Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in a turbulent bulk flow.

The impact of turbulent mixing on an ensemble of initially monodisperse water droplets is studied in a turbulent bulk that serves as a simplified setup for the interior of a turbulent ice-free cloud. A mixing model was implemented that summarizes the balance equations of water vapor mixing ratio and temperature to an effective advection-diffusion equation for the supersaturation field s(x,t). Our three-dimensional direct numerical simulations connect the velocity and scalar supersaturation fields in the Eulerian frame of reference to an ensemble of cloud droplets in the Lagrangian frame of reference. The droplets are modeled as point particles with and without effects due to inertia. The droplet radius is subject to growth by vapor diffusion. We report the dependence of the droplet size distribution on the box size, initial droplet radius, and the strength of the updraft, with and without gravitational settling. In addition, the three finite-time Lyapunov exponents λ_{1}≥λ_{2}≥λ_{3} are monitored which probe the local stretching properties along the particle tracks. In this way, we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. For the present parameter range, the mixing process in terms of the droplet evaporation is always homogeneous, while it is inhomogeneous with respect to the relaxation of the supersaturation field. The probability density function of the third finite-time Lyapunov exponent, λ_{3}<0, is related to the one of the supersaturation s by a simple one-dimensional aggregation model. The probability density function (PDF) of λ_{3} and the droplet radius r are found to be Gaussian, while the PDF of the supersaturation field shows sub-Gaussian tails.

Erratum: Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection [Phys. Rev. Lett. 128, 164501 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.164501.

Characterizing and demonstrating the role of Klebsiella SSN1 exopolysaccharide in osmotic stress tolerance using neutron radiography.

Exopolysaccharides (EPS) are organic macromolecules naturally secreted by many microorganisms. EPS is increasingly used for agriculture and industrial purposes. This study focuses on isolate Klebsiella pneumonia SSN1, Klebsiella quasipeumonniae SGM81 isolated from rhizosphere to explore its water retention efficiency under drought conditions. Neutron Radiography was used to visualise water distribution in the sand under normal and drought conditions in the presence and absence of EPS producing bacteria. The EPS production was studied by applying Box Behnken design (BBD) under drought stress which was artificially induced by using polyethene glycol 6000 under osmotic stress condition 3.65% w/v of EPS dry weight was obtained. The relative water content (RWC) is used to calculate the amount of water present in the sand and was further studied by Neutron Radiography imaging with appropriate controls. FTIR and HPLC were also carried out for the characterisation of the extracted EPS. The sand experiments revealed that after 24 h of evaporation, the highest RWC was maintained by SSN1 at 29.7% compared to SGM81 (19.06%). SSN1 was found to release L-arabinose as the main sugar of its EPS under drought stress conditions by HPLC method. The FTIR data indicated the presence of ß-glucans and polysaccharide α-pyranose between wavenumber 700 cm-1-1500 cm-1 and 1017 cm-1-1200 cm-1 respectively. The HPLC characterization of extracted EPS from osmotic stressed cells (run 3) displayed a peak designated to L-arabinose at 10.3 retention time (RT) for 132.4 mM concentration. While from run 5 with the controlled condition indicated the presence of L-rhamnose at 7.3 RT for 87 mM concentration. Neutron radiography enables the visualisation of water distribution in the sand as well as water transport in root-soil systems in situ. SSN1 has elicited EPS production in drought conditions with a low level of nitrogen and carbon.

Generalizability of reservoir computing for flux-driven two-dimensional convection.

We explore the generalization properties of an echo state network applied as a reduced-order model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain with constant height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-Bénard case, thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input of the echo state network is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.

Molecular Origins of Transcriptional Heterogeneity in Diazotrophic Klebsiella oxytoca.

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of bacterial systems; however, the molecular origins of such heterogeneity and its magnitude are not well understood. Under conditions of extreme low-nitrogen stress in the model diazotroph Klebsiella oxytoca, we found remarkably high heterogeneity of nifHDK gene expression, which codes for the structural genes of nitrogenase, one key enzyme of the global nitrogen cycle. This heterogeneity limited the bulk observed nitrogen-fixing capacity of the population. Using dual-probe, single-cell RNA fluorescent in situ hybridization, we correlated nifHDK expression with that of nifLA and glnK-amtB, which code for the main upstream regulatory components. Through stochastic transcription models and mutual information analysis, we revealed likely molecular origins for heterogeneity in nitrogenase expression. In the wild type and regulatory variants, we found that nifHDK transcription was inherently bursty, but we established that noise propagation through signaling was also significant. The regulatory gene glnK had the highest discernible effect on nifHDK variance, while noise from factors outside the regulatory pathway were negligible. Understanding the basis of inherent heterogeneity of nitrogenase expression and its origins can inform biotechnology strategies seeking to enhance biological nitrogen fixation. Finally, we speculate on potential benefits of diazotrophic heterogeneity in natural soil environments. IMPORTANCE Nitrogen is an essential micronutrient for both plant and animal life and naturally exists in both reactive and inert chemical forms. Modern agriculture is heavily reliant on nitrogen that has been "fixed" into a reactive form via the energetically expensive Haber-Bosch process, with significant environmental consequences. Nitrogen-fixing bacteria provide an alternative source of fixed nitrogen for use in both biotechnological and agricultural settings, but this relies on a firm understanding of how the fixation process is regulated within individual bacterial cells. We examined the cell-to-cell variability in the nitrogen-fixing behavior of Klebsiella oxytoca, a free-living bacterium. The significance of our research is in identifying not only the presence of marked variability but also the specific mechanisms that give rise to it. This understanding gives insight into both the evolutionary advantages of variable behavior as well as strategies for biotechnological applications.

Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection.

The large-scale flow structure and the turbulent transfer of heat and momentum are directly measured in highly turbulent liquid metal convection experiments for Rayleigh numbers varied between 4×10^{5} and ≤5×10^{9} and Prandtl numbers of 0.025≤Pr≤0.033. Our measurements are performed in two cylindrical samples of aspect ratios Γ=diameter/height=0.5 and 1 filled with the eutectic alloy GaInSn. The reconstruction of the three-dimensional flow pattern by 17 ultrasound Doppler velocimetry sensors detecting the velocity profiles along their beam lines in different planes reveals a clear breakdown of coherence of the large-scale circulation for Γ=0.5. As a consequence, the scaling laws for heat and momentum transfer inherit a dependence on the aspect ratio. We show that this breakdown of coherence is accompanied with a reduction of the Reynolds number Re. The scaling exponent ß of the power law Nu∝Ra^{ß} crosses eventually over from ß=0.221 to 0.124 when the liquid metal flow at Γ=0.5 reaches Ra≳2×10^{8} and the coherent large-scale flow is completely collapsed.

Large-scale flow in a cubic Rayleigh-Bénard cell: long-term turbulence statistics and Markovianity of macrostate transitions.

We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for single flow trajectories up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows.

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allows individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows, which are typically based on sparse information from drifters and probes.

Resource Allocation During the Transition to Diazotrophy in Klebsiella oxytoca.

Free-living nitrogen-fixing bacteria can improve growth yields of some non-leguminous plants and, if enhanced through bioengineering approaches, have the potential to address major nutrient imbalances in global crop production by supplementing inorganic nitrogen fertilisers. However, nitrogen fixation is a highly resource-costly adaptation and is de-repressed only in environments in which sources of reduced nitrogen are scarce. Here we investigate nitrogen fixation (nif) gene expression and nitrogen starvation response signaling in the model diazotroph Klebsiella oxytoca (Ko) M5a1 during ammonium depletion and the transition to growth on atmospheric N2. Exploratory RNA-sequencing revealed that over 50% of genes were differentially expressed under diazotrophic conditions, among which the nif genes are among the most highly expressed and highly upregulated. Isotopically labelled QconCAT standards were designed for multiplexed, absolute quantification of Nif and nitrogen-stress proteins via multiple reaction monitoring mass spectrometry (MRM-MS). Time-resolved Nif protein concentrations were indicative of bifurcation in the accumulation rates of nitrogenase subunits (NifHDK) and accessory proteins. We estimate that the nitrogenase may account for more than 40% of cell protein during diazotrophic growth and occupy approximately half the active ribosome complement. The concentrations of free amino acids in nitrogen-starved cells were insufficient to support the observed rates of Nif protein expression. Total Nif protein accumulation was reduced 10-fold when the NifK protein was truncated and nitrogenase catalysis lost (nifK 1 - 1 203), implying that reinvestment of de novo fixed nitrogen is essential for further nif expression and a complete diazotrophy transition. Several amino acids accumulated in non-fixing ΔnifLA and nifK 1 - 1203 mutants, while the rest remained highly stable despite prolonged N starvation. Monitoring post-translational uridylylation of the PII-type signaling proteins GlnB and GlnK revealed distinct nitrogen regulatory roles in Ko M5a1. GlnK uridylylation was persistent throughout the diazotrophy transition while a ΔglnK mutant exhibited significantly reduced Nif expression and nitrogen fixation activity. Altogether, these findings highlight quantitatively the scale of resource allocation required to enable the nitrogen fixation adaptation to take place once underlying signaling processes are fulfilled. Our work also provides an omics-level framework with which to model nitrogen fixation in free-living diazotrophs and inform rational engineering strategies.

Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection.

Recurrent neural networks are machine learning algorithms that are well suited to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-Bénard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations to obtain training and test data for the algorithm. Both sets are preprocessed by a proper orthogonal decomposition (POD) using the snapshot method to reduce the amount of data. Training data comprise long time series of the first 150 most energetic POD coefficients. The reservoir is subsequently fed by these data and predicts future flow states. The predictions are thoroughly validated by original simulations. Our results show good agreement of the low-order statistics. This incorporates also derived statistical moments such as the cloud cover close to the top of the convection layer and the flux of liquid water across the domain. We conclude that our model is capable of learning complex dynamics which is introduced here by the tight interaction of turbulence with the nonlinear thermodynamics of phase changes between vapor and liquid water. Our work opens new ways for the dynamic parametrization of subgrid-scale transport in larger-scale circulation models.

Genomic appraisal of Klebsiella PGPB isolated from soil to enhance the growth of barley.

BACKGROUND: PGPR has substituted chemical fertilizers to enhance the nutrient profile of the soil. Although gene encoding for PGP activity is present in PGPB their activity changes in response to conditions. OBJECTIVE: To study comparative genomics for three Klebsiella strains and their PGPR activity in response to in vitro and soil condition. METHODS: We evaluated the activity of three Klebsiella spp. in two different conditions, specific nitrogen-deficient MS media and greenhouse experiment. Applying comparative genomics, genes encoding for PGP traits were identified from the whole-genome sequencing of the three strains. With the help of the RAST tool kit and functional annotation, a total number of genes encoding for cell wall capsule, nitrogen metabolism, sulfur genes and many other functional groups were identified. With the help of blast circular genome, similarity between GC content, pseudogene and tRNA was represented. The percentage of gene similarity of SSN1 was generated against BLAST with M5a1 and SGM81. Other methods like synteny alignment and orthologous gene clusters were applied to understand the homologous present in three strains. RESULTS: SSN1 was actively producing the maximum amount of ammonia 10.97 ± 0.29 µmol/mL compared to the other two strains. K. oxytoca M5a1 was considered negative for all PGP traits except ammonia production. The activity of SSN1 was showing a consistent pattern both the conditions whereas M5a1 was only active in vitro condition. Gene encoding for allantoin metabolism allD, allC, allB, allA, allE, allR, allH were identified in SSN1 and M5a1 but was absent in SGM81. The highest COG was shared between SGM81 and SSN1 predicting a maximum number of similar genes. The nif gene cluster was 98 % identical to the M5a1 strain. CONCLUSIONS: Comparatively, SSN1 expressed the additional gene for various PGP traits which suggest higher efficiency of strain in nitrogen deficiency stress.

Bacterial Indole-3-Acetic Acid Influences Soil Nitrogen Acquisition in Barley and Chickpea.

Farming of barley and chickpea is nitrogen (N) fertilizer dependent. Using strategies that increase the nitrogen use efficiency (NUE) and its components, nitrogen uptake efficiency (NUpE) and nitrogen utilization efficiency (NUtE) would reduce the N fertilizer application in the soil and its adverse environmental effects. We evaluated the effects of three different strains of diazotroph Klebsiella (K.p. SSN1, K.q. SGM81, and K.o. M5a1) to understand the role of biological nitrogen fixation (BNF) and bacterial indole-3-acetic acid (IAA) on NUE of the plants. A field study revealed that K.p. SSN1 results in profound increment of root surface area by eightfold and threefold compared to uninoculated (control) in barley and chickpea, respectively. We measured significant increase in the plant tissue nitrogen, chlorophyll content, protein content, nitrate reductase activity, and nitrate concentration in the inoculated plants (p ≤ 0.05). Treated barley and chickpea exhibited higher NUE and the components compared to the control plants (K.p. SSN1 ≥ K.q. SGM81> K.o. M5a1). Specifically, K.q. SGM81 treatment in barley increased NUpE by 72%, while in chickpea, K.p. SSN1 increased it by 187%. The substantial improvement in the NUpE and NUE by the auxin producers K.p. SSN1 and K.q. SGM81 compared with non-auxin producer K.o. M5a1 was accompanied by an augmented root architecture suggesting larger contribution of IAA over marginal contribution of BNF in nitrogen acquisition from the soil.

Systemic reprogramming of phytohormone profiles and metabolic traits by virulent Diplodia infection in its pine (Pinus sylvestris L.) host.

The widespread ascomycetous fungus Diplodia pinea is a latent, necrotrophic pathogen in Pinus species causing severe damages and world-wide economic losses. However, the interactions between pine hosts and virulent D. pinea are largely not understood. In the present study, systemic defence responses were investigated in non-inoculated, asymptomatic needles and roots of D. pinea infected saplings of two P. sylvestris provenances under controlled greenhouse conditions. Here, we show that D. pinea infection induced a multitude of systemic responses of the phytohormone profiles and metabolic traits. Shared systemic responses of both pine provenances in needles and roots included increased abscisic acid and jasmonic acid levels. Exclusively in the roots of both provenances, enhanced salicylic acid and reduced indole-3-acetic acid levels, structural biomass, and elevated activities of anti-oxidative enzymes were observed. Despite these similarities, the two pine provenances investigated different significantly in the systemic responses of both, phytohormone profiles and metabolic traits in needles and roots. However, the different systemic responses did not prevent subsequent destruction of non-inoculated needles, but rather prevented damage to the roots. Our results provide a detailed view on systemic defence mechanisms of pine hosts that are of particular significance for the selection of provenances with improved defence capacity.

Classical 1/3 scaling of convection holds up to Ra = 1015.

The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh number [Formula: see text]-the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for [Formula: see text] have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh-Bénard convection flows in a slender cylindrical cell of aspect ratio [Formula: see text], that the Nusselt number-the dimensionless measure of heat transport-follows the classical power law of [Formula: see text] up to [Formula: see text] Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all [Formula: see text] considered here, increasing with increasing [Formula: see text], and suggest that an abrupt transition of the boundary layer to turbulence does not take place.

Lagrangian coherent sets in turbulent Rayleigh-Bénard convection.

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number Ra=10^{6} and at a Prandtl number Pr=10. Three different Lagrangian analysis techniques based on graph Laplacians (distance spectral trajectory clustering, time-averaged diffusion maps, and finite-element based dynamic Laplacian discretization) are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set framework is extended to study heat transport.

A low-potential terminal oxidase associated with the iron-only nitrogenase from the nitrogen-fixing bacterium Azotobacter vinelandii.

The biological route for nitrogen gas entering the biosphere is reduction to ammonia by the nitrogenase enzyme, which is inactivated by oxygen. Three types of nitrogenase exist, the least-studied of which is the iron-only nitrogenase. The Anf3 protein in the bacterium Rhodobacter capsulatus is essential for diazotrophic (i.e. nitrogen-fixing) growth with the iron-only nitrogenase, but its enzymatic activity and function are unknown. Here, we biochemically and structurally characterize Anf3 from the model diazotrophic bacterium Azotobacter vinelandii Determining the Anf3 crystal structure to atomic resolution, we observed that it is a dimeric flavocytochrome with an unusually close interaction between the heme and the FAD cofactors. Measuring the reduction potentials by spectroelectrochemical redox titration, we observed values of -420 ± 10 and -330 ± 10 mV for the two FAD potentials and -340 ± 1 mV for the heme. We further show that Anf3 accepts electrons from spinach ferredoxin and that Anf3 consumes oxygen without generating superoxide or hydrogen peroxide. We predict that Anf3 protects the iron-only nitrogenase from oxygen inactivation by functioning as an oxidase in respiratory protection, with flavodoxin or ferredoxin as the physiological electron donors.

Deep learning in turbulent convection networks.

We explore heat transport properties of turbulent Rayleigh-Bénard convection in horizontally extended systems by using deep-learning algorithms that greatly reduce the number of degrees of freedom. Particular attention is paid to the slowly evolving turbulent superstructures-so called because they are larger in extent than the height of the convection layer-which appear as temporal patterns of ridges of hot upwelling and cold downwelling fluid, including defects where the ridges merge or end. The machine-learning algorithm trains a deep convolutional neural network (CNN) with U-shaped architecture, consisting of a contraction and a subsequent expansion branch, to reduce the complex 3D turbulent superstructure to a temporal planar network in the midplane of the layer. This results in a data compression by more than five orders of magnitude at the highest Rayleigh number, and its application yields a discrete transport network with dynamically varying defect points, including points of locally enhanced heat flux or "hot spots." One conclusion is that the fraction of heat transport by the superstructure decreases as the Rayleigh number increases (although they might remain individually strong), correspondingly implying the increased importance of small-scale background turbulence.

Analysis of Indole-3-acetic Acid (IAA) Production in Klebsiellaby LC-MS/MS and the Salkowski Method.

Many rhizobacteria isolated from plant rhizosphere produce various phytohormones in the form of secondary metabolites, the most common of which is Indole-3-acetic acid (IAA). Here, we detail analytical protocols of IAA detection and quantification, in vitro and in situ, as recently applied to Klebsiella SGM 81, a rhizobacterium isolated from the rhizosphere of Dianthus caryophyllus (a commercially important flower across the globe). Specifically, we describe a detailed protocol for a colorimetric assay using the Salkowski reagent method, which can be used to screen for the presence of Indole compounds. To further detect and quantify IAA, a highly accurate analytical approach of LC-MS/MS is used. To detect the presence of IAA around the root system of Dianthus caryophyllus, in situ staining of plant roots is done using Salkowski reagent.

Turbulent superstructures in Rayleigh-Bénard convection.

Turbulent Rayleigh-Bénard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 107. We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.