compare levels of a given RNA in two conditions (induced and uninduced cells). The primers used for xylS were (xylS 141: 5’TAAT CCAGGCGAGATTACCC and 3’AACCAGTATGTCGGTACGCA; xylS 108: 5’CGAGTT GCTGGAGATTGTGT and 3’TCGTTAAATTGCCCTCAGTG; rpoN: 5’TCGACCCGGAG CTGGATA and 3’CGGCTCGAACTGCTGGAT). Results were normalised relative to for the rpoN gene, the expression of which remains constant throughout the growth curve.

Kinetic reactions, simulation and optimisation

The kinetic reactions that describe the model depicted in Figure 3 are:

$$Activation/deactivation:Pm+Xyl{S}^a\underset{k_{-1}}{\stackrel{k_1}{\rightleftarrows }}P{m}^a$$ (1)

$$Transcription:P{m}^a\stackrel{k_2}{\to }P{m}^a+mRNA$$ (2)

$$Translation:mRNA\stackrel{k_3}{\to }mRNA+GFP$$ (3)

$$Degradation:mRNA\stackrel{k_4}{\to }Ø$$ (4)

$$Degradation:GFP\stackrel{k_5}{\to }Ø$$ (5)

$$BasalTranscription:Pm\stackrel{k_6}{\to }Pm+mRNA$$ (6)

where Pm^a and Pm are the promoter with and without bound XylS^a, respectively, XylS^a denotes the regulator in its active form, mRNA is the output of the transcription process and GFP is the final green fluorescent protein. The description of the rates is as follows: k₁ is the binding rate of XylS^a to Pm (molecules^-1 hour^-1), k_-1, the unbinding rate of XylS^a from the promoter (hour^-1), k₂ and k₃, the transcription and translation rates (hour^-1), k₄ and k₅ are the degradation rates of mRNA and GFP (hour^-1) and k₆, the basal transcription of the promoter, which is Pm activity with no regulator bound (hour^-1). Stochastic simulations were performed using the Gillespie algorithm⁷¹. To obtain cytometry-like graphs (Figure 3C), the values Gillespie’s algorithm returns must be converted into a time-course array in which time intervals are fixed, τ_a, and are small enough to have cells (each time point) that correctly represent (in terms of frequency) all possible molecular levels⁷². Here we used τ_a = 0.01 h (Supplementary Figure S7). The values in Figure 3C where optimised within the ranges k₁ ∈ [0.001 - 1.2], k_-1 ∈ [0.2 - 80], k₂ ∈ [100 - 1000], k₃ ∈ [10 - 120] and XylS^a ∈ [20 - 1500], were each combination was weighted following the fitness parameters width and flatness (Figure 3B). Each combination of rates was assigned a fitness value. The width of the output distribution was measured as the difference between maximum and minim protein values. The flatness parameter corresponds to the minimum probability that represents any given protein value of a given run. Such value would be 0 in a one-peak Gaussian-like distribution while higher for a flat surface. Therefore, the goal (for 3MBz induction) was to maximize width while at the same time maximizing flatness. Five runs per combination of rates assisted the process to discard outlier values (not representative of the final distribution). Different degradation rates were tested, as well as affinity values, in the stress analysis of Supplementary Text S1 to test system robustness. The full TOL network was formalized, including reactions and rates, and simulated in Supplementary Text S2.

The multi-agent simulation of Supplementary Figure S2 was performed using our software DiSCUS^{72, 73}. XylS^a entry rate (k₇ = 400 molecules hour^-1) and degradation (k₈ = 2 hour^-1) were added to reactions 1-6. Extrinsic noise was simulated by changing the rates vector after division to reflect fluctuations in environmental conditions. Every new rate was the result of a Gaussian distribution where the mean was the previous rate value and the standard deviation a 20% of the original rate. Dilution was simulated by dividing by two the number of molecules in each daughter cell compared with the mother.

Differential variability (DV), the relation between the variance of the noise under two different conditions⁷⁴, was used to measure the simulations of Figure 3D. This value was defined as $f={\sigma }_1^2/{\sigma }_2^2$ where ${\sigma }_1^2$ and ${\sigma }_2^2$ are the variances of the signal at low induction (3MBz) and high induction (m-xyl), respectively.

Spatial protein trajectories

For the spatial simulation of regulators shown in Figures 5 we implemented a two-dimensional Brownian motion instance, written as an iteration scheme as follows:

$$X(t+dt)=X(t)+N\left(0,{\delta }^2\times dt;t,t+dt\right)$$ (10)

where t identifies the last time event, dt is the time step (dt = T/N with T the total time per iteration and N the number of steps, 15.0 and 1.0, respectively, in this case) and δ the so-called Wiener process parameter (here, 0.25). Each protein ran for 400 iterations. Time parameters were dimensionless and the simulated cell area was based on a 60 x 20 2D lattice. The target region monitored to obtain the graphs of Figure 5B (right) was a 10 x 5 lattice situated on a pole (source region at the middle). The numbers of trajectory points (not TF numbers, but TF crossings) in the target region for the ‘variable TF’ simulation were obtained during 16 spatial simulations: 147, 87, 47, 128, 103, 71, 12, 26, 91, 35, 47, 0, 214, 21, 29, 152. These numbers updated the TF variable within a single Gillespie simulation to generate the wide-rage plateau-like signal. To simulate the low mobility areas of the heterogeneous spatial distribution (Figure S5) the time step was set to 1.0 in such areas in contrast with the 15.0 of the normal mobility regions.

All computational simulations were written in Python. The source code is available in Supplementary File S1.

Visualization of the TOL plasmid (Figure 6C)

The plasmid was labelled using the fluorescent operator repressor system tetO-TetR-EYFP⁷⁵ to investigate its localization within the cell P.putida mt-2. Tandemly repeated tetO sequences were introduced into specific locus of the TOL plasmid. Given TetR fused EYFP chimera, the labelled DNA was visualized using epifluorescent microscopy. Cells were grown on succinate amended agarose pad.