This article presents a dataset on nitrate, nitrite and dissolved organic carbon (DOC) losses measured for 4 years using lysimeters at the EFELE long-term experimental site . This ongoing long-term study was designed to provide information on effects of organic waste product (OWP) application and soil tillage on crop production, soil properties, biodiversity, greenhouse gas emissions and water quality. Forty wick-fiber lysimeters were installed at depths of 40 and 90 cm to document effects of organic and/or mineral fertilization, vegetation cover and weather conditions on dynamics of nitrate, nitrite and DOC concentrations of water collected during the drainage season (winter). These data help analyze the effects of winter plant cover (wheat vs. mustard catch crop) on these dynamics and fill a knowledge gap on effects of organic waste product supply on DOC losses. These dynamic data over several years are also of great interest for calibrating and evaluating models . Specification table•The dataset, acquired over 4 consecutive years, provides a reference for dynamics of nitrate concentration and DOC under annual crops.•This dataset is of particular interest to soil scientists and modelers who work with soil-plant models .•The data help fill a knowledge gap on effects of OWP supply on DOC losses, which is little documented in the literature. Analysis of losses at 2 depths should help understand processes that influence DOC flows in the soil.•These dynamic data over several years are particularly useful for calibrating and evaluating models.1This article includes descriptive tables and figures on dynamics of nitrate and dissolved organic carbon (DOC) concentrations of the water collected by EFELE's lysimeters during drainage seasons from 2014 to 2015 to 2017–2018. The data include amounts of organic waste product (OWP) and of carbon (C) and nitrogen (N) applied to the experimental treatments from 2014 to 2017 , intra- The dataset is composed of 1 PDF document and 4 Excel files that contain raw data . It incl22.1https://www6.inra.fr/valor-pro_eng). It is used to measure long-term evolutions of agrosystems after repeated applications of organic residues derived from animal wastes that undergo a variety of treatments .EFELE is an experimental site of the SOERE PRO network  and a control treatment with mineral N fertilization (MIN). The OWP are i) cattle farmyard manure (CM), ii) pig manure composted on straw (CPigM), iii) poultry manure (PoM), iv) pig slurry (PS) and v) the digestate obtained after anaerobic digestion of the studied pig slurry (PS-DIG). Since the short-term N fertilizing value of cattle manure and composted pig manure may not be high enough to satisfy the crop's N requirements, particularly during the first few years of the trial, the OWP received a mineral N supplement .PROs, a complete randomized-block trial with 4 replicates, each block composed of 9 plots of 109 m2-TS/MO, a split-plot trial with 3 replicates. Two tillage methods  are combined with mineral or organic fertilization. Four treatments are studied: conventional tillage and mineral N fertilization (CT_MIN), conventional tillage and cattle manure application (CT_CM), reduced tillage and mineral N fertilization (RT_MIN) and reduced tillage and cattle manure application (RT_MIN). Conventional tillage (CT) consists of moldboard plowing with full soil inversion to a depth of 25 cm, followed by harrowing to 12 cm before seeding. Reduced tillage (RT) consists of soil tillage with notched-edge discs, without soil inversion, to a depth of 8–10 cm.Two trials are underway at the EFELE experimental site :Zea mays L.) and winter wheat (Triticum aestivum L.), with a N catch crop (CC) of white mustard  sown at the beginning of September, 2 months after the wheat harvest. Rates of mineral N fertilizer applied to crops were calculated using the mineral N balance-sheet method recommended in France The crop rotation consists of maize  and the 4 plots of block 1 of the TS/MO trial, 2 pairs of fiberglass-wick lysimeters were installed in each plot . Each is made of a 50 × 25 × 2 cm stainless steel plate with a fiberglass wick spread over the plate before the plate is pressed up against the soil layers above. The whole wick goes through a hole in the center of the plate, through a TygonⓇ tube and down to a receiving glass flask (10 l). Fourteen flasks are equipped with ultrasonic sensors (Telemecanique Sensor XX918A3C2M12) that monitor filling of the flasks, so that water can be sampled soon after drainage has stopped to minimize changes in water composition.In pits dug into 6 plots of block 1 of the PROs trial . Total rainfall from November to mid-April was significantly lower in 2016–2017 than that during the 3 other winters, and the drainage periods varied from 1 month in 2016–2017 to 4.5 months in 2014–2015 .62 l − 1, 6.4% lay below the quantification threshold of 0.15 mg NO2 l − 1, and only 5.4% had a concentration greater than 5 mg NO2 l − 1. Concentrations of DOC were determined with a TOC-VCSH analyzer  using thermal oxidation Water was collected and sampled as a function of drainage events, with the objective of collecting water as soon as possible after drainage had stopped (within 2–7 days). Water samples were filtered at 0.45 µm and stored at 4 °C until analysis. Nitrate and nitrite concentrations were determined by ion chromatography  Not applicable.The authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the work reported in this article.


In this study, we aimed to investigate the contribution of respiratory gas exchange (RGE) metrics  to low frequency CHF during spontaneous breathing.The origin of low frequency cerebral hemodynamic fluctuations (CHF) in the resting state remains unknown. Breath-by breath OTwenty-two healthy adults were included. We used transcranial Doppler sonography to evaluate CHF by measuring the changes in cerebral blood flow velocity (ΔCBFv) in bilateral middle cerebral arteries. The regional CHF were mapped with blood oxygenation level dependent (ΔBOLD) signal changes using functional magnetic resonance imaging. Temporal features and frequency characteristics of RGE metrics during spontaneous breathing were examined, and the simultaneous measurements of RGE metrics and CHF (ΔCBFv and ΔBOLD) were studied for their correlation.2 and ΔPCO2 were interdependent but not redundant. The oscillations of RGE metrics were coherent with resting state CHF at the frequency range of 0.008–0.03Hz. Both bER and ΔPO2 were superior to ΔPCO2 in association with CHF while CHF could correlate more strongly with bER than with ΔPO2 in some brain regions. Brain regions with the strongest coupling between bER and ΔBOLD overlapped with many areas of default mode network including precuneus and posterior cingulate.We found that the time courses of ΔPOAlthough the physiological mechanisms underlying the strong correlation between bER and CHF are unclear, our findings suggest the contribution of bER to low frequency resting state CHF, providing a novel insight of brain-body interaction via CHF and oscillations of RGE metrics. Low frequency components below 0.05 Hz) in the cerebral hemodynamic fluctuations (CHF) are used to characterize functional connectivity of cerebral resting state networks including the default mode network (DMN) , 2. The  Hz in th2) as a metabolic waste from the blood and replenishing oxygen (O2) for energy consumption. Breath-by-breath RGE metrics include parameters like end-tidal partial pressures of O2 (PETO2) and CO2 (PETCO2), changes of the partial pressure of O2 (ΔPO2) and CO2 (ΔPCO2) [2 and PCO2 as regulated variables, peripheral and central chemoreceptors as sensors, brain stem as the control center, and diaphragm and respiratory muscles as effectors, to optimize systemic blood gases. While the detailed mechanisms between the change in central chemoreceptor activities and the change in cerebral blood flow (CBF) are topics of on-going research [2 and PCO2 which are sensed by chemoreceptors are maintained within a range (or fluctuate) around the physiological ‘set point’ (i.e. mean) by the feedback control of diaphragm and respiratory muscles for ventilation in the homeostatic regulatory system. Spontaneous breathing is, therefore, part of a vital homeostatic process to optimize the systemic blood gases which can presumably regulate in turn CBF and O2 delivery to the brain [2 or PCO2 may interact synergistically and contribute to fluctuations of CHF during spontaneous breathing at rest.Fluctuations of respiratory gas exchange (RGE) are of particular interest because RGE is a physiological process of removing carbon dioxide (CO (ΔPCO2) , 8. Accoresearch –11, artehe brain . Such hoETO2, PETCO2, respiratory exchange ratio) had been reported to be below 0.05Hz in humans [2 to ΔPCO2 between end inspiration and end expiration which we named breath-by-breath exchange ratio (bER), to quantify RGE as well [2, ΔPCO2 and bER. It is interesting that bER was superior to either ΔPO2 or ΔPCO2 alone in coupling with the changes of global/regional cerebral hemodynamic response in our breath hold study. In this manuscript, we hypothesized a brain-body interaction during spontaneous breathing where various RGE metrics would separately contribute to CHF and the coupling of CHF with bER would be the strongest. Our study was different from previous works by Wise et al. [2 and PO2 were redundant.RGE may be related to CHF because oscillations of RGE metrics  and CO2 (PCO2) are simply mirror image of each other [2, CO2 and their ratio bER on CHF during spontaneous breathing.The oscillations of Pch teams , 17, 18 hallenge . Notablyt et al. . The nond PETCO2 , 17, 18 ch other , and encETO2 and PETCO2, we focused more on the contribution of RGE metrics including ΔPO2 and ΔPCO2 and bER in this manuscript. We preferred to use the ratio of ΔPO2/ΔPCO2 for the respiratory gas exchange instead of PETCO2/PETO2 with two reasons that we have explained with the findings in our recent breath hold study [2 and ΔPCO2, but not to both PETCO2 and PETO2. The time courses of PETCO2 and PETO2 oscillate out of phase, while ΔPO2 oscillates in phase with ΔPCO2. Second, bER is a breath-by-breath dynamic form related to the steady-state respiratory exchange ratio (RER) described in the alveolar gas equation introduced by Fenn et al. [2 and not PETO2 is the designated term used in RER from the alveolar air equation [2 is used as numerator in bER in this manuscript because of the strong positive correlation found previously between bER and cerebral hemodynamic responses under brief breath hold challenge [In addition to the more commonly used Pld study . First, ld study  common tn et al. ; the timequation , 19. ΔPOhallenge . RER hashallenge –22. Therhallenge . Traditi2 and PCO2 breath-by-breath in humans, we studied RGE metrics as surrogates of arterial blood gases with the recognition of the difference between respiratory metrics and blood gases. We studied the interaction between RGE metrics and CHF measured with transcranial Doppler sonography (TCD) and functional magnetic resonance imaging (fMRI). TCD has an advantage of acquiring data at high temporal resolution (~100 Hz), eliminating the concern of unwanted high frequency cardiovascular signal being aliased into the low frequency range which has a potential association with the minute-long oscillation of RGE metrics. The cerebral blood flow velocities (CBFv) were measured by TCD in the middle cerebral arteries (MCA) which supply most parts of the brain. The application of TCD allows the subjects to have measurements in an upright seated position, which is the usual position in respiratory physiology studies. Although TCD offers a high temporal resolution to evaluate CHF, it does not provide regional information. Regional mapping of spontaneous CHF was carried out instead with blood oxygen level-dependent (BOLD) signal changes measured by fMRI. We used BOLD-fMRI instead of arterial spin labeling (ASL) in MRI perfusion studies for two major reasons. ASL perfusion-related signal has a low contrast to noise ratio in comparison with the BOLD signal, especially in white matter area. ASL image acquisition at a temporal resolution of 4 seconds also under-samples the spontaneous fluctuations within the respiratory cycle of 4–6 seconds, which hampers the dynamic analyses between CHF and RGE metrics. While CBFv and BOLD signals are not equivalent surrogates for CBF, combining their strengths would be powerful to study the temporal and spatial features in the association between RGE and CHF.Given the dynamic changes in PO2, ΔPO2, PETCO2 and PETO2. In the TCD study, we measured the correlation of CBFv in the MCA with RGE metrics of bER, ΔPO2 and ΔPCO2. We also examined the temporal features and frequency characteristics of these RGE metrics and their coherence with CBFv. In the fMRI study, we mapped the association between regional BOLD signal changes and RGE metrics of bER, ΔPO2 and ΔPCO2. Brain regions showing a significant association between regional BOLD signal changes and RGE metrics were then compared with regions within the default mode network (DMN) outlined by the resting state connectivity analysis with the seed at the left precuneus. DMN encompasses brain regions responsible for the constant background activities at rest, showing higher metabolic and hemodynamic level than the other parts of the cortex [2 challenge, the potential of using the interaction between CHF and RGE metrics to evaluate CVR to the elements in spontaneous breathing was also discussed.In the present study, we aimed to evaluate the contribution of breath-by-breath RGE metrics to the CHF indicated by CBFv and BOLD signal changes during spontaneous breathing. To address the question of redundancy among RGE metrics during spontaneous breathing, we examined the correlations among bER, ΔPCOe cortex . The temTwenty-two volunteers aged from 19 to 48 years  were included. Eleven of them participated in both TCD and MRI sessions, while the remaining participated in either one of the sessions. Subject demographics were shown in 2 and ΔPO2 with CBFv in MCAs which serve as CHF in the major cerebral arterial supply during spontaneous breathing. We also examined the temporal features and frequency characteristics of these RGE metrics and their coherence with CBFv. Thirteen subjects participated in TCD sessions. In Part II MRI study, we aimed to map the association between these RGE metrics  and BOLD signal changes which serve as regional CHF during spontaneous breathing. Twenty subjects participated in MRI sessions. Ten out of 20 subjects had additional exogenous CO2 challenge in the MRI sessions. Before we correlated the changes of RGE with CBFv and BOLD signal changes, we examined the correlations among the respiratory metrics  acquired in both TCD and MRI sessions.Our study was divided into two parts: Part I and Part II. In Part I TCD study, we aimed to correlate the RGE metrics including bER, ΔPCOBefore the study of blood flow velocity in intracranial arteries, the subject was allowed to rest at least 20–30 minutes in an upright seated position for hemodynamic stabilization. The blood pressure measured in the subject was within the normal range of systolic blood pressure below 130 mmHg . With thA white crosshair in the black background was presented visually to the subject by a computer using the software Eprime Professional 2.0  to fixate their eye movement. The total duration of the CBFv data acquisition lasted 10 minutes.2, PO2, electrocardiogram (ECG) and peripheral blood pressure were measured simultaneously with TCD acquisition. A biological amplifier  and a finometer  were used to measure ECG and peripheral blood pressure, respectively. A small nasal tubing was placed at the subject’s nostril to sample PCO2 and PO2 via gas analyzers  after calibrating to the barometric pressure on the day of TCD session and correcting for vapor pressure. Small nasal tubing was chosen to sample PCO2 and PO2 because of several reasons. In the current study, we standardized all the physiological set-up in both TCD and MRI sessions. We did not measure PCO2 and PO2 from a facemask connected to a closed breathing circuit with non-rebreathing valves because of the space constraint of the MRI head coil, or from the expired gases collected in Douglas bag because of the slow sampling of gases in the units of minutes. Sampling gases with small nasal tubing has an advantage that the subjects breathe normally through the nose. In the gas sampling circuit, the same gas sample volume was used in both CO2 and O2 analyzers at the same gas sampling flow rate. The CBFv and physiological measurements were synchronized using trigger signals from E-prime. All the CBFv time series and physiological recordings were stored for offline data analysis.Physiological changes including PCO2 and PO2 in the MRI session were the same as those used in the TCD session. The gas analyzers were again calibrated to the barometric pressure on the day of MRI session and corrected for vapor pressure. ECG was measured using a Siemens physiological monitoring unit . Physiological changes including PCO2, PO2, ECG and respiration were measured simultaneously with MRI acquisition. All the physiological measurements, including those of PCO2, PO2 and ECG were synchronized using trigger signals from the MRI scanner. BOLD-fMRI images and physiological recordings were stored for offline data analysis.MRI brain scanning was performed on a 3-Tesla scanner . The head was immobilized in a standard head coil with foam pads. The following whole brain MRI datasets were acquired on each subject: 1) standard high-resolution sagittal images acquired with volumetric T1-weighted 3D-MEMPRAGE ; 2) BOLD-fMRI images acquired with gradient-echo echo planar imaging (EPI) sequence  while the subject was at rest. The visual presentation of the crosshair, the physiological set-up for the sampling of PCO2 challenge in the MRI sessions. An in-house gas delivery and mixing system comprising of a medical gas mixer in series with a manifold of flow meters was used to mix and deliver gas mixture for exogenous CO2 challenge. Given that there is significant inter-individual variance in resting PETCO2 [, resting PETCO2 was assessed in subjects via calibrated capnograph before the exogenous CO2 challenge. The subject wore nose-clip and breathed through a mouth-piece on an MRI-compatible circuit designed to maintain the PETCO2 within ± 1–2 mmHg of target PETCO2 [. The fraction of inspired carbon dioxide was adjusted to produce steady-state conditions of normocapnia and mild hypercapnia (4–8 mmHg above the subject’s resting PETCO2). The CO2 challenge paradigm consisted of 2 consecutive phases (normocapnia and mild hypercapnia) repeating 6 times with 3 epochs of 4 mmHg increase and 3 epochs of 8 mmHg increase of PETCO2. The normocapnic phase lasted 60–90 seconds, while the mild hypercapnic phase lasted 30 seconds. The same paradigm was also used and described in our other study [2 hypercapnic challenge lasted 10 minutes.Ten out of 20 subjects had additional exogenous COg PETCO2 , restingt PETCO2 , 27. Theer study . The tot2 challenge in MRI session, BOLD-fMRI images were acquired using the same EPI sequence for resting state. The PCO2 and PO2 were sampled through the air filter connected with the mouthpiece, and the sampled gases were measured by calibrated gas analyzers. The respiratory flow was measured with respiratory flow head  on the breathing circuit via calibrated spirometer . The physiological measurements were synchronized with MRI images using trigger signals from the MRI scanner. All the BOLD-fMRI images and physiological recordings were stored for offline data analysis.When the subject had exogenous CO2 and PO2 was corrected by cross-correlating the time series of PCO2 and PO2 with respiratory phases determined from the artifactual displacement due to chest excursion on ECG time series in the TCD sessions, with the respiratory phases from respiratory bellow or respiratory flow measured with respiratory flow head via spirometer in the MRI sessions.The physiological data from both TCD and MRI sessions were analyzed using Matlab R2014a . Technical delay of PCO2 and PCO2 (ETCO2 and PETO2 were extracted at the end expiration of PCO2 and PO2 time series respectively. ΔPO2 is defined as (inspired PO2 –expired PO2) and ΔPCO2 is defined as (expired PCO2 –inspired PCO2). Breath-by-breath O2-CO2 exchange ratio (bER) is defined as the ratio of ΔPO2 to ΔPCO2 measured between end inspiration and end expiration at each breath, whereas RER at steady state from alveolar air equation introduced by Fenn et al. [2 to ΔPO2 over minutes. The product of ΔPO2 and ΔPCO2 was not used to evaluate the interaction with CHF because the effects of fluctuations due to ventilation would be exacerbated in ΔPO2×ΔPCO2 (End inspiration (I) and end expiration (E) were defined on the time series of POand PCO2 . The bren et al.  is formuO2×ΔPCO2 .2, and ΔPO2) in pairs. The correlation was considered significant at p<0.05.Simple correlation analyses were applied to the time series of RGE metrics . A median filter was applied to the data to reduce artifactual spikes. Beat-by-beat systolic peaks and end-diastolic troughs were determined using custom Matlab function and corrected on the graphical user interface incorporated in the function. Systolic peaks and diastolic troughs of cardiac cycles on the CBFv time series showing persistent artifacts were excluded in the following analysis. TCD data in both left and right MCAs were acquired on 13 subjects. One of the 13 TCD datasets had persistent artifacts in over one-third of the CBFv time series acquired in the LMCA, and another one had persistent artifacts in CBFv data acquired in RMCA. The CBFv time series of those particular TCD runs that showed persistent artifacts were excluded in further analysis, and the CBFv time series acquired in the contralateral MCA that did not show persistent artifacts were retained. Time series of mean CBFv were derived by integrating the CBFv over each cardiac cycle. To reduce the large inter-individual variations of absolute blood flow velocities , 29 and 2 and ΔPO2 separately. The correlation indicated by Pearson's correlation coefficient was considered significant at p<0.05. Fisher’s Z-transformation was used to transform Pearson’s correlation coefficients to Fisher’s z scores for group analysis. Paired t-tests were used to compare the Fisher’s z scores representing the correlation between ΔCBFv and bER with those indicating the correlation between ΔCBFv and other physiological parameters besides bER. Differences were considered to be significant at p<0.05. We did not apply a low pass filter to CHF before our correlation analyses, even though applying a low pass filter to CHF is a standard preprocessing step in the resting state analysis [The time series of ΔCBFv were correlated with those of bER, ΔPCOanalysis .2, and ΔPO2, as well as the phase lag of ΔCBFv to bER, ΔPCO2 and ΔPO2. We used the Matlab wavelet cross-spectrum toolbox developed by Grinsted et al. [Wavelet transform coherence (WTC) was employed to demonstrate the dynamic interaction between ΔCBFv and RGE metrics  in the td et al. . Squaredd et al. . An arroTime-averaged coherence is defined as the total significant coherence at each scale of Fourier periods (converted into frequency) where the wavelet coherence magnitude exceeded 95% significance level, normalized by the maximum possible coherence outside the cone of influence at that particular scale . It is i2 and ΔPO2) when they were at rest.Interpreting the time-averaged coherence irrespective of phase lag raised the question that the coherence with positive correlation between two time series (at phase lag of 0±π/2) and the coherence with negative correlation (at phase lag of π±π/2) might be mixed together. Therefore, mean time-averaged coherence at the phase lags of 0±π/2 and π±π/2 were separately averaged across all the subjects who participated in the TCD sessions to explore the Fourier periods/frequency bandwidths that oscillations of ΔCBFv were in synchrony with the time series of each RGE metric  for time-shift correction, motion correction, normalization and detrending. Details of preprocessing with AFNI are given as follows. The first 12 volumes in the first 12 time points of each functional dataset, collected before equilibrium magnetization was reached, were discarded. Each functional dataset was corrected for slice timing, motion-corrected and co-registered to the first image of the functional dataset using three-dimensional volume registration. Components of motion were removed from the co-registered functional dataset using orthogonal projection. The clean functional dataset was then normalized to its mean intensity value across the time-series. Voxels located within the ventricles and outside the brain defined in the parcellated brain volume using FreeSurfer [http://surfer.nmr.mgh.harvard.edu) were excluded from the following analyses of functional images. Individual subject brain volumes with time series of percent BOLD signal changes (ΔBOLD) were derived.All the BOLD-fMRI data were imported into the software Analysis of Functional NeuroImage (AFNI)   value was defined as the percent BOLD signal changes per unit change of the regressor . Individual subject brain volumes with β magnitudes were registered onto their own anatomical scans and transformed to the standardized space of Talairach and Tournoux [3 contiguous volume would provide the significance level α<0.05, which met the overall corrected threshold of p<0.05.Linear regression analysis was used to evaluate the association between ΔBOLD, bER, ΔPOTournoux . Monte CTournoux . To protTournoux , it was bER), ΔBOLD on ΔPO2 (βΔPO2) and ΔBOLD on ΔPCO2 (βΔPCO2) were separately averaged in each of the 160 brain regions parcellated by the software FreeSurfer. One-sample t-tests were used to analyze regional βbER, βΔPO2 and βΔPCO2 in the subject group. False discovery rate was used to correct for multiple comparisons [fdr<0.05.For each subject who participated in MRI scanning, β magnitude values derived by regressing ΔBOLD on bER , ΔPO2 (voxelβΔPO2) and ΔPCO2 (voxelβΔPCO2) were obtained. One-sample t-tests were used to analyze regional voxelβbER, voxelβΔPO2 and voxelβΔPCO2 in the subject group. False discovery rate was used to correct for multiple comparisons [fdr<0.05.For each brain region, we also calculated the number of voxels with significant ΔBOLD that reached cluster-corrected threshold p<0.05 in the individual subject analysis. The number of voxels with significant ΔBOLD were then normalized to the total number of voxels in each brain region. The percentage of voxels in each brain region with significant ΔBOLD, namely voxelβparisons , 42. SigbER, βΔPO2 and βΔPCO2 instead of the commonly used voxel-by-voxel analysis because the maps of β values were compared side-by-side with the maps of voxelβbER, voxelβΔPO2 and voxelβΔPCO2 which require the ROI analysis to evaluate the percentage of voxels in each brain region with significant ΔBOLD.In the group analysis, we preferred the ROI analysis of 160 brain regions for βfdr<0.05.Seed-based analysis with the seed at the left precuneus was used to generate the functional connectivity map for an individual subject. For each subject, after preprocessing of BOLD data, a low pass filtering at 0.03Hz was applied onto the brain volume with time series of ΔBOLD. The time series of ΔBOLD in the voxels within left precuneus were averaged. The averaged ΔBOLD time series of left precuneus was correlated with the ΔBOLD time series of each voxel in the brain volume. Pearson's correlation coefficient was used to indicate the strength of correlation and converted to z scores using the Fisher’s Z transformation. For the comparison with the regional β and voxelβ maps, the Fisher’s z scores in each of the 160 brain regions were averaged for each subject. Individual subject brain volumes with regional Fisher's z scores from all the subjects who participated in MRI sessions were subjected to group analysis using a one-sample t-test. False discovery rate was again used to correct for multiple comparisons , 41, 42.2, and ΔPO2) and ΔBOLD in three brain regions within DMN. They included inferior parietal lobule (IPL), posterior cingulate (PCC) and precuneus (PCun). The analysis procedures were the same as those described for the dynamic analysis of coherence between ΔCBFv and RGE metrics. The mean time-averaged coherence between each RGE metric and ΔBOLD from each of the three brain regions at the phase lag of 0±π/2 was averaged across all the subjects who participated in MRI sessions. Similarly, the mean time-averaged coherence between each RGE metric and ΔBOLD from each of the three brain regions at the phase lags of π±π/2 were averaged across the same group of the subjects.To further verify the dynamic coupling between bER and CHF in DMN, we used the WTC method to examine the dynamic changes in coupling between the time series of RGE metrics  were separately averaged in each of the 160 brain regions parcellated by the software FreeSurfer. To study the CVR in group, one-sample t-tests were applied onto the brain volumes with regional CVRCO2-PETCO2. False discovery rate was used to correct for multiple comparisons.For each subject who participated in exogenous COETCO2, PETO2, ΔPCO2, ΔPO2 and bER measured in the TCD and MRI sessions are summarized in Subject demographics are shown in 2 and ΔPCO2) in TCD and MRI sessions are shown in 2 and ΔPCO2 ranged from 0.7 to 0.9 in TCD sessions and from 0.2 to 0.9 in MRI sessions, demonstrating that ΔPO2 and ΔPCO2 are not necessarily redundant in either TCD or MRI sessions. The range of correlation strength between ΔPO2 and ΔPCO2 in the MRI sessions was larger than that in TCD sessions. Correlation between bER and ΔPO2 was stronger than that between bER and ΔPCO2.The correlations among the RGE metrics  for all 13 subjects who participated in TCD sessions are shown in 2 with ΔCBFv showed that ΔPO2 plays an essential role in bER correlation with CHF.With the simple correlation analyses, 2 and ΔPCO2  during spontaneous breathing in a representative subject are shown in bER), ΔPO2 (βΔPO2) and ΔPCO2 (βΔPCO2) .Brain maps on the association between ΔBOLD and RGE metrics  . ComparibER), ΔPO2 (βΔPO2) and ΔPCO2 (βΔPCO2) for all 20 subjects who participated in MRI sessions    did not emporal) .bER), ΔPO2 (voxelβΔPO2) and ΔPCO2 (voxelβΔPCO2) were analyzed in the same group of 20 subjects. Significant association of ΔBOLD with bER and ΔPO2 was shown in more than 50% of the voxels in the gray matter regions , left and right posterior cingulate (PCC), and left and right precuneus (PCun) in all 20 subjects participated in MRI sessions. At the phase lag of 0±π/2, we showed that the mean time-averaged coherence between bER and ΔBOLD and that between ΔPOTo confirm that the RVT had little contribution to CHF within the DMN, we used the WTC method to examine the dynamic coupling between RVT and ΔBOLD extracted from IPL, PCC and PCun in 10 subjects who had their respiratory tracings measured by a respiratory bellow. We showed that the mean time-averaged coherence between RVT and ΔBOLD at the phase lag of 0±π/2 increased between 0.016 and 0.031Hz, and reduced at the frequency below 0.016Hz where the mean time-averaged coherence started to increase at the phase lag of π±π/2 . The fre2 challenge, most of the brain regions showed increased CVRCO2-PETCO2 in the subject group, especially thalamus, insula and putamen  and were coherent with CHF in this frequency range. The coherence of CHF with bER or with ΔPO2 was much stronger than the coherence of CHF with ΔPCO2 in the frequency range between 0.008Hz and 0.03Hz. bER was shown in some brain regions to be superior to ΔPO2 in the association with CHF. Brain regions with the strongest bER-CHF coupling overlapped with many areas of DMN. Taken together, our study provides evidence that resting state CHF at low frequency show the strongest association with fluctuations attributed to bER.There has been no previous study on the dynamic interactions between low frequency fluctuations of resting state CHF (ΔCBFv and ΔBOLD) and those of all three RGE metrics of bER, ΔPO2 and ΔPCO2 were often considered to be redundant [2 and ΔPCO2 demonstrated that while ΔPO2 and ΔPCO2 were interdependent they were not redundant to each other  showed association between ΔPCO2 and ΔBOLD  and RGE metrics of bER, ΔPOTCD Figs  and MRI TCD Figs  and 4. Hth ΔCBFv . The mapnd ΔPCO2 . Group and ΔBOLD  but suchnd ΔBOLD . Our gro2 and CHF is accompanied by an interaction between ΔPO2 and CHF. However, the mechanisms behind the superiority of ΔPO2 over ΔPCO2 in association with CHF, especially at the frequency range of 0.008–0.03Hz, remain unclear. A possible factor may be related to the difference in the O2 and CO2 dissociation curves, which are associated with the magnitude of the PO2 and PCO2 variations in time [2 varies from approximately 150mmHg in inspired air to 100mmHg in expired air at the top horizontal asymptote of the sigmoidal O2 dissociation curve, where it is associated with only a small change in oxygen saturation. On the contrary, the CO2 dissociation curve is more linear. With the Haldane effect, O2 affects the affinity of hemoglobin for CO2. Given the small fluctuations of oxygen saturation, a rather significant change in PO2 can, therefore, be associated with a minor change in PCO2. The larger oscillation amplitude of ΔPO2 in comparison with that of ΔPCO2 was observed by our team  have been reported to be related to autoregulation of microvasculature, spontaneous rhythmic oscillations in intracranial pressure (ICP), and intrinsic brainstem rhythm that leads to cerebral blood volume modulation , 66. B-wle cells –70. SincThe coherence of CHF with RGE metrics at the frequency of 0.008–0.03Hz may also be related to a proposed mechanism to remove cerebral metabolic waste. In the glymphatic model , cerebraIn the peripheral circulation, laser Doppler measurements showed that the endothelial activity oscillated at the frequency of 0.0096–0.021Hz , 74, whiSeparate from the B-waves and glymphatic model, we do not consider heart rate (HR) or heart rate variability (HRV) to be a major contributing factor for the role of RGE metrics in CHF. Even though HR and HRV had been reported to contribute to low frequency fluctuations, the peaks of coherence between ΔBOLD and HR/HRV were at the frequency of 0.05Hz or above (period ~30–42 seconds)  which ar2 and ΔPCO2 in their interaction with CHF. First, RVT would be expected to have the same effect on the time courses of ΔPO2 and ΔPCO2. Second, bER, being a ratio of ΔPO2/ΔPCO2, reduces the contribution of ventilatory volume fluctuations to the interaction between bER and CHF. Previous studies showed that the relationship between the time courses of PETCO2 and RVT was unclear [ETCO2 and RVT [ETCO2 [ETCO2 is supposed to play a more direct role than ventilation to modulate CHF [2  with ΔBOLD. If the application of RRF improves the correlation of ΔPCO2 with ΔBOLD, it will also improve the correlation of ΔPO2 or bER with ΔBOLD. There is no justification for applying RRF to only ΔPCO2 and not to ΔPO2. Applying the same RRF to all of the RGE metrics should have little effect on how one RGE metric ranks against other RGE metrics in its association with ΔBOLD. Another approach to state that convolution of RGE metrics with RRF is not applicable in our case because our research question is ‘Which RGE metric contributes more to ΔBOLD?’ whereas studies that took up RRF [ETCO2?’ With a different research question, it was reasonable for those previous studies to focus on convolving the RVT or PETCO2 time series with RRF which identified the portion of the ΔBOLD that was not directly accounted for by the time series of RVT or PETCO2.In our fMRI regression analysis, we did not convolve the RGE metrics with a specific respiratory response function (RRF) which was commonly used to convolve with RVT or Pth ΔBOLD , 6, 16. k up RRF , 6, 16 f2 is related to the partial pressure of O2 utilized in the whole body, we cannot simply substitute ΔPO2 and ΔPCO2 for O2 uptake (VO2) and CO2 release (VCO2). O2 uptake and CO2 release require extra elements like respiratory minute volume  and are typically evaluated as a steady state of RGE data obtained by averaging the breath-by-breath signal over minutes. A measurement of breath-by-breath VO2 and VCO2 inside the MRI scanner in addition to the collection of ΔPO2 and ΔPCO2 was not included in our study. Given the physical constraint of the MRI settings, we collected ΔPO2 and ΔPCO2 using a nasal tubing. We will leave the possibility of measuring VO2 and VCO2 during MRI to future neuroimaging research. However, under specific conditions, some information extracted from ΔPO2 and ΔPCO2 can be related to that from VO2 and VCO2. As mentioned above, bER has the explicit influence on suppressing the ventilatory volume when we are taking the ratio of ΔPO2 and ΔPCO2. We, therefore, consider the possibility of bER or equivalently ΔPO2/ΔPCO2 being a surrogate for breath-by-breath VO2/VCO2 at rest.Even though ΔPO2 to modulate CBF is an entrenched belief, it is natural to gravitate towards the explanation that association between RGE metrics and CHF must be resulting from “the effect of CO2 which reflects in O2”. However, the model of CO2 being the sole agent to interact with CHF remains at variance with our findings of non-redundancy between ΔPO2 and ΔPCO2 in this study. Therefore, further investigations on the roles of bER, ΔPO2 and ΔPCO2 in their association with CHF would be warranted.As the vasodilatory role of CO2 as a regressor to evaluate CVR to spontaneous breathing  measured by respiratory bellow in a representative subject during spontaneous breathing in TCD session. Open circles represent end expiration while closed circles represent end inspiration. Positive phases with deflection above zero on the respiration time series represent inspiration and negative phases with deflection below zero represent expiration. The inspiratory and expiratory phases of each respiratory cycle on the time series of PETO2 and PETCO2 are verified by those on respiration time series. The timing for open (end expiration) and closed (end inspiration) circles in green is the same as those in red and blue.A segment of 90-second time series of ΔCBFv in left MCA and physiological changes including breath-by-breath bER, ΔPO(TIF)Click here for additional data file.S2 Figupper left). Moderate correlation was shown between ΔCBFv and bER (upper right). Time series of ΔCBFv and the product of ΔPO2 and ΔPCO2 (ΔPO2×ΔPCO2) normalized to its mean (lower left). Weak correlation was shown between ΔCBFv and ΔPO2×ΔPCO2 (lower right).Time series of ΔCBFv and bER normalized to its mean ((TIF)Click here for additional data file.S3 Fig(A) Time series of bER and ΔCBFv measured in right MCA of a representative subject at rest. (B) The squared wavelet coherence between these two time series. Squared wavelet coherence is plotted with x-axis as time and y-axis as scale which has been converted to its equivalent Fourier period. The magnitude of wavelet transform coherence ranges between 0 and 1, where warmer color represents stronger coherence and cooler color represents weaker coherence. Areas inside the ‘cone of influence’, which are locations in the time-frequency plane where edge effects give rise to lower confidence in the computed values, are shown in faded color outside of the conical contour. The statistical significance level of the wavelet coherence is estimated using Monte Carlo methods and the 5% significance level against red noise is shown as thick contour. The phase angle between the two time series, with bER leading ΔCBFv, at particular samples of the time-frequency plane is indicated by an arrow . There are four different ranges of phase lags: 0+π/2, 0-π/2, π-π/2, and π+π/2. (C) Time-averaged coherence at four different phase lags of 0+π/2, 0-π/2, π-π/2, and π+π/2. At each phase lag range, time-averaged coherence was defined as the total significant coherence at each scale where the wavelet coherence magnitude exceeded 95% significance level, normalized by the maximum possible coherence outside the cone of influence, i.e. inside the conical contour, at that particular scale and phase lag range.(TIF)Click here for additional data file.S4 FigbER, βΔPO2 and βΔPCO2 in a representative subject after correcting for multiple comparisons. (B) Group maps of regional βbER, βΔPO2 and βΔPCO2 before correcting for multiple comparisons for all the subjects included in the MRI sessions.(A) Brain maps of β(TIF)Click here for additional data file.S5 Figleft panel) and of the right brain (right panel) (n = 10). Color shaded areas represent standard error of the mean. Coherence between two time series at the phase lag of 0±π/2 indicates positive correlation, while negative correlation is represented by the coherence at the phase lag of π±π/2.The mean time-averaged coherence between time series of RVT and ΔBOLD at the phase lags of 0±π/2 and π±π/2 (thick color lines) in the brain regions of the inferior parietal lobule (IPL), posterior cingulate (PCC) and precuneus (PCun) of the left brain ((TIF)Click here for additional data file.S6 FigbER changes resembled the CVR map under exogenous CO2 challenge indicated by CVRCO2-PETCO2.The CVR map during spontaneous breathing indicated by β(TIF)Click here for additional data file.S1 Table2 and ΔPCO2 in all subjects who participated in TCD sessions (n = 13), and those who participated in MRI sessions (n = 20).Strength of correlation indicated by Pearson’s correlation coefficients among respiratory metrics including bER, ΔPO(DOCX)Click here for additional data file.S2 Table2, ΔPCO2 and PETCO2 (n = 13). Numbers in brackets next to Pearson’s correlation coefficients indicate p values from individual correlation analyses. The bottom row shows the mean values of Fisher’s Z scores transformed from Pearson’s correlation coefficients in groups. Numbers in brackets next to mean Fisher’s Z scores indicate p values in the paired comparisons.Strength of correlation indicated by Pearson’s correlation coefficients between ΔCBFv and RGE metrics including bER, ΔPO(DOCX)Click here for additional data file.


Reverse intersystem crossing (RISC), the uphill spin-flip process from a triplet to a singlet excited state, plays a key role in a wide range of photochemical applications. Understanding and predicting the kinetics of such processes in vastly different molecular structures would facilitate the rational material design. Here, we demonstrate a theoretical expression that successfully reproduces experimental RISC rate constants ranging over five orders of magnitude in twenty different molecules. We show that the spin flip occurs across the singlet–triplet crossing seam involving a higher-lying triplet excited state where the semi-classical Marcus parabola is no longer valid. The present model explains the counterintuitive substitution effects of bromine on the RISC rate constants of previously unknown molecules, providing a predictive tool for material design. Understanding and predicting the kinetics of reverse intersystem crossing (RISC) facilitates the design of materials. Here, the authors demonstrate a theoretical expression that reproduces experimental RISC rate constants ranging over five orders of magnitude in selected molecules. A relevant example is reverse intersystem crossing (RISC), the uphill transition of a non-emissive triplet excited state to an emissive singlet excited state. This process leads to E-type delayed fluorescence, also known as thermally activated delayed fluorescence (TADF), and allows an internal charge-to-photon conversion efficiency of nearly 100% in organic light-emitting diodes10. Although materials have typically been discovered experimentally, a fundamental understanding of RISC kinetics and strategy for predicting the rate constants may open vast opportunities for theory-driven materials discovery.Electronic spin-flip processes in molecular excited states have attracted increasing interest for optoelectronics14. If the spin–orbit coupling HSO between the initial triplet and final singlet excited states is weak, meaning that the spin-flip only occurs on the crossing seam between their potential energy surfaces (PESs)  follows a Marcus-like nonadiabatic expression:ћ is the reduced Planck constant, kB is the Boltzmann constant, T is the temperature, λ is the reorganization energy, and EA is the activation energy to reach the crossing seam. In the case of simple parabolic PESs with equal force constants, which is a crucial assumption of Marcus theory, EA can be analytically expressed asEST as the adiabatic singlet–triplet energy difference. A key implication of Eqs.  Fig. , the RISentclass1pt{minimae19 Fig. . Since Eentclass1pt{minimakRISC values from differential rate equations of the population densities of their singlet and triplet excited states /2 while simultaneously fulfilling the crossing condition of the energy difference ES − ET = 0. ES and ET were calculated at the level of time-dependent density functional theory (TDDFT) within the Tamm–Dancoff approximation24 (see the Methods for details).Directly computing from Eq.  requiresHSO of 0.17–3.61 cm–1 with fairly small EA of 0.11–0.32 eV, corresponding to kRISC of 102–107 s–1 calculated using Eq.  reaches only 0.23, whereas a larger MALE of 1.2, corresponding to an error of 1.2 orders of magnitude, is observed for the values based on the conventional model shown in Fig. kRISC.For the MESX geometries of the twenty molecules shown in Fig. 1) does not cross the lowest triplet state (T1) and instead crosses the higher-lying triplet state (T2) at the obtained MESX geometry, consistent with the model shown in Fig. 1 and T1 to a nonzero exchange interaction between the singlet and triplet states, which leads to T1 always lying below S1 if the two states have the same electronic configuration25. In accordance with El-Sayed’s rule26, a large change in the orbital angular momentum between S1 and T2 consisting of different electronic configurations induces an effective HSO and thus enables spin flipping via the MESX. These results are consistent with the RISC picture anticipated based on recent theoretical and experimental studies using ACRXTN16 and 4CzIPN19. It must be stressed that S1–T2 MESX is present in every molecule examined in this quantitative study despite their wide variety of excited-state electronic configurations, including intramolecular charge transfer (CT) states and locally excited (LE) states of π–π* and n–π* on either donor or acceptor units, illustrating the generality of RISC via S1–T2 crossing in organic donor–acceptor molecules.Closer inspection of the data further reveals that the lowest singlet excited state xanthone (Br-ACRXTN) and 3-xanthone (Br-3-PXZ-XO)  Fig. . Althoug ns Fig. , which iues Fig. , and thikRISC by bromination of ACRXTN is due to a decrease in HSO from 0.88 cm–1 to 0.72 cm–1 at the S1–T2 MESX geometries. This counterintuitive substitution effect of bromine on HSO can be rationalized by two factors. First, the S1–T2 spin flipping in Br-ACRXTN is compensated by a smaller change in the orbital angular momentum than that in ACRXTN 2 and the mean energy (ES + ET)/2 are minimized, were obtained by the gradient projection method23 using a composed gradient vector G for the nuclear coordinates Q:The geometries of the singlet–triplet MESXs, where the square energy difference  basis set within the Tamm–Dancoff approximation24. The range-separated parameters for the LC-BLYP functional were non-empirically optimized for each molecule to incorporate a reasonable amount of exact exchange34. The geometry optimization of the MESXs was performed with the GRRM17 program35, which refers to the energy and gradient calculated by the Gaussian 16 program36. The HSO values were calculated perturbatively using the Breit–Pauli spin–orbit Hamiltonian with an effective charge approximation implemented in the PySOC program37 interfaced to the Gaussian 16 program. The EA values were calculated as the electronic energy difference between the MESX and the equilibrium T1. The λ values were calculated as the difference between the T1 electronic energies at the equilibrium T1 and S1 geometries.In Eq. , the firThe synthetic procedures and characterization data of the compounds are detailed in Supplementary Information Section 2 using a Fluorolog-3 fluorescence lifetime spectrometer (HORIBA) with a 370 nm LED excitation source. The absolute PL quantum yields were determined under a flow of N2 using a C9920 integrating sphere system (Hamamatsu Photonics). The method for determining the experimental kRISC values is detailed in Supplementary Information Section Steady-state photoluminescence spectra were acquired using a Fluoromax-4 spectrophotometer (HORIBA) with 370 nm photoexcitation from a Xe arc lamp. Transient photoluminescence decay measurements were performed by time-correlated single photon counting under a flow of NSupplementary InformationPeer Review File


E. coli single cell mRNA levels for two stress responses that depend on bacterial sigma factors with different mode of transcription initiation (σ70 and σ54). By fitting a stochastic model to the observed mRNA distributions, we show that the transition from low to high expression of the σ70-controlled stress response is regulated via the burst size, while that of the σ54-controlled stress response is regulated via the burst frequency. Therefore, transcription initiation involving σ54 differs from other bacterial systems, and yields bursting kinetics characteristic of eukaryotic systems.Transcription is fundamentally noisy, leading to significant heterogeneity across bacterial populations. Noise is often attributed to burstiness, but the underlying mechanisms and their dependence on the mode of promotor regulation remain unclear. Here, we measure  Transcription noise in bacteria is often attributed to burstiness, but the mechanisms are unclear. Here, the authors show that the transition from low to high expression can be regulated via burst size or burst frequency, depending on the mode of transcription initiation determined by different sigma factors. As a consequence, transcription is stochastic4 and may follow either a Poisson distribution —mRNA is synthesized in random, uncorrelated events, with a uniform probability over time—or is described as bursty—mRNA is synthesised in episodes of high transcriptional activity7. Cell-to-cell variability (noise) within a population3 is increased through bursty transcription7. Noise underpins bacterial bet hedging whereby genetically identical cells display population-wide divergent phenotypes11. Bet hedging may offer a competitive advantage ensuring survival and is important in responses of bacteria to antibiotics, acquisition of drug-tolerant persistence and the use of cells harbouring non-native gene control circuits in synthetic biology11. Gene-specific and genome-wide sources of noise have been described7. However, the contributions of many molecular events involved in transcription—in particular those occuring during transcription initiation—are currently largely unknown12.Transcription is a series of discrete interactions of transcription factors and RNA polymerase with the promoter alongside any biochemical steps that these factors undertake13. Specificity factors comprise two distinct classes: the σ70 family combines all sigma factors that bind to −10/−35 promoter elements and in E. coli includes σ70, σ19, σ24, σ28, σ32 and σ38; in contrast, σ54 binds to −12/−24 promoter elements and forms a class of its own. Transcription initiation from σ70-dependent promoters involves the spontaneous isomerisation of the closed RNA polymerase-promoter complex to the open complex14 , for the promoter DNA opening event19  and how it occurs is currently unknown.One major aspect of transcription initiation in bacteria is the need for a specificity factor termed sigma (σ) to direct RNA polymerase to the promoterSuf and Psp, each dependent upon a contrasting σ-factor class. One response manages stress arising from exposure to oxidants28 and iron starvation29, the other manages membrane stress27.In order to evaluate the impact of σ-factors in cell-to-cell variability, we analyse two paradigmatic stress responses, 30 and the Spätzcells software30 31 and burstiness 32. A Fano factor value of 1 corresponds to Poisson distribution (non-bursty), while Fano greater than 1 indicates bursty transcription. We also elaborated a model to provide a conceptual framework for interpreting our data. In the two-state Telegraph model of transcription35 the promoter transitions between an active and inactive state at rates λ and ν respectively. Transcription only occurs in the active state with a mean rate Κ, while mRNA decays at a rate δ. Transcription is bursty if ν ≫ λ and Κ, ν ≫ δ whereby bursts occur at an average frequency of λ/δ and an average size of Κ/ν. In line with previous propositions36 we considered that there may be multiple (nested) regulatory mechanisms at play, operating at different timescales to each other. This leads to a model in which there are multiple states of the transcription apparatus, only one of which is active in initiation  and a primed but inactive state (B). A single active state (A) then exists from which transcription can occur. If switching between states (C) and (B) is relatively slow, this leads to the behaviour displayed in Fig. 38 expressed mathematically as:We used RNA fluorescence in situ hybridizationω refers to the fraction of time in which the gene is in the deep inactive state (C), and is related to the parameters by ω = β/(α + β). This fraction is also the proportion of cells within a measured sample that are in this deeply inactive state. The parameters of the Negative binomial are related to the model parameters via r = λ/δ, and p = ν/(ν + Κ).Here, r, p, ω and consequently burst frequency λ/δ and burst size Κ/ν. Further details are given in the methods section.We then performed parameter estimation via model fitting. To infer parameters we used Bayesian inference via a custom Markov chain Monte Carlo (MCMC) algorithm, in order to obtain the probability distribution of these parameters, in light of the experimental data 39. We investigated the expression profile of the σ70 controlled Suf system to establish whether the behaviour of stress responses under the control of a more complex regulation deviates from that of simpler adaptive systems such as lactose utilisation. Suf is encoded in a single operon (sufABCDSE) and enables the assembly of Fe-S clusters under oxidative stress and iron limitation29. Expression from the PsufA promoter is induced in presence of hydrogen peroxide (H2O2) and/or the iron-chelator bipyridyl (BP)29. Regulation of PsufA in response to these stressors involves the interplay between two activators (OxyR and IscR) and one repressor (Fur)43  to the promoter43  or oxyR (ΔoxyR), under unstressed basal conditions and in presence of H2O2 and BP applied singly and in combination. Cells lacking iscR consistently showed nearly no expression at any condition (data not shown), suggesting that IscR is the major regulator of PsufA, in line with previous findings42. The lack of expression meant that no further insight could be gained from this mutant in understanding the source of noise and burstiness of this promoter.We measured the level of gene expression, transcriptional noise and bursting of native PsufABCD mRNA levels per cell are small         Fig.  suggesti50) Fig.  we inter29) Fig.  with a n20) Fig.  but not 49) Fig. . In cont04) Fig.  or oxyR 97) Fig.  is deletfur) the mean mRNA copy numbers per cell increase several fold  reduced the noise , since noise in wildtype and ΔoxyR under these conditions was largely the same. Generally, the levels of noise and burstiness correlate with the strength of the inducing signal. Application of the stronger inducer BP (singly and in combination with H2O2) resulted in stronger noise reduction and a stronger increase in burstiness than application of the weaker inducer H2O2. Interestingly, noise was slightly lower when BP was applied alone than in combination with H2O2. This was slightly more pronounced in Δfur     to cells that harboured the repressor  Fig.  than in 22) Fig. , while i64) Fig. . Our dation Fig. . Overallω, λ and K/ν underpinning bursty transcription  in which the σ70 controlled promoter is in the deep inactive state (C) is linked to the repression by Fur, since the value of ω is high when Fur is operating (i.e. in wildtype cells in absence of stress) yet ω is always low when cells are lacking Fur . Furthermore, the value of ω in presence of H2O2 showed a strong dependence on OxyR. Indeed, this was one of the strongest effects of OxyR in our entire data set. We thus conclude that a major role for OxyR in the regulation of PsufA transcription is to reduce the time and proportion of cells in which PsufA is in the deep inactive state and thus to prime PsufA for expression under oxidative stress.Fitting our extended Telegraph model to the experimental data of mRNA distributions  of PsufA was largely similar and did not scale with mean mRNA numbers per cell at higher levels of expression, i.e., when repression was removed e.g. through fur deletion or addition of BP (singly or with H2O2) in wildtype and ΔoxyR cells. We note however some modest burst frequency modulation at low expression in unstressed wildtype and ΔoxyR cells and also in ΔoxyR in presence of H2O2  from PsufA was small at low expression (e.g. in unstressed wildtype cells). Burst size scaled however with signal strength and mean mRNA numbers per cell to yield large bursts at high expression , the mean mRNA levels per cell produced from PpspA are low        Fig.  and burs19) Fig. . This ba74) Fig. ; strikin40) Fig.  compared54-dependent promoters strictly requires the mechanochemical action of an enhancer binding transcriptional activator (here PspF)16 .Recall that transcription initiation from σ)16 Fig. . Consequ45. This is due to autoregulation via a negative feedback exerted by PspF on its own expression45    Fig.  than at 92) Fig. . We prop54-dependent promoters, activation (and hence open complex formation) is a multi-step process that involves (i) ATP hydrolysis (inhibited by negative regulation) and (ii) sustained contact of the activator with the closed complex (RNA polymerase/σ54/promoter DNA)19  expressed at low levels which is unable to interact with the negative regulator PspA and thus escapes its inhibitory function49   . We presume that these differences arise from some residual negative regulation that occurs in the native system under stress. Strikingly however, removal of negative regulation of the activator has no marked effect on the burstiness of the σ54 controlled promoter  that has reduced affinity for the closed complex formed by RNA polymerase and σ54 at the promoter51  . Notably however, the promoter is markedly less bursty in presence of PspFT86S (FPspF_T86S = 7.57) , noise (CV2PspF_W56A+T86S = 0.58)     is due to the inefficient remodelling of the closed to the transcriptionally active open complex. Taken together, the quality of the contact between the activator and the closed complex is a determinant of the burstiness but not the level of noise during transcription from σ54 controlled promoters.We utilised a variant form of the activator PspF PspFW6A expres56) Fig.  than in ter Fig. . Followi96) Fig.  is simil57) Fig.  than und58) Fig.  returns 56) Fig. . The mRN89) Fig.  is large54 controlled promoter correlate with the level of expression as is seen with σ70  and increases exponentially with increasing expression level  , indicating non-Poisson mRNA production at all levels of expression  Fig. 4–7,39. Iion Fig. .54 controlled promoter is in the deep inactive state (C) correlates with the level of negative regulation of the activator. It is lowest in the W56A mutant where negative regulation is absent, ATP hydrolysis constitutively active and remodelling of the closed to the transcriptionally active open complex efficient due to the proficient contact of this constitutive activator with the closed complex.Model fitting to the experimental data , but only modest at high level of expression in absence of negative regulation (compare PspFW56A+T86S with PspFW56A) . It increased in wildtype in presence of stress as well as at high activator levels (PspFhigh), in both cases some low level negative regulation still occurs. Yet, burst frequency was highest when negative regulation was completely abolished in the W56A and W56A + T86S mutant. The efficiency of the contact between activator and the closed complex however appears to have no major effect on the burst frequency. We discounted that our observations were simply due to differences in (i) gene dosage  Fig. . In contion Fig. . Burst f4 given that in contrast to other domains, in bacteria burstiness as well as burst size increased with higher expression in all promoters studied to date. This was further interpreted as being indicative of a global control of transcriptional bursting. Contradictory to this idea of gene-independent determinants of burst kinetics, it was shown that burstiness and burst size can be modulated by changing the efficiency of transcription regulation of an individual bacterial gene39.Although it is well established that noise and bursting is a fundamental property of inducible gene transcription, a precise picture of the underlying molecular events has not yet emerged. It is implied that domain specific differences in burst kinetics exist58. Yet, the contribution of sigma factors—whose role is to facilitate transcription initiation—has so far been overlooked. All bacterial promoters studied to date for noise and bursting are controlled by σ70. However, the evolutionarily distinct σ54 drives a fundamentally different mode of open complex formation. Whether or not the two sigma factor classes differ in the generation of noise and bursting is currently unknown. Yet, such knowledge is critical in order to gain a better appreciation of the scope of noisy and bursty transcription displayed by bacteria. It also enables a better understanding of the mechanisms underpinning cell-to-cell variability and thus phenotypic variation of σ54 controlled adaptive responses, e.g., biofilm formation, nitrogen fixation, virulence or antimicrobial persistence; such an understanding is essential when aiming to manipulate beneficial and pathogenic interactions of bacteria with their human, animal and plant hosts.A fuller understanding of the sources of transcriptional noise and bursting in bacteria requires an appreciation of the biochemical complexity of transcription regulation to avoid oversimplified views of the events that lead to open complex formation during transcription initiation. The impact of transcription initiation on noise and bursting has been acknowledged70-dependent promoters or from infrequent large bursts with high variability at σ54-dependent promoters  at σ70-dependent promoters or by increasing the burst frequency λ/δ at σ54-dependent promoters  and unregulated access of RNA polymerase to the promoter, both hallmarks of transcription initiation involving σ54. Strikingly, a similar behaviour is also observed in enhancer-dependent transcription in mamalian cells56. This implies that the type of regulation and not domain-specific constraints determine the transcriptional burst kinetics of a gene.The present study demonstrates that in bacteria the class of sigma factors, and as such the route to open complex formation during transcription initiation, determines the level and kinetics of transcriptional bursting. Low mean expression results from frequent small transcription bursts with low variability at σ59.While the two sigma factor classes yield opposing burst kinetics, noise (cell-to-cell variability of transcription within a population) simply correlates with the level of gene expression irrespective of the sigma factor. Our results imply that under basal and stress conditions bacteria utilise a universal adaptive behaviour. Prior to stress, transcription is noisier and hence cells are more heterogeneous; presumably reflecting opportunity to bet hedge. Upon stress perception, transcriptional noise is reduced through elevated gene expression yielding a more homogeneous cell population. Our observations therefore suggest a mixed strategy to cope with stress, using both environmental sensing and bet hedging. Environmental sensing is arguably more cost effective in that gene expression only occurs in presence of stress. Here we assume the low level expression of the sensory apparatus before stress is less costly than the full stress response. Examples where this may not be so can be envisaged, but is not the case for those studied here. The applicability of environmental sensing however is limited to stress conditions that are neither too sudden nor too severe given the phenotypic lag between sensing and responding. Bet hedging (gene expression in absence of stress) may be more costly but eliminates the phenotypic lag and thus provides an escape route for sudden and severe stress by priming the cells for less favourable conditions. This strategy may represent an adaptation to more stringent environmental pressure in line with the idea that gene expression noise may be subject to evolutionary selectionEscherichia coli K12 MG1655 strains. Genes were deleted by P1 transduction using strains from the KEIO collection of Escherichia coli mutants60 as donors or by lambda red recombineering61. Strains were typically grown in Luria-Bertani (LB) broth or on agar at 37 °C. For RNA fluorescence in situ hybridization, strains were grown in M9 minimal medium (Teknova) at 37 °C, from an inoculum of 150 μl from an LB overnight culture to a final OD600 of 0.4 in a culture volume of 30 ml in a 250 ml flask. The bacterial cultures were supplemented as required with antibiotics at the following concentrations: chloramphenicol 30 μg/ml; kanamycin 25 μg/ml. Exposure to isopropyl β-D-1-thiogalactopyranoside (IPTG) at 1 mM final concentration for 1 hour was used to express pIV from plasmid pGZ119EH. Arabinose 0.02–0.2% (w/v) and glucose 0.4–1% (w/v) were used to express PspF  from pBAD18-cm in cells lacking chromosomally encoded pspF.All experiments were performed with sufABCD and pspABC structural genes were designed using the Stellaris® Probe Designer version 4.2; the oligo length was set at 20 nt, the minimal spacing length at 2 nt and the masking level at 1–2. The probes were labelled by 6-carboxytetramethylrhodamine, succinimidyl ester (6-TAMRA).Fluorescent DNA probes (purchased from LGC Biosearch Technology) to detect the mRNA of 600 of 0.4 and collected by centrifugation. Cells were fixed in 1 ml of ice-cold 1× PBS in DEPC-treated water with 3.7% (v/v) formaldehyde (30 min incubation at room temperature), washed twice in 1 ml 1× PBS in DEPC-treated water, permeabilised in 1 ml 70% (v/v) ethanol in DEPC-treated water (1 h gently mixing at room temperature) and washed again in 1 ml 2× SSC in DEPC-treated water with 40% (w/v) formamide. Hybridisation was performed through incubation of the cells overnight at 30 °C in hybridisation buffer  formamide, 10% (w/v) dextran sulfate, 2 mM ribonucleoside-vanadyl complex, 0.2 mg/ml BSA and 1 mg/ml carrier E. coli tRNA) with 1 μM of the appropriate fluorescent probe(s). Subsequently, 10 μl of cells in hybridisation buffer were washed twice in 200 μl 2× SSC in DEPC-treated water with 40% (w/v) formamide and incubated for 30 min at 30 °C. Chromosomes were stained by incubating the cells for 30 min at 30 °C with 10 μg/ml DAPI  in 200 μl 2× SSC in DEPC-treated water with 40% (w/v) formamide. The cells were washed again in 200 μl 2× SSC in DEPC-treated water with 40% (w/v) formamide and resuspended in 10 μl 2× SCC in DEPC-treated water. For imaging, 2 μl of the cell suspension were immobilized using 1% (w/v) agarose pads on 35 mm, high μ-Dishes (ibidi).Bacterial cells were grown in M9 medium to an OD62. Cell segmentation masks from brightfield or DAPI images were generated via Schnitzcells63 in MATLAB (MathWorks). The mRNA copy number per cell was determined via Spätzcells30 in MATLAB (MathWorks) using images acquired through the Cy3 (6-TAMRA) channel in combination with the cell segmentation masks. Fluorescent spots within selected cells were detected automatically and differentiation of specific from nonspecific probe binding was achieved by selecting a false-positive threshold using non-expressing cells . The probability distribution of peak height and intensity of fluorescent spots was extracted   we assume therefore that 50 mRNAs per cell would be towards the top end of what might accumulate if the usual parameters of promoter activity and mRNA stability were being met. We note that some cells however appeared to accumulate several hundred target mRNAs. We propose that these high content mRNA cells are imaging or hybridisation artefacts e.g. through probe aggregation or non-specific genome-wide hybridisation. These cells were therefore omitted from the analyses presented in the main text. For completenesss however, we have included the data derived from the analyses including these cells . If the copy number of mRNA in the π(θ) are our prior distributions. Priors for ω and p were uniform  and therefore flat across the range of permissable values. The prior for r(=λ) was set as the half-Normal, truncated to positive values. This prior has minimal effect around the region of the inferred distribution, but ensures good convergence properties for the MCMC. A custom Metropolis-Hastings MCMC scheme was implemented to sample from the posterior distribution, the code for which is freely available. A multivariate Gaussian proposal distribution was used, in which the standard deviation was set at 5% of the current parameter values to ensure a reasonable acceptance ratio and good convergence. Chains were generally run to collect 500,000 samples with 100,000 dicarded as burn-in and thinning applied at a factor of 100. Each chain was examined for good convergence and restarted from the old chain when necessary. Outputs from the MCMC are displayed in Supplementary Figs. where 2) and Fano factor (F) as a function of the mean expression level and the other (non-varying) kinetic parameters. Expressions for the Fano factor are provided through Eqs.   2) and Fλ, and therefore the burst frequency, the following expression hold for each of the squared noise and Fano factor,If regulation is performed only via Conversely, if regulation is only via ν, and therefore the burst size, the following expressions hold,Suf data in which we infer variation in only the burst size, an average value of λ = 1.89 is obtained. For the Psp data, we take an average value of the ratio K/ν as 11.3. One must then still choose a value for K/δ, which here we set as 1000, although the results are not very sensitive to this choice.In plotting the predictions of these equations for Fig. Further information on research design is available in the Supplementary InformationReporting Summary