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Transcription closed and open complex dynamics studies reveal balance between genetic determinants and co-factors

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Phys. Biol. 12 036003 (http://iopscience.iop.org/1478-3975/12/3/036003) View the table of contents for this issue, or go to the journal homepage for more

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Phys. Biol. 12 (2015) 036003

doi:10.1088/1478-3975/12/3/036003

PAPER

RECEIVED

28 November 2014

Transcription closed and open complex dynamics studies reveal balance between genetic determinants and co-factors

REVISED

9 March 2015 ACCEPTED FOR PUBLICATION

26 March 2015 PUBLISHED

Adrien Sala1, Muhammad Shoaib1, Olga Anufrieva1, Gnanavel Mutharasu1, Rawnak Jahan Hoque1, Olli Yli-Harja1,2 and Meenakshisundaram Kandhavelu1 1

19 May 2015 2

Molecular Signaling Lab, Computational Systems Biology Research Group, Signal Processing Department, Tampere University of Technology, PO Box 553, 33101, Tampere, Finland Institute for Systems Biology, 1441 N 34th Street, Seattle, WA 98103-8904, USA

E-mail: meenakshisundaram.kandhavelu@tut.fi Keywords: single cell imaging, single molecule study, transcription dynamics, lac promoter, molecular modeling, bio physical interactions

Abstract In E. coli, promoter closed and open complexes are key steps in transcription initiation, where magnesium-dependent RNA polymerase catalyzes RNA synthesis. However, the exact mechanism of initiation remains to be fully elucidated. Here, using single mRNA detection and dual reporter studies, we show that increased intracellular magnesium concentration affects Plac initiation complex formation resulting in a highly dynamic process over the cell growth phases. Mg2+ regulates transcription transition, which modulates bimodality of mRNA distribution in the exponential phase. We reveal that Mg2+ regulates the size and frequency of the mRNA burst by changing the open complex duration. Moreover, increasing magnesium concentration leads to higher intrinsic and extrinsic noise in the exponential phase. RNAP-Mg2+ interaction simulation reveals critical movements creating a shorter contact distance between aspartic acid residues and Nucleotide Triphosphate residues and increasing electrostatic charges in the active site. Our findings provide unique biophysical insights into the balanced mechanism of genetic determinants and magnesium ion in transcription initiation regulation during cell growth.

1. Introduction Transcription initiation of Escherichia coli is regulated by multiple factors, such as the sequence of the promoter, regulatory molecules, RNA polymerase (RNAP) and structural properties of the DNA sequence [1, 2]. RNAP has to follow several steps, namely formation of the closed complex, open complex and initiation of RNA synthesis to begin transcription. Analysis of the transcription initiation process from several bacterial promoters suggests the existence of several rate-limiting steps in the initiation process [1, 3, 4]. The activation of the promoter and the process of initial steps of transcription tend to have complex effects, affecting the mean duration of closed and open complex formations [2, 3]. This complex formation in initiation involves different sequence regions of the promoter and variation of ionic strength [5–7], as well as activator and repressor proteins, temperature [5], and degree of supercoiling of the DNA template [8, 9]. Among several ions, magnesium © 2015 IOP Publishing Ltd

is the only molecule identified as a co-factor actively involved in the transcription complex [5, 6]. Mg2+ is an essential ion affecting the transition of transcription open and closed complex formation [10–13]. Several reports suggest that Mg2+ is regulating the rate of isomerization and open complex formation of λPR, G3b, lac, gal, and Pα promoters [10, 14, 15]. It also determines the stability of RNAP in the transcription complex, facilitating the addition of nucleotide to the growing RNA chain and leading to the successive mRNA production [11, 12]. It also determines the stability of RNAP in the transcription complex, facilitating the addition of nucleotides to the growing RNA chain and leading to the successive mRNA production [11, 12]. The actual contribution of Mg2+ in transcriptional regulation and its role throughout the cell phases is yet to be clarified. In particular, cell phase has an important role in transcription and translation regulation, which helps survival of the population in fluctuating environments [16, 17]. It is also unclear whether the gene sequence or

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biochemical nature of the cellular environment leads to the variation in transcript production [18]. Tracking the transcription open complex transition of the promoter over the phases would unravel new mechanistic insights of initiation. Investigation of gene expression dynamics by a delayed stochastic model confirms that by regulating the kinetics of the closed and open complex formations, it is possible to regulate both mean and variations in RNA numbers independently [19]. However, kinetics of the transcription closed and open complex transition of any promoter region, including lac promoter in E. coli, remains yet to be fully understood [20]. Recent studies on the lac promoter reported that mRNAs are produced in bursts and then promoter is turned off for a long time at full induction [21]. Yet, most of the studies aimed to examine the mechanism in specific cell phases. The present study aims to understand how transcription open complex formation is regulated by the lac promoter in different cell phases. More specifically, we address how transcriptional bursts are regulated by Mg2+ in the transcription complex at the single-cell, single-molecule level. The successful recruitment of incoming nucleotides is dependent on the availability of the Mg2+ ion nearby the transcription start site, +1 site, of the promoter open complex. In this work we also set up to test the model predictions by studying the effects of additional Mg2+ ions in the open complex formation and during transcription.

2. Material and methods 2.1. Plasmids, strains and media Escherichia coli Dh5α-PRO strain was used as a host system to study the gene expression over the phases. To study mRNA transcription at the single-cell level, we co-transformed the cells with two vectors: (1) single copy reporter bacterial artificial chromosome, pTRUEBLUE-BAC2, expressing 96 target binding sites (96xbs) for the MS2 protein. It is under the control of the wild-type lac promoter with the catabolic activator protein (CAP) site in the upstream for the binding of CAP and the Operator 1 site in the downstream for the binding of lac repressor [22]. The CAP and lac repressor are inducible by cyclic AMP (cAMP) and isopropyl-D-1-thiogalactopyranoside (IPTG), respectively. (2) A medium-copy plasmid, pPROTET.E, expressing bacteriophage MS2 coat protein was tagged with a fluorescent protein coding gene (GFP-mut3) under the control of PLtetO-1 [22] (generously provided by Prof. Ido Golding, University of Illinois). The cells without the BAC were used as a negative control (supplementary figure 4). The strain was grown in a liquid Lysogeny Broth (LB) medium composed of 10 g L−1 of tryptone (T7293-Sigma Aldrich-USA), 5 g L−1 of yeast extract (MC 001-LabM-UK) and 10 g L−1 of NaCl (S30142

LabM-UK). Antibiotics were used to grow the cells according to the respective antimicrobial resistance. The strain information is as follows: deoR, endA1, gyrA96, hsdR17(rk−mk+), recA1, relA1, supE44, thi-1, Δ(lacZYA-argF)U169, Φ80δlacZΔM15, F-, λ-, PN25/ tetR, PlacIq/lacI, and SpR. Frag1A: F-, rha-, thi, gal, lacZam, ΔacrAB::kanR, PN25/tetR, PlacIq/lacI, and SpR. Frag1B: F-, rha-, thi, gal, lacZam, PN25/tetR, Placiq/lacI, and SpR. The PN25/tetR, Placiq/lacI, SpR cassette was transferred from DH5αPRO to Frag1 to generate Frag1B by P1 transduction. The ΔacrAB:kanR cassette was transferred from KZM120 to Frag1B to generate Frag1A. 2.2. Cell phase determination and gene activation Generation time of the E. coli DH5a-PRO strain was calculated to determine the phases of the cells. Cells were grown overnight in an orbital shaker (Labnet) at 30 °C with aeration at 250 RPM. Following overnight culture, cells were diluted in fresh media to reach an optical density (OD600) of 0.05 using a spectrophotometer (Ultraspec 10- Amersham Biosciences) and grown at 37 °C at 250 RPM. Cell growth was measured every 30 min and OD600 values were used to calculate the generation time as described in earlier literature [23] (supplementary figure 2 and table 1). Cell phases were defined as suggested from the Jacob–Monod study based on the state of the cells’ division time, i.e., lag, acceleration, exponential, retardation and stationary phases [24]. To study the regulation of the lac and lac variant promoter over the phases, cells were induced in the state of a particular phase. To detect the single mRNA molecule, the tet promoter was activated with 50 ng/ ml of anhydrotetracycline (aTc) (lot number 2-0401001, IBA GmbH, Germany) for 20 min incubation. Full induction of the target Plac was achieved by the activation of Downstream Region of Promoter Sequence (DRS) with 1 mM IPTG (L6758-Sigma Aldrich-USA) and Upstream Region of Promoter Sequence (URS) by endogenous cAMP [22] (supplementary table 2). In the population study, to observe single mRNAs the cells were incubated with inducers for 15 min depending on the induction scheme in each phase. In the population study, the cells were observed under microscope immediately (3 min) after the division time of every phase. In the case of time-lapse microscopy imaging, cell observation was started 10 min before the time of division. For the time-trace experiments, cells were induced with aTc as explained earlier and corresponding inducers for 10 min following the induction scheme of the target promoter (supplementary table 2). In order to monitor the synchronously dividing cells, we started to image the cells prior to the division time and captured this under a microscope over the duration of 120 minutes. For the population and time lapse microscopy study, over

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100 cells were analyzed in each induction (supplementary table 3). 2.3. Single-cell fluorescence microscopy Cells were pelleted by centrifugation at 6000 RPM and then suspended in the required volume of LB to facilitate the observation of several cells under the microscope. Suspended cells were then placed on a microscopy slide between a 1% LB-agarose gel pad and a microscopic cover slip. For the image acquisition of the produced mRNA molecules in the cells, we used an inverted fluorescence microscope (Nikon, Eclipse Ti-E) with 100× N.A. 1.49 oil immersion objective. The microscope is equipped with a hardware autofocus module, motorized z-drive and Nikon’s Perfect Focus System to maintain the cells in focus during the image acquisition. Built-in microscope software (Nikon, NIS-Elements C) was used to acquire the images. Fluorescence was measured using a 488 nm laser (Melles-Griot) and a 515/30 nm detection filter. For the real-time observation of mRNA production, we followed the previously described method. Cells were then placed between a gel pad and a cover slip in an FCS2 temperature-controlled perfusion chamber (Bioptechs), maintained at 37 °C during the measurement. The pad was supplemented with required inducers as well to maintain the induction conditions under the time-lapse microscope. 2.4. Single-cell signal processing Cells producing mRNAs were selected from microscopic images using semi-automated methods. This method consists of manually masking the region of the images displaying cells containing fluorescent spots (supplementary figure 3). Further, principal component analysis (PCA) was applied to extract information about locations, dimensions and orientations of masked cells, assuming that the fluorescence intensity is relatively uniformly distributed within cells and close to zero in the background [25, 26]. Fluorescent spots within the cells were then segmented by sub-cell object detection methods [4, 26], i.e., kernel density estimation (Gaussian kernel) and Otsu’s threshold method [26]. Importantly, precise segmentation of fluorescent spots reduces enlarged noise in intensity signals of spots in the cells. The threshold value was selected to minimize the intraclass variance. In this analysis, the spot detection algorithm detected 0.74% of false-positive and 2.9% of false-negative spots. Segmented cells were then connected in lineage across time by matching their closest centroids from one frame to the following in the time-lapse images in order to quantify the mRNA production kinetics. As quenching does not occur throughout the experiment, absolute total intensities from background-corrected spots fit as a monotonic piecewise-constant curve [4, 26]. From there, tracking significant increase in intensity visible in the monotonic step-like curve 3

allowed us to determine the time of appearance of new mRNA and intervals between production of consecutive RNA molecules (supplementary figures 7 and 8). Jumps in the curve indicate the appearance of newly produced mRNA molecules and the transcription interval between two consecutive events. However, such a jump detection method does not quantify mRNA molecules produced in the event. In order to determine the quantity of mRNAs produced from each event, the mean total intensity of each intensity jump was used and mRNAs numbers were calculated as described next. 2.5. Absolute mRNAs quantification and burstiness at the single-molecule level To quantify the single mRNA intensity, we tracked the production of the first mRNA in weak induction. For this, cells were grown at 37 °C at 250 RPM, with the aTc for tet promoter activation and without inducers for the target mRNA production. From time-series images, we find the first appearance of a fluorescent spot in 50 random cells that did not present spots at the beginning of the imaging. Then the fluorescence intensity of each mRNA spot and mean intensity was calculated, which is defined as the mean intensity value of a single mRNA molecule. Combining information from the jump detection method, cell backgroundcorrected spot intensities and the mean intensity of a single mRNA molecule allowed us to calculate the number of mRNAs produced from the transcription events. As a positive control we also quantified LacZ mRNA expression using quantitative Polymerase Chain Reaction (PCR) (detailed methods and results are included in the supplementary file). To study the transcriptional bursting behavior over phases, we investigated the transcription events of individual cells. The production interval between the burst also was estimated from the intensity jump. The model for its examination was implemented in Matlab R2013a software. From the data we calculated the burst size (number of mRNA produced in a burst) and frequency (occurrence of event in a population). 2.6. Quantification transcriptional noise To measure the noise in the mRNA level from the population of the cells, we used the ratio between the variance and mean of the distribution of mRNA number per cell, i.e., Fano, b = σ 2 / n . To calculate the total noise in transcriptional events from the time series, identical analysis was performed using the squared root of variance over the mean, i.e., CV = σ 2 / n 2 . 2.7. Quantification of intracellular magnesium To measure intracellular Mg2+ concentration, E. coli Dh5α-PRO cells were taken from each specific phase and pre-incubated at 37 °C for 10 min to allow the stabilization and equilibration of ion gradients.

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Following this, 10 μM of Mag-fluo-4 (Invitrogen, Lot, 108 1211) was added to the cells and they were incubated at 37 °C for 30 min. Cells were then washed with physiological saline buffer (PBS) three times and incubated in PBS at 37 °C for 30 min. Cells were centrifuged at 6000 RPM and imaged under the microscope. Fluorescence was measured using a 488 nm laser and 515/30 nm detection filter. Acquired images were analyzed with semi-automated and automated methods to detect cells and extract intensities of individual cells. From the obtained values of intensities, intracellular Mg2+ concentration was calculated using the following formula:

⎡ Mg2 + ⎤ = Kd + * F − Fmin / Fmax − F ⎣ ⎦

(

)(

)

where F is the observed fluorescence intensity, Fmin is the fluorescence of minimum ion concentration, Fmax is the fluorescence of maximum ion concentration and Kd is the dissociation constant for the ionindicator complex (Mg2+, Kd = 4.7 mM) (reference). Fmin and Fmax intensities were calculated from the mean of minimum and maximum fluorescence intensities per cell (supplementary figure 9). 2.8. Effect of Mg2+ on transcriptional dynamics Following the identification of intracellular Mg2+ concentration over the phases, we increased the level of Mg2+ by adding extra cellular magnesium. To observe the effect of Mg2+ we added 2.5 and 5 mM solution of MgCl2 to the cells in 15 min prior to the division, and we followed the same induction scheme and protocols as described earlier to see the changes in mRNA numbers. From the total population we calculated the mRNA number, their distribution and its noise. Further, we also performed a time-series experiment to see the changes in transcriptional events. Following the induction of the target promoter with different condition time series experiments were executed as explained in supplementary table 1. From the measurements we calculated the burst intervals, frequency, size, mean mRNA/burst and transcriptional noises as described earlier. At least 100 cells were observed in each condition (supplementary table 2). 2.9. Intrinsic/extrinsic noise To study the roles of intrinsic and extrinsic noises in the observed behavior of transcriptional noise, we determined transcriptional total noise (ηtot) as the standard deviation divided by mean mRNA number [21, 27]. We decomposed it into intrinsic (ηint) and extrinsic (ηext) noise classes, defining extrinsic noise as the difference of mRNA numbers between the cells and intrinsic noise as the squared difference of total and extrinsic noises, such as η2ext = η2tot – η2int. Treating the noise in an orthogonal manner as proposed by [27] provides evidence that changes in either of the noise classes correspondingly affect another noise part. 4

2.10. Molecular docking and modeling Our molecular dynamics study started with the x-ray crystal structure of the E. coli RNAP in a complex with rifampin (PDBID: 4KMU) [28]. The ligand molecule was removed from the complex, while the Mg ion was kept intact. Form this original structure, two Mg ions were introduced subsequently to the active site using Molegro [29], a molecular modeling tool. Energy minimization of RNAP with 2 Mg2+ and 3 Mg2+ configurations was performed independently. To study the conformational change in the active site upon increased Mg ion concentration and Adenosine Triphosphate (ATP), both structures were docked with ATP into active site around ASP 460, ASP 462 and ASP 464 [11, 12]. To see the stability of the interaction between ATP and RNAP with increased Mg ion concentration, molecular dynamics simulations were performed. Simulations were set up at 300 K in a water medium using Gromacs [30] for both two Mg2+ and three Mg2+ bound complexes for 5 nanoseconds. The simulation was repeated by increasing +10 K from the standard temperature. Minimized conformations were compared using the structural alignment method, and interaction distances and energy difference were calculated. 2.11. Model and statistical tests To prove the existence of bimodality, we also fit the mRNA distribution with the Gaussian mixture model. To determine if the trend of the cell phase follows the trend of mean mRNA distributions and Fano factor, the Wilcoxon–Mann–Whitney test was used with the threshold parameter of 0.05. The Pearson correlation coefficient test was used to study the correlation between mean mRNA and production interval. The significance in fold changes in mRNA and total noises in different induction conditions were measured using the Kolmogorov–Smirnov test with a threshold of 0.05.

3. Results 3.1. Magnesium-induced transcriptional response Here we study the role of Mg2+ in transcription open complex formation of the lac promoter and its regulatory mechanism in determination of the transcriptional events and transcript numbers of the target gene at the single-molecule level in distinct cell growth phases (lag, acceleration, exponential, retardation and stationary) [24]. In full induction of the wild-type lac promoter, we observed a single-mode distribution of mRNAs produced in all the phases, except the exponential phase (figure 1(a)). Exponential phase data show the existence of bimodal distribution of populations. In detail, the cells with 1 to 2 mRNAs appeared as a distinct population, while remaining cells with >2 molecules appeared as another population, indicating the existence of bimodal-like

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Figure 1. Transcriptional response of lac with the additional magnesium ions in multiple cell growth phases of E. coli. (a) Distributions of mRNA number of population. Wild-type lac promoter, Plac, was activated by cAMP in URS and by IPTG in DRS. Bimodal-like distribution of the mRNA number is observed in the exponential phase. Small numbers of mRNA (1 to 2) appear as one population (green), and cells producing more than 2 mRNAs appear as another population (gray). (b) Transcriptional response of Plac with the additional 2.5 mM Mg2+ observed over the cell phases. Figure shows the bimodal-like distribution of mRNA numbers is observed only 2.5 mM Mg2+ in the exponential phase. The cells with ∼1 to 3 mRNAs (blue color) appeared as one population, and cells producing more than 3 appeared as another population (gray color). (c) Transcriptional response of Plac in the presence of 5 mM Mg2+ over the cell phases. The figure shows probability distributions of the mRNA number among different cells over the phases. Bimodal-like distribution of mRNA numbers was not observed in exponential phase. (d) Bimodal distribution fit: distribution of mRNA per cell in the population under full induction of the wild-type lac promoter (control) in exponential phase is shown as black dots. The fitting of the Gaussian mixture distribution results in a higher sum of square error (SSE = 0.001403) and R-square = 0.4778 compared to the Gaussian distribution fit (SSE = 0.001646, R-square = 0.3873). It significantly indicates the existence of two mRNAs population distribution. (e) In the presence of 2.5 mM Mg2+ the distribution of bimodality is increased compared to the control. The fitting of the Gaussian mixture distribution results in higher SSE = 0.001584 and R-square = 0.572 compared to the Gaussian distribution fit SSE = 0.002005, R-square = 0.4581. Goodness of fit (R-square) is increased by 10% in the presence of Mg2+ compared to the control.

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Figure 2. Dynamic changes in mRNA noise at the single-cell level. (a) Mean mRNA/cell of Plac in fully activated (control), 2.5 and 5 mM Mg2+ added conditions in all the phases. Increase in Mg2+ concentration increased the mRNA production. (b) Example of mean versus Fano figure shows the changes in observed Fano values as a function of the mean in the exponential phases of Plac (data points are originated from seven technical repeats). (c) Decreasing trend in mRNA noise with the addition of Mg2+ in acceleration and exponential phases. (d) Increasing trend in mRNA noise with the addition of Mg2+ in lag, retardation and stationary phases. Kolmogorov–Smirnov test further supports the statistical significance of observed changes (supplementary tables 4 and 5).

distribution of mRNAs. This finding suggests that in some fraction of the exponential phase, cells have a slower transcription open complex rate, while another fraction has a faster open complex to produce more mRNAs. Previously, several studies explained how the specific extrinsic noise sources, i.e., RNAP, repressor protein and temperature, influence the initiation of transcription [31]. As discussed earlier, Mg2+ is another important molecule to the cells involved in cell phases, registering an increasing trend up to the exponential phase followed by a decreasing trend (supplementary figure 10). The observed trend follows the mean mRNA ( m ) production of cells in each phase, suggesting the counter-play of co-factor concentration in regulating the mRNA production (figure 2(a)). Given changes in concentration of Mg2+ over the phases, we further investigated how magnesium would determine the mRNA numbers and the transcriptional noise given their significant role in initiation. Figures 1(b) and (c) show how the fully activated lac promoter is further able to increase 〈m〉 per cell when it receives higher concentrations of Mg2+, i.e., 2.5 and 5 mM in all phases when compared to the control. The addition of Mg2+ up to 5 mM exerts a greater effect than at 2.5 mM on the production of mRNA, which confirms the efficient role of Mg in transcriptional regulation. At 5 mM Mg2+ concentration, the existence of bimodal-like behavior noticed in the exponential phase with no additional Mg and with 2.5 mM Mg2+ disappears (figure 1(c)). To validate the existence of bimodality, we fit the Gaussian mixture distribution in the mRNA population and compared it to the Gaussian fit. The parameters of the Gaussian mixture distribution fit are greater than the parameters of Gaussian fit in both cases, indicating existence of bimodality (figures 1(d) and (e)). Presence of 6

2.5 mM Mg2+ increases bimodality by 10% compared to the control (R-square = 0.572 and R-square = 0.4778, respectively). 3.2. Impact of Mg in mRNA noise Figure 2(a) shows the trend of produced mRNA per cell from endogenous lac, with 2.5 mM and 5 mM Mg2+. The trend of m is first increasing and then decreasing over the phases. Gradual addition of Mg concentration increased the m per cell. The dynamic changes of LacZ-mRNA expression are also independently validated by the quantitative PCR (qPCR) method. The observed result shows that the trend of absolute mRNA number/cell detected by the MS2-FP method follows the trend of mRNA expression quantified by qPCR (supplementary figure 5). Further, we calculated the cell-to-cell heterogeneity using Fano 〈b〉: (variance (σ2)/mean n ). Figure 2(b) shows the changes in observed Fano values follow the mean in Plac WT control. The trend of 〈b〉 follows the cell division (supplementary tables 1 and 4). In slowgrowing cells, higher Mg concentration results in an increasing mRNA noise 〈b〉 while it decreases in fastgrowing cells (figures 2(c) and (d)). We next performed the Kolmogorov–Smirnov test to assess the distinctiveness between the trend of induction conditions of the two promoters over the phases, resulting in the changes in mean mRNA and Fano, which are statistically distinguishable (supplementary table 5). 3.3. Transcriptional burst regulation by co-factor To further investigate whether the observed changes in 〈m〉 and 〈b〉 are the output of variations in the transition of the promoter open complex in a specific cell phase, we monitored the kinetics of transcription at single-event levels of individual cells for all inductions and phases. From the data analysis, we addressed

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Figure 3. Tracking of real-time dynamics of mRNA burst regulation by co-factor. (a) Levels of mean burst intervals over the phases are modulated by the presence of different Mg2+ concentrations. 2.5 mM Mg2+ causes the mean burst interval to decrease, while 5 mM Mg2+ increases it. Over 100 cells were analyzed in each induction (supplementary table 3). (b) Mean mRNA/burst in all phases of Plac with the addition of 2.5 and 5 mM Mg2+ over the phases. Increasing the Mg concentrations increases the noise in all phases, except the exponential phase. (c) and (d) Probability distributions of the number of mRNAs produced from bursts, showing an exponential trend in frequency and size at 2.5 and 5 mM Mg2+ concentrations. It shows the increased burst size and frequency in 5 mM Mg2+ compared to 2.5 mM Mg2+ condition.

the following questions: does a cell phase change the intracellular Mg concentration? If it changes, does it correlate with the mean mRNA per cell? Are the burst of mRNAs controlled by Mg2+ or not? Does Mg2+ affect the rate of the open complex and thus determine population diversity? To address these questions, we tracked the appearance of new mRNA in individual cells using time-lapse microscopy (supplementary figure 6 and movie 1). Data were obtained by fitting a monotonic piecewiseconstant curve in the least-squares sense to the corrected intensity of signals obtained from a cell (supplementary figure 7) [26]. Figure 3(a) shows a gradual decrease in the production interval. It provides evidence that Mg2+ increases the probability of the addition of nucleotides by RNAP in the open complex, thus changing the behavior of the transcription transition. Figure 3(b) shows the mean mRNA produced per burst for Plac with the addition of 2.5 and 5 mM Mg2+ over the phases. Increasing the Mg2+ concentrations increases the noise in all phases, except the exponential phase. Further analysis uncovers coherent monotonic increases in burst frequency and m per burst (figures 3(c) and (d)) compared to the control, fully induced wild-type lac. Also, the data show increasing

7

burst size results in decreased frequency that reveals an exponentially decreasing trend under the present conditions. 3.4. Mg-regulated transcriptional noise From the time series, transcriptional ‘noise’ was quantified by the proportion of the squared coefficient of variance CV2 = σ2/〈n〉2 and the mean of transcription interval. Figure 4(a) presents the linear regression fit (equation of the fit is y = 0.101 09*x + 0.4368) for the coefficient of variation (CV2) and the mean production interval, where dots represent the individual cells. Fit, plotted so that the mean square error is minimized, allows for conclusion of bursty-like behavior in Plac WT because the mean production interval per cell increases with the increase of CV2. The fit approximates the distribution of the mean intervals of the transcription event from many cells versus the coefficient of variation. Additional Mg2+ changes the mean mRNA per cell and thus affects the CV2. Upon the addition of 2.5 mM and 5 mM Mg2+ (figure 4(b)) the trend of CV2 decreased compared to the control. It is also noted that a gradual increase of Mg2+ concentration increases the noise in all the phases, except exponential phase (figure 4(b)) due to the higher

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Figure 4. Transition of CV2 as a function of mean mRNA. (a) CV2 of transcription burst intervals was calculated. The figure shows the changes in CV2 depending on mean burst production intervals in Plac WT in the presence of 2.5 mM and 5 mM Mg2+. (b) Transcriptional noise from the transcription production intervals. Noise is proportional to the Mg concentration and mRNA production. Except for exponential phase, all phases have an increasing trend. (c) Fold change in total noise and its decomposition to intrinsic and extrinsic noises. The noises increase with the increasing concentration of Mg2+.

a

b

c

Figure 5. RNAP structural conformation in the open complex. (a) Active site of the E. coli RNA polymerase (PDB ID: 4KMU) with ATP molecule and Mg ions. RNAP with 2 Mg ions shown in dark cyan and RNAP with 3 Mg ions shown in yellow. Increased concentration of Mg ion shows movement in the side chains of Asp 460, 462 and 464 towards the ATP molecule. Hydrogen bond length becomes shorter (difference of 0.591 Å and 0.322 Å in bond length), implying stronger interactions with RNAP. (b) Molecular dynamics simulations of RNAP and ATP complex with Mg ions shows the interactions are intact in a 5-nanosecond simulation. Trends of movements in the backbone and all atoms of RNAP are similar in the 2 Mg2+ and 3 Mg2+ state, but a significant difference is observed between the states. (c) Molecular dynamics simulation of RNAP with Mg ion in the active site at 310 K. Root mean square deviation (RMSD) of atom movements in RNA polymerase from molecular dynamics simulations at 310 K (+10 K from standard temperature 300 K). 3 Mg configuration still shows large movements in all atoms, as well as in backbone (excluding side chain), including backbone of the protein.

mRNA production frequency and burst size (figures 3(c) and (d)) [32]. We noticed that in exponential phase, addition of 5 mM Mg2+ increases the probability of the production of single mRNA, as well as the frequency of bursts (figures 3(c) and (d)) and the mean mRNAs per burst (figure 3(b)) when compared to 2.5 mM. It provides evidence that transcription noise dynamics have been regulated by the concentration of Mg2+ in the cell. The observed changes in mean mRNA and noise are statistically distinguishable (supplementary tables 4 and 5). Further, we used mRNA numbers per cell to calculate intrinsic and extrinsic noise analysis that shows greater intrinsic noise than extrinsic noise (figure 4(c)). It indicates that cell populations with an increased mRNA number have higher homogeneity in the presence of 5 mM Mg2+ than 2.5 mM Mg2+ (figure 4(c)). It points out that Mg2+ is an important source that affects dynamics of the noise. 8

3.5. Conformational change in RNAP in the open complex To sum up, the data indicate that Mg2+, as an extrinsic noise source, regulates mRNA and protein noise. However, it does not explain the changes at the +1 site (one nucleotide prior to initiation site) of the open complex. For better resolution, we extended our work to see the thermodynamic changes of RNAP at +1 site. RNAP with two Mg ions in the active site docked with the ATP (endogenous ligand) molecule shows interactions similar to the previous observations [11, 12]; the stability of this complex was found even after 5 nanosecond simulation. The complex with three Mg ions shows similar interactions with better hydrogen bonding distance (figure 5(a)) between the ligand and critical (aspartic acid) Asp residues in the active site. It suggests that the increased Mg ion concentration induces the interaction of ATP by the increased polarity in the active site. The positively charged Mg2+

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with the valency of +2 drags the Asp residues (460 and 462) and ligand atoms together. It helps to make shorter and stronger hydrogen bonding. When compared to the structure having 3 Mg2+ ions in the active site to the structure with 2 Mg ions, the length of the hydrogen bond decreases by 0.34 Å and 0.322 Å (from 2.112 Å to 1.768 Å) between the oxygen atom in ATP and Asp 460 (figure 5(a)). We also observed a rotational change in the 3 Mg2+ state at the side chain of Asp 460, which makes both of its terminus oxygen atoms (2.359 Å) interact with ATP, whereas in the 2 Mg2+ state, only one atom (1.768 Å) makes the contact. From molecular dynamics simulation, it is observed that the middle Asp 462 changes its confirmation to make Mg2+ move towards Asp 464 from Asp 460 (supplementary movie 2). Significant movements observed in the RNAP side chains and the main chain in the 3 Mg2+ state when compared to the 2 Mg2+ state suggest a dynamic environment influenced by Mg ions (figure 5(b)). Interactions were not disturbed even when the simulation was repeated with +10 K difference to the standard temperature (figure 5(c)). This observation gives better assumption towards the mechanism of RNAP in the dynamics of the transcriptional open complex formation with increased Mg concentrations.

4. Discussion We have studied the effect of Mg in the formation of the transcription open complex in live cells at the single-molecule level over the phases. This complex formation depends on the stability of RNAP, which holds and adds Nucleotide Triphosphate (NTP)s to synthesize mRNA [33]. Several experiments also prove that higher concentrations of Mg could possibly inhibit the initiation by abortive initiation in the open complex [10, 13, 34]. The present study provides new insight on how Mg2+ affects the open complex during cell growth and thus changes in the duration of the open complex as well as mRNA burst size and frequency. A closed to open complex switch is favored by conditions that destabilize the closed complex of DNA in the promoter region, i.e., quantity of Mg2+ and its availability near the catalytic center determine the rate of open complex formation as well as successful completion of RNA synthesis [33]. Consistent with this notion is the trend of mean mRNA increases with the increasing Mg2+. Greater availability decreased the rate of open complex formation duration and increased the read of RNAP in the open complex, and, thus, changes in the burst size and frequency. Although it is known that the lac promoter regulates the production of lower and higher numbers of mRNA, the role of Mg2+ in the transcription open complex formation and their regulatory mechanism on bimodal distribution is not clear [35]. It was 9

hypothesized that the phenotypic switch is a singlemolecule event [9, 36]. So far, bimodal distribution of lac gene expression has been observed at the protein level and not at the mRNA level. The present study further suggests that bimodal distribution is arising from mRNA distribution. Moreover, the present study provides evidence that this switching highly depends on the biochemical reaction involved in the open complex. Since we observe the disappearance of bimodallike distribution of mRNAs in the population with the presence of higher Mg2+ concentration, we suggest that it could be a significant extrinsic noise source that determines the rate-limiting step in the promoter open complex [1, 37]. Recent reports also provide evidence that DNA unlooping, as a rate-limiting step, triggers the stochastic events in transcription to determine the phenotype switching [9, 37]. Also, mechanism of transcriptional bursting studies in bacteria show that bursting is primarily caused by reversible gyrase dissociation from and rebinding to a DNA region, which changes the supercoiling of the region. Extensive review of transcription and supercoiling reported that RNAP initiating the transcription depends on positive and negative supercoiling of DNA. It may have some relevance with the Mg ion, which binds in the upstream of the promoter region, inducing structural conformation in the DNA. Our experiment does not show what is happening in the promoter upstream; rather, we show the changes in the speed of the open complex once RNAP is attached to the DNA. From the quantification of endogenous intracellular Mg2+, we confirm that Mg2+ concentration is correlated with the cell phase and the gene expression. Yet, in the exponential phase, we are not able to discriminate how, within a population, cells produce small or large numbers of mRNAs. One possible hypothesis is that in the exponential phase, a subpopulation of cells may have variable nutrition transport machinery that determines the intracellular Mg2+ concentration. The observed experimental and computational models provide evidence that the co-factor has a significant role in changing the transcription open complex and determining stochasticity in mRNA burst frequency and size during cell growth. Based on the computational model, we reveal that the interaction of an extra Mg2+ with ASP 460 and the next incoming nucleotide, involving additional charges to the nucleotidyl transfer reaction of RNAP on DNA, improves transcription kinetics. RNAP-induced DNA strand opening at the +1 site depending on Mg2+ is well-established. In addition, it is noted that the concentration of Mg2+ of the cells differs depending on the cell. From the Molecular Dynamics simulation we show that if there is higher Mg2+ concentration in the environment, it changes speed in access and holding of NTP, thus changing the frequency of transcription kinetics. Higher concentration of the Mg2+ state is the identical environment as the exponential phase where

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cells also have increased Mg2+ in the cell population. This observation gives insight into the mechanism of RNAP in the dynamics of the transcriptional open complex formation with higher Mg2+. Overall, the tendency of Mg2+ influenced stochastic transcription open complex in gene activation and their changes during the growth phases of the cells are crucial to understanding the phenotypic diversity. The all-or-nothing characteristic of the β-galaactosidase enzyme induction system was observed in E. coli [36]. It has been observed that when thiomethyl-β-D-galactoside (TMG), inducer of the lac promoter, was added to E. coli culture, the cells exhibit two mixed populations [35, 37, 38]. It was also shown that these mixed populations are either cells uninduced or fully induced when induced with a low concentration of TMG [39]. More recently, it has been observed that the all-or-nothing characteristic has at least single mRNA transcript and a remaining population with multiple transcripts [37]. It also suggests that the DNA looping mechanism could have an important role in the all-or-nothing mechanism. These reports reason out the positive feedback mechanism of the lac permease for bimodality. While this mechanism is not well studied, our report extends the current view where intracellular magnesium plays a crucial role. The strain that we used has the genotype of ΔlacZYA [3, 40]. While lacking lacZYA, we observed bimodal distribution of mRNAs most likely regulated by promoter open and closed complex dynamics, where magnesium is modulating the frequency of these complexes. As discussed earlier, when the promoter is activated by an inducer, it has to follow several sequential steps to produce the transcript. Thus, the promoter transition or promoter open and closed complex also plays a significant role in stochastic gene expression. Stochasticity in gene expression is mostly regulated by cell state and cell type diversification [27, 41, 42]. Although it remains unclear, several reports also suggest that promoter transition might have an important role in stochasticity [18, 41]. In particular, ON and OFF state transition of the promoter and its rate could be a rate-limiting step in transcript production, and thus it is determining the quantity of the protein numbers. Reports also suggest that random transitions between ON and OFF states could modulate the bimodal distribution of the cell population [21, 38]. While the analytical model does not include many variables, our data suggest how the magnesium variable affects the state of the promoter transition and burst of RNA production [43]. The stochastic transcription initiation model also was used to predict the duration of the promoter open and closed complex as well as isomerization. The magnesium variable is suggested to have a role in promoter isomerization and open complex formation [6, 14]. More recently, we found that lac and lac variant promoters transcripts production appeared to have a bimodal distribution [38]. In the present report we 10

identify that magnesium is also one of the important variables that changes the frequency of transcription transition and thus modulates the bistablity of the promoter. It demonstrates that magnesium has an important role in stochastic transcription and thus population diversity. Santillan et al also report that the bistablity behavior of the lac system in E. coli plays an important role in consuming glucose and lactose, which helps the bacterial population survive [36, 39]. Several reports also suggest that a switch between the unimodal and bimodal state depends on the concentration of the inducers or repressors [35–37, 44]. In addition to inducer concentration, we provide evidence that intracellular magnesium affects the rate of promoter transition. Our findings may have important implications in understanding the strategy of cell populations surviving in the ion-changing environment.

Supplementary data Supplementary data are available online: supplementary figures 1–10, supplementary tables 1–5, supplementary movies 1–2, supplementary methods, and supplementary references.

Acknowledgments We thank Professor I Golding for the generous gift of the lac and lac variant MS-FP system and C Balasundaram for helpful discussion and critical reading. This work was supported by the Academy of Finland. The authors declare no competing financial interests.

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