Background

Climate change increases global temperatures. Some regions experience droughts and immediately thereafter a sudden burst of excessive rainfalls [1]. Excessive rainfalls result in further destructive and dangerous natural hazards, that is, floods, which cause serious damage to life and soils every year. An increase in crop flooding area from 10 to 20% by 2080 is expected [2]. In soils, excess rainfall promotes leaching of cations, especially K, decreasing its availability in the soil solution [3]. This is more serious in weathered soils containing source materials of low nutrient availability. Also, soils in some regions of the southern hemisphere are currently running out of K due to the expansion and intensification of agriculture and a lack of access to potassium [4]. It is estimated that the amount of potassium required by agricultural crops is ten times greater than the amount extracted annually by the fertilizer industry [5], resulting in a deficiency of this nutrient in a large part of crops. On the other hand, drought decreases the movement of ions in the soil, including K+, reducing its uptake by plants [6]. Therefore, it is evident that climate change may accentuate problems of potassium deficiency in crops. Losses by K deficiency are more drastic in K-demanding species, such as beans, a crop of global importance, as it causes damage to the sustainability of the crop [7] and leads to food insecurity.

Thus, K deficiency causes well-known physiological damages [8, 9]. Examples are osmotic imbalance and losses in photosynthetic rates due to low water use efficiency [10, 11]. In addition, K activates dozens of enzymes in different metabolic pathways in plants [12,13,14,15], with an emphasis on N metabolism [16]. This consequently reduces plant growth. However, little is known about the damage caused by K deficiency to the stoichiometric homeostasis of C:N:P and its effects on nutritional efficiency, that is, on the plant's ability to use nutrients in physiological and biochemical processes that are vital for conversion into dry mass. There is recent strong evidence for other species that stresses such as saline [17] and water deficit [18, 19], associated with increased temperature [20], are responsible for elemental imbalances in stoichiometry enough to decrease the nutritional efficiency of crops and plant growth This may occur with K deficiency, but there is not enough evidence of it. Additionally, potassium is also known to reduce the impacts of stressful conditions in plants. Its deficiency is severe, as it reduces plant tolerance to other stresses and consequently leads to yield losses [21].

An innovative and sustainable strategy to mitigate stress caused by K deficiency can be the use of Si. This is because Si is known to mitigate different abiotic stresses, including in legumes [22,23,24,25]. Little is known about the potential of Si to attenuate the biological damage of K deficiency in bean plants. Recently, researchers discovered that Si improves the uptake of K in soybean plants, improving the response of plants under saline stress [26]. There is only one study reporting the benefits of Si to the photosynthetic apparatus [27], a fact also observed for maize plants [28], basil plants [29], peanut (Arachis hypogaea) [24], and barley (Hordeum vulgare L.) [30, 31]. However, it is necessary to advance in the research on elementary stoichiometric homeostasis for a better understanding of the effects of Si on this nutritional balance for a possible neutralization of damages arising from K deficiency.

Studies have shown the role of Si in replacing C in organic compounds that make up the cell wall of plants, especially lignin and cellulose [32]. Recent research indicates that Si uptake can lead to a new homeostatic balance of C:N:P, as observed in different species such as Sorghum bicolor (L.) Moenchand, Helianthus annuus L. [17, 33], Chenopodium quinoa Willd. [34], Triticum aestivum L. [35], Panicum maximum L. [36], Phragmites australis [37], Medicago sativa [38], and Saccharum officinarum L. [19, 39,40,41,42,43]. In this scenario, there are indications that this new elemental homeostasis of C, N, and P promoted by Si plays a role in minimizing biomass losses in plants of different species under stress conditions [39,40,41] or enhancing plant growth without stress [41, 44]. However, this is not yet studied in bean plants.

In this context, studies are needed to understand the biological damages that K deficiency causes to the homeostatic balance of C:N:P and the role of Si in attenuating nutritional deficiency. For this, it is relevant to test the following hypotheses: (i) K deficiency can cause damage to the homeostatic balance of C:N:P, reducing the use efficiency of these nutrients, (ii) Si can reverse these nutritional damages and improve the nutritional efficiency and growth of K-deficient bean plants, which may mean a possible benefit to agriculture in underdeveloped economies with restricted use of K, or (iii) Si could improve nutritional balance and efficiency in a level that is enough to increase dry mass production of common beans cultivated under K sufficiency, meaning a possible use of Si in agriculture in developed economies with no nutritional restrictions.

This research aims to evaluate whether K deficiency changes the stoichiometric ratio C:N:P of bean plants and whether the supply of Si can modify the homeostatic balance of C:N:P, attenuating the damage caused by K nutritional deficiency and increasing the use efficiency of nutrients and the production of dry mass of bean plants with deficiency and sufficiency of K.

If these hypotheses above are true, they should reveal one more benefit of Si in mitigating stresses such as potassium deficiency in bean plants resulting from the improvement in the nutritional efficiency of C, N, and P. Thus, this research may pave the way for further studies on different species. It may open ways to evaluate the role of Si in the stoichiometric homeostasis of C, N, and P, which are vital structural nutrients for plant metabolism, in order to better explain the optimal performance of nutritionally deficient crops that received Si, which is still little discussed in studies on Si.

Results

Si, C, N, and P concentrations

K deficiency decreased the concentration of Si and C in roots (Fig. 1b and h), decreased the concentration of P in shoots (Fig. 1e) and increased the concentration of N and P in roots in the absence of application of the beneficial element (Fig. 1d and f). The application of Si to bean plants with K deficiency led to an increase in the concentration of Si in shoots (Fig. 1g) and N, P, and Si in roots (Fig. 1b, d and h). There was also a decrease in the concentrations of N and P in shoots (Fig. 1c and e). Regarding the nutritional sufficiency of K, the application of Si decreased the concentration of C in shoots (Fig. 1a) and C, N, and P in roots (Fig. 1b, d and f) and increased the concentration of Si in shoots and roots (Fig. 1g and h).

Fig. 1
figure 1

C (a, b), N (c, d), P (e, f), and Si (g, h) concentration in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution). Different uppercase letters indicate differences in K supply (deficiency or sufficiency) and different lowercase letters indicate differences in Si application (absence and presence of Si) by Tukey test (p < 0.05). Error bars indicate mean standard error (n = 5)

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Homeostatic balance of C, N, P, and Si

The stoichiometric ratios C:N and C:P in shoots (Fig. 2a and c) and C:Si, N:Si, and P:Si in roots (Fig. 3b, d and 3f) decreased, and the stoichiometric ratios P:Si in shoots (Fig. 3e) and C:N and C:P in roots (Fig. 2b and d) increased due to K deficiency in bean plants without Si application. However, there was no change in N:P and N:Si ratios in shoots (2e and 3c) and N:P in roots (Fig. 2f). In K-deficient plants, the supply of Si increased the stoichiometric ratios of C:N in shoots (Fig. 2a) and C:P and N:P in roots (Fig. 2d and f), but it decreased the ratios N:P, C:Si, N:Si, and P:Si in shoots (Figs. 2e, 3a, c and e) and C:N, C:Si, N:Si and P:Si in roots of bean plants (Figs. 2b, 3b, d and f). In plants with K sufficiency, there was a reduction in the stoichiometric ratios C:N, C:P, C:Si, N:Si, and P:Si in shoots (Figs. 2a, c, 3a, c and e) and C: Si, N:Si and P:Si in roots (Fig. 3b, d and f) and an increase in the stoichiometric ratios N:P (shoots) and C:N (roots) (Fig. 2e and b).

Fig. 2
figure 2

Stoichiometric ratios C:N (a, b), C:P (c, d), and N:P (e, f) in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution). Different uppercase letters indicate differences in K supply (deficiency or sufficiency) and different lowercase letters indicate differences in Si application (absence and presence of Si) by Tukey test (p < 0.05). Error bars indicate mean standard error (n = 5)

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Fig. 3
figure 3

Stoichiometric ratios C:Si (a, b), N:Si (c, d), and P:Si (e, f) in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution). Different uppercase letters indicate differences in K supply (deficiency or sufficiency) and different lowercase letters indicate differences in Si application (absence and presence of Si) by Tukey test (p < 0.05). Error bars indicate mean standard error (n = 5)

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C, N, P, and Si contents

K deficiency caused a reduction in C, N, P, and Si content in shoots and roots in the absence of Si supply in bean plants (Fig. 4). The application of Si increased the contents of C, N, P, and Si in shoots and roots in plants under K deficiency, while in bean plants under K sufficiency there was an increase in Si content in shoots (Fig. 4g) and of C, N, P, and Si in roots (Fig. 4b, d, f and h).

Fig. 4
figure 4

C (a, b), N (c, d), P (e, f), and Si (g, h) content in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution). Different uppercase letters indicate differences in K supply (deficiency or sufficiency) and different lowercase letters indicate differences in Si application (absence and presence of Si) by Tukey test (p < 0.05). Error bars indicate mean standard error (n = 5)

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C, N, and P use efficiency and biomass production

C, N, and P use efficiency in shoots and roots of bean plants decreased in plants under K deficiency in relation to K sufficiency and in the absence of Si supply (Fig. 5). The supply of Si increased the use efficiency of C, N, and P in shoots and roots of K-deficient plants (Fig. 5). In plants with K sufficiency, the addition of Si to the nutrient solution also increased the C and P use efficiency in shoots (Fig. 5a and e) and C, N, and P in roots (Fig. 5b, d and f).

Fig. 5
figure 5

C (a, b), N (c, d), and P (e, f) use efficiency and production of dry mass (g, h) in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution). Different uppercase letters indicate differences in K supply (deficiency or sufficiency) and different lowercase letters indicate differences in Si application (absence and presence of Si) by Tukey test (p < 0.05). Error bars indicate mean standard error (n = 5)

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K deficiency in common bean plants in the absence of Si supply caused a reduction in the production of shoot and root dry matter (Fig. 5g and h). The supply of Si increased the production of shoot and root mass in K-deficient plants, while in plants with K sufficiency there was only an increase in the dry mass of roots (Fig. 5h).

Hierarchical cluster analysis

The hierarchical cluster analysis of shoots showed that there was a greater dissimilarity in the absence of Si supply in K-deficient plants in treatments that received application of Si and in the treatment with K sufficiency in the absence of Si (Fig. 6a). In the analysis of hierarchical clustering in roots, the greatest dissimilarity in the Si supply condition in K-deficient plants occurred in treatments that did not receive Si application and in the treatment with K sufficiency and application of Si (Fig. 6b).

Fig. 6
figure 6

Correlogram of the stoichiometric ratio C:N:P, C, N and P use efficiency, dry mass production (a, b), and hierarchical cluster heat map of independent variables in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution)

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For shoots, the hierarchical cluster analysis showed a greater similarity of variables of the stoichiometric ratios C:N and C:Si and concentrations of C, N, and P in the absence of supply of Si to plants deficient in K, while Si concentration was associated with treatments that received Si application (Fig. 6a). The use efficiency of C, N, and P, the stoichiometric ratio N:P, and the contents of N and Si were associated with the treatment that received a supply of Si under K sufficiency. The increase in the stoichiometric ratio C:N and C:P and in the contents of C and P were associated with treatments with absence of Si supply under K sufficiency (Fig. 6a).

In the roots of bean plants, there was a greater similarity of P use efficiency, Si concentration and content, and the stoichiometric ratios C:P and N:P with the treatment with Si supply under K deficiency. On the other hand, there was a greater association of C concentration and the stoichiometric ratio C:N with treatments without Si supply under K deficiency (Fig. 6b). Concentrations of N and P and the stoichiometric ratio C:Si were associated with the treatment without Si supply under K sufficiency Finally, the contents of C, N and P, the use efficiency of C and N, and the dry mass production were associated with a greater similarity to the treatment with Si supply under K sufficiency (Fig. 6b).

Principal component analysis

The principal component analysis (PCA) of shoots and roots of common bean plants explained 81% and 83% (principal component 1 + 2) (Fig. 7a, b). As for the PCA of shoots, dry mass, P concentration, N and P content, and C, N and P use efficiency explained the variance in PC1 and Si concentration; C:N, C:P and N:P and Si content explained the variance in PC2 (Fig. 6a); and C and N concentrations, C content and C:Si, N:Si and P:Si ratios explained the variance in PC1 and PC2 (Fig. 7a). As for the PCA of roots, dry mass, P concentration, N and P content, C, N and P use efficiency explained the variance in PC1; Si concentration and content and the ratios C:N, C: P and C:Si explained the variance in PC2; and C and N concentrations, C content, and N:P, N:Si and P:Si ratios contributed with mean values ​​to explain the variance in PC1 and PC2 (Fig. 7b).

Fig. 7
figure 7

PCA of the stoichiometric ratio C:N:P, C, N and P use efficiency, dry mass production (a, b), and hierarchical cluster heat map of independent variables in leaves and roots of bean plants cultivated under deficiency (-K) and sufficiency (+ K) of K in the absence (-Si) and presence of supply of Si (via nutrient solution)

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In shoots, the PCA showed an association of increased N and P concentrations with the treatment with K deficiency in the absence of Si The increased C:N and C:P ratios was associated with treatments with K sufficiency in the absence of Si. Increased C, N and P use efficiency, C content, and dry mass were associated with treatments with K sufficiency and the presence of Si (Fig. 7a). Also, the increase in Si concentration and content and the N:P ratio was associated with treatments with the presence of Si in K deficiency and K sufficiency (Fig. 7a).

For the root system, there was an association of increased C concentration and C:N ratio, C:P and N:P ratios, P use efficiency, and P concentration and content to treatments with K deficiency and absence of Si. Si associated with treatments with K deficiency and presence of Si (Fig. 7b). The C:Si, N:Si and P:Si ratios and the N and P concentrations were associated with treatments with K sufficiency and Si absence, while C and N use efficiency, C, N and P contents, and dry mass were associated with treatments sufficient in K and the presence of Si (Fig. 7b).

Discussion

Silicon in the stoichiometry of C:N:P and nutritional efficiency in K-deficient beans

K deficiency in bean plants begins with a reduction in C, N, P, and Si contents in shoots and roots (Fig. 3), that is, a decrease in the uptake of these elements. This is because K deficiency can impair the water status of plants [11, 45] and decrease the activity of aquaporins, causing a reduction in the hydraulic conductance of roots [46] and resulting in less transpiration, consequently in less uptake of nutrients and physiological damage [46,47,48]. These processes are widely known, but it is necessary to explain whether the lack of this element causes loss of stoichiometric homeostasis of vital structural nutrients for plant metabolism, such as C, N and P. A study conducted on barley (Hordeum vulgare L.) aimed to evaluate the impact of potassium deficiency on the dynamics of other nutrients. The authors found changes in the dynamics of Ca, Fe, and Zn but did not observe any impact on the homeostasis of C, N, and P [30]. We argue here that the disturbance of the metabolism of these key nutrients could result in important losses in the use efficiency of these elements in plants, thus explaining the loss of dry mass in common beans.

Potassium is crucial for balancing homeostasis in plants [49]. The results show that K deficiency in bean plants results in changes in the homeostatic balance of C:N:P, decreasing the stoichiometric ratios C:N and C:P in shoots (Fig. 2a and c) and C:Si, N:Si and P:Si in roots (Fig. 3b, d and f It also increases the P:Si ratio in shoots (Fig. 3c) and C:N and C:P in roots (Fig. 2b and d).

Impairments to the homeostatic balance of C:N:P may be related to low C assimilation resulting from K deficiency [3]. This was probably due to impaired N and P metabolism, essential for an optimal C assimilation [8, 38, 50, 51].

The losses by K deficiency in bean plants causes changes in stoichiometric homeostasis of C, N and P This results in a decrease in the use efficiency of C, N and P, that is, there is a low capability of the plant to use these nutrients to ensure an optimal metabolism. It consequently decreases the plant's ability to convert dry mass in shoots and roots (Fig. 5g and h). The hierarchical cluster analysis complements this information by showing that the increase in the stoichiometric ratio C:N is the most limiting factor to the production of dry mass (Fig. 5g). This reinforces that the lower N content in relation to C points to the importance of K for N metabolism and the dry mass production of beans. Studies conducted under water deficit conditions have also shown that dry mass loss is related to a modification of the C:N:P homeostatic balance and the loss of carbon use efficiency [39, 42, 43]. The results of our work, together with the results reported in the literature, show that under stressful conditions there is damage to the plant's homeostatic balance and loss of nutrient use efficiency, such as C, N, and P.

In this context, our results show that the first hypothesis is true since K deficiency in bean plants can cause damage to the homeostatic balance of C:N:P, reducing the use efficiency of these nutrients. This shows, for the first time, that studies on the role of K in common beans should not stop in physiological evaluations involving gas exchanges or enzymatic metabolism.

The application of Si was efficient in increasing the concentration of Si in shoots and roots (Fig. 1h), indicating that there is an increase in the uptake of the beneficial element (Fig. 3g). The uptake of Si that occurs in the form of H4SiO4 is favored even under nutritional stress conditions [29], as the present study shows (Fig. 3g and h). It is a passive movement, which is common in legumes [52]. It is noteworthy that the uptake of Si, observed here by its content in roots, is greater in plants under nutritional stress, that is, deficient rather than sufficient in K. Similar results were found for peanuts, with a higher Si content in the roots of plants that were under a high K restriction [24, 53].

The Si uptake by K-deficient bean plants promoted a change in the homeostatic balance of C:N:P, resulting in an increase in the stoichiometric ratio C:N in shoots and C:P and N:P in roots, and in a decrease in the ratios C:Si, N:Si, P:Si and N:P in shoots and C:N, C:Si, N:Si and P:Si in roots (Fig. 2). Other studies have shown the benefits of Si in changing the homeostatic balance of C:N:P in different species. such as Saccharum officinarum L. [19, 39, 41,42,43,44], Chenopodium quinoa Willd. [34], Sorghum bicolor (L.) Moench [17, 33], and Triticum aestivum L. [35]. However, this is the first study to detect the role of Si in changing the stoichiometric ratio C:N:P in bean plants. These changes are expected, because Si modifies the concentration of carbon in plants, causing alterations in the rates of accumulation and use efficiency, especially under stress conditions [42, 54]. However, the extent of the changes induced by Si in beans is poorly understood. Si can reduce the changes caused by K deficiency in the C:N:P homeostatic balance.

We also evidence the benefit of Si in increasing the contents of N and P, that is, in the uptake of these nutrients by K-deficient bean plants (Fig. 4c, d, e and f). This is probably because Si increases the efficiency of NH4+ transporters (OsAMT) and the expression of NO3 transporters (BnaNTR2.1), in addition to improving the gene expression of inorganic phosphorus transporters (TaPHT1;1 andTaPHT1;2) [23]. Other studies on Si also support our results, showing the beneficial role of Si in improving N use efficiency [55, 56]. However, such studies did not investigate the implications of Si on the homeostatic balance of C, N, and P in plants.

The principal component analysis showed that the increase in the use efficiency of C, N, and P in bean plants is related to the presence of Si and the increase in the stoichiometric ratios C:Si, N:Si and P:Si (Fig. 7). Thus, the greater use efficiency of C, N and P modulated by Si makes clear the role of this beneficial element in increasing the ability of plants to use them in metabolism [12]. It consequently favors the conversion into dry mass of the shoots and roots of bean plants with potassium deficiency (Fig. 5g and h).

It becomes clear that a bean plant under K deficiency favors its ability to absorb more Si through the roots and accumulate less C in shoots because the plant in such a situation has a high C cost. Therefore, beans use a strategy that replaces Si for C, leading to a decrease in the stoichiometric ratio C:Si (Fig. 3a and b). This replacement of Si for C in the organic compounds of the cell wall has a low energy cost and may represent an energy saving ten to twenty times lower compared to the incorporation of C [57]. The energy balance resulting from the economy of replacing C and Si can be directed to the mechanisms of attenuation of nutritional stress caused by K deficiency. The latest evidence suggests that mono-silicic acid is complexed in the cell wall, forming Si–O-C bonds from the hydroxyl complexation between H2SiO4 and cisdiols [58].

Therefore, the beneficial effects of Si in mitigating a known K deficiency result not only from its role in restoring physiological activity impaired by nutritional deficiency [28, 59], as we show the underlying role of Si in the elementary stoichiometric homeostasis of C:N:P in bean plants. However, the hierarchical cluster analysis shows that despite the benefits of Si in attenuating the deleterious effects of K deficiency, such changes are still not enough to fully reverse the biological damage caused by deficiency of this macronutrient (Fig. 6a). This is because Si does not completely replace K functions in plants; it significantly mitigates the damage caused by K deficiency, improving plant growth, which has a great practical relevance.

In this scenario, our second hypothesis is true. It shows that the biological role of Si in attenuating K deficiency in bean plants occurs through the modification of the homeostatic balance of C:N:P, which increases the content and use efficiency of these nutrients, resulting in attenuation of biomass production losses.

Studies using Si in bean plants analyzed a predominance of different stresses [27, 60,61,62]. However, studies on this element in plants without stress are scarce, especially with legumes, as they are not Si-accumulating species but have the capacity to absorb this element.

Silicon in the stoichiometry of C:N:P and nutritional efficiency in K-sufficient beans

The present study allows for an additional approach to the role of Si in the stoichiometry of C:N:P in bean plants without stress, that is, in plants with sufficient K. This helps to better understand why the use of this beneficial element can improve growth in plants in this situation.

The Si uptake capacity of bean plants with sufficient K was evidenced, as there was an increase in the concentration and content of the beneficial element (Fig. 1g, h, 4g, and h). This indicates a good application efficiency and there is no evidence of polymerization of the beneficial element in the solution. Si absorbed in plants predominates in the form of amorphous silica in the cell wall [58] and a small amount in the form of polysilicic acid [27].

The higher uptake of Si in bean plants with K sufficiency changed the homeostatic balance C:N:P, causing reductions in the C:N, C:P, C:Si, N:Si and P:Si ratios in shoots (Fig. 2a, c, 3a, c and e) and C:Si, N:Si and P:Si in roots (Fig. 3b, d and f). It also increased the N:P ratio in shoots (Fig. 2e) and C:N in roots (Fig. 2b).

Si can improve the efficiency of N use in roots and P in shoots and roots of plants (Fig. 5). The presence of this beneficial element contributes to the uptake and assimilation of these nutrients [23]. These results support the role of Si in alleviating N and P deficiency in plants by improving the uptake and accumulation of these nutrients [55, 63, 64]. Si caused changes in the homeostatic balance C:N:P in shoots and roots of bean plants. However, such stoichiometric modifications are not enough to improve the dry mass biosynthesis in plant shoots, restricting increases in dry mass only in roots (Fig. 5). This result may be related to the absence of an increase in the efficiency of N use in plant shoots (Fig. 5c), indicating that the modification of the stoichiometric ratios C:N and N:Si are not enough to improve the use of this admittedly important nutrient in plant physiological processes [20, 65, 66], which is vital for dry mass biosynthesis.

In addition, a greater effect of Si on root growth of a plant under no nutritional stress happens because the greatest benefit of Si in this organ arises from the replacement of C for Si in organic compounds, immobilizing Si in cell walls [67] with lower energy costs for biosynthesis [68]. Other authors reported the benefits of Si for root growth in plants without stress [69, 70], but these benefits did not reflect on a growth of bean shoots. Thus, our results reinforce the thesis that the greatest benefits of Si occur in plants under stress rather than in plants under no stress [71].

In this scenario, the third hypothesis is not true. The results, although they may indicate that Si generally potentiates the balance, the nutritional efficiency and the production of dry mass of roots, do not point to an increase in the production of shoot dry mass of common bean cultivated under K sufficiency. Therefore, a direct implication is that its use is not recommended for intensive agriculture without K restriction.

In general, our research makes it clear that the greatest benefit of Si in bean plants occurs under K deficiency. This finding has global implications given the low availability of this nutrient in crops, which occurs due to inadequate K fertilization caused, mainly, by an underdeveloped economy and scarcity of resources of soluble K [72], which are unevenly distributed in the world [73]. There is growing evidence that some agricultural systems have a limited availability of Si in soils [74], justifying the need to supply this element to obtain benefits in plants cultivated under K deficiency.

This research may pave the way for further studies with different species aiming to analyze the role of Si in the stoichiometric homeostasis of C, N and P, which are vital structural nutrients for plant metabolism, in order to better explain the optimal performance of crops, especially in soils with low potassium availability.

In conclusion, our study shows that K deficiency in bean plants causes biological damage to the homeostatic balance C:N:P, reducing the efficiency of nutrient use and causing losses in biomass production. Si is an alternative that can mitigate the damage caused by K deficiency, modifying the stoichiometric ratio C:N:P, increasing the use efficiency of nutrient, and reducing the loss of biomass production in bean plants. In plants with K sufficiency, Si also induces changes in the stoichiometric ratio C:N:P. However, these changes are not enough to increase shoot biomass, restricting gains only to the root system.

The future perspective is that the use of Si may be more intense in agriculture in underdeveloped economies with restriction of use of K. It may be a sustainable strategy to increase the productivity of bean crops and ensure food security.

Methods

Experimental conditions and design

The experiment was carried out in a controlled greenhouse at the Agricultural Production Science Department of the Faculty of Agrarian and Veterinary Sciences (FCA) of the São Paulo State University (UNESP), Jaboticabal, São Paulo, Brazil. During the experiment, the monitoring of climatic conditions was carried out using a digital thermohygrometer recording minimum temperature (19.5 ± 5 °C), maximum temperature (38.6 ± 7 °C), and relative humidity (32.8 ± 8%).

The factorial design was 2 × 2 randomized blocks, with two K supply conditions (deficiency at 0.2 mmol and sufficiency at 6 mmol) and two Si supply conditions (absence at 0.0 mmol and presence at 2 mmol), with five replications.

Installation and conduction of experimental plots

Sowing was carried out in plastic seed trays in November 2017. The cultivar was BRS Estilo. Five days after seedling emergence, transplanting was carried out in 10-L polypropylene pots (0.44 × 0.19 × 0.14 m) containing sand, sand washed with water, and a solution of 0.5 mol HCl. The substrates of the experimental plots were washed weekly to eliminate excess salt using 700 mL of deionized water in each pot and pH adjusted to 5.5. The nutrient solution used in the experiment was that proposed by Hoagland and Arnon [75], that is, 10% concentration of the solution in the first week, 25% in the second week, and 50% from the third week until the end of the experiment.

The pH of the nutrient solution was kept between 5.5 and 6.5, correcting it with a solution of NaOH (1 mmol) and HCl (1 mmol). Si was supplied to the nutrient solution using SiNaK (1.8 mmol of Si and 0.2 mmol of K), balancing with K in treatments with no application of Si.

Production of plant biomass

Twenty five days after seedling transplanting, the plants were collected and separated into shoots and root. They were washed in deionized water, neutral detergent solution (0.1%), HCl solution (0.3%), and deionized water. After washing, the samples were dried in a forced air oven until constant mass, determining the dry mass of shoots and roots.

C, N, P, and Si concentrations

The determination of C was carried out by oxidation with K dichromate in acidic medium and titration of excess Cr6+. The concentration of N was determined by the Kjeldahl method of wet oxidation [76]. P concentration was determined by the nitric-perchloric digestion method and colorimetry (ammonium metavanadate method) [77]. Finally, Si was determined by alkaline digestion and reading was taken by colorimetry with ammonium molybdate [78].

C:N:P:Si homeostatic balance

To determine stoichiometric ratios, the concentrations of elements in shoots and roots were used to estimate the stoichiometric ratios C:N, C:P, C:Si, N:P, N:Si, and P:Si.

C:N:P:Si content and use efficiency

The contents of C, N, P, and Si were determined by multiplying dry mass by the concentration of the nutrient in shoots and roots. The use efficiency of C, N, and P was determined by the quadratic ratio of dry mass and nutrient content in shoots and roots [79].

Statistical analysis of data

Shapiro–Wilk normality [80] and Levene homogeneity [81] tests were performed. Subsequently, an analysis of variance was performed (p < 0.05); when significant, a Tukey mean comparison test was performed (p < 0.05). Hierarchical cluster analysis was performed using the Euclidean distance coefficient, the group connection by single linkage, and principal component analysis (PCA) by covariance matrix. All data analysis procedures were performed using Python programming language (version 3.9.7; Python Software Foundation).