Research article

Analysis of an HTLV/HIV dual infection model with diffusion

  • In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD4+T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.

    Citation: A. M. Elaiw, N. H. AlShamrani. Analysis of an HTLV/HIV dual infection model with diffusion[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 9430-9473. doi: 10.3934/mbe.2021464

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  • In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD4+T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.



    Abbreviations: AMF: Arbuscular mycorrhizal fungi; BSR: basal soil respiration; EO: essential oil; GC/MS: gas chromatography/mass spectrometry; MBC: microbial biomass carbon; N: nitrogen; P: phosphorus; PCA: principal component analysis; qCO2: metabolic quotient; RDW: root dry weight; SFW: shoot fresh weight; SDW: shoot dry weight; TDW: total dry weight

    Medicinal, aromatic, and spice plants have fundamental value for humanity, having been widely used in traditional medicine for the treatment of diseases [1,2]. These plants are rich in essential oils (EOs) with great economic and industrial potential [3].

    Melissa officinalis L. is an aromatic medicinal plant belonging to the family Lamiaceae. Native to Europe, the plant is commonly known as lemon balm, in allusion to its lemon-like odor stemming from the presence of volatile oils [4]. The aerial parts of lemon balm are consumed as herbal tea, prepared by infusion. This method prevents the decomposition of active compounds, particularly EO components [3].

    Lemon balm has been used for the treatment of a multitude of diseases, with some reports dating back to more than 2,000 years [5]. In traditional medicine, the species is used to treat mental disorders such as anxiety and depression, as well as for memory improvement and prevention of heart disease. Such effects are attributed to the presence of flavonoids, alkaloids, polyphenols, and other products of secondary metabolism [3,6]. Lemon balm EO has high commercial value, as it finds application in the pharmaceutical, cosmetic, and food industries [7].

    Studies indicated that lemon balm EO may be a promising antimicrobial agent [3,8]. In a clinical study [9], the EO was effective in preventing insulin resistance and obesity. Several pharmacological properties have been reported for lemon balm EO, including anxiolytic, antidepressant, neuroprotective, cardiovascular protective, cytotoxic, anti-inflammatory, and antioxidant, among others [3,5].

    Given its several applications and widespread use, lemon balm should ideally be produced in sustainable systems. An interesting strategy is to apply arbuscular mycorrhizal fungi (AMF), organisms that form mutualistic symbiotic associations with the roots of most plant species. Such relationships favor plant growth and development by attenuating biotic and abiotic stresses, increasing the absorption of water and nutrients such as phosphorus (P) by plant roots, and enhancing secondary metabolism, ultimately improving EO production [10,11,12,13,14,15,16].

    Assis et al. [17] investigated the inoculation of AMF together with organic fertilization in the cultivation of M. officinalis and identified that the chemical characteristics of the soil, such as P content, interfere with the colonization of roots by AMF. In addition, the combination of these practices increased the production of biomass and the active ingredient of the plants. Merlin et al. [18] also observed that inoculation with R. clarus and high phosphorus content in the cultivation of Plectranthus amboinicus (coarse mint) increased the dry matter content, however the extracted essential oil content was higher with R. clarus and low phosphorus.

    The EO content of lemon balm ranges from 0.05% to 0.52%, which is low compared to that of other members of the family Lamiaceae [19]. In light of the growing industrial and consumer demands for EOs, AMF inoculation has been proposed as a means of enhancing biomass production, increasing EO yield, and improving the chemical composition of medicinal and aromatic plants [13,17]. In addition to being an environmentally friendly practice, AMF treatment stimulates plant growth without compromising the quality of the plant or its EO [12,17,18,19,20].

    Considering that AMF inoculation may improve plant growth, EO production, and EO quality, this study aimed to investigate the EO yield and chemical composition, as well as vegetative growth parameters, of lemon balm inoculated with Rhizophagus clarus or Claroideoglomus etunicatum under different P rates.

    The experiment was carried out at the Medicinal Garden (23°46′09.1″S, 53°16′38.4″W) of Paranaense University (UNIPAR), located in Umuarama, Paraná, Brazil. A mixture containing 50% substrate and 50% sand + vermiculite (1:1) was fumigated with 10 mL chloroform (CHCl3) kg−1, according to a method adapted Endlweber and Scheu [21]. The experimental design was completely randomized with 8 replications per treatment arranged in a 3 × 2 factorial (inoculation or not of R. clarus or C. etunicatum at high or low soil P levels), totaling 48 experimental units. Cuttings of lemon balm measuring about 5 cm in length were planted in 3.5 dm−3 pots and grown for 4 months.

    Inoculated treatments received approximately 200 spores of R. clarus or C. etunicatum, which were obtained from the Bank of Glomales of UNIPAR. For the pots assigned to the high P rate treatment, 0.88 g of monopotassium phosphate (KH2PO4) was added per kilogram of substrate, equivalent to 200 mg of P kg−1 of substrate, however the solution also contains about 253 mg of potassium (K) kg−1 of substrate Therefore, in the pots assigned to a low P rate were treated with 0.38 g of potassium chloride (KCl), corresponding to 199 mg of K kg−1 substrate. Thus, all treatments had approximately the same soil K content (at low and high P rate), differing only in P levels, according to the method described by Urcoviche et al. [22]. Plants were irrigated every two days (or as needed) with a modified P-free Hoagland and Arnon [23] nutrient solution.

    Chlorophyll index were measured at the center of three leaves per plant using a chlorophyll meter (CFL 1030, ClorofiLOG®). When they complete their vegetative cycle, after 4 months of planting samples were dried in a forced-air oven at 65 ℃ for 24 h. Then, shoot dry weight, root dry weight, and total dry weight were quantified by weighing the samples on a semi-analytical scale.

    Dried plant shoots were ground and subjected to determination of P and N [24,25]. The P was estimated by colorimetry with ammonium molybdate + ascorbic acid in a spectrophotometer, using a red filter and a wavelength of 660 nm [24]. N content was determined by sulfuric acid digestion at 450 ℃, followed by the Kjeldahl method of distillation and titration with 0.05 mol·L−1 HCl [23,24].

    AMF spores were extracted from 10 g subsamples of substrate by wet sieving (0.710–0.053 mm mesh) [26], and transferred to Petri dishes for counting under a stereoscopic microscope (40 × magnification) [15]. For determination of colonization percentage, fine roots were collected, bleached, stained, and acidified with trypan blue, according to the method of Phillips and Hayman [27]. The number of colonized root segments was counted using slides overlaid with coverslips [28]. In total, about 100 segments were numbered and counted using a stereoscopic microscope (40–100 × magnification) [15].

    Soil microbial biomass carbon (MBC) was determined by the fumigation-extraction method proposed by Vance et al. [29] and modified by Tate et al. [30]. Extracted MBC was estimated according to Lermen et al. [25] and Ferrari et al. [15]. Basal soil respiration (BSR) was determined according to Jenkinson and Powlson [31], using 30 g of soil sample. According to Anderson and Domsch [32], metabolic quotient (qCO2) was estimated as the ratio of BSR to MBC.

    EO extraction, yield determination (%, g 100 g−1 fresh shoots), and chemical identification by gas chromatography/mass spectrometry (GC/MS) were performed according to Cruz et al. [33].

    Data were subjected to analysis of variance (ANOVA). Means were compared by Duncan's test (p ≤ 0.05) using SPSS for Windows version 22.0 (SPSS Inc. Chicago, IL, USA). Hierarchical clustering and principal component analysis (PCA) were performed using Statistica software version 13.0 Statsoft [34] to discriminate EO composition according to treatment.

    Shoot fresh and dry weights increased significantly with R. clarus and C. etunicatum inoculation and low P rate (Table 1). R. clarus inoculation and low P rate led to an increase in root dry weight and total dry weight. In the control treatment with low P, were observed a significant decrease in shoot fresh weight, shoot dry weight, root dry weight, and total dry weight (Table 1).

    Table 1.  Shoot fresh weight (SFW, g·plant−1), shoot dry weight (SDW, g·plant−1), root dry weight (RDW, g·plant−1), total dry weight (TDW, g·plant−1) of lemon balm inoculated with arbuscular mycorrhizal fungi (Rhizophagus clarus or Claroideoglomus etunicatum) under low and high phosphorus rates.
    Treatment SFW SDW SDW TDW
    T1 12.28 ± 0.92c 2.85 ± 0.21c 0.68 ± 0.05c 3.53 ± 0.23c
    T2 24.57 ± 1.62a 4.66 ± 0.40a 3.88 ± 0.67a 8.55 ± 0.71a
    T3 24.57 ± 1.62a 4.25 ± 0.31ab 2.15 ± 0.57b 6.41 ± 0.70b
    T4 18.59 ± 1.12b 3.41 ± 0.24bc 1.55 ± 0.15bc 4.97 ± 0.36bc
    T5 19.56 ± 0.63b 3.63 ± 0.21bc 1.43 ± 0.27bc 5.06 ± 0.40bc
    T6 15.99 ± 1.57bc 3.55 ± 0.34bc 2.39 ± 0.30b 5.94 ± 0.57b
    p-value < 0.001 0.002 < 0.001 < 0.001
    Notes: Mean values (n = 8 ± standard error). Means within columns followed by the same letter are not significantly different by Duncan's test (p ≤ 0.05). T1: uninoculated control under low P rate; T2: R. clarus under low P rate; T3: C. etunicatum under low P rate; T4: uninoculated control under high P rate; T5: R. clarus under high P rate; T6: C. etunicatum under high P rate.

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    Shoot N and chlorophyll index did not differ significantly among the treatments. R. clarus + low P and C. etunicatum + high P increased significant P content in shoot (Table 2).

    Table 2.  Chlorophyll index shoot nitrogen content (mg·g−1), and shoot phosphorus content (mg·g−1) of lemon balm inoculated with arbuscular mycorrhizal fungi (Rhizophagus clarus or Claroideoglomus etunicatum) under low and high phosphorus rates.
    Treatment Chlorophyll index Shoot N content Shoot P content
    T1 26.28 ± 0.77a 33.87 ± 1.86a 1.56 ± 0.03b
    T2 26.16 ± 0.69a 39.75 ± 3.27a 2.21 ± 0.03a
    T3 26.27 ± 0.87a 40.06 ± 2.59a 1.42 ± 0.10b
    T4 26.95 ± 0.68a 40.82 ± 2.35a 2.27 ± 0.08a
    T5 26.64 ± 0.75a 40.36 ± 2.66a 1.57 ± 0.03b
    T6 26.82 ± 0.74a 35.07 ± 1.41a 2.33 ± 0.07a
    p-value 0.966 0.196 < 0.001
    Notes: Mean values (n = 8 ± standard error). Means within columns followed by the same letter are not significantly different by Duncan's test (p ≤ 0.05). T1: uninoculated control under low P rate; T2: R. clarus under low P rate; T3: C. etunicatum under low P rate; T4: uninoculated control under high P rate; T5: R. clarus under high P rate; T6: C. etunicatum under high P rate.

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    Spore density and root colonization were significantly higher in treatments with AMF inoculation, particularly under low P rates (Table 3). MBC was higher with AMF inoculation, regardless of P rates (Table 3). C. etunicatum inoculation combined with high P rate led to a significant increase in BSR (Table 3). qCO2 decreased significantly with AMF inoculation compared with the controls (Table 3).

    Table 3.  Spore density (spores g–1 dry soil) and root colonization (%) by arbuscular mycorrhizal fungi, microbial biomass carbon (MBC, µg CO2·g–1), basal soil respiration (BSR, µg CO2-C·g–1·h–1), and soil metabolic quotient (qCO2, µg CO2·µg–1·Cmic h–1) for lemon balm inoculated with Rhizophagus clarus or Claroideoglomus etunicatum under low and high phosphorus rates.
    Treatment Spore density Root colonization MBC BSR qCO2
    T1 0.05 ± 0.01c 1.62 ± 0.32c 88.57 ± 6.14b 0.94 ± 0.10ab 11.09 ± 1.56a
    T2 1.94 ± 0.39b 63.86 ± 6.92ab 129.12 ± 8.81a 0.65 ± 0.11b 5.45 ± 1.22b
    T3 3.48 ± 0.39a 72.64 ± 3.07a 129.22 ± 5.86a 0.81 ± 0.06ab 6.33 ± 0.55b
    T4 0.05 ± 0.02c 1.87 ± 0.29c 80.88 ± 6.49b 0.76 ± 0.08ab 10.24 ± 1.81a
    T5 2.06 ± 0.35b 55.66 ± 6.00b 148.79 ± 10.55a 0.97 ± 0.15ab 6.53 ± 0.91b
    T6 2.40 ± 0.34b 67.05 ± 5.39ab 133.24 ± 4.67a 1.04 ± 0.07a 7.85 ± 0.51ab
    p-value < 0.001 < 0.001 < 0.001 0.046 0.009
    Notes: Mean values (n = 8 ± standard error). Means within columns followed by the same letter are not significantly different by Duncan's test (p ≤ 0.05). T1: uninoculated control under low P rate; T2: R. clarus under low P rate; T3: C. etunicatum under low P rate; T4: uninoculated control under high P rate; T5: R. clarus under high P rate; T6: C. etunicatum under high P rate.

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    EO yield ranged from 0.04% to 0.12% and was highest with R. clarus inoculation, regardless of P rates (Figure 1). In treatments inoculated with C. etunicatum, P rate did not significantly influence EO yield; nevertheless, the yields of C. etunicatum-inoculated plants were higher than those of the control.

    Figure 1.  Essential oil content (%) of lemon balm inoculated with arbuscular mycorrhizal fungi (Rhizophagus clarus or Claroideoglomus etunicatum) under low (–) and high (+) phosphorus (P) rates.
    Notes: Different letters indicate significant differences by Duncan's test (p ≤ 0.05); Bars = standard error.

    GC/MS analysis revealed 18 chemical compounds in EOs (Table 4). The major compounds were geranial (43.96% to 54.93%), followed by neral (29.25% to 34.66%), geraniol (3.11% to 12.85%), and (E)-caryophyllene (2.62% to 6.66%).

    Table 4.  Chemical composition (%) of essential oils from lemon balm inoculated with Rhizophagus clarus or Claroideoglomus etunicatum under low and high phosphorus rates.
    Peak Compound RT literature RT T1 T2 T3 T4 T5 T6
    1 trans-2-Hexenal 3.99 5.619 0.75 0.93 0.83 0.75 0.85 0.83
    2 Methyl heptanoate 8.57 9.698 0.41 0.60 0.58 0.41 0.58 0.30
    3 Citronellal 13.58 12.115 1.74 1.78 t 1.55 t t
    4 α-Cyclogeraniol 28.02 12.174 0.29 t t t t t
    5 Linalool 11.32 13.743 0.96 0.83 0.97 0.96 0.55 0.90
    6 Isocitral 14.82 16.597 0.42 0.55 1.51 0.42 1.76 t
    7 Neral 17.32 18.763 29.25 34.62 32.48 29.25 34.66 34.66
    8 Geraniol 17.95 19.286 12.85 3.11 3.28 12.85 3.51 3.31
    9 Geranial 18.62 19.831 43.96 52.71 47.42 43.96 51.13 54.93
    10 Linalool oxide acetate 19.64 20.091 t 0.79 t t t t
    11 Terpinyl acetate 20.22 20.222 1.19 0.64 1.53 1.19 0.58 1.24
    12 Methyl geranate 21.19 21.458 0.49 0.77 0.80 0.49 0.87 0.58
    13 2, 6-Dimethyl-2, 8-octanediol 22.83 22.049 t t 0.38 t t t
    14 8-Hydroxymenthol 21.44 23.245 t t 0.54 t 0.57 t
    15 (E)-caryophyllene 25.36 24.623 4.97 2.62 6.66 4.94 4.87 3.14
    16 ar-Turmerone 35.51 31.982 1.53 t t 2.23 T t
    17 Ledol 32, 99 32.982 0.97 t t 0.97 T t
    18 Farnesoic acid 40.98 40.991 t t 1.00 t T t
    Citral (neral + geranial) 73.21 87.33 79.90 73.21 85.79 89.59
    Total identified 99.78 99.95 97.98 99.97 99.93 99.89
    Notes: Compounds were identified by comparison of their retention indices and mass spectra with literature data [35]. RT: Retention time; T1: uninoculated control under low P rate; T2: R. clarus under low P rate; T3: C. etunicatum under low P rate; T4: uninoculated control under high P rate; T5: R. clarus under high P rate; T6: C. etunicatum under high P rate; t: traces.

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    Geranial and neral contents increased with AMF inoculation, regardless of P rates. However, the content of geraniol did not increase with inoculation, being higher in the control treatments, while (E)-caryophyllene increased with the inoculation of C. etunicatum under low P rate (Table 5). Data on EO composition (Table 5) were subjected to hierarchical cluster analysis to assess the variability in major compounds between treatments.

    Table 5.  Major components (%) of essential oils from lemon balm inoculated with Rhizophagus clarus or Claroideoglomus etunicatum under low and high phosphorus rates.
    Treatment Neral Geraniol Geranial (E)-caryophyllene Citral (neral + geranial) Yield
    T1 29.25 12.85 43.96 4.97 73.21 0.065
    T2 34.62 3.11 52.71 2.62 87.33 0.124
    T3 32.48 3.28 47.42 6.66 79.9 0.072
    T4 29.25 12.85 43.96 4.94 73.21 0.050
    T5 34.66 3.51 51.13 4.87 85.79 0.121
    T6 34.66 3.31 54.93 3.14 89.59 0.073
    Literature, data from 32 articles
    Mean 26.07 2.21 37.65 5.14 62.35 0.32
    SE 0.68 0.38 1.06 0.45 1.42 0.03
    Range 4–38.9 0.12–19.16 4.6–63.7 0.3–45.07 8.6–92.46 0.008–1.2
    n 144 75 153 146 142 114
    Notes: T1: uninoculated control under low P rate; T2: R. clarus under low P rate; T3: C. etunicatum under low P rate; T4: uninoculated control under high P rate; T5: R. clarus under high P rate; T6: C. etunicatum under high P rate; SE: standard error; n: number of observations.

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    EO composition was grouped into two main groups (Figure 2) and plotted on a dendrogram obtained by the unweighted pair group method with arithmetic mean. The first cluster included plants inoculated with AMF and the second cluster comprised the controls.

    Figure 2.  Hierarchical clustering dendrogram of essential oils of lemon balm inoculated with arbuscular mycorrhizal fungi (Rhizophagus clarus or Claroideoglomus etunicatum) under low and high phosphorus (P) rates.
    Notes: Treat 1: uninoculated control under low P rate; Treat 2: R. clarus under low P rate; Treat 3: C. etunicatum under low P rate; Treat 4: uninoculated control under high P rate; Treat 5: R. clarus under high P rate; Treat 6: C. etunicatum under high P rate.

    PCA of EO data revealed two components (PCA1 and PCA2), which explained 82.50% and 16.47%, respectively, of the variance in chemical composition (Figure 3 and Table 5). As observed in the PCA loading biplot (Figure 3), control treatments (treatments 1 and 4) were clearly separated from treatments inoculated with AMF, corroborating the results of hierarchical clustering (Figure 2). Factor loadings demonstrated that geraniol was highly correlated with treatments 1 and 4 in PCA1 (plotted near −1). Citral, geranial, and neral were highly correlated with PC1 (plotted near +1). (E)-caryophyllene and treatment 3 were correlated with PCA2. Overall, the results of PCA underscore the effect of AMF inoculation (treatments 2, 3, 5 and 6) on the production of monoterpenes, such as geranial, which was lower in the controls (treatments 1 and 4) (Figure 3 and Table 5).

    Figure 3.  Principal component analysis (PCA) biplot for essential oils of lemon balm inoculated with arbuscular mycorrhizal fungi (Rhizophagus clarus or Claroideoglomus etunicatum) under low and high phosphorus (P) rates.
    Notes: Treat 1: uninoculated control under low P rate; Treat 2: R. clarus under low P rate; Treat 3: C. etunicatum under low P rate; Treat 4: uninoculated control under high P rate; Treat 5: R. clarus under high P rate; Treat 6: C. etunicatum under high P rate.

    An increase in shoot fresh and dry weights was observed with R. clarus inoculation. Root dry weight and total dry weight increased with R. clarus inoculation and addition of P at a low rate. Salgado et al. [36] attributed an increase in root dry weight to R. clarus inoculation and enhanced nutritional status, leading to an overall improvement in plant development. Silva et al. [37] found similar results for total dry weight of tomato (Solanum lycopersicum L.) inoculated with R. clarus. AMF inoculation significantly increased the shoot dry weight of lemon balm plants in a study conducted by Shamizi et al. [38]. Engel et al. [1], however, observed no significant increase in shoot fresh or dry weight in lemon balm inoculated with AMF.

    Addition of P did not stimulate biomass production. Similar results were reported by Carneiro et al. [39] for embauba (Cecropia pachystachya Trécul). The authors observed that AMF inoculation combined with absence of P2O5 enhanced shoot dry weight, given that, the higher the P rate, the lower the root colonization, leading to a decrease in plant growth [39]. By contrast, Urcoviche et al. [22] found that inoculation of Mentha crispa with AMF combined with high P rate increased shoot fresh weight.

    An increase in shoot P content was observed with low P rate and R. clarus inoculation, as well as with C. etunicatum inoculation under high P rate. Lermen et al. [40], in assessing the effects of different P rates on Cymbopogon citratus (DC.) Stapf. (lemongrass), found similar root and shoot P contents in AMF-inoculated and uninoculated plants.

    AMF inoculation combined with low P rate significantly increased spore density and root colonization, which ranged from 55.66% to 72.64%. Engel et al. [1] observed a mean root colonization of 62% in lemon balm. Similar results were reported for Plectranthus amboinicus Lour. inoculated with R. clarus and C. etunicatum and treated with low P rates [20] and Lippia alba (Mill.) N.E.Br. [25].

    P is essential for plant-soil-fungi interactions, which promote plant development and influence secondary metabolism [20,22,25]. However, addition of high P rates to the soil decreased spore density and root colonization by R. clarus and C. etunicatum (Table 3). Therefore, low P rates are sufficient to ensure good nutritional performance in plants inoculated with AMF.

    MBC was higher in AMF-inoculated plants, demonstrating that inoculation favored plant development. High MBC rates are indicative of high absorption and storage of C, nutrients, and minerals in the soil [11,15,25]. Inoculation with C. etunicatum and high P rate increased BSR, resulting in greater loss of C to the atmosphere. As argued by Balota et al. [41], treatment of plants with high rates of inorganic nutrients, such as P, may lead to a reduction in soil C, possibly causing nutrient deficiencies.

    qCO2 decreased with AMF inoculation compared with the controls. This finding shows that AMF enhanced soil quality, given that the lower the qCO2, the better the soil quality [15,42].

    The EO yield (0.12%) of plants inoculated with R. clarus and treated with low P rates was below the average reported in the literature for lemon balm (0.32%). Even lower EO yields were observed in the controls, although values were within the range reported by Sodré et al. [43] and Szabó et al. [17], ranged from 0.07% to 0.3%. Cruz et al. [44], in studying Salvia officinalis L., and Merlin et al. [20], in studying P. amboinicus, observed that EO yield increased with R. clarus inoculation under both high and low P rates.

    The main constituents of lemon balm EO are citral (geranial + neral), geranial, neral, geraniol, and (E)-caryophyllene (Table 5). Citral content generally ranges from 8.6% to 92.46%, with a mean of 62.35%; here, we obtained values of 73.21% to 89.59%, being slightly above the average (Table 5). Similar results were observed for geranial (43.96%–54.93%) and neral (29.25%–34.66%), whose contents were within ranges reported in the literature (Table 5) and in the studies of Sodré et al. [43], Szabó et al. [17], Abdellatif et al. [45], Silva et al. [46], Chrysargyris et al. [47], and Petrisor et al. [3]. Assis et al. [18] inoculated lemon balm with AMF and organic manure rates, but did not observe significant changes in geranial or neral contents with AMF inoculation. Karagiannidis et al. [19], in assessing the effects of AMF on oregano and mint development, found that inoculation promotes the growth of plants in soils with low fertility, minimizing the need for agricultural inputs and increasing EO production and quality.

    The major EO component identified here was citral, as also observed in previous studies under different plant cultivation and processing methods [18,46] (Behbahani and Shahidi, 2019; Assis et al., 2020). Citral was the major compound of lemongrass EO [16,33]. This compound is responsible for the characteristic citric odor of lemon balm, very similar to that of lemongrass [48]. The cosmetic and perfume industries use citral in formulations of colognes, deodorants, body moisturizers, and soap. Citral is an important ingredient in the pharmaceutical industry, being used as a starting material for the production of ionone, vitamin A, and beta-carotene [5,45]. Its main pharmacological activities include antibacterial, antifungal and soothing effects [3,18,49].

    AMF inoculation of lemon balm under low P rates increased shoot fresh and dry weights, soil quality, and plant development. Furthermore, AMF inoculation enhanced root colonization and spore density.

    EO yield ranged from 0.04% to 0.12% and increased with R. clarus inoculation. Eighteen compounds were identified in EOs, with the major compounds being geranial (43.96% to 54.93%), neral (29.95% to 34.66%), geraniol (3.11% to 12.85%), and (E)-caryophyllene (2.62% to 6.66%). On the basis of the results, it is recommended to inoculate lemon balm with R. clarus under low P conditions, being a sustainable, safe, and efficient strategy for farmers to reduce costs and increase yields.

    Due to the increase in the global population, the demand for food, agro-industrial and medicinal products is increasing. Several studies have contributed to the investigation of AMFs in the cultivation of different medicinal species. This unprecedented study identified a significant increase in the EO yield and content of active compounds of M. officinalis when inoculated with R. clarus, opening opportunities for future research that may contribute to the implementation of more sustainable agronomic techniques in the production of industrially important species.

    The authors acknowledge UNIPAR for the financial support. M. M. Pinc and R. U. Lastra thanks PROSUP/ CAPES for the scholarship. C. da Silva and O. Alberton acknowledge a research fellowship from the CNPq (National Council for Scientific and Technological Development). The authors thanks the Fundação Araucária by supporting research.

    All authors declare no conflicts of interest in this paper.



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