Quantum algorithms for geologic fracture networks

Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10-1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

Inference-Based Quantum Sensing

In a standard quantum sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response R(θ) (i.e., changes in the measurement outcomes). For simple cases the form of R(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this Letter, we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, R(θ) can be fully characterized by only measuring the system response at 2n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Ω(log^{3}(n)/δ^{2}). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

Challenges and opportunities in quantum machine learning

At the intersection of machine learning and quantum computing, quantum machine learning has the potential of accelerating data analysis, especially for quantum data, with applications for quantum materials, biochemistry and high-energy physics. Nevertheless, challenges remain regarding the trainability of quantum machine learning models. Here we review current methods and applications for quantum machine learning. We highlight differences between quantum and classical machine learning, with a focus on quantum neural networks and quantum deep learning. Finally, we discuss opportunities for quantum advantage with quantum machine learning.

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as [Formula: see text]. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to [Formula: see text]. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

Tomato Systemin induces resistance against Plectosphaerella cucumerina in Arabidopsis through the induction of phenolic compounds and priming of tryptophan derivatives

Phytocytokines are endogenous danger peptides that are actively released after a pest or pathogen attack, triggering an amplification of plant immune responses. Here, we found that Systemin, a peptide from tomato, has a substantial impact at the molecular level in Arabidopsis plants that leads to induced resistance against Plectosphaerella cucumerina. Using transcriptional and metabolomics approaches, and loss-of-function mutants to analyse the molecular mechanisms underlying induced resistance against the necrotroph, we decipher the enhanced molecular responses in Systemin-treated plants following infection. Some protein complexes involved in the response to other damage signals, including the BAK1-BIK1 protein complex and heterotrimeric G proteins, as well as MPK activation, were among the early signalling events triggered by Systemin in Arabidopsis upon infection. Non-targeted analysis of the late responses underlying Systemin-Induced Resistance¹ (Sys-IR) showed that phenolic and indolic compounds were the most representative groups in the Systemin metabolic fingerprint. Lack of flavonoids resulted in the impairment of Sys-IR. On the other hand, some indolic compounds showed a priming profile and were also essential for functional Sys-IR. Evidence presented here shows that plants can sense heterologous peptides from other species as danger signals driving the participation of common protein cascades activated in the PTI and promoting enhanced resistance against necrotrophic fungus.

Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we call dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed. Our work represents the first rigorous analysis of the scalability of a perceptron-based QNN.

Reformulation of the No-Free-Lunch Theorem for Entangled Datasets

The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training dataset. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this Letter, we show that entangled datasets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our Letter establishes that entanglement is a commodity in quantum machine learning.

Noise-induced barren plateaus in variational quantum algorithms

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Computable and Operationally Meaningful Multipartite Entanglement Measures

Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state |ψ⟩ for these applications is often directly related to the degree or type of entanglement present in |ψ⟩. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called concentratable entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under local operations and classical communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is [Formula: see text]. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

Mycorrhizal tomato plants fine tunes the growth-defence balance upon N depleted root environments

In low nutritive environments, the uptake of N by arbuscular mycorrhizal (AM) fungi may confer competitive advantages for the host. The present study aims to understand how mycorrhizal tomato plants perceive and then prepare for an N depletion in the root environment. Plants colonized by Rhizophagus irregularis displayed improved responses to a lack of N than nonmycorrhizal (NM) plants. These responses were accomplished by a complex metabolic and transcriptional rearrangement that mostly affected the gibberellic acid and jasmonic acid pathways involving DELLA and JAZ1 genes, which were responsive to changes in the C/N imbalance of the plant. N starved mycorrhizal plants showed lower C/N equilibrium in the shoots than starved NM plants and concomitantly a downregulation of the JAZ1 repressor and the increased expression of the DELLA gene, which translated into a more active oxylipin pathway in mycorrhizal plants. In addition, the results support a priorization in AM plants of stress responses over growth. Therefore, these plants were better prepared for an expected stress. Furthermore, most metabolites that were severely reduced in NM plants following the N depletion remained unaltered in starved AM plants compared with those normally fertilized, suggesting that the symbiosis buffered the stress, improving plant development in a stressed environment.

Factorization and Criticality in Finite XXZ Systems of Arbitrary Spin

We analyze ground state (GS) factorization in general arrays of spins s_{i} with XXZ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GSs can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero-bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for d-dimensional arrays. The definite magnetization-projected GSs at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization-compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.

Identification of indole-3-carboxylic acid as mediator of priming against Plectosphaerella cucumerina

Plant resistance against the necrotrophic pathogen Plectosphaerella cucumerina is mediated by a combination of several hormonal-controlled signalling pathways. The priming agent β-aminobutyric acid (BABA) is able to induce effective resistance against this pathogen by stimulating callose-rich cell wall depositions. In the present research it is demonstrated that BABA-Induced Resistance (BABA-IR) against P. cucumerina in Arabidopsis has additional components such as the induction of defences mediated by indolic derivatives. Chromatographic approach for the detection and characterization of metabolites enhanced by BABA compared with water-treated plants only when the challenge is present has been developed. The metabolites matching this criteria are considered to be primed by BABA. The analytic procedure is based on the combination of liquid chromatography (LC) with a triple quadrupole (TQD) detector in a precursor ion scanning mode. Using this analytical system a signal in negative electro-spray mode of 160 m/z is primed by BABA in infected plants. A subsequent exact mass analysis in a quadrupole time-of-flight mass spectrometer demonstrated that this ion was the indole-derivative metabolite indole-3-carboxylic acid (I3CA). The identity of indole-3-carboxilic acid was definitively confirmed by comparing its retention time and fragmentation spectra with a commercial standard. Quantification of I3CA in primed plants showed that this indolic metabolite is specifically primed by BABA upon P. cucumerina infection, while other indolic compounds such as IAA and camalexin are not. Taking together these observations with the known role of callose in priming against this pathogen, suggests that priming is not a single mechanism but rather a multicomponent defence.

Testing the performance of mtSNP minisequencing in forensic samples

There is a growing interest among forensic geneticists in developing efficient protocols for genotyping coding region mitochondrial DNA (mtDNA) SNPs (mtSNPs). Minisequencing is becoming a popular method for SNP genotyping, but it is still used by few forensic laboratories. In part, this is due to the lack of studies testing its efficiency and reproducibility when applied to real and complex forensic samples. Here we tested a minisequencing design that consists of 71 mtSNPs (in three multiplexes) that are diagnostic of known branches of the R0 phylogeny, in real forensic samples, including degraded bones and teeth, hair shafts, and serial dilutions. The fact that amplicons are short coupled with the natural efficiency of the minisequencing technique allow these assays to perform well with all the samples tested either degraded and/or those containing low DNA amount. We did not observe phylogenetic inconsistencies in the 71 mtSNP haplotypes generated, indicating that the technique is robust against potential artefacts that could arise from unintended contamination and/or spurious amplification of nuclear mtDNA pseudogenes (NUMTs).

The mtDNA ancestry of admixed Colombian populations

A total of 185 individuals from Colombia were sequenced for the first hypervariable region (HVS-I) of the mitochondrial DNA (mtDNA) genome, and a subset of these individuals were additionally genotyped for the second hypervariable segment (HVS-II). These individuals were collected according to their "self-reported ethnicity" in Colombia, comprising "Mestizos," "Mulatos," and "Afro-Colombians." We used databases containing more than 4,300 Native American lineages, 6,800 Africans, and 15,600 Europeans for population comparisons and phylogeographic inferences. We observe that Mulatos and Afro-Colombians have a dominant African mtDNA component, whereas Mestizos carry predominantly Native American haplotypes. All the populations analyzed have high diversity indices and there are no signatures of dramatic genetic drift episodes. Central and South America are the main candidate source populations of the Colombian Native American lineages, whereas west-central, southwest, and southeast Africa are the main original mtDNA sources for the African Colombian mtDNAs. We found that our results differ from those obtained in other studies for the same "population groups" in terms of haplogroup frequencies. This observation leads us to conclude that (i) self-reported ancestry is not a reliable proxy to indicate an individual's "ethnicity" in Colombia, (ii) our results do not support the use of outmoded race descriptions (Mestizos, Mulatos, etc.) mainly because these labels do not correspond to any genetically homogeneous population group, and (iii) studies relying on these terms to describe the population group of the individual, which then treat them as genetically homogeneous, carry a high risk of type I error (false positives) in medical studies in this country and of misinterpretation of the frequency of observed variation in forensic casework.

Case report: identification of skeletal remains using short-amplicon marker analysis of severely degraded DNA extracted from a decomposed and charred femur

Applying two extraction protocols to isolate DNA from a charred femur recovered after a major forest fire, a range of established and recently developed forensic marker sets that included mini-STRs and SNPs were used to type the sample and confirm identity by comparison to a claimed daughter of the deceased. Identification of the remains suggested that the individual had been dead for 10 years and the DNA was therefore likely to be severely degraded from the combined effects of decomposition and exposure to very high temperatures. We used new marker sets specifically developed to analyze degraded DNA comprising both reduced-length amplicon STR sets and autosomal SNP multiplexes, giving an opportunity to assess the ability of each approach to successfully type highly degraded material from a challenging case. The results also suggest a modified ancient DNA extraction procedure offers improved typing success from degraded skeletal material.

2006 GEP-ISFG collaborative exercise on mtDNA: reflections about interpretation, artefacts, and DNA mixtures

We report the results of the seventh edition of the GEP-ISFG mitochondrial DNA (mtDNA) collaborative exercise. The samples submitted to the participant laboratories were blood stains from a maternity case and simulated forensic samples, including a case of mixture. The success rate for the blood stains was moderate ( approximately 77%); even though four inexperienced laboratories concentrated about one-third of the total errors. A similar success was obtained for the analysis of mixed samples (78.8% for a hair-saliva mixture and 69.2% for a saliva-saliva mixture). Two laboratories also dissected the haplotypes contributing to the saliva-saliva mixture. Most of the errors were due to reading problems and misinterpretation of electropherograms, demonstrating once more that the lack of a solid devised experimental approach is the main cause of error in mtDNA testing.

Characterization and regulation of ammonium transport systems in Citrus plants

We have investigated both the kinetics and regulation of 15NH4+ influx in roots of 3-month-old hydroponically grown Citrus (Citrus sinensis L. Osbeck x Poncirus trifoliata Blanco) seedlings. The 15NH4+ influx is saturable below an external ammonium concentration of 1 mM, indicating the action of a high-affinity transport system (HATS). The HATS is under feedback repression by the N status of the plant, being down-regulated in plants adequately supplied with N during growth, and up-regulated by N-starvation. When assayed between 1 and 50 mM [15NH4+]0, the 15NH4+ influx showed a linear response typical of a low-affinity transport system (LATS). The activity of the LATS increased in plants supplied with NH4+ as compared with plants grown on an N-free medium. Transfer of the plants to N-free solution resulted in a marked decrease in the LATS-mediated 15NH4+ influx. Accordingly, resupply of NH4+ after N-starvation triggered a dramatic stimulation of the activity of the LATS. These data provide evidence that in Citrus plants, the LATS or at least one of its components is inducible by NH4+. Even when up-regulated, both the HATS and the LATS displayed a limited capacity, as compared with that usually found in herbaceous species. The use of various metabolic uncouplers or inhibitors indicated that 15NH4+ influx mediated by the HATS is strongly dependent on energy metabolism and H+ transmembrane electrochemical gradient. By contrast, the LATS is not affected by protonophores or inhibitors of the H(+)-ATPase, suggesting that its activity is mostly driven by the NH4+/NH3 transmembrane gradient. In agreement with these hypotheses, the HATS-mediated 15NH4+ influx was strongly inhibited when the solution pH was raised from 4 to 7, whereas influx mediated by the LATS was slightly stimulated.

Characterization of the signal transduction pathways mediating morphine withdrawal-stimulated c-fos expression in hypothalamic nuclei

The transcription factor, Fos, is considered as a functional marker of activated neurons. We have shown previously that acute administration of morphine induces the expression of Fos in hypothalamic nuclei associated with control of the hypothalamus-pituitary-adrenocortex axis, such as the paraventricular nucleus and the supraoptic nucleus. In the current study, we examined the role of protein kinase A, protein kinase C and Ca2+ entry through L-type Ca2+ channels in naloxone-precipitated Fos expression in the paraventricular and supraoptic nuclei. After 7 days of morphine treatment, we did not observe any modification in Fos production. However, when opioid withdrawal was precipitated with naloxone a dramatic increase in Fos immunoreactivity was observed in the parvocellular division of the paraventricular nucleus and in the supraoptic nucleus. Chronic co-administration of chelerythrine (a selective protein kinase C inhibitor acting at its catalytic domain) with morphine did not affect the increase in Fos expression observed in nuclei from morphine withdrawn rats. In addition, infusion of calphostin C (another protein kinase C inhibitor, which interacts with its regulatory domain) did not modify the morphine withdrawal-induced expression of Fos. In contrast, when the selective protein kinase A inhibitor, N-(2'guanidinoethyl)-5-isoquinolinesulfonamide (HA-1004), was infused it greatly diminished the increased Fos production observed in morphine-withdrawn rats. Furthermore, chronic infusion of the selective L-type Ca2+ channel antagonist, nimodipine, significantly inhibited the enhancement of Fos induction in the paraventricular and supraoptic nuclei from morphine-withdrawn animals. Taken together, these data might indicate that protein kinase A activity is necessary for the expression of Fos during morphine withdrawal and that an up-regulated Ca2+ system might contribute to the activation of Fos. The present findings suggest that protein kinase A and Ca2+ influx through L-type Ca2+ channels might contribute to the activation of neuroendocrine cells in the paraventricular and supraoptic nuclei.

Major alterations of the regulation of root NO(3)(-) uptake are associated with the mutation of Nrt2.1 and Nrt2.2 genes in Arabidopsis

The role of AtNrt2.1 and AtNrt2.2 genes, encoding putative NO(3)(-) transporters in Arabidopsis, in the regulation of high-affinity NO(3)(-) uptake has been investigated in the atnrt2 mutant, where these two genes are deleted. Our initial analysis of the atnrt2 mutant (S. Filleur, M.F. Dorbe, M. Cerezo, M. Orsel, F. Granier, A. Gojon, F. Daniel-Vedele [2001] FEBS Lett 489: 220-224) demonstrated that root NO(3)(-) uptake is affected in this mutant due to the alteration of the high-affinity transport system (HATS), but not of the low-affinity transport system. In the present work, we show that the residual HATS activity in atnrt2 plants is not inducible by NO(3)(-), indicating that the mutant is more specifically impaired in the inducible component of the HATS. Thus, high-affinity NO(3)(-) uptake in this genotype is likely to be due to the constitutive HATS. Root (15)NO(3)(-) influx in the atnrt2 mutant is no more derepressed by nitrogen starvation or decrease in the external NO(3)(-) availability. Moreover, the mutant also lacks the usual compensatory up-regulation of NO(3)(-) uptake in NO(3)(-)-fed roots, in response to nitrogen deprivation of another portion of the root system. Finally, exogenous supply of NH(4)(+) in the nutrient solution fails to inhibit (15)NO(3)(-) influx in the mutant, whereas it strongly decreases that in the wild type. This is not explained by a reduced activity of NH(4)(+) uptake systems in the mutant. These results collectively indicate that AtNrt2.1 and/or AtNrt2.2 genes play a key role in the regulation of the high-affinity NO(3)(-) uptake, and in the adaptative responses of the plant to both spatial and temporal changes in nitrogen availability in the environment.

Effect of a novel chemical mixture on senescence processes and plant--fungus interaction in Solanaceae plants

The effects of exogenous application of a chemical mixture consisting of adipic acid monoethyl ester, furfurylamine, and 1,2,3,4-tetra-O-acetyl-beta-D-glucopyranose (FGA) on various metabolic pathways and the plant-fungus interaction have been studied in Solanaceae plants. Tomato and pepper plants were sprayed with the FGA mixture, and different biochemical parameters such as gas exchange, chlorophyll concentration, protein, cell wall sugar and phenolics contents, and peroxidase and phenylalanine ammonia lyase (PAL) activities were measured. FGA-treated plants showed, in general, an increase in cell wall sugar content and decreases in the chlorophyll degrading rate and the peroxidase activity. These results suggest that FGA (a possible synthetic regulator) could act as a retardant--antisenescence agent in Solanaceae plants. The FGA mixture increased the PAL activity and promoted an overall rise in the concentration of flavonoids and phenolic compounds. Therefore, FGA induced the synthesis of compounds that could give protection to plants against pathogens or insects. To further verify this putative protection, several fungi were inoculated in intact plants. Exogenous FGA applications on intact plants delayed fungus-provoked lesion development. In addition, data also showed that applications of 1,2,3,4-tetra-O-acetyl-beta-D-glucopyranose inhibited fungal growth in vitro. These results confirm that FGA can activate protective mechanisms in plants upon contact with invaders such as fungi.

An arabidopsis T-DNA mutant affected in Nrt2 genes is impaired in nitrate uptake

Expression analyses of Nrt2 plant genes have shown a strict correlation with root nitrate influx mediated by the high-affinity transport system (HATS). The precise assignment of NRT2 protein function has not yet been possible due to the absence of heterologous expression studies as well as loss of function mutants in higher plants. Using a reverse genetic approach, we isolated an Arabidopsis thaliana knock-out mutant where the T-DNA insertion led to the complete deletion of the AtNrt2.1 gene together with the deletion of the 3' region of the AtNrt2.2 gene. This mutant is impaired in the HATS, without being modified in the low-affinity system. Moreover, the de-regulated expression of a Nicotiana plumbaginifolia Nrt2 gene restored the mutant nitrate influx to that of the wild-type. These results demonstrate that plant NRT2 proteins do have a role in HATS.

Characterization of the low affinity transport system for NO(3)(-) uptake by Citrus roots

Three-month old citrange Troyer (hybrid of Citrus sinensis x Poncirus trifoliata) seedlings were grown hydroponically and, after a period of NO(3)(-) starvation, plants were transferred to solutions enriched with K(15)NO(3) (96% atoms 15N excess) to measure 15NO(3)(-) uptake rates as a function of external 15NO(3)(-) concentrations. Two different NO(3)(-) uptake systems were found. Between 1 and 50 mM 15NO(3)(-) in the uptake solution medium, the uptake rate increased linearly due to the low affinity transport system (LATS). Nitrate reductase activity showed the same response to external [NO(3)(-)], and also appears to be regulated by the rate of nitrate uptake. Nitrate pre-treatments had a represive effect on NO(3)(-) uptake rate measured at 5 or 30 mM external [15NO(3)(-)]. The extent of the inhibition depended on the [NO(3)(-)] during the pre-treatment and in the uptake solution. These results suggest that the LATS of Citrus seedlings is under feedback control by the N status of the plant. Accordingly, addition of amino acids (Glu, Asp, Asn, Gln) to the uptake solution resulted in a decrease in 15NO(3)(-) uptake rate. However, the inactivation of nitrate reductase activity after treatment of the seedlings with either 100 or 500 µM WO(4)(2-) did not affect the activity of the LATS. Metabolic uncouplers, 2,4-DNP and KCN, reduced the uptake rate by 43.3% and 41.4% respectively at 5mM external [15NO(3)(-)]. However, these compounds had little effect when 15NO(3)(-) uptake was assayed at 30 mM external concentration. The ATPase inhibitors DCCD and DES reduced 15NO(3)(-) uptake by 68.8%-35.6%, at both external [15NO(3)(-)]. Nitrate uptake by the LATS declined with the increase of the solution pH beyond pH 4. The data presented are discussed in the context of the kinetics, energy dependence and regulation of NO(3)(-) uptake.