Label-Free Functional Analysis of Root-Associated Microbes with Dynamic Quantitative Oblique Back-illumination Microscopy

The increasing global demand for food, coupled with concerns about the environmental impact of synthetic fertilizers, underscores the urgency of developing sustainable agricultural practices. Nitrogen-fixing bacteria, known as diazotrophs, offer a potential solution by converting atmospheric nitrogen into bioavailable forms, reducing the reliance on synthetic fertilizers. However, a deeper understanding of their interactions with plants and other microbes is needed. In this study, we introduce a recently developed label-free 3D quantitative phase imaging technology called dynamic quantitative oblique back-illumination microscopy (DqOBM) to assess the dynamic activity of diazotrophs in vitro and in situ. Our experiments involved three different diazotrophs (Sinorhizobium meliloti, Azotobacter vinelandii, and Rahnella aquatilis) cultured on media with amendments of carbon and nitrogen sources. Over five days, we observed increased dynamic activity in nutrient-amended media. These results suggest that the observed bacterial dynamics correlate with their metabolic activity. Furthermore, we applied qOBM to visualize bacterial activity within the root cap and elongation zone of Arabidopsis thaliana primary roots. This allowed us to identify distinct areas of microbial infiltration in plant roots without the need for fluorescent markers. Our findings demonstrate that DqOBM can effectively characterize microbial activity and provide insights into plant-microbe interactions in situ, offering a valuable tool for advancing our understanding of sustainable agriculture.


Introduction
An expanding world population and the need for economic growth are increasing the demand for food, fuel, and renewable feedstocks.Nitrogen availability often limits crop yields 1 -a problem typically counteracted through the application of synthetic fertilizers.But despite their widespread use, almost half of the nitrogen added through chemical fertilizers is lost to the surrounding environment, resulting in cascades of adverse ecological and societal effects. 2 Consequently, new approaches are needed to improve nitrogen use efficiency, balance the global nitrogen cycle, and make agriculture more sustainable.
Nitrogen-fixing bacteria, known as diazotrophs, naturally reside in the rhizosphere and offer a process that can be leveraged to reduce the need for synthetic fertilizers.Diazotrophs associate with plants symbiotically and commensalistically by converting atmospheric nitrogen, N 2 , into biologically usable forms such as NH 3 .In addition to providing fixed nitrogen, diazotrophs improve plant productivity and biomass by influencing their hormone levels in plants. 3,4 n return, plants provide fixed carbon compounds like sugars and organic acids to the bacteria.In addition to the exchange of metabolites and signaling molecules, plants support diazotrophs in other ways, most notably by the creation of root nodules that provide a favorable microaerobic environment for nitrogen fixation in legumes.Whether equivalent root morphological features favor nitrogen fixation by non-symbiotic endophytic diazotrophs remains an open question. 5,6  order to leverage microbial nitrogen fixation to develop more sustainable agricultural practices, more research is needed to understand the complex interactions between plants and soil microbes. 7,8 0][11][12] Although genomics and proteomics provide an understanding of gene and protein expression in this system, they employ destructive techniques that can not yet provide real-time or holistic spatial information on microbial activity in situ.As such, imaging modalities have emerged as a tool to study root colonization.These imaging tools primarily consist of brightfield microscopy [13][14][15] and fluorescence-based imaging. 9,12,13,16 Whle brightfield microscopy is easy to implement, it alone lacks the contrast needed to visualize structural details of plant and bacterial cells.Consequently, the microbial cells are often tagged with fluorescent markers or stained histochemically for imaging.However, these methods suffer from a number of limitations, including photobleaching, phototoxicity, and biological tissue alterations from the exogenous agents.Thus, there remains a need for a label-free imaging modality capable of characterizing microbial inoculation of plant samples in situ.
To enable functional imaging with qOBM, we have developed dynamic-qOBM (DqOBM). 25In DqOBM, a sample is imaged over a period of time, and the resulting temporal signal for each spatial pixel is analyzed based on its temporal frequency response, which exhibits an exponential-like behavior that can be characterized using phasor analysis, as illustrated in Fig. 1B-C.The final DqOBM image is a functional map, depicting temporal changes in the refractive index (and thus dry mass) that correlate to patterns of cellular and metabolic activity within the sample (Fig. 1C-D).
Here, we exhibit the ability of DqOBM to assess the metabolic activity of known nitrogen-fixing bacteria both in vitro and in situ in Arabidopsis thaliana roots.First, we show that amendments of nitrogen and carbon elicit an appreciable rise in the dynamic activity of cultured bacteria as measured with DqOBM.Second, we used DqOBM to identify spatial patterns of bacterial colonization in Arabidopsis thaliana roots.These results demonstrate the potential of DqOBM to serve as a label-free and non-destructive imaging modality capable of detecting microbial activity and endophytic behavior in plant roots.This work paves the way for qOBM, and/or other imaging tools that can assess refractive index/dry-mass dynamic in scattering samples, to provide a deeper understanding of nitrogen-fixing diazotrophs in natural soil environments.

DqOBM analysis of bacteria culture activity in vitro
To test the hypothesis that the addition of carbon and nitrogen-containing compounds leads to observable changes in microbial activity, DqOBM images were collected of different diazotrophs (Sinorhizobium meliloti, Azotobacter vinelandii, and Rahnella aquatilis) grown in eight media treatments over five days.The plated media treatments included additions of glucose (0.25 g/L, 0.5 g/L, 1 g/L), casamino acids (5 g/L, 10 g/L,20 g/L), or a combination of both (20 g/L casamino acids, 2 g/L glucose).Carbon substrate was already present in our base media; thus, small concentrations of glucose were used.Casamino acids served as a source of organic nitrogen compounds, and it was previously shown that the chosen concentrations of 5-20 g/L of casamino acids lead to the repression of nitrogenase activity. 29,30 bserved dynamic activity of A. vinelandii was shown to increase with additions of both glucose and casamino acids, with peak activity detected 2-3 days after plating (Fig. 2).S. meliloti and R. aquatilis also exhibit increased microbial activity with increases in carbon and nitrogen-containing compounds (Fig. 3 and 4), but optimal activity was generally observed 1-2 earlier.
The observed results are in line with expectations: first, an increase in glucose concentration leads to a general increase in energy availability for the cells. 31This is reflected in Fig. 2, 3, and 4, where a higher dynamic response is seen with DqOBM in all bacteria cultured with higher concentrations of glucose.Similarly, nitrogen fixation is metabolically expensive, 32 thus we expect to see an increase in microbial activity when the competing energy demand for nitrogenase activity is reduced due to a surplus of casamino acids.Results in Fig. 2, 3, and 4 show that, indeed, when bacteria are no longer required to expend energy fixing atmospheric nitrogen, rates of other microbial processes increase.These processes may include motility, cell growth, division, and respiration -all of which are encapsulated within the DqOBM signal.Increases in microbial activity due to increases in available energy are further supported by the high activity recorded when excess carbon and nitrogen-containing   compounds are supplied together and by the lack of microbial activity recorded when excess compounds were not provided (Fig. 2, 3, and 4).
Changes in dynamic activity were observed as an initial peak in activity followed by a decrease in activity over time, mirroring growth patterns (Fig. 2, 3, and 4).R. aquatilis grows faster than A. vinelandii or S. meliloti and thus consumes its nutrients faster, which is reflected in the large reduction of microbial activity on day 3 for R. aquatilis compared with day 4 or 5 for A. vinelandii, S. meliloti, respectively (Fig. 2, 3, and 4).All phasor plots and end-member decays from the phasor plots of the different cultured plates can be seen in the Supplemental Section S1.It is important to note that we currently lack the ability to distinguish which exact set of microbial dynamic processes are being measured with DqOBM.Again, we simply define microbial activity as any combination of the following: metabolism, growth, proliferation, nitrogen fixation, motility, and any other dynamic cellular processes.While we are not yet able to directly link DqOBM dynamic responses to nitrogen fixation, we show that dynamic activity is nitrogen and carbon-limited (Supplemental Section S2).Further, nitrogen fixation rates were highest in glucose-amended treatments in comparison to the casamino acid treatments.shows some increased activity from the casamino acid groups.(C) shows increased prolonged dynamic activity for the casamino acid S. meliloti variants.Error in the plot is demonstrated from the shaded area surrounding the lines and represents the standard deviation of the energy from three replicates.
Figures 2, 3, and 4 provide a spatial representation of the dynamic activity, with red signifying higher activity and blue lower.This response can be further represented in a quantitative manner by computing the total energy (Eq.3) captured in the frequency response of the dynamic signals.Here, we take the frequency response of the most dynamic signal within a group, as determined by the endmember of the phasor plot (Supplemental Section S1).These results allow us to quantitatively visualize the dynamic activity of a culture over time.The highest energy signal was observed in cultures amended with glucose and casamino acids (Fig. 5A-C).Further, the lowest activity observed was from cultures grown in Jensen's media without any nutrient additions.In Fig. 5A, the peak energy signal of A. vinelandii was observed after 2 days in cultures supplemented with glucose.This peak was followed by a sharp decline in energy between Days 3-4 of culture.In contrast, A. vinelandii produced a higher and more prolonged period of activity when cultured in media containing casamino acids additions.These observations are consistent with the growth rate and nitrogen fixation data found in the Supplemental Section S2.As discussed above, we hypothesize that differences in cumulative energy may be the result of enhanced energy conservation through respiration stimulated by supplements of carbon and nitrogen-containing substrates.The initial increase in cumulative energy reflects the use of the added substrates which provide the bacteria with greater amounts of energy since abundant nutrients are available and nitrogen fixation is not required.The decline following peak cumulative energy implies that the added carbon and nitrogen compounds have been depleted and the ability of cells to produce/conserve energy is diminished.Similarly for R. aquatilis, in Fig. 5B, high activity is observed for cultures with glucose and casamino acids additions followed by a return to dormancy.Here, we do not see the same increased glucose activity.This may be due to the fast growth of R. aquatilis which means that the sampling of R. aquatilis at D2 is more similar to D4 of the A. vinelandii (this fast growth rate is also seen in the growth rate curves in Supplemental Section S2).In future experiments, imaging at earlier time points may reveal similar peaks as seen in Fig. 5A.Finally, in Fig. 5C with S. meliloti, a similar pattern is observed as in Fig. 5A with A. vinelandii -high dynamic activity is observed media with high glucose and high casamino acid additions.Unlike A. vinelandii and R. aquatilis, S. meliloti is a symbiont, which are reported to be more carbon efficient than their free-living counterparts and explains the prolonged growth of S. meliloti. 33

DqOBM imaging of bacteria in inoculated Arabidopsis thaliana roots
After establishing that DqOBM provides quantitative information on microbial dynamic activity, our next goal was to image colonized roots.The Arabidopsis thaliana primary root, a well-studied organism, acted as our model experimental system.Seedlings were inoculated with either A. vinelandii or R. aquatilis and imaged 7 days post-inoculation.DqOBM images were taken along seedling roots at the elongation zone and root cap, as illustrated in Fig. 6.As a control, uninoculated plants were imaged (Fig. 6A-D).
Results show that the uninoculated plants have low levels of activity.These changes in the phase of the images can be attributed to normal plant root activity, including the transport of water, minerals, and nutrients in the vascular cylinder.This is localized using qOBM images where we can visually identify the endodermal cells encasing the xylem and phloem, as indicated by arrows in Fig. 6A, B, and I.
In the elongation zone, many of the same patterns were observed in the inoculated and uninoculated plants -small amounts of dynamic activity within the endodermal region, and otherwise low dynamic activity, as seen in Fig. 6E, F, and I. Further, in the plants inoculated with R. aquatilis, we observed small areas of high dynamic activity from microbial cells that have colonized into the elongation zone.These are indicated by the white arrows in Fig. 6J-K.Further, in K, microbial cells located outside of the plant root exhibited high dynamic activity can be observed.These results are indicative of qOBM's ability to detect the microbial activity and the sparsity of microbial cells that have infiltrated more centrally into the root.In other areas of the elongation zone, microbial cells are either not present in the qOBM image or show lower dynamic activity and thus are not seen in the DqOBM image.
For comparison, we also imaged the root cap, which has been shown to be the first point of contact for bacterial cells attempting to colonize the root. 34Additionally, the root cap may act as a filter that prevents further microbial colonization in the root. 35Here, we would expect to see increased microbial activity and infiltration of microbial cells into the plant.Indeed, in both the plant inoculated with A. vinelandii and R. aquatilis, we observe (as expected) higher dynamic activity than in the uninoculated plant or in the elongation zone, as seen in Fig. 6G-H and L-N.Dynamic activity, and by association microbial cells, are predominantly present in intercellular spaces (white arrows in Fig. 6M and the red in N).This level of increased dynamic activity suggests higher levels of plant-secreted carbon compounds in the root cap.Such a possibility is consistent with reports of higher production of arabinogalactan-proteins and certain organic acids at root tips, 36,37 which can serve as carbon and energy sources for the bacteria.Phasor plots from the colonized roots can be seen in Supplemental Section S3.
Finally, to compare the images obtained by DqOBM to those from an end-point analysis, we converted the qOBM microscope into a multimodal system with an added fluorescence channel to excite 4',6-diamidino-2-phenylindole (DAPI).As seen in Fig. 6 and Fig. 7, qOBM and DqOBM imaging can be used to extract structural information based on the refractive index distribution (Fig. 7A, E, I, & M) and functional dynamic information (Fig. 7 B, F, J, & N).To confirm that regions of measured high dynamic activity with DqOBM in plants indeed correspond to the bacteria, we labeled the bacteria with DAPI.These fluorescence images (green channel) can be overlaid on the phase (or refractive index) qOBM images (red channel) as seen in Fig. 7 C, G, K, & O.To compare the DAPI fluorescence images with DqOBM, a similar overlay method was employed in Fig. 7D, H, L, & P, where the DqOBM can be visualized in green and the phase images in red.Again, we notice that less A. vinelandii is observed in the elongation zone (Fig. 7B-D) than in the root cap (Fig. 7F-H) in both the DqOBM and DAPI images.Similar results could be observed with R. aquatilis, albeit the overall levels of dynamic activity, and consequently bacteria, were higher in these samples.We note that the images obtained in D, H, L, & P closely resemble those seen with current imaging modalities like confocal imaging; 9 however, unlike confocal, qOBM is a label-free analysis.We also see some minor differences between the bright field fluorescence and DqOBM images (K&L and O&P respectively) where the DAPI-stained image shows higher, more diffuse fluorescence than in the DqOBM images.We believe this points to the differences in axial sectioning of the images.In DqOBM, the axial resolution is on the order of 2-3 µm (depending on the microscope objective used).With the DAPI bright field fluorescence imaging, there are no cross-sectional capabilities; therefore, the fluorescence would be summed from across the entire depth of light penetrating into the sample.Thus, these images may not present a perfect one-to-one match, but they show clear similarities to confirm that DqOBM regions of high activity correspond to the active bacteria.Phasor plots from the roots colonized with the labeled bacteria can be seen in Supplemental Section S4.

Discussion
This paper presents DqOBM as a label-free imaging modality capable of monitoring microbial dynamics in real time.No prior label-free imaging modalities have been able to provide the level of detail seen with qOBM in situ in plants.By collecting DqOBM images, we can assess microbial activity in vitro and in situ during plant colonization.By observing microbial activity in response to changes in carbon and nitrogen substrate amendments, we were able to begin to characterize the underlying mechanisms that control carbon and nitrogen exchange.Our resulting qOBM and DqOBM approach also provides an opportunity to characterize free-living bacterial behavior in a system comparable to their natural environment.We again note that the energy level measured by DqOBM is likely a sum of all microbial activities.As such, research is needed to directly link microbial dynamics observed by imaging with rates of growth or nitrogen fixation (Supplemental Section S2).Nonetheless, the trends in dynamic activity observed here are consistent with a dependence of energy level on carbon and nitrogen.Further, in vivo experiments using A. thaliana allow us to observe complex plant-microbe interactions non-invasively.While the approach is unable to differentiate between the different types of microbial activities or the different bacteria types, DqOBM imaging allows for the visualization of "hotspots," which we believe colocalize with sites of active polysaccharides and organic acids secretion.The sustainable optimization of bioenergy crop yields requires a better understanding of nutrient transport and metabolic transport in the rhizosphere, and the method described here represents a novel tool with which to gain new insights into these complex processes.
While DqOBM is able to provide label-free functional imaging to assess the dynamic activity of bacterial cells, the penetration depth of qOBM has been shown to be limited to ∼200 µm in tissues, 28 so it will not able to penetrate deep into the natural environment of roots, such as soil.Nevertheless, this work demonstrates that dynamic activity, as measured by temporal fluctuations of phase (or refractive index), can be applied as a surrogate to study bacteria and their metabolic activity in plants.We hope that the dynamic analysis presented in this paper will continue to inspire the development or application of other imaging modalities capable of penetrating deeper into the soil to employ similar dynamic analyses in soil.

Bacteria Growth Conditions and Techniques
Three bacterial cultures were used in this study: Rahnella aquatilis strain OV588 was kindly gifted to us by our collaborators at Oak Ridge National Research Laboratory, the Sinorhizobium meliloti strain SM1021 was generously provided by Sharon R. Long, and the Azotobacter vinelandii which was isolated from peatlands in northern Minnesota / obtained from ATCC (Catalog number BAA-1303).To study nitrogen fixation activity, the bacteria were continuously cultured on Jensen's nitrogen-free media.Cultures were kept on Jensen's plates in a room-temperature incubator between experiments.
Carbon and nitrogen-containing compounds were varied through the addition of glucose and casamino acids to the media.To prepare media containing different concentrations of glucose and casamino acids, fresh nitrogen-free Jensen's with agar was prepared using Milli-Q water.Three glucose concentrations (0.25, 0.5, and 1 g/L) were added to freshly prepared media before being autoclaved.Similarly, three casamino acid concentrations (5, 10, and 20 g/L) were added to fresh media.In addition, unaltered Jensen's media was used as a control.In an effort to observe maximum activity, media containing large amounts of glucose (2 g/L) and casamino acids (20 g/L) was prepared.Cultures of S. meliloti, A. vinelandii, and R. aquatilis were carried out in triplicate started.Microbial activity was then measured using qOBM imaging every 24 hours for five days.Sterile inoculation loops were used to select colonies from each plate and to lightly streak colonies onto glass slides.Streaking was completed with the goal of creating a uniform layer of cells and colonies of like size were selected for imaging.Once the colonies were streaked out, a cover slip was placed on the glass slide.

Plant Growth Conditions and Techniques
Arabidopsis thaliana wild-type (ecotype Columbia) seed was used.Seeds were surface sterilized with 2% sodium hydroxide along with 0.05% Triton X-100 for 5 min and then washed five times with sterile water.Seeds were then kept at 4°C for two days for vernalization.Seeds were grown in liquid ½ strength nitrogen-free Murashige and Skoog media supplemented with 1% (w/v) sucrose in a 6-well plate at 23°C and 50% relative humidity under 16 hr-light/8 hr-dark conditions for 7 days.All in-planta experiments were conducted with 7-day-old seedlings.

Bacterial Growth and Inoculation
To prepare for inoculation, S. meliloti, A. vinelandii, and R. aquatilis cultures were grown to an OD of 1 to 1.5 at 28°C in liquid Jensen's nitrogen-free media.Before inoculation, each culture was pelleted through centrifugation and washed in Milli Q water before being resuspended in Milli Q water.The bacterial suspensions were diluted to 10% and then used to inoculate either M. truncatula or A. thaliana roots on nitrogen-free MS plates.

Acetylene Reduction Assay
A. vinelandii was grown in 5 ml of each media treatment (Jensen's, 0.25 g/L glucose, 0.5 g/L glucose, 1g/L glucose, 5 g/L casamino acids, 10 g/L casamino acids, 20 g/L casamino acids, and 2 g/L glucose 20 g/L casamino acids) for 3 days at 25°C.Cells were washed, harvested and diluted to 10% before being added to fresh aliquots of the amended media treatments in 30 mL serum bottles.Serum bottles were sealed to be gas-tight and then flushed with argon for 10 minutes.The serum bottle headspace was injected with 10% vol oxygen and 10% vol acetylene.Nitrogen fixation activity was then measured using the acetylene reduction assay method based on acetylene reduction into ethylene by nitrogenase. 38Ethylene concentrations were measured over a 5-day time series using gas chromatography.

Growth Curve Culture
Bacteria were precultured in eight media treatments (Jensen's, 0.25 g/L glucose, 0.5 g/L glucose, 1g/L glucose, 5 g/L casamino acids, 10 g/L casamino acids, 20 g/L casamino acids, and 2 g/L glucose 20 g/L casamino acids).Fresh aliquots of amended media were then inoculated with precultured cells at a 10% dilution in triplicate.Cultures were then loaded onto a 96-well plate and the plate was loaded into a BioTek Synergy H1 microplate reader where cultures were kept at 25°C and continually shaken.OD600 was measured at 30-minute intervals over 5 days.

qOBM Imaging System
9]26 In contrast to the traditional transmission-based illumination utilized in both brightfield microscopy and QPI, the qOBM approach employs an epi-mode illumination strategy using a quartet of LED light sources emitting at 720 nm.These LEDs are strategically positioned around the objective at 90°intervals, as depicted in Fig. 1A, and are coupled via optical multimode fibers.In the epi-mode configuration, ∼45 mW of light is directed onto the sample.Within the sample, photons undergo multiple scattering interactions, resulting in changes in their trajectory, with a subset being redirected back toward the microscope objective.This phenomenon effectively establishes a virtual light source within the sample, leading to oblique back-illumination, a phenomenon previously termed oblique back-illumination. 39Fluctuations in the refractive index across the sample guide the light either towards or away from the microscope objective.This refractive index-induced modulation induces intensity variations that encode the sample's refractive index properties.In our investigations, we employ Nikon S Plan Fluor LWD 20X (numerical aperture 0.45) and Nikon S Plan Fluor LWD 40X (numerical aperture 0.6) objectives.The light collected by the microscope is captured by an sCMOS camera (pco.edge4.2 LT).
To achieve quantitative phase imaging with qOBM, we first subtract the intensity images obtained from opposing illumination angles (these intermediate images are called differential phase constrast or DPC images).Subsequently, two orthogonal DPC images, acquired through a total of four distinct acquisitions, are deconvolved using the optical transfer function of the system.This process, previously elaborated upon in references, 17-19, 26, 27 ultimately yields quantitative phase contrast images.Leveraging the rich quantitative phase information acquired, we achieve the capability to both visualize and quantify cellular and subcellular structures within the sample, enabling comprehensive tracking of their developmental progression over time.

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Imaging Procedure To assess whether or not we could use qOBM dynamics to assess microbial dynamics, we first imaged the bacteria plates over the course of 5 days (D0-5) with 8 different glucose and nitrogen concentrations.Each day, representative streaks were taken from each plate and restreaked onto a glass slide.On each slide, 2 different fields of view were taken with 600 images at 8Hz.This was repeated for each bacteria type (A.vinelandii, R. aquatilis, and S. meliloti).
Next, we went to image plants inoculated with the same bacteria strains.A. thaliana was inoculated with R. aquatilis and A. vinelandii and imaged at D1 and D7 after inoculation.We studied FOV with inoculated and uninoculated roots and with bacteria outside of the root.Again the same dynamic imaging procedure was followed collecting 600 images at 8Hz.

Dynamic Image Analysis
To conduct functional imaging with qOBM, we have developed Dynamic qOBM (DqOBM). 25In DqOBM a sample is imaged over a period of time -for all samples in this work this time period is 75 seconds at 8 Hz to obtain 600 images.From these images, we obtain a pixel-wise dynamic frequency response given by the absolute value of the Fourier transform of the temporal phase signal, φ ( f ) = |F {φ (t)}| for each spatial pixel in the image.We observe that the frequency response of the pixels exhibits an exponential or multi-exponential decay indicative of subcellular mass movement that more prominently oscillates at low frequencies and dampens exponentially with increasing frequency.This functional behavior is expected for cell structures such as cell membranes 40 and mitochondria, 41 among other structures. 42As expected, the dynamic response in background regions show a mostly flat near-zero amplitude dynamic response, indicative of static behavior.
To visualize the cell dynamics, we utilize phasor analysis, 43,44 as it aligns well with the exponential nature of the dynamic phase frequency response, φ ( f ).Phasor analysis is a widely-used technique for examining spectral and dynamic signals, especially those with exponential characteristics, such as those encountered in fluorescent lifetime and pump-probe microscopy. 43,44 his method involves decomposing signals into two variables, typically referred to as g and s, which are derived from the cosine and sine transforms (real and imaginary components of the Fourier Transform) of the dynamic signals (here φ ( f )) for each spatial pixel in the image at a particular period, τ.In our case, we choose τ=0.5 s depending on the net acquisition rate to decompose the signals into g and s following Eq. 1 and 2, respectively: In phasor space, the two components, g and s, act as coordinates, uniquely defining each pixel in the image.As a result, the phasor plot represents a 2D histogram that captures the distribution of g and s values across the image.Similar dynamic signals tend to cluster together in this space, while mixtures of exponential signals create linear mappings between regions.The boundary points of these distributions are termed endmembers.
The cumulative phasor plot in Fig. 1C-D shows signals that lie mostly within the universal semicircle (black dotted line in Fig. 1C-D), which signifies that the frequency response of the cellular dynamics, for the most part, follows an exponential behavior. 43,44 ut because the frequency response is not physically constrained to be strictly exponential, some signals are observed outside the universal semi-circle (but they are within the unit circle due to the normalization of g and s). Figure 1C-D also shows the average responses from two distinct regions in phasor space.
Energy of the dynamic signal can also be accounted for by taking the sum of the area under the curve of the phasor line decay signal. 45Here, we integrate the phase signal from 0.1 Hz (to remove the DC component of the signal) to 4 Hz (half of our sampling frequency).This is: The summation of the energy via Eq. 3 quantifies the decay signals visualized in Fig. 2, 3, & 4 and Supplemental Section S1.Plots of energy can be seen in Fig. 5.

Figure 1 .
Figure 1.(A) Overview of the qOBM imaging approach which consists of an inverted brightfield microscope with epi-illumination.The sample (cultured bacteria streaked onto a glass slide) is sequentially illuminated by 4 optical fibers connected to 720 nm LEDs, followed by quantitative phase recovery.(B) Time-lapsed qOBM image stack of cultured Azotobacter vinelandii bacteria.(C) Blue: temporal phase fluctuations of a pixel corresponding to the boxed area of bacteria in B. Green: log-log representation of the Fourier transform of the temporal phase value.This plot is used to generate the phasor plot (middle) and the colorized DqOBM image (right) demonstrating areas of high and low dynamic activity.(D) Representative phasor plots and DqOBM images of areas with low dynamic activity (left) and high dynamic activity (right).

Figure 2 .
Figure 2. Representative colorized DqOBM images of the nitrogen-fixing bacteria A. vinelandii.Columns represent culture treatments with varying carbon and nitrogen concentrations.Rows indicate the time expired relative to inoculation.

Figure 3 .
Figure 3. Representative colorized DqOBM images of the nitrogen-fixing bacteria Rahnella aquatilis.Columns represent culture treatments with varying carbon and nitrogen concentrations.Rows indicate the time expired relative to inoculation.

Figure 4 .
Figure 4. Representative colorized DqOBM images of the nitrogen-fixing bacteria Sinorhizobium meliloti.Columns represent culture treatments with varying carbon and nitrogen concentrations.Rows indicate the time expired relative to inoculation.

Figure 5 .
Figure 5.The cumulative energy over time of A. vinelandii, R. aquatilis and S. meliloti, respectively.(A) shows a sharp decline to a dormant state of the glucose variants between D3-4 whereas the casamino variants show continued energy.(B)shows some increased activity from the casamino acid groups.(C) shows increased prolonged dynamic activity for the casamino acid S. meliloti variants.Error in the plot is demonstrated from the shaded area surrounding the lines and represents the standard deviation of the energy from three replicates.

Figure 6 .
Figure 6.Representative qOBM (left) and DqOBM (right) images from uninoculated A. thaliana plants (A-D), A. thaliana inoculated with A. vinelandii (E-H) and A. thaliana inoculated with R. aquatilis (I-N).We look at regions from the elongation zone (A-B, E-F, & I-K) and from the root cap (C-D, G-H, & L-N).In the uninoculated plant (A-D), we see minimal fluctuations in the phase of the images, corresponding to little dynamic activity.Similarly, E and F show the elongation zone inoculated by A. vinelandii with minimal dynamic activity.I demonstrates increased dynamics activity (as indicated by the arrow) in the center of the root, which may be indicative of nutrient flow through the Xylem rather than microbe activity.J and K show isolated dynamic activity from individual microbial cells in the elongation zone and higher dynamic activity and microbe inoculation in the root cap (indicated by arrows in J and K).Further, K shows high dynamic activity from a large number of bacteria growing outside of the root.In the root cap, we see colonization of intercellular spaces as indicated by the arrows in H and M and the red in N.All samples were prepared from uncut roots.All scale bars are 100 µm.