Review Special Issues

Plant probiotic bacteria: solutions to feed the world

  • The increasing human population expected in the next decades, the growing demand of livestock products—which production requires higher amounts of feed products fabrication, the collective concern about food quality in industrialized countries together with the need to protect the fertility of soils, in particular, and the environment, in general, constitute as a whole big challenge that worldwide agriculture has to face nowadays. Some soil bacteria harbor mechanisms to promote plant growth, which include phytostimulation, nutrient mobilization, biocontrol of plant pathogens and abiotic stresses protection. These bacteria have also been proved as promoters of vegetable food quality. Therefore, these microbes, also so-called Plant Probiotic Bacteria, applied as biofertilizers in crop production, constitute an environmental friendly manner to contribute to produce the food and feed needed to sustain world population. In this review, we summarize some of the best-known mechanisms of plant probiotic bacteria to improve plant growth and develop a more sustainable agriculture.

    Citation: Esther Menendez, Paula Garcia-Fraile. Plant probiotic bacteria: solutions to feed the world[J]. AIMS Microbiology, 2017, 3(3): 502-524. doi: 10.3934/microbiol.2017.3.502

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  • The increasing human population expected in the next decades, the growing demand of livestock products—which production requires higher amounts of feed products fabrication, the collective concern about food quality in industrialized countries together with the need to protect the fertility of soils, in particular, and the environment, in general, constitute as a whole big challenge that worldwide agriculture has to face nowadays. Some soil bacteria harbor mechanisms to promote plant growth, which include phytostimulation, nutrient mobilization, biocontrol of plant pathogens and abiotic stresses protection. These bacteria have also been proved as promoters of vegetable food quality. Therefore, these microbes, also so-called Plant Probiotic Bacteria, applied as biofertilizers in crop production, constitute an environmental friendly manner to contribute to produce the food and feed needed to sustain world population. In this review, we summarize some of the best-known mechanisms of plant probiotic bacteria to improve plant growth and develop a more sustainable agriculture.


    1. Introduction

    Current techniques for observing bacterial motility are effectively two-dimensional because of the small depth of field provided by high numerical aperture objectives. Measurement of 3D trajectories is performed by approximating the third dimension from measured 2D trajectories, or by inferring the organisms' z positions as they travel into and out of focus. This severe limitation gives an incomplete image of the motility patterns observed. For example, a bacterium travelling vertically, parallel to the optical axis, will appear stationary using conventional techniques. A 2015 paper [1] calculated the systematic errors associated with observing bacterial motility when using conventional microscopic techniques and found that in addition to the effects of localization errors, 2D projection of the same volume introduce systematic errors in speed and turning angle measurements, compared to the correct speed and turning angle measurements found in 3D tracking. Similarly, observations obtained from 2D slicing are constrained to a thin focal plane thickness and ignore the vast majority of turning events; a bias against turning angles near 90° is also introduced. Finally, the boundaries of the sample chambers required for high-resolution imaging constrain motion in the z direction and affect the hydrodynamics of motility and the organisms' possible swimming ranges. Because of this, 2D methods do not capture the entire complexity of bacterial motility and shed doubt upon models of motility such as "run and tumble" or "flick" [2,3] the swimming patterns of most bacteria in an unconstrained 3D volume remain largely unknown.

    Digital Holographic Microscopy (DHM) is based on the technique of holographic interferometry. In this technique, two physically separate beams of monochromatic and collimated light are used to create interference patterns at the digital detector when recombined at an angle. One beam passes through the sample of interest, which encodes its morphology and phase characteristics in the curvature of the transmitted light while the second beam remains undisturbed. This beam serves as a reference for the plane wave curvature before the light interacted with the sample. The digitally recorded hologram can then be reconstructed back into the original object wavefront using numerical methods [4].

    The amplitude and phase distribution in the plane of the real image can be found from the hologram by the Fresnel-Kirchhoff integral [4,5]. If a plane wave illuminates the hologram located in the plane z=0, with an amplitude transmittance t(x,y), the Fresnel-Kirchhoff integral gives the complex wavefront, Γ(ξ,η), in the plane of the real image. The amplitude, A, in the real image can be calculated as the magnitude of the complex wavefront:

    A=|Γ(ξ,η)| (1)

    The phase information, ϕ, of the complex wavefront is obtained by:

    ϕ=arctan((Γ)(Γ)) (2)

    Where (Γ) and (Γ) are the imaginary and real parts of the complex wavefront, respectively.

    These methods allow for capture of an entire sample volume in a single hologram, followed by plane-by-plane reconstruction. This is ideal for sparse samples moving in three dimensions. Samples with multiple scatterers complicate the reconstruction; we have found that bacterial concentrations > 108 cells per ml are too dense for reconstruction using a Mach-Zehnder style DHM [6]. Reconstructed amplitude images correspond to brightfield images in ordinary light microscopy. Phase images have no direct counterpart and are an emerging field in and of themselves. Quantitative phase microscopic imaging has shown promise in diagnostics, label-free cell biology and more [7]. Because phase is recorded as modulo 2π, the problem of "unwrapping" multiples of 2π to calculate the true phase shift is one of the major challenges in this field.

    DHM has been used to study distribution and swimming patterns of microorganisms on the scale of 10 µm: Algae in the laboratory [8] and plankton in the open ocean [9], to investigate dinoflagellate feeding behavior [10,11], to study the motility of algal zoospores [12] and to study cultured cells in the laboratory [13]. Nevertheless, papers on DHM imaging of micron-sized bacteria are few. We have constructed a DHM specifically for bacterial imaging, with sub-micron resolution, and have demonstrated its utility for detection of bacteria in extreme environments [14]. However, obtaining automated 3D tracks of bacterial cells with this instrument is still very challenging. Low contrast does not allow images to be thresholded and the presence of out-of-focus airy rings confuses detection algorithms. Amplitude images show a large amount of laser speckle noise, which is inherit to any imaging technique using coherent light sources. Some solutions have been presented in the literature. One paper successfully tracked bacteria using de-noising algorithms [2,15], but this approach is computationally intensive as well as labor-intensive. Holographic microscopy using incoherent light can eliminate speckle [16], but at the expense of depth of field, so that it is less useful for 3D tracking than coherent DHM. Synthetic aperture techniques can also improve resolution [17], but are used to improve images taken through low NA lenses. Operating at the diffraction limit makes such techniques difficult. Other super-resolution techniques, such as angular or wavelength multiplexing [18,19], require the sample to be stationary. Because studies of live bacteria require imaging at the order of the size of the wavelength of illumination light in a large volume, and because they move at tens to hundreds of microns per second, identifying and tracking them remains a challenge.

    Phase images contain less speckle noise than amplitude images, but are subject to temporal phase noise, which results from the uncorrelated noise between the two beams of the interferometer. Most importantly, the contrast provided by bacterial cells is low. The contrast in phase images at a point (x,y) is provided by the spatially averaged phase difference Δϕ, which is related to the difference in indices of refraction between the medium (nm) and cell (nc) [20]:

    Δϕ=2πλh(x,y)(nc(x,y)nm) (3)

    Where λ is the wavelength of illuminating light and h is the thickness of the specimen at (x,y).

    For bacteria, refractive indices differ from water only at the second decimal place (~1.38 vs. 1.33 for water) [21]. Thus, a typical phase shift for a 1 µm cell imaged at 405 nm is about π/4 or 45°, which can be difficult to resolve. The advantage to such small objects is that unwrapping is not required since phase shifts do not exceed 2π.

    Automated particle tracking can generally be divided into two steps: Particle identification/detection (the spatial aspect), followed by particle tracking/linking (the temporal aspect). In 2014, Chenouard et al. [22] provided an objective comparative study of the most common particle tracking methods used in bioimaging. First, the authors identified three main factors that affect tracking performance: Dynamics (type of motion), density (number of particles per field of view), and signal-to-noise ratio (SNR). Second, they simulated a set of 2D and 3D image data based on these different factors. They then sent these image datasets to 14 teams who took up the challenge of identifying and tracking the particles using state-of-the-art methods. The teams then sent back their results, which showed that no one particle tracking method performed best for all data. The best identification methods were based on careful implementation and parameter tuning of any algorithm. The best tracking methods were the ones that used multiframe/multitrack optimization instead of the simpler nearest-neighbor linking. In addition, methods that made explicit use of the prior knowledge about the particle motion in each scenario were more successful than methods that did not.

    In this work, a high precision machine-learning particle identification/detection algorithm based on linear logistic regression [23] is implemented for tracking of two test bacterial strains: Bacillus subtilis and Collwellia psychrerythraea. This algorithm is available in MATLAB as part of the Statistics and Machine Learning toolbox. This algorithm was used as a proof of concept; other machine learning algorithms such as decision tree model, support vector machine, or k-nearest neighbor classification model could also be implemented. The strains were chosen to represent relative extremes of prokaryotic size and motility. B. subtilis is large (5 µm long) and shows slow (~20 µm/s), undulating motility. C. psychrerythraea is a marine psychrophile that is very small (<1 µm) and swims at rapid speeds (over 40 µm/s even at subzero temperatures) [24].

    The algorithm requires an expert user to identify bacteria from a training dataset, which is a small subset of the recorded data. Once trained using just a few examples, the algorithm is able to automatically detect organisms from the entire dataset. Performance is compared to manual tracking and found to give a precision of 91%. Once identified, bacteria may be tracked by the simple nearest-neighbor Hungarian linking algorithm [25]. This represents the first demonstration of an automated algorithm for tracking of bacteria using DHM. While much work on the subject remains to be done, this is a promising area of inquiry for anyone studying 3D bacterial motility.


    2. Materials and methods


    2.1. Design specifications of the Digital Holographic Microscope (DHM)

    The DHM used in this study has been described elsewhere [14]. It is a twin-beam off-axis DHM, suitable for extreme environments in terms of mechanical and thermal stress. Specifications of this instrument are summarized in Table 1.

    Table 1. Design specifications of the DHM instrument.
    Property Value Unit
    Operating Wavelength 405 nm
    Objective focal length f0 7.6 mm
    Objective Numerical Aperture 0.30
    Relay lens focal length fr 150 mm
    System magnification 19.7
    Lateral resolution 0.7 µm
    CCD pixel size 3.45 × 3.45 µm × µm
    Sample imaging volume 360 × 360 × > 600 µm × µm × µm
    Sampling Rate 15 Frames per second
    Instrument length 400 mm
     | Show Table
    DownLoad: CSV

    2.2. Sample preparation

    Bacillus subtilis was grown to mid-log phase in lysogeny broth (LB) in a shaking incubator at 30 ℃. Cultures were then diluted into motility medium (10 mM potassium phosphate, 10 mM NaCl, 0.1 mM EDTA, 0.1 mM glucose, pH 7.0) immediately before being inserted into the sample chamber and imaged using the DHM at room temperature.

    Colwellia psychrerythraea was maintained in half-strength 2216 marine broth (Difco) at 6 ℃. Cultures were then diluted using the same Difco broth immediately before being inserted into the sample chamber and imaged using the DHM at room temperature.

    The sample chamber consisted of high optical quality glass etalons separated by a PDMS gasket. Sample chamber depth was 800 µm with a total sample volume of 0.25 µL. Bacterial samples were pipetted into the chamber and videos were recorded using the commercial software KOALA (LynceeTec) [26] at maximum acquisition speed (7–15 frames per second).

    Three separate datasets were acquired and analyzed. The first two consisted of either Bacillus subtilis or Colwellia psychrerythraea at low concentrations (on the order of 102 cells per mL), while the third consisted of Bacillus subtilis at a much higher concentration (on the order of 106 cells per mL). The two low concentration datasets were used to compare to "manually identified gold standard" tracks that were obtained by manually tracking each bacterium through (x,y,z,t) in order to quantify the level of error in the algorithm, while the high concentration data set was used to investigate its ability to track higher concentration samples. A summary of each dataset's properties are listed in Table 2.

    Table 2. Properties of all three datasets acquired and analyzed.
    Property Dataset 1 Dataset 2 Dataset 3
    Sample Volume [µm3] 360 × 360 × 252 360 × 360 × 392 360 × 360 × 500
    Bacteria Species Bacillus subtilis Colwellia psychrerythraea Bacillus subtilis
    Concentration [cells per mL] ≈ 102 ≈ 102 ≈ 106
    Object Volume and Shape ≈ 8 µm3, elongated ≈ 2 µm3, comma-shaped ≈ 8 µm3, elongated
    Number of z-planes 201 157 201
    Number of time frames 84 18 85
    Axial Resolution [µm] 1.25 2.5 2.5
    Total Number of Bacteria in FOV 8 6 149
     | Show Table
    DownLoad: CSV

    2.3. Hologram reconstruction

    KOALA (LynceeTec) was used for the holographic reconstruction of all datasets. The holograms of all datasets were numerically reconstructed into amplitude and phase images at a z spacing of 1.25 µm/slice and 2.50 µm/slice, respectively. Images were saved as 8-bit TIFF files. The phase reconstructions were used in the tracking of Dataset 1 and Dataset 2, while Dataset 3 was tracked by analyzing images obtained by the multiplication of the amplitude and phase reconstructions. By doing so, it was seen to increase contrast, which aids in the automated tracking of higher concentration datasets without introducing false positives.


    2.4. Manual object identification

    All analysis was performed on a custom built desktop computer, with an Intel Core i7-7800x CPU @ 3.50 GHz, 32.0 GB of Installed memory (RAM), running Windows 10 Pro and using MATLAB R2017b with the Image-Processing Toolbox and the Statistics and Machine Learning Toolbox installed.

    Prior to the automated tracking of Datasets 1 and Datasets 2, manual tracks were compiled in order to quantify the performance of the automated tracking routine. Manual tracking was accomplished in two stages, both involving a human observer that would individually identify bacteria. In the first stage, raw holograms are analyzed by the observer. Because this is done before any numerical reconstruction, the raw holograms only provide (x,y,t) locations for a particular bacterium. The open source data visualization software FIJI (is just imageJ) was used with the "Manual Tracking" plugin [27]. Once these (x,y,t) coordinates are recorded, KOALA was used to numerically reconstruct the holograms at various focal planes. By knowing the (x,y,t) locations of bacteria, their respective z location can be found by cycling through the reconstructed focal planes and identifying the z-plane where a particular bacterium is in focus. With (x,y,z,t) coordinates for the bacteria in Datasets 1 and 2 compiled manually, quantifying the performance of the automated tracking routine is possible.


    2.5. Validation metrics

    To quantify the performance of the automated tracking algorithm, the manual tracks of Datasets 1 and 2 were used in order to calculate an Fβ score (F-score). The F-score is defined as:

    Fβ=(1+β2)PRβ2P+R (4)

    Where β is a weighting factor, P is the statistical precision, and R is the statistical recall. Statistical precision is defined as:

    P=TpTp+Fp (5)

    And statistical recall is defined as:

    R=TpTp+Fn (6)

    Where Tp is the number of true positives, Fp is the number of false positives, and Fn is the number of false negatives.

    The motivations that led to the development of this algorithm were to be able to extract statistically relevant motility characteristics of bacteria from a given dataset and not necessarily identify all bacteria present in the field of view. For this reason, precision is weighted higher than recall by defining β=0.5.


    2.6. Automated particle identification and tracking


    2.6.1. Pre-processing

    All images that were analyzed with the automated tracking routine were subject to a pre-processing step in order to reduce noise in the image as well as normalize average pixel values from image to image. De-noising included calculating the mean image for a time sequence of images and subtracted that image from all images in that time sequence. By subtracting a temporally averaged image, all stationary artifacts of an image (e.g. speckle noise) are removed. Next, these mean subtracted images were band-pass filtered. This band-pass filtering was done by multiplying the Fourier Transform of an image with a binary mask matrix. The DHM used has been shown to operate at diffraction limited resolution, and so this absolute resolution limit was used as the upper cut-off frequency of the band pass filter, while the lower cut-off frequency was set to eliminate zero-frequency artifacts. For Dataset 3, the pre-processed amplitude and phase images were then multiplied together in order to further increase contrast.


    2.6.2. Training

    The linear logistic regression pixel classifier is a supervised learning algorithm that was implemented using MATLAB's Statistics and Machine Learning Toolbox. In order to train this classifier, a sample dataset is used to generate a classifier hw(x) as well as a pixel features matrix Xt. The pixel features that are used to construct Xt are summarized in Table 3.

    Table 3. Pixel features used to train the classifier.
    Importance (descending order) Pixel Feature
    1 Absolute difference of pixel values |xˉx|
    2 Local image gradient
    3 Local standard deviation
    4 Absolute difference of pixel values (in z)
    5 Local neighborhood median value
    6 Total image standard deviation
     | Show Table
    DownLoad: CSV

    For a given sample dataset (x,y,z,t) coordinates are provided to the algorithm corresponding to the location of particles of interest. Pixel feature matrices are constructed near these coordinates along with a binary probability matrix ft, where ft{0,1}. Because absolute particle coordinates are known, this probability matrix contains zeros everywhere except for the pixels where a particle is located. Both the pixel feature matrix and the binary probability matrix are used to calculate the classifier, which is defined as:

    hw(x)=(1+ewT)1 (7)

    Where wT is the transpose of a linear weighting matrix. There is no closed form solution for w and as a result a gradient descent iterative minimization approach is used such that:

    wkm+1=wk1m+αmi=1(ft,ihk1w(xi))xi (8)

    Where wkm+1 is the (m+1)th element of the kth iteration of the linear weighting matrix and α is gradient descent learning parameter. This learning parameter must be predefined and was chosen as α=0.1.


    2.6.3. Particle identification

    With the classifier trained, arbitrary datasets can be used to construct pixel feature matrices (X). These matrices are then subsequently multiplied by the classifier to yield the probability matrix:

    f=Xhw(x) (9)

    Where 0f1 the values of this matrix correspond to the probability that a particular pixel contains a particle of interest. A minimum probability threshold is then employed to decide whether or not a pixel is indeed a particle of interest.


    2.6.4. Particle tracking

    With (x,y,z,t) coordinates found for all particles of interest in the dataset, a "nearest neighbor" particle tracking algorithm is employed to identify identical particles across time sequences [25]. This algorithm requires inputs of spatial locations of particles at each time point to be analyzed. The tracking algorithm then operates in two stages. First, the algorithm compares the coordinates of particles in time point i to the coordinates in time point (i+1) and defines two coordinates as belonging to the same particle as the points with the smallest Euclidean distance between them across i and (i+1). The second step involves dealing with gaps. These gaps arise when a particle was not successfully identified in one or multiple frames, but reappears in subsequent frames. This stage is an iterative loop that identifies the location where trajectories end and searches subsequent time points for trajectories that begin near where the other ended. If the function is able to find a close enough pair of trajectories, then the two tracks become stitched together and the locations of the particle within the gap are calculated as a linear interpolation between the two known locations.


    3. Results and discussion

    With the manually tracked bacteria in Datasets 1 and 2, calculating an F-score was possible to quantify the performance of the automated tracking algorithm discussed in this work. For Dataset 1, the tracking algorithm yielded a precision of 98.9%, a recall of 57.1% and an F-score of 0.863. For Dataset 2, the tracking algorithm yielded a precision of 91.5%, a recall of 76.5% and an F-score of 0.880. The statistical performance of the automated tracking routine is summarized in Table 4.

    Table 4. Performance statistics of automated tracking algorithm.
    Dataset 1 Dataset 2
    Total number of points 324 98
    Total number of points identified 187 82
    True positives 185 75
    False positives 2 7
    False negatives 139 23
    Precision 98.8% 91.5%
    Recall 57.1% 76.5%
    F-score 0.863 0.880
     | Show Table
    DownLoad: CSV

    Of the bacteria that were identified in Datasets 1 and 2, the localization errors were quantified as the absolute Euclidean distance between the coordinates found by the algorithm and the coordinates obtained by manual tracking. The root-mean-squared (RMS) localization error of Dataset 1 was found to be 7 µm and 6 µm for Dataset 2. Figure 1 shows the histogram of localization errors from (a) Dataset 1 and (b) Dataset 2.

    Figure 1. Localization error of the automated tracking algorithm of (a) Dataset 1 and (b) Dataset 2.

    The tracking algorithm was also employed to track a dataset with a higher concentration of Bacillus subtilis (on the order of 106 cells per mL). At such a concentration, there are expected to be a range of 100 to 200 cells in the field of view of the DHM instrument at any one time. The tracking algorithm was able to identify 149 unique bacteria in this dataset, while a human observer was only able to identify 127 bacteria. The remaining 22 bacteria were noticed by the human observer only after they knew there were bacteria there. Figure 2 shows a three-dimensional plot of the trajectories extracted from the tracking algorithm of this dense sample. The trajectories are color coded with respect to time.

    Figure 2. Three-dimensional trajectories of Bacillus subtilis from Dataset 3.

    Swimming speeds of the tracked dataset were calculated as the root-sum-squared (RSS) of the x,y and z component velocities, such that:

    vix(τ)=ΔxΔt=xi(τ+1)xi(τ)t(τ+1)t(τ) (10A)
    viy(τ)=ΔyΔt=yi(τ+1)yi(τ)t(τ+1)t(τ) (10B)
    viz(τ)=ΔzΔt=zi(τ+1)zi(τ)t(τ+1)t(τ) (10C)
    |vi|=v2x+v2y+v2z (10D)

    Where vij(τ) is the j-component velocity at time vij(τ) of the ith bacterium and |vi| is the absolute swimming speed of the ith bacterium. A histogram of the results is shown in Figure 3. The mean swimming speed was 23 ± 17 µm/s (standard deviation, n = 149) and the median swimming speed was 10 µm/s.

    Figure 3. Distribution of swimming speeds of Bacillus subtilis from Dataset 3.

    This shows that there were a considerable number of outliers, which is consistent with the experimental data. There were multiple very fast swimmers that shifted the mean. These values are in agreement with the literature on wild-type B. subtilis [28].

    The motivations behind the development of this algorithm were to extract statistically significant motility characteristics of bacteria from a dataset in an automated manner. In doing so it was clear that statistical precision is more important than recall because in order to extract statistics from a dataset, not all bacteria need to necessarily be tracked, only a sufficient number of them to form an acceptable sample size. This reason justifies the relatively high number of false negatives in Datasets 1 and 2. Furthermore, although DHM allows three-dimensional imaging in real-time, it is susceptible to sources of noise that result in low signal to noise (SNR) ratios. The low SNR associated with DHM also helps explain the false negatives.

    In the quantification of localization errors of this algorithm, it was found that there are RMS errors of 7 µm and 6 µm for Datasets 1 and 2, respectively. Because these errors were calculated relative to manual tracks, they are susceptible to human error as well. Any error in the centroid identification during manual tracking will affect the RMS error reported here.

    Errors associated with Dataset 3 were not explicitly quantified, but rather are inferred upon by the error analysis conducted on the Dataset 1. This assumption is valid because Dataset 1 and 3 are identical other than the fact that Dataset 3 is at a higher bacterial concentration. It has been found that the average SNR obtained in DHM reconstructions is in fact a function of sample concentration, but the degradation of SNR from the concentration of Dataset 1 to Dataset 3 was found to be negligible [29].

    A large hindrance of three-dimensional particle tracking is the data volumes associated with it. In the particular setup used in this work, 4 megapixel holograms (roughly 4 MB per hologram) were acquired at roughly 10 frames per second. Each hologram was then reconstructed into about 200 separate focal planes in both amplitude and phase. This results in a 400× increase in data size after numerical reconstruction (e.g. Dataset 3 was over 100 GB in size). Non-trivial software techniques must be employed in order to be able to analyze this volume of data with a modest computer. The algorithm described in this work employs these techniques in order to only occupy 8 GB of RAM at any one given time throughout the tracking process.


    4. Conclusions

    This work presents and validates a machine-learning identification algorithm based on linear logistic regressions that can identify microorganisms within DHM image reconstructions, with a precision of over 90% and localization error of roughly 7 µm. Identification was validated using two species of microorganisms of different sizes, without the use of any chemical contrast enhancement (e.g. fluorescent dyes).

    The theoretical and mathematical foundation of this algorithm was introduced and discussed as well as the method in which it was implemented as a MATLAB routine.

    A total of three datasets were analyzed using this algorithm consisting of Bacillus subtilis and Colwellia psychrerythraea. Two of the three datasets contained low concentrations of bacteria in order to allow for the quantization of error, while the third dataset contained a much higher concentration to illustrate its usefulness in practical biological imaging applications.

    Although the data sizes associated with high spatial and temporal resolution three dimensional imaging are cumbersome, the algorithm developed in this work is able to track particles in arbitrarily large datasets (>100 GB) while only occupying 8 GB of RAM and modest CPU requirements. A fully annotated version of the software developed and used throughout this work is available for public use at: https://github.com/mbedross/MachineLearningObjectTracking.


    Acknowledgments

    The authors would like to acknowledge the Gordon and Betty Moore Foundation Grant Numbers 4037/4038 as the source of funding for this work, as well as the Keck Center at Caltech for hosting our collaborations.


    Conflict of interest

    The authors declare no conflicts of interest in this paper.


    [1] Pimentel D (2012) World overpopulation. Environ Dev Sustain 14: 151. doi: 10.1007/s10668-011-9336-2
    [2] Tilman D, Balzer C, Hill J, et al. (2011) Global food demand and the sustainable intensification of agriculture. Proc Natl Acad Sci USA 108: 20260–20264. doi: 10.1073/pnas.1116437108
    [3] Béné C, Barange M, Subasinghe R, et al. (2015) Feeding 9 billion by 2050-Putting fish back on the menu. Food Sec 7: 261. doi: 10.1007/s12571-015-0427-z
    [4] Khush G (2001) Green revolution: the way forward. Nat Rev Genet 2: 815–822.
    [5] Araus J, Li J, Parry M, et al. (2014) Phenotyping and other breeding approaches for a New Green Revolution. J Integr Plant Biol 56: 422–424. doi: 10.1111/jipb.12202
    [6] Garcia-Fraile P, Carro L, Robledo M, et al. (2012) Rhizobium promotes non-legumes growth and quality in several production steps: towards a biofertilization of edible raw vegetables healthy for humans. PLoS One 7: e38122. doi: 10.1371/journal.pone.0038122
    [7] Flores-Felix JD, Silva LR, Rivera LP, et al. (2015) Plants probiotics as a tool to produce highly functional fruits: the case of Phyllobacterium and vitamin C in strawberries. PLoS One 10: e0122281. doi: 10.1371/journal.pone.0122281
    [8] Haas D, Keel C (2003) Regulation of antibiotic production in root-colonizing Pseudomonas spp. and relevance for biological control of plant disease. Ann Rev Phytopathol 41: 117–153.
    [9] Kloepper J, Schrot M (1978) Plant growth-promoting rhizobacteria on radishes. Proceedings of the 4th International Conference on Plant Pathogenic Bacteria 2: 879–882.
    [10] Gray EJ, Smith DL (2005) Intracellular and extracellular PGPR: commonalities and distinctions in the plant-bacterium signaling processes. Soil Biol Biochem 37: 395–412. doi: 10.1016/j.soilbio.2004.08.030
    [11] Hardoim PR, van Overbeek LS, Berg G, et al. (2015) The hidden world within plants: ecological and evolucionary considerations for defining functioning of microbial endophytes. Microbiol Mol Biol Rev 79: 293–320. doi: 10.1128/MMBR.00050-14
    [12] Brewin NJ (1991) Development of the legume root nodule. Ann Rev Cell Biol 7: 191–226. doi: 10.1146/annurev.cb.07.110191.001203
    [13] Suzaki T, Kawaguchi M (2014) Root nodulation: a developmental program involving cell fate conversion triggered by symbiotic bacterial infection. Curr Opin Plant Biol 21: 16–22. doi: 10.1016/j.pbi.2014.06.002
    [14] Pawlowski K, Demchenko KN (2012) The diversity of actinorhizal symbiosis. Protoplasma 249: 967–979. doi: 10.1007/s00709-012-0388-4
    [15] Vessey JK, Pawlowski K, Bergman B (2005) Root-based N2-fixing symbioses: Legumes, actinorhizal plants, Parasponia sp. and cycads. Plant Soil 274: 51–78. doi: 10.1007/s11104-005-5881-5
    [16] Khalid A, Arshad M, Shaharoona B, et al. (2009) Plant Growth Promoting Rhizobacteria and Sustainable Agriculture, In: Microbial Strategies for Crop Improvement, Berlin: Springer, 133–160.
    [17] Bhattacharyya PN, Jha DK (2012) Plant growth-promoting rhizobacteria (PGPR): emergence in agriculture. World J Microbiol Biotechnol 28: 1327–1350. doi: 10.1007/s11274-011-0979-9
    [18] García-Fraile P, Menéndez E, Rivas R (2015) Role of bacterial biofertilizers in agriculture and forestry. AIMS Bioeng 2: 183–205. doi: 10.3934/bioeng.2015.3.183
    [19] Vejan P, Abdullah R, Khadiran T, et al. (2016) Role of plant growth promoting rhizobacteria in agricultural sustainability-a review. Molecules 21: 573. doi: 10.3390/molecules21050573
    [20] Malusá E, Vassilev N (2014) A contribution to set a legal framework for biofertilisers. Appl Microbiol Biotechnol 98: 6599–6607. doi: 10.1007/s00253-014-5828-y
    [21] Reinhold-Hurek B, Hurek T (1998) Interactions of gramineous plants with Azoarcus spp. and other Diazotrophs: identification, localization, and perspectives to study their function. Crit Rev Plant Sci 17: 29–54.
    [22] Sabry SRS, Saleh SA, Batchelor CA, et al. (1997) Endophytic establishment of Azorhizobium caulinodans in wheat. Proc Biol Sci 264: 341–346. doi: 10.1098/rspb.1997.0049
    [23] Tejera N, Lluch C, Martínez-Toledo MV, et al. (2005) Isolation and characterization of Azotobacter and Azospirillum strains from the sugarcane rhizosphere. Plant Soil 270: 223–232. doi: 10.1007/s11104-004-1522-7
    [24] Yadegari M, Rahmani HA, Noormohammadi G, et al. (2010) Plant growth promoting rhizobacteria increase growth, yield and nitrogen fixation in Phaseolus vulgaris. J Plant Nutr 33: 1733–1743. doi: 10.1080/01904167.2010.503776
    [25] Isawa T, Yasuda M, Awazaki H, et al. (2010) Azospirillum sp. strain B510 enhances rice growth and yield. Microbes Environ 25: 58–61.
    [26] Hungria M, Nogueira MA, Araujo RS (2013) Co-inoculation of soybeans and common beans with rhizobia and azospirilla: strategies to improve sustainability. Biol Fert Soils 49: 791–801. doi: 10.1007/s00374-012-0771-5
    [27] Sahoo RK, Ansari MW, Pradhan M, et al. (2014) Phenotypic and molecular characterization of native Azospirillum strains from rice fields to improve crop productivity. Protoplasma 251: 943–953. doi: 10.1007/s00709-013-0607-7
    [28] Ramakrishnan K, Selvakumar G (2012) Effect of biofertilizers on enhancement of growth and yield on Tomato (Lycopersicum esculentum Mill.) Int. J Res Bot 2: 20–23.
    [29] Wani SA, Chand S, Ali T (2013) Potential use of Azotobacter chroococcum in crop production: an overview. Curr Agri Res J 1: 35–38. doi: 10.12944/CARJ.1.1.04
    [30] Sahoo RK, Ansari MW, Dangar TK, et al. (2014) Phenotypic and molecular characterisation of efficient nitrogen-fixing Azotobacter strains from rice fields for crop improvement. Protoplasma 251: 511–523. doi: 10.1007/s00709-013-0547-2
    [31] Beneduzi A, Peres D, Vargas LK, et al. (2008) Evaluation of genetic diversity and plant growth promoting activities of nitrogen-fixing bacilli isolated from rice fields in South Brazil. App Soil Ecol 39: 311–320. doi: 10.1016/j.apsoil.2008.01.006
    [32] Habibi S, Djedidi S, Prongjunthuek K, et al. (2014) Physiological and genetic characterization of rice nitrogen fixer PGPR isolated from rhizosphere soils of different crops. Plant Soil 379: 51–66. doi: 10.1007/s11104-014-2035-7
    [33] Rana A, Saharan B, Joshi M, et al. (2011) Identification of multi-trait PGPR isolates and evaluating their potential as inoculants for wheat. Ann Microbiol 61: 893–900. doi: 10.1007/s13213-011-0211-z
    [34] Kao CM, Chen SC, Chen YS, et al. (2003) Detection of Burkholderia pseudomallei in rice fields with PCR-based technique. Folia Microbiol (Praha) 48: 521–552. doi: 10.1007/BF02931334
    [35] Govindarajan M, Balandreau J, Kwon SW, et al. (2007) Effects of the inoculation of Burkholderia vietnamensis and related endophytic diazotrophic bacteria on grain yield of rice. Microb Ecol 55: 21–37.
    [36] Berge O, Heulin T, Achouak W, et al. (1991) Rahnella aquatilis, a nitrogen-fixing enteric bacterium associated with the rhizosphere of wheat and maize. Can J Microbiol 37: 195–203. doi: 10.1139/m91-030
    [37] Taulé C, Mareque C, Barlocco C, et al. (2012) The contribution of nitrogen fixation to sugarcane (Saccharum officinarum L.), and the identification and characterization of part of the associated diazotrophic bacterial community. Plant Soil 356: 35–49.
    [38] Simonet P, Normand P, Moiroud A, et al. (1990) Identification of Frankia strains in nodules by hybridization of polymerase chain reaction products with strain-specific oligonucleotide probes. Arch Microb 153: 235–240. doi: 10.1007/BF00249074
    [39] Muñoz-Rojas J, Caballero-Mellado J (2003) Population dynamics of Gluconacetobacter diazotrophicus in sugarcane cultivars and its effect on plant growth. Microb Ecol 46: 454–464. doi: 10.1007/s00248-003-0110-3
    [40] Elbeltagy A, Nishioka K, Sato T, et al. (2001) Endophytic colonization and in planta nitrogen fixation by a Herbaspirillum sp. isolated from wild rice species. Appl Environ Microbiol 67: 5285–5293.
    [41] Valverde A, Velazquez E, Gutierrez C, et al. (2003) Herbaspirillum lusitanum sp. nov., a novel nitrogen-fixing bacterium associated with root nodules of Phaseolus vulgaris. Int J Syst Evol Microbiol 53: 1979–1983.
    [42] Alves GC, Videira SS, Urquiaga S, et al. (2015) Differential plant growth promotion and nitrogen fixation in two genotypes of maize by several Herbaspirillum inoculants. Plant Soil 387: 307–321. doi: 10.1007/s11104-014-2295-2
    [43] Puri A, Padda KP, Chanway CP (2016) Evidence of nitrogen fixation and growth promotion in canola (Brassica napus L.) by an endophytic diazotroph Paenibacillus polymyxa P2b-2R. Biol Fert Soils 52: 119–125.
    [44] Peix A, Ramírez-Bahena MH, Velázquez E, et al. (2015) Bacterial associations with legumes. Crit Rev Plant Sci 34: 17–42. doi: 10.1080/07352689.2014.897899
    [45] Aloni R, Aloni E, Langhans M, et al. (2006) Role of cytokinin and auxin in shaping root architecture: regulating vascular differentiation, lateral root initiation, root apical dominance and root gravitropism. Ann Bot 97: 883–893. doi: 10.1093/aob/mcl027
    [46] Ahmed A, Hasnain S (2010) Auxin producing Bacillus sp.: Auxin quantification and effect on the growth Solanum tuberosum. Pure Appl Chem 82: 313–319.
    [47] Sokolova MG, Akimova GP, Vaishlya OB (2011) Effect of phytohormones synthesized by rhizosphere bacteria on plants. App Biochem Microbiol 47: 274–278. doi: 10.1134/S0003683811030148
    [48] Liu F, Xing S, Ma H, et al. (2013) Cytokinin-producing, plant growth-promoting rhizobacteria that confer resistance to drought stress in Platycladus orientalis container seedlings. Appl Microbiol Biotechnol 97: 9155–9164. doi: 10.1007/s00253-013-5193-2
    [49] Ortiz-Castro R, Valencia-Cantero E, López-Bucio J (2008) Plant growth promotion by Bacillus megaterium involves cytokinin signaling. Plant Signal Behav 3: 263–265. doi: 10.4161/psb.3.4.5204
    [50] Kang SM, Khan AL, Waqas M, et al. (2015) Gibberellin-producing Serratia nematodiphila PEJ1011 ameliorates low temperature stress in Capsicum annuum L. Eur J Soil Biol 68: 85–93. doi: 10.1016/j.ejsobi.2015.02.005
    [51] Asaf S, Khan MA, Khan AL, et al. (2017) Bacterial endophytes from arid land plants regulate endogenous hormone content and promote growth in crop plants: an example of Sphingomonas sp. and Serratia marcescens. J Plant Interact 12: 31–38. doi: 10.1080/17429145.2016.1274060
    [52] Suarez C, Cardinale M, Ratering S, et al. (2015) Plant growth-promoting effects of Hartmannibacter diazotrophicus on summer barley (Hordeum vulgare L.) under salt stress. Appl Soil Ecol 95: 23–30.
    [53] Bent E, Tuzun S, Chanway CP, et al. (2001) Alterations in plant growth and in root hormone levels of lodgepole pines inoculated with rhizobacteria. Can J Microbiol 47: 793–800. doi: 10.1139/w01-080
    [54] Bakaeva MD, Chetverikov SP, Korshunova TY, et al. (2017) The new bacterial strain Paenibacillus sp. IB-1: A producer of exopolysaccharide and biologically active substances with phytohormonal and antifungal activities. App Biochem Microbiol 53: 201–208.
    [55] Galland M, Gamet L, Varoquaux F, et al. (2012) The ethylene pathway contributes to root hair elongation induced by the beneficial bacteria Phyllobacterium brassicacearum STM196. Plant Sci 190: 74–81. doi: 10.1016/j.plantsci.2012.03.008
    [56] Shaharoona B, Naveed M, Arshad M, et al. (2008) Fertilizer-dependent efficiency of Pseudomonas for improving growth, yield, and nutrient use efficiency of wheat (Triticum aestivum L.). Appl Microbiol Biotechnol 79: 147–155. doi: 10.1007/s00253-008-1419-0
    [57] Ahmad M, Zahir ZA, Khalid M, et al. (2013) Efficacy of Rhizobium and Pseudomonas strains to improve physiology, ionic balance and quality of mung bean under salt-affected conditions on farmer's fields. Plant Physiol Biochem 63: 170–176. doi: 10.1016/j.plaphy.2012.11.024
    [58] Flores-Felix JD, Menendez E, Rivera LP, et al. (2013) Use of Rhizobium leguminosarum as a potential biofertilizer for Lactuca sativa and Daucus carota crops. J Plant Nutr Soil Sci 176: 876–882. doi: 10.1002/jpln.201300116
    [59] Brígido C, Nascimento FX, Duan J, et al. (2013) Expression of an exogenous 1-aminocyclopropane-1-carboxylate deaminase gene in Mesorhizobium spp. reduces the negative effects of salt stress in chickpea. FEMS Microbiol Lett 349: 46–53.
    [60] Flores-Félix JD, Marcos-García M, Silva LR, et al. (2015) Rhizobium as plant probiotic for strawberry production under microcosm conditions. Symbiosis 67: 25–32. doi: 10.1007/s13199-015-0373-8
    [61] Menéndez E, Escribano-Viana R, Flores-Félix JD, et al. (2016) Rhizobial biofertilizers for ornamental plants, In: Biological Nitrogen Fixation and Beneficial Plant-Microbe Interaction, Springer International Publishing, 13–21.
    [62] Brígido C, Glick BR, Oliveira S (2016) Survey of plant growth-promoting mechanisms in native Portuguese Chickpea Mesorhizobium isolates. Microb Ecol 73: 900–915.
    [63] Kong Z, Glick BR, Duan J, et al. (2015) Effects of 1-aminocyclopropane-1-carboxylate (ACC) deaminase-overproducing Sinorhizobium meliloti on plant growth and copper tolerance of Medicago lupulina. Plant Soil 391: 383–398. doi: 10.1007/s11104-015-2434-4
    [64] Khan AL, Waqas M, Kang SM, et al. (2014) Bacterial endophyte Sphingomonas sp. LK11 produces gibberellins and IAA and promotes tomato plant growth. J Microbiol 52: 689–695.
    [65] Verma VC, Singh SK, Prakash S (2011) Bio-control and plant growth promotion potential of siderophore producing endophytic Streptomyces from Azadirachta indica A. Juss. J Basic Microb 51: 550–556. doi: 10.1002/jobm.201000155
    [66] Boudjeko T, Tchinda RAM, Zitouni M, et al. (2017) Streptomyces cameroonensis sp. nov., a Geldanamycin producer that promotes Theobroma cacao growth. Microbes Environ 32: 24–31.
    [67] Estrada GA, Baldani VLD, de Oliveira DM, et al. (2013) Selection of phosphate-solubilizing diazotrophic Herbaspirillum and Burkholderia strains and their effect on rice crop yield and nutrient uptake. Plant Soil 369: 115–129. doi: 10.1007/s11104-012-1550-7
    [68] Jog R, Pandya M, Nareshkumar G, et al. (2014) Mechanism of phosphate solubilization and antifungal activity of Streptomyces spp. isolated from wheat roots and rhizosphere and their application in improving plant growth. Microbiology 160: 778–788.
    [69] Sheng XF (2005) Growth promotion and increased potassium uptake of cotton and rape by a potassium releasing strain of Bacillus edaphicus. Soil Biol Biochem 37: 1918–1922. doi: 10.1016/j.soilbio.2005.02.026
    [70] Han HS, Lee KD (2005) Phosphate and potassium solubilizing bacteria effect on mineral uptake, soil availability and growth of eggplant. Res J Agric Biol Sci 1: 176–180.
    [71] Han HS, Supanjani S, Lee KD (2006) Effect of co-inoculation with phosphate and potassium solubilizing bacteria on mineral uptake and growth of pepper and cucumber. Plant Soil Environ 52: 130–136.
    [72] Sugumaran P, Janarthanam B (2007) Solubilization of potassium containing minerals by bacteria and their effect on plant growth. World J Agric Sci 3: 350–355.
    [73] Singh G, Biswas DR, Marwaha TS (2010) Mobilization of potassium from waste mica by plant growth promoting rhizobacteria and its assimilation by maize (Zea mays) and wheat (Triticum aestivum L.): a hydroponics study under phytotron growth chamber. J Plant Nutr 33: 1236–1251.
    [74] Velázquez E, Silva LR, Ramírez-Bahena MH, et al. (2016) Diversity of potassium-solubilizing microorganisms and their interactions with plants, In: Potassium Solubilizing Microorganisms for Sustainable Agriculture, Springer India, 99–110.
    [75] Zhang C, Kong F (2014) Isolation and identification of potassium-solubilizing bacteria from tobacco rhizospheric soil and their effect on tobacco plants. Appl Soil Ecol 82: 18–25. doi: 10.1016/j.apsoil.2014.05.002
    [76] Subhashini DV (2015) Growth promotion and increased potassium uptake of tobacco by potassium-mobilizing bacterium Frateuria aurantia grown at different potassium levels in vertisols. Commun Soil Sci Plant Anal 46: 210–220. doi: 10.1080/00103624.2014.967860
    [77] Bagyalakshmi B, Ponmurugan P, Marimuthu S (2012) Influence of potassium solubilizing bacteria on crop productivity and quality of tea (Camellia sinensis). Afr J Agric Res 7: 4250–4259.
    [78] Beneduzi A, Ambrosini A, Passaglia LM (2012) Plant growth-promoting rhizobacteria (PGPR): Their potential as antagonists and biocontrol agents. Genet Mol Biol 35: 1044–1051. doi: 10.1590/S1415-47572012000600020
    [79] Radzki W, Gutierrez Manero FJ, Algar E, et al. (2013) Bacterial siderophores efficiently provide iron to iron-starved tomato plants in hydroponics culture. Anton Van Leeuw 104: 321–330. doi: 10.1007/s10482-013-9954-9
    [80] Ghavami N, Alikhani HA, Pourbabaei AA, et al. (2016) Effects of two new siderophore producing rhizobacteria on growth and iron content of maize and canola plants. J Plant Nutr 40: 736–746.
    [81] Egamberdiyeva D (2007) The effect of plant growth promoting bacteria on growth and nutrient uptake of maize in two different soils. Appl Soil Ecol 36: 184–189. doi: 10.1016/j.apsoil.2007.02.005
    [82] El-Akhal MR, Rincon A, Coba de la Pena T, et al. (2013) Effects of salt stress and rhizobial inoculation on growth and nitrogen fixation of three peanut cultivars. Plant Biol (Stuttg) 15: 415–421. doi: 10.1111/j.1438-8677.2012.00634.x
    [83] Lee SW, Lee SH, Balaraju K, et al. (2014) Growth promotion and induced disease suppression of four vegetable crops by a selected plant growth-promoting rhizobacteria (PGPR) strain Bacillus subtilis 21-1 under two different soil conditions. Acta Physiol Plant 36: 1353–1362. doi: 10.1007/s11738-014-1514-z
    [84] Sivasakthi S, Usharani G, Saranraj P (2014) Biocontrol potentiality of plant growth promoting bacteria (PGPR)-Pseudomonas fluorescens and Bacillus subtilis: A review. Afr J Agric Res 9: 1265–1277.
    [85] Li H, Ding X, Wang C, et al. (2016) Control of Tomato yellow leaf curl virus disease by Enterobacter asburiae BQ9 as a result of priming plant resistance in tomatoes. Turk J Biol 40: 150–159. doi: 10.3906/biy-1502-12
    [86] Singh RP, Jha PN (2016) The multifarious PGPR Serratia marcescens CDP-13 augments induced systemic resistance and enhanced salinity tolerance of wheat (Triticum aestivum L.). PloS One 11: e0155026. doi: 10.1371/journal.pone.0155026
    [87] Calvo J, Calvente V, de Orellano ME, et al. (2007) Biological control of postharvest spoilage caused by Penicillium expansum and Botrytis cinerea in apple by using the bacterium Rahnella aquatilis. Int J Food Microbiol 113: 251–257. doi: 10.1016/j.ijfoodmicro.2006.07.003
    [88] Allard S, Enurah A, Strain E, et al. (2014) In situ evaluation of Paenibacillus alvei in reducing carriage of Salmonella enterica serovar Newport on whole tomato plants. App Environ Microbiol 80: 3842–3849. doi: 10.1128/AEM.00835-14
    [89] Xu S, Kim BS (2016) Evaluation of Paenibacillus polymyxa strain SC09-21 for biocontrol of Phytophthora blight and growth stimulation in pepper plants. Trop Plant Pathol 41: 162–168. doi: 10.1007/s40858-016-0077-5
    [90] Yao L, Wu Z, Zheng Y, et al. (2010) Growth promotion and protection against salt stress by Pseudomonas putida Rs-198 on cotton. Eur J Soil Biol 46: 49–54. doi: 10.1016/j.ejsobi.2009.11.002
    [91] Kumar H, Bajpai VK, Dubey RC, et al. (2010) Wilt disease management and enhancement of growth and yield of Cajanus cajan (L) var. Manak by bacterial combinations amended with chemical fertilizer. Crop Protect 29: 591–598.
    [92] Pastor N, Masciarelli O, Fischer S, et al. (2016) Potential of Pseudomonas putida PCI2 for the protection of tomato plants against fungal pathogens. Curr Microbiol 73: 346–353. doi: 10.1007/s00284-016-1068-y
    [93] Raymond J, Siefert JL, Staples CR, et al. (2004) The natural history of nitrogen fixation. Mol Biol Evol 21: 541–554. doi: 10.1093/molbev/msh047
    [94] Grady EN, MacDonald J, Liu L, et al. (2016) Current knowledge and perspectives of Paenibacillus: a review. Microb Cell Fact 15: 203. doi: 10.1186/s12934-016-0603-7
    [95] Borriss R (2015) Bacillus, a plant-beneficial bacterium, In: Principles of Plant-Microbe Interactions, Springer International Publishing, 379–391.
    [96] Hurek T, Reinhold-Hurek B (2003) Azoarcus sp. strain BH72 as a model for nitrogen-fixing grass endophytes. J Biotechnol 106: 169–178.
    [97] Kao CM, Chen SC, Chen YS, et al. (2003) Detection of Burkholderia pseudomallei in rice fields with PCR-based technique. Folia Microbiol (Praha) 48: 521–552. doi: 10.1007/BF02931334
    [98] Tan Z, Hurek T, Vinuesa P, et al. (2001) Specific detection of Bradyrhizobium and Rhizobium strains colonizing rice (Oryza sativa) roots by 16S-23S ribosomal DNA intergenic spacer-targeted PCR. Appl Environ Microbiol 67: 3655–3664. doi: 10.1128/AEM.67.8.3655-3664.2001
    [99] Yanni YG, Rizk RY, El-Fattah FKA, et al. (2001) The beneficial plant growth-promoting association of Rhizobium leguminosarum bv. trifolii with rice roots. Aust J Plant Physiol 28: 845–870.
    [100] Yanni YG, Dazzo FB, Squartini A, et al. (2016) Assessment of the natural endophytic association between Rhizobium and wheat and its ability to increase wheat production in the Nile delta. Plant Soil 407: 367–383. doi: 10.1007/s11104-016-2895-0
    [101] Moulin L, Munive A, Dreyfus B, et al. (2001) Nodulation of legumes by members of the beta-subclass of Proteobacteria. Nature 411: 948–950. doi: 10.1038/35082070
    [102] Oldroyd GE, Downie JA (2008) Coordinating nodule morphogenesis with rhizobial infection in legumes. Annu Rev Plant Biol 59: 519–546. doi: 10.1146/annurev.arplant.59.032607.092839
    [103] Santi C, Bogusz D, Franche C (2013) Biological nitrogen fixation in non-legume plants. Ann Bot 111: 743–767. doi: 10.1093/aob/mct048
    [104] Spaepen S (2015) Plant Hormones Produced by Microbes, In: Lugtenberg B, Editor, Principles of Plant-Microbe Interactions, Switzerland: Springer International Publishing, 247–256.
    [105] Costacurta A, Vanderleyden J (1995) Synthesis of phytohormones by plant-associated bacteria. Crit Rev Microbiol 21: 1–18. doi: 10.3109/10408419509113531
    [106] Trewavas A (1981) How do plant growth substances work? Plant Cell Environ 4: 203–228. doi: 10.1111/j.1365-3040.1981.tb01048.x
    [107] Spaepen S, Vanderleyden J, Remans R (2007) Indole-3-acetic acid in microbial and microorganism-plant signaling. FEMS Microbiol Rev 31: 425–448. doi: 10.1111/j.1574-6976.2007.00072.x
    [108] Hayat R, Ali S, Amara U, et al. (2010) Soil beneficial bacteria and their role in plant growth promotion: a review. Ann Microbiol 60: 579–598. doi: 10.1007/s13213-010-0117-1
    [109] Arkhipova TN, Prinsen E, Veselov SU, et al. (2007) Cytokinin producing bacteria enhance plant growth in drying soil. Plant Soil 292: 305–315. doi: 10.1007/s11104-007-9233-5
    [110] Bottini R, Cassán F, Piccoli P (2004) Gibberellin production by bacteria and its involvement in plant growth promotion and yield increase. App Microbiol Biotechnol 65: 497–503.
    [111] Nagahama K, Ogawa T, Fujii T, et al. (1992) Classification of ethylene-producing bacteria in terms of biosynthetic pathways to ethylene. J Ferment Bioeng 73: 1–5. doi: 10.1016/0922-338X(92)90221-F
    [112] Glick BR, Penrose DM, Li J (1998) A model for the lowering of plant ethylene concentrations by plant growth-promoting bacteria. J Theor Biol 190: 63–68. doi: 10.1006/jtbi.1997.0532
    [113] Joo GJ, Kim YM, Kim JT, et al. (2005) Gibberellins-producing rhizobacteria increase endogenous gibberellins content and promote growth of red peppers. J Microbiol 43: 510–515.
    [114] Ghosh PK, Sen SK, Maiti TK (2015) Production and metabolism of IAA by Enterobacter spp. (Gammaproteobacteria) isolated from root nodules of a legume Abrus precatorius L. Biocatal Agric Biotechnol 4: 296–303.
    [115] Ma W, Penrose DM, Glick BR (2002) Strategies used by rhizobia to lower plant ethylene levels and increase nodulation. Can J Microbiol 48: 947–954. doi: 10.1139/w02-100
    [116] Saleem M, Arshad M, Hussain S, et al. (2007) Perspective of plant growth promoting rhizobacteria (PGPR) containing ACC deaminase in stress agriculture. J Ind Microbiol Biotechnol 34: 635–648. doi: 10.1007/s10295-007-0240-6
    [117] Glick BR, Cheng Z, Czarny J, et al. (2007) Promotion of plant growth by ACC deaminase-producing soil bacteria. Eur J Plant Pathol 119: 329–339. doi: 10.1007/s10658-007-9162-4
    [118] Glick BR (2014) Bacteria with ACC deaminase can promote plant growth and help to feed the world. Microbiol Res 169: 30–39. doi: 10.1016/j.micres.2013.09.009
    [119] Gamalero E, Glick BR (2015) Bacterial modulation of plant ethylene levels. Plant Physiol 169: 13–22. doi: 10.1104/pp.15.00284
    [120] Nascimento FX, Brígido C, Glick BR, et al. (2016) The role of rhizobial ACC deaminase in the nodulation process of leguminous plants. Int J Agron 2016.
    [121] Honma M, Shimomura T (1978) Metabolism of 1-aminocyclopropane-1-carboxylic acid. Agric Biol Chem 42: 1825–1831.
    [122] Magnucka EG, Pietr SJ (2015) Various effects of fluorescent bacteria of the genus Pseudomonas containing ACC deaminase on wheat seedling growth. Microbiol Res 181: 112–119. doi: 10.1016/j.micres.2015.04.005
    [123] Zerrouk IZ, Benchabane M, Khelifi L, et al. (2016) A Pseudomonas strain isolated from date-palm rhizospheres improves root growth and promotes root formation in maize exposed to salt and aluminum stress. J Plant Physiol 191: 111–119. doi: 10.1016/j.jplph.2015.12.009
    [124] Zahir ZA, Ghani U, Naveed M, et al. (2009) Comparative effectiveness of Pseudomonas and Serratia sp. containing ACC-deaminase for improving growth and yield of wheat (Triticum aestivum L.) under salt-stressed conditions. Arch Microbiol 191: 415–424.
    [125] Schachtman DP, Reid RJ, Ayling SM (1998) Phosphorus uptake by plants: from soil to cell. Plant Physiol 116: 447–453. doi: 10.1104/pp.116.2.447
    [126] Sharma SB, Sayyed RZ, Trivedi MH, et al. (2013) Phosphate solubilizing microbes: sustainable approach for managing phosphorus deficiency in agricultural soils. Springerplus 2: 587. doi: 10.1186/2193-1801-2-587
    [127] Zaidi A, Khan M, Ahemad M, et al. (2009) Plant growth promotion by phosphate solubilizing bacteria. Acta Microbiol Immunol Hungarica 56: 263–284. doi: 10.1556/AMicr.56.2009.3.6
    [128] Dastager SG, Deepa CK, Pandey A (2010) Isolation and characterization of novel plant growth promoting Micrococcus sp NII-0909 and its interaction with cowpea. Plant Physiol Biochem 48: 987–992. doi: 10.1016/j.plaphy.2010.09.006
    [129] Pindi PK, Satyanarayana SDV (2012) Liquid microbial consortium-a potential tool for sustainable soil health. J Biofertil Biopest 3: 1–9.
    [130] Peix A, Rivas-Boyero AA, Mateos PF, et al. (2001) Growth promotion of chickpea and barley by a phosphate solubilizing strain of Mesorhizobium mediterraneum under growth chamber conditions. Soil Biol Biochem 33: 103–110. doi: 10.1016/S0038-0717(00)00120-6
    [131] Liu FP, Liu HQ, Zhou HL, et al. (2014) Isolation and characterization of phosphate-solubilizing bacteria from betel nut (Areca catechu) and their effects on plant growth and phosphorus mobilization in tropical soils. Biol Fert Soils 50: 927–937. doi: 10.1007/s00374-014-0913-z
    [132] Panda P, Chakraborty S, Ray DP, et al. (2016) Screening of phosphorus solubilizing bacteria from tea rhizosphere soil based on growth performances under different stress conditions. Int J Biores Sci 3: 39–56. doi: 10.5958/2454-9541.2016.00005.0
    [133] Jaiswal DK, Verma JP, Prakash S, et al. (2016) Potassium as an important plant nutrient in sustainable agriculture: a state of the art, In: Potassium Solubilizing Microorganisms for Sustainable Agriculture, Springer India, 21–29.
    [134] Sheng XF, He LY (2006) Solubilization of potassium-bearing minerals by a wild-type strain of Bacillus edaphicus and its mutants and increased potassium uptake by wheat. Can J Microbiol 52: 66–72. doi: 10.1139/w05-117
    [135] Sangeeth KP, Bhai RS, Srinivasan V (2012). Paenibacillus glucanolyticus, a promising potassium solubilizing bacterium isolated from black pepper (Piper nigrum L.) rhizosphere. J Spices Arom Crops 21.
    [136] Basak BB, Biswas DR (2009) Influence of potassium solubilizing microorganism (Bacillus mucilaginosus) and waste mica on potassium uptake dynamics by sudan grass (Sorghum vulgare Pers.) grown under two Alfisols. Plant Soil 317: 235–255.
    [137] Neilands JB (1995) Siderophores: structure and function of microbial iron transport compounds. J Biol Chem 270: 26723–26726. doi: 10.1074/jbc.270.45.26723
    [138] Ahmed E, Holmstrom SJ (2014) Siderophores in environmental research: roles and applications. Microb Biotechnol 7: 196–208. doi: 10.1111/1751-7915.12117
    [139] Saha M, Sarkar S, Sarkar B, et al. (2016) Microbial siderophores and their potential applications: a review. Environ Sci Poll Res 23: 3984–3999. doi: 10.1007/s11356-015-4294-0
    [140] Wang W, Vinocur B, Altman A (2003) Plant responses to drought, salinity and extreme temperatures: towards genetic engineering for stress tolerance. Planta 218: 1–14. doi: 10.1007/s00425-003-1105-5
    [141] Zubair M, Shakir M, Ali Q, et al. (2016) Rhizobacteria and phytoremediation of heavy metals. Environ Technol Rev 5: 112–119. doi: 10.1080/21622515.2016.1259358
    [142] Liddycoat SM, Greenberg BM, Wolyn DJ (2009) The effect of plant growth-promoting rhizobacteria on asparagus seedlings and germinating seeds subjected to water stress under greenhouse conditions. Can J Microbiol 55: 388–394. doi: 10.1139/W08-144
    [143] Paul D, Nair S (2008) Stress adaptations in a Plant Growth Promoting Rhizobacterium (PGPR) with increasing salinity in the coastal agricultural soils. J Basic Microbiol 48: 378–384. doi: 10.1002/jobm.200700365
    [144] Yaish MW, Antony I, Glick BR (2015) Isolation and characterization of endophytic plant growth-promoting bacteria from date palm tree (Phoenix dactylifera L.) and their potential role in salinity tolerance. Anton Van Leeuw 107: 1519–1532.
    [145] Burd GI, Dixon DG, Glick BR (2000) Plant growth-promoting bacteria that decrease heavy metal toxicity in plants. Can J Microbiol 46: 237–245. doi: 10.1139/w99-143
    [146] Pérez-Montaño F, Alías-Villegas C, Bellogín RA, et al. (2014) Plant growth promotion in cereal and leguminous agricultural important plants: from microorganism capacities to crop production. Microbiol Res 169: 325–336. doi: 10.1016/j.micres.2013.09.011
    [147] Abou-Shanab RA, Angle JS, Delorme TA, et al. (2003) Rhizobacterial effects on nickel extraction from soil and uptake by Alyssum murale. New Phytol 158: 219–224. doi: 10.1046/j.1469-8137.2003.00721.x
    [148] Ma Y, Rajkumar M, Freitas H (2009) Isolation and characterization of Ni mobilizing PGPB from serpentine soils and their potential in promoting plant growth and Ni accumulation by Brassica spp. Chemosphere 75: 719–725. doi: 10.1016/j.chemosphere.2009.01.056
    [149] Dimkpa C, Svatoš A, Merten D, et al. (2008) Hydroxamate siderophores produced by Streptomyces acidiscabies E13 bind nickel and promote growth in cowpea (Vignaunguiculata L.) under nickel stress. Can J Microbiol 54: 163–172.
    [150] Carrillo-Castaneda G, Juarez MJ, Peralta-Videa J, et al. (2002) Plant growth-promoting bacteria promote copper and iron translocation from root to shoot in alfalfa seedlings. J Plant Nutr 26: 1801–1814. doi: 10.1081/PLN-120023284
    [151] Thomashow LS (1996) Biological control of plant root pathogens. Curr Opin Biotechnol 7: 343–347. doi: 10.1016/S0958-1669(96)80042-5
    [152] Ulloa-Ogaz, AL, Muñoz-Castellanos LN, Nevárez-Moorillón GV (2015) Biocontrol of phytopathogens: Antibiotic production as mechanism of control, In: Méndez-Vilas A, The Battle Against Microbial Pathogens: Basic Science, Technological Advances and Educational Programs, 305–309.
    [153] Fernando WD, Nakkeeran S, Zhang Y (2005) Biosynthesis of antibiotics by PGPR and its relation in biocontrol of plant diseases, In: PGPR: Biocontrol and Biofertilization, Springer Netherlands, 67–109.
    [154] Mazzola M, Fujimoto DK, Thomashow LS, et al. (1995) Variation in sensitivity of Gaeumannomyces graminis to antibiotics produced by fluorescent Pseudomonas spp. and effect on biological control of take-all of wheat. Appl Environ Microbiol 61: 2554–2559.
    [155] Durán P, Acuña JJ, Jorquera MA, et al. (2014) Endophytic bacteria from selenium-supplemented wheat plants could be useful for plant-growth promotion, biofortification and Gaeumannomyces graminis biocontrol in wheat production. Biol Fert Soils 50: 983–990. doi: 10.1007/s00374-014-0920-0
    [156] Maksimov IV, Abizgil'dina RR, Pusenkova LI (2011) Plant growth promoting rhizobacteria as alternative to chemical crop protectors from pathogens (review). Appl Biochem Microbiol 47: 333–345. doi: 10.1134/S0003683811040090
    [157] Silo-Suh LA, Lethbridge BJ, Raffel SJ, et al. (1994) Biological activities of two fungistatic antibiotics produced by Bacillus cereus UW85. Appl Environ Microbiol 60: 2023–2030.
    [158] Araújo FF, Henning AA, Hungria M (2005) Phytohormones and antibiotics produced by Bacillus subtilis and their effects on seed pathogenic fungi and on soybean root development. World J Microbiol Biotechnol 21: 1639–1645. doi: 10.1007/s11274-005-3621-x
    [159] Arora NK, Khare E, Oh JH, et al. (2008) Diverse mechanisms adopted by Pseudomonas fluorescens PGC2 during the inhibition of Rhizoctonia solani and Phytophthora capsici. World J Microbiol Biotechnol 24: 581–585. doi: 10.1007/s11274-007-9505-5
    [160] El-Tarabily KA, Sykes ML, Kurtböke ID, et al. (1996) Synergistic effects of a cellulase-producing Micromonospora carbonacea and an antibiotic-producing Streptomyces violascens on the suppression of Phytophthora cinnamomi root rot of Banksia grandis. Can J Bot 74: 618–624. doi: 10.1139/b96-078
    [161] El-Tarabily KA (2006) Rhizosphere-competent isolates of streptomycete and non-streptomycete actinomycetes capable of producing cell-wall-degrading enzymes to control Pythium aphanidermatum damping-off disease of cucumber. Can J Bot 84: 211–222. doi: 10.1139/b05-153
    [162] Martínez-Hidalgo P, Galindo-Villardón P, Trujillo ME, et al. (2014) Micromonospora from nitrogen fixing nodules of alfalfa (Medicago sativa L.). A new promising Plant Probiotic Bacteria. Sci Rep 4: 6389.
    [163] Martínez-Hidalgo P, García JM, Pozo MJ (2015) Induced systemic resistance against Botrytis cinerea by Micromonospora strains isolated from root nodules. Front Microbiol 6.
    [164] Hirsch AM, Valdés M (2010) Micromonospora: An important microbe for biomedicine and potentially for biocontrol and biofuels. Soil Biol Biochem 42: 536–542. doi: 10.1016/j.soilbio.2009.11.023
    [165] Schnepf E, Crickmore N, Van RJ, et al. (1998) Bacillus thuringiensis and its pesticidal crystal proteins. Microbiol Mol Biol Rev 62: 775–806.
    [166] Chattopadhyay A, Bhatnagar NB, Bhatnagar R (2004) Bacterial insecticidal toxins. Crit Rev Microbiol 30: 33–54. doi: 10.1080/10408410490270712
    [167] Muqarab R, Bano A (2016) Plant defence induced by PGPR against Spodoptera litura in tomato. Plant Biol 19: 406–412.
    [168] Sharma IP, Sharma AK (2017) Effective control of root-knot nematode disease with Pseudomonad rhizobacteria filtrate. Rhizosphere 3: 123–125. doi: 10.1016/j.rhisph.2017.02.001
    [169] Schippers B, Bakker AW, Bakker PAHM (1987) Interactions of deleterious and beneficial rhizosphere microorganisms and the effect of cropping practices. Ann Rev Phytopathol 25: 339–358. doi: 10.1146/annurev.py.25.090187.002011
    [170] Pal KK, Tilak KVBR, Saxcna AK, et al. (2001) Suppression of maize root diseases caused by Macrophomina phaseolina, Fusarium moniliforme and Fusarium graminearum by plant growth promoting rhizobacteria. Microbiol Res 156: 209–223. doi: 10.1078/0944-5013-00103
    [171] Yu X, Ai C, Xin L, et al. (2011) The siderophore-producing bacterium, Bacillus subtilis CAS15, has a biocontrol effect on Fusarium wilt and promotes the growth of pepper. Eur J Soil Biol 47: 138–145. doi: 10.1016/j.ejsobi.2010.11.001
    [172] Gamalero E, Marzachì C, Galetto L, et al. (2016) An 1-Aminocyclopropane-1-carboxylate (ACC) deaminase-expressing endophyte increases plant resistance to flavescence dorée phytoplasma infection. Plant Biosyst 151: 331–340.
    [173] Borriss R (2011) Use of plant-associated Bacillus strains as biofertilizers and biocontrol agents in agricultura, In: Bacteria in agrobiology: Plant growth responses, Springer Berlin Heidelberg, 41–76.
    [174] Senthilkumar M, Swarnalakshmi K, Govindasamy V, et al. (2009) Biocontrol potential of soybean bacterial endophytes against charcoal rot fungus, Rhizoctonia bataticola. Curr Microbiol 58: 288. doi: 10.1007/s00284-008-9329-z
    [175] Herrera SD, Grossi C, Zawoznik M, et al. (2016) Wheat seeds harbour bacterial endophytes with potential as plant growth promoters and biocontrol agents of Fusarium graminearum. Microbiol Res 186: 37–43.
    [176] Andreolli M, Lampis S, Zapparoli G, et al. (2016) Diversity of bacterial endophytes in 3 and 15 year-old grapevines of Vitis vinifera cv. Corvina and their potential for plant growth promotion and phytopathogen control. Microbiol Res 183: 42–52.
    [177] Pretty J, Sutherland WJ, Ashby J, et al. (2010). The top 100 questions of importance to the future of global agriculture. Int J Agric Sust 8: 219–236. doi: 10.3763/ijas.2010.0534
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