Investigation of Defensive Role of Silicon during Drought Stress Induced by Irrigation Capacity in Sugarcane: Physiological and Biochemical Characteristics

Abstract

Water stress may become one of the most inevitable factors in years to come regulating crop growth, development, and productivity globally. The application of eco-friendly stress mitigator may sustain physiological fitness of the plants as uptake and accumulation of silicon (Si) found to alleviate stress with plant performance. Our study focused on the mitigative effects of Si using calcium metasilicate (wollastonite powder, CaO·SiO₂) in sugarcane (Saccharum officinarum L.) prior to the exposure of water stress created by the retention of 50–45% soil moisture capacity. Si (0, 50, 100, and 500 ppm L^–1) was supplied through soil irrigation in S. officinarum L. grown at about half of the soil moisture capacity for a period of 90 days. Water stress impaired plant growth, biomass, leaf relative water content, SPAD value, photosynthetic pigments capacity, and photochemical efficiency (F_v/F_m) of photosystem II. The levels of antioxidative defense-induced enzymes, viz., catalase, ascorbate peroxidase, and superoxide dismutase, enhanced. Silicon-treated plants expressed positive correlation with their performance index. A quadratic nonlinear relation observed between loss and gain (%) in physiological and biochemical parameters during water stress upon Si application. Si was found to be effective in restoring the water stress injuries integrated to facilitate the operation of antioxidant defense machinery in S. officinarum L. with improved plant performance index and photosynthetic carbon assimilation.

1. Introduction

The water stress may be recorded as one of the major adverse variables affecting plant performance. It causes loss in crop productivity and quality both. The stability in crop growth and production during stress conditions rated a big challenge for plant biologists.¹⁻³ The mineral nutrients conferred a crucial role in maintaining desirable growth and also stress tolerance.⁴

Water stress impairs physiological and biochemical mechanisms such as photosynthetic capacity, photochemical efficiency of photosystem II, chlorophyll biosynthesis, nutrient uptake, translocation of ions, and respiration.^3,5−8 The stressed plants provoke anatomical and ultracellular injuries of subcellular organelles, viz., chloroplasts and mitochondria.^9,10 Water stress induces biosynthesis of reactive oxygen species (ROS) in plants to cause oxidative damage which leads to enzyme inactivation, loss of protein, and ionic imbalance^6,11 because plants possess an efficient antioxidant defense system.¹² Photosynthetic leaf gas exchange and growth characteristics are regulated by environmental variables. Water stress is one of the biggest problems which inhibit plant development and crop productivity.^7,13−15 The growth phases of plants may also get affected throughout by atmospheric air temperature, irradiance, and water supply,^8,16 while CO₂ enrichment in ambient air may be beneficial for biomass accumulation in sugarcane (Saccharum officinarum L).¹⁶⁻¹⁸

Silicon is considered as a bioactive beneficial element in providing benefits for plant development during stress.^9,10,19,20 Different forms of silicon could be used as biotic and abiotic stress mitigators^8,13,21 along with its beneficial effects on plant growth and productivity during stress.^8,10,22 It has also been noted that Si may get accumulated in the walls of the epidermal and vascular tissues of monocots^22,23 to enhance water uptake transport^13,24,25 along with antioxidant enzymes²⁶ and photosynthetic capacity.^14,19,27

S. officinarum L. is a major agricultural cash crop for sugar and bioethanol production worldwide. It requires mineral nutrients adequately to achieve the maximum crop production.^3,8,28 It is a C₄ crop based on carbon metabolism with various growth stages, viz., sprouting, tillering, grand growth period, and maturity, which may experience various levels of water stress.^19,29 These days, S. officinarum L. acquired attention to be used upland for expansion of its cultivation where inadequate soil moisture prevails as unfavorable atmospheric variables for its production.^8,17,30

Keeping such priorities in view, our study was conducted to explore the protective role of Si during water stress with improved photosynthetic efficiency, antioxidative machinery, and biomass and crop productivity.

2. Results

2.1. Silicon Alleviates the Effects of Water Stress on Photosynthetic Responses

The exposure of S. officinarum L. plants to water stress significantly increased the percent gain in photosynthesis (P_N), stomatal conductance (g_s), and transpiration rate (E), as shown in Figure 1A–I.

Figure 1.

Effect of water stress and calcium metasilicate (Si) on (A–C) photosynthesis (P_N), (D–F) stomatal conductance (g_s), and (G–I) transpiration rate (E) of Saccharum officinarum L. at specific time durations (30, 60, and 90 days). Average (%) mean values are each point (n = 3). Blue ovals denote the actual values, and red lines show the predicted values. S = standard error, r = correlation coefficient, and DASA = days after silicon application.

The water-stressed plants increased P_N (28–31%), g_s (31–41%), and E (50–54%). The water stress (50–45% SMC) with exogenous soil irrigation of Si (50, 100, and 500 ppm) significantly reduced percent loss in P_N by 29–25, 26–20, and 20–17%, g_s by 38–28, 34–24, and 28–19%, and E by 52–49, 51–48, and 47–43%, respectively, in comparison with control plants (Figure 1). Application of Si to water-stressed plants showed remarkably favored photosynthetic responses, viz., P_N, g_s, and E, in case Si was applied (500 ppm) for 30, 60, and 90 days.

2.2. Silicon Mitigates the Effects of Water Stress on Chl a Fluorescence, Chlorophyll Content, and Chlorophyll Index

Dark-adapted chl a fluorescence (F_v/F_m) of photosystem II decreased (11–∼14%) at 30, 60, and 90 days under water-stress conditions. The maximum loss (∼14%) was found in 90 days after drought, while minimum loss (13–10%) was observed in stressed plants with Si application (50, 100, and 500 ppm) at 30, 60, and 90 days after stress (Figure 2A–C). The Chl a + b and chlorophyll index (SPAD units) significantly reduced in water-stressed plants with increase in these parameters from 6 to 26 and 9–18% compared to the control. The chlorophyll content and SPAD values noted slightly enhanced, after Si application. The optimal enhancement was recorded in 500 ppm of Si application (Figure 2D–I). Silicon mitigated the total chlorophyll and SPAD units by 25–3 and 18–7%, respectively, in stressed plants.

Figure 2.

Effect of water stress and calcium metasilicate (Si) on Chl a fluorescence (F_v/F_m, A–C), SPAD units (D–F), and chlorophyll content (Chl a + b, G–I) of sugarcane plants at specific time durations (30, 60, and 90 days). Average (%) mean values are each point (n = 3). Blue ovals denote the actual values, and red lines show the predicted values. S = standard error, r = correlation coefficient, and DASA = days after silicon application.

2.3. Si Improves Leaf Area Expansion, Relative Leaf Water Content, and Biomass during Stress

Silicon application triggered leaf area expansion (LAE) in S. officinarum L. under water stress as about 51% loss was found in stressed plants at 90 days after treatment. Soil irrigation of Si mitigated 46–15% reduction in LAE in stressed plants (Figure 3A–C) with enhancement in relative leaf water content (RLWC) ca. 29–34% during stress (Figure 3D–F). The reduction in RLWC of stressed S. officinarum L. was mitigated by soil irrigation of Si (50, 100, and 500 ppm), resulting in the reduction of 34–24% at 30, 60, and 90 days after water stress, respectively. The S. officinarum L. showed a drastic gain in plant biomass (44–53%) subjected to water stress for 30, 60, and 90 days (Figure 3G–I). Gradually, Si application mitigated the loss in biomass significantly.

Figure 3.

Effect of water stress and calcium metasilicate (Si) on LAE (A–C), relative water content (D–F), and biomass (G–I) of sugarcane plants at specific time durations (30, 60, and 90 days). Average (%) mean values are each point (n = 3). Blue ovals denote the actual values, and red lines show the predicted values. S = standard error, r = correlation coefficient, and DASA = days after silicon application.

2.4. Effects of Limited Irrigation and Si on Antioxidative Enzyme Activities

The antioxidative enzyme activities such as CAT, SOD, and APx enhanced in response to stress conditions (Figure 4). The water stress induced the activities of CAT (102–132%), SOD (34–98%), and APx (135–263%). The application of Si (50, 100, and 500 ppm) could express a quite different pattern for improving the activities of various antioxidative enzymes as SOD activity enhanced from 26–98% with Si levels (Figure 4D–F). The enhancement in CAT activity (67–131%) was found similar to that in SOD influenced by Si (Figure 4A–C). Ascorbate peroxidase (APx) activity was found positively correlated by Si application with its acquired higher values about 133–259% (Figure 4G–I).

Figure 4.

Effect of water stress and calcium metasilicate (Si) on antioxidant enzyme activities such as catalase (CAT, A–C), SOD (D–F), and APx (G–I) of sugarcane plants at specific time durations (30, 60, and 90 days). Average (%) mean values are each point (n = 3). Blue ovals denote the actual values, and red lines show the predicted values. S = standard error, r = correlation coefficient, and DASA = days after silicon application.

The coefficients of determination (R²) for each set of data, that is, P_N, g_s, E, F_v/F_m, relative water content (RWC), Chl a + b, LAE, SPAD, biomass, and antioxidant enzymes such as SOD, CAT, and APx with the exogenous amendment of Si with soil moisture capacity (moderate, 50–45%), were found in the range of 0.939–0.999 (Table 1).

Table 1. Regression Analysis of Growth, Photosynthetic and Antioxidant Enzyme Activities during Soil Moisture Capacity, and Exogenous Si Application in Sugarcane Plants at Specific Time Durations.

parameters	stress (days)	model constants	R(2)
PN	30	Penz_r_si = 7.529Si2 + 6.060Si + 3.114	0.992
	60	Penz_r_si = 1.544Si2 + 1.006Si + 3.159	0.999
	90	Penz_r_si = 1.018Si2 + 1.238Si + 3.134	0.998
gs	30	Penz_r_si = 1.270Si2 + 9.160Si + 4.195	0.996
	60	Penz_r_si = 1.024Si2 + 7.544Si + 3.197	0.999
	90	Penz_r_si = 1.251Si2 + 8.337Si + 3.211	0.997
E	30	Penz_r_si = 2.728Si2 + 2.235Si + 5.059	0.998
	60	Penz_r_si = 4.445Si2 + 3.520Si + 5.396	0.999
	90	Penz_r_si = 4.226Si2 + 3.875Si + 5.227	0.999
Fv/Fm	30	Penz_r_si = 3.038Si2 + 1.988Si + 1.234	0.991
	60	Penz_r_si = 1.667Si2 + 1.140Si + 1.151	0.990
	90	Penz_r_si = 2.646Si2 + 1.772Si + 1.388	0.978
RWC	30	Penz_r_si = 3.241Si2 + 2.630Si + 2.962	0.992
	60	Penz_r_si = 5.314Si2 + 3.456Si + 3.245	0.980
	90	Penz_r_si = 5.983Si2 + 3.923Si + 3.422	0.999
Chl a + b	30	Penz_r_si = 1.926Si2 + 1.747Si + 6.688	0.998
	60	Penz_r_si = 3.760Si2 + 2.767Si + 1.593	0.998
	90	Penz_r_si = 5.831Si2 + 3.857Si + 2.619	0.989
LAE	30	Penz_r_si = 1.000Si2 + 8.218Si + 3.171	0.987
	60	Penz_r_si = 2.207Si2 + 1.447Si + 3.803	0.999
	90	Penz_r_si = 1.760Si2 + 1.182Si + 5.221	0.999
SPAD	30	Penz_r_si = 1.185Si2 + 9.757Si + 9.544	0.998
	60	Penz_r_si = 1.072Si2 + 9.093Si + 1.231	0.978
	90	Penz_r_si = 1.088Si2 + 1.086Si + 1.818	0.999
biomass	30	Penz_r_si = 9.861Si2 + 2.910Si + 4.465	0.998
	60	Penz_r_si = 2.146Si2 + 1.351Si + 5.196	0.939
	90	Penz_r_si = 9.354Si2 + 1.881Si + 5.364	0.999
CAT	30	Penz_r_si = 2.969Si2 + 2.285Si + 1.074	0.974
	60	Penz_r_si = 1.098Si2 + 1.365Si + 1.203	0.993
	90	Penz_r_si = 4.610Si2 + 3.124Si + 1.386	0.952
APx	30	Penz_r_si = 9.726Si2 + 2.296Si + 3.513	0.946
	60	Penz_r_si = 8.068Si2 + 8.195Si + 4.757	0.991
	90	Penz_r_si = 2.320Si2 + 1.921Si + 1.025	0.978
SOD	30	Penz_r_si = 6.125Si2 + 4.500Si + 1.441	0.971
	60	Penz_r_si = 1.884Si2 + 4.395Si + 1.731	0.999
	90	Penz_r_si = 9.805Si2 + 1.861Si + 2.662	0.999

Our derived model explains the loss or gain of physiological and biochemical activities in a perfect way. The hypothesis also explains well the rate of change in either loss or gain (%) of physio-biochemical activities upon subjecting the S. officinarum L. to soil moisture capacity with Si application.

3. Discussion

Water stress is a serious problem for impairment of morphological and physiological characteristics in plants.^3,13,31,32 The low soil moisture in the soil elicits a range of responses that permit plants to avoid loss of water through physiological, biochemical, and cellular processes.³³ The leaf water status depends upon the water absorption, transport, and its loss through transpiration.^3,34,35 Morphological and anatomical changes are the initial effects associated with water stress, while photosynthetic efficiency observed was majorly affected.^1,9,14,19 Similar findings were noted in Saccharum spp.,^8,10,36,37Eucalyptus camaldulensis,³⁸Triticum boeoticum,³⁹Oryza sativa,⁴⁰ and Nicotiana tabacum.⁴¹ Photosynthetic efficiency of the plants was detected to be more sensitive under water-stress conditions.³ However, an exogenous application of Si was found to sustain the photosynthetic capacity in several plants during stress,^{1,3,13,30,42,43} with favorable regulation of stomatal transpiration.^10,43

Si application enhances endogenous growth factors, resulting in the development of denser roots (root diameter, area, volume, and length) and the shoot biomass of stressed plants. Si also stimulated an increase in cell wall extensibility in the growth region,^1,2,7,44,45 along with root/shoot ratio and water uptake ability.^34,46 Silicon played an essential role in balancing the uptake, transport, and distribution of minerals to the aerial parts of plants during stress^8,43 as it expanded the accretion of nutrients, viz., Mg, N, K, P, Ca, Fe, Zn, Mn, and Cu, in plants during stress conditions.⁴⁷⁻⁵⁵

Chl a fluorescence (F_v/F_m) is generally accepted as a basic approach to examine the structure and role of the photosynthetic apparatus.⁵⁶ Hence, assessment of the F_v/F_m value was considered significant to observe the quality and integrity of the photosynthetic machinery of chloroplasts for photosynthesis.¹³ In this study, F_v/F_m values were found to be influenced by the duration and severity of stress as seen in O. sativa,⁵⁷Citrullus lanatus,⁵⁸ and Triticum aestivum.⁵⁹ The growth and biomass of sugarcane found markedly decreased, in case subjected to water stress,^60,61 almost similar to our findings. The high concentration of Si in plant leaves enhances the biosynthesis of chlorophyll pigments and decreases its decomposition, initiated due to water stress. The increase in pigment levels conferred improved photosynthetic responses.^3,8−10

Several studies demonstrated the involvement of Si to mitigate biotic and abiotic stresses^1,13,62 in growing plant cultivars under unfavorable atmospheric circumstances.^2,8,63,64 Similarly, our findings also favor the protective role of Si in sugarcane plants in case grown under water stress. The application of Si reduced the stress-induced injuries and also enhanced plants’ immunity for stress resistance by balancing sugarcane plant development. The increase in biomass accumulation and growth capacity is endorsed to the balanced carbon assimilation due to enhanced leaf photosynthetic responses of the stressed plants.^2,8,40,63,65 In O. sativa plants, Si extended protection from water stress by controlling plant water uptake, photosynthesis, and uptake of essential mineral nutrients.^40,64 The protective role of Si on plant leaf transpiration found to be correlated with the varieties of plants and atmospheric variables,³⁵ in few plants, the transpiration rate enhanced,^10,19,40 while in others, it declined⁶⁶ and also with no change in transpiration.⁶⁷ Such variations suggest that there are various adaptation strategies and plant varieties because they balance water level absorption and the water loss through the leaf surface.⁶⁸

Melatonin, selenium (Se), and nitric oxide (NO) are considered to be involved in various stress responses such as biotic and abiotic stresses.^7,69−74 However, applying melatonin, Se, and NO as foliar spray and soil irrigation reduced the severity of stress-induced growth inhibition. It enhanced the maize plant’s resistance to water deficiency to promote the plant’s growth and development. The enhancement in biomass accumulation and growth traits is endorsed to the improved carbon assimilation due to increased photosynthetic responses in treated plants.^74,75 The application of melatonin and Se mitigated water deficiency and significantly affected plant growth in kiwifruit, watermelon, pea, tomato, potato, and olive plants.^{69,72,73,76−78} Exogenous application of melatonin, Se, and NO preserves photosynthetic pigments with improved leaf gas exchange and delayed senescence of leaves during stress conditions.^{7,15,71,74,79} The optimum concentration of melatonin and Se improved the stomatal dynamics by enabling plants to reopen their stomata subjected to water stress in wheat, cucumber, malus, black gram, and maize, suggesting a significant role of melatonin and Se in stomatal regulation.^7,15,74,76 Melatonin and Se treatment also resulted in an increased transpiration rate, possibly driven by the increased stomatal conductance to maintain a steady state of the photosynthetic CO₂ assimilation rate during stress.^7,74,80

The pronounced loss in chlorophyll content may be due to either reduced biosynthesis of the chlorophyll or its enhanced degradation.^3,7,81 Water stress results in acute reduction in LAE, total chlorophyll content, and photosynthesis linked with plant development.^8,13,82 An exogenous application of Si improves chlorophylls and photosynthetic efficiency in the plants during water stress.^2,20,24,63 Water-deficit resistance is frequently associated with the balance of LRWC in sugarcane plants^31,83 to follow the enzymatic activities of tolerance species.^8,84

The increase in antioxidative enzymes in response to drought has largely been used as a sign of stress resistance.^5,8,17 An enhanced antioxidative enzyme activity has been found in response to water stress in our case. The severe water and oxidative stress are often interconnected with cellular mechanisms, that is, antioxidative enzyme activities and the accumulation of compatible solutes.^20,83,85 However, these processes are strongly linked with the duration and severity of stress and plant species.⁸⁶ Thus, our priority was to understand the variations of biochemical activities that conferred resistance to sugarcane cultivars during progressive water-deficit stress. The ROS production and accumulation in the plants result in a serious loss in the ultrastructure of cellular organelles, their functions, and mechanisms in relation to the antioxidative system to balance homeostasis through enzymatic and nonenzymatic strategies of the plants to recover the injury caused by ROS.^63,87 The function of the antioxidative defense machinery is closely associated with scavenging excess ROS production in the cell when redox state gets disrupted by stress conditions.^13,19,88 ROS are central to cell signaling and influence a broad range of critical and cascading processes, including the expression of genes, growth, development, and programmed cell death during stress.^2,89,90

Silicon application in stressed plants may increase CAT, APx, and SOD enzyme activities.^8,63 Hence, Si positively regulates antioxidative defense systems in plants²⁶ along with detoxification of ROS by antioxidative enzymatic systems⁹⁰ to mitigate oxidative damage in plants under stress.^2,8,87 The antioxidative enzyme activities demonstrated by increased CAT, APx, and SOD seemed to be more effective to balance photosynthetic responses for stress resistance in plants.

In conclusion, our observations revealed that the exogenous application of Si mitigated drought stress in sugarcane plants with improved plant growth, performance, biomass, juice quality, and plant productivity which may sustain agroeconomy under climatic variables.

4. Experimental Section

4.1. Plants and Growth Conditions

Sugarcane stems (S. officinarum L. cultivar GT 44) were cut into small pieces, that is, single bud sets and then treated with fungicide (carbendazim, 10% for 10 min) and planted in an experimental field for germination. Fifty day old plants were transferred to plastic pots (1 plants pot^–1) filled with fertile soil (5 kg) and kept in a greenhouse under natural atmospheric variables. The basal dose of fertilizer in soil as nitrogen, potassium, and phosphorous (N/P/K, 70, 50, and 100 mg kg^–1 soil) was applied in each pot. The plants were moistened once a day manually up to field capacity during the initial growth stage (upto 90 days) and then exposed to water stress by withdrawing irrigation after exogenous Si application. The control (C) plants irrigated upto 90–85% soil moisture capacity without Si. Water stress (50–45%) was maintained at almost half of the soil moisture level. The concentrations of Si soil irrigation were chosen as 50, 100, and 500 ppm Si L^–1.

The soil moisture level was determined using a moisture meter (Top Instrument Co. Ltd., Zhejiang, China). The experimental soil was sandy clay. The soil of the experiment was collected from the experimental station and sieved to homogenize the soil and eliminate unnecessary materials. The soil profile was assessed before transplanting with pH (5.89), organic carbon (0.69%), total N (0.10%), available P (9.11 mg kg^–1), S (11.87 mg kg^–1), Si (85.3 mg kg^–1), Cu (0.80 mg kg^–1), Fe (10.9 mg kg^–1), Zn (1.23 mg kg^–1), Mn (17.1 mg kg^–1), B (0.11 mg kg^–1), exchangeable K (2.72 cmol(+) kg^–1), Ca (3.6 cmol(+) kg^–1), Mg (1.4 cmol(+) kg^–1), Na (0.083 cmol(+) kg^–1), and Al (0.004 cmol(+) kg^–1). The plants were selected uniformly for each experiment. The Si concentrations such as 0, 50, 100, and 500 ppm Si L^–1 were applied as soil irrigation in water-stressed sugarcane plants. Calcium metasilicate (Wollastonite powder, CaO·SiO₂) was chosen as a source of silicon. Silicon was applied at 40 days after potting and after one month up to three months (90 days) and then observations were taken after 30, 60, and 90 days.

4.2. Leaf Area Expansion and Growth Parameters

The LAE was observed using a leaf area meter (CI-203 Area Meter, CID, Inc., USA) after 30, 60, and 90 days after Si treatment. Harvested plants cleaned with ground tap water and oven-dried (65 ± 2 °C) in paper envelopes to determine dry mass weight.

4.3. Leaf Relative Water Content, Chlorophyll Content, and SPAD Unit

Leaf discs (diameter 2.5 cm) were sampled from the photosynthetically mature leaf of sugarcane plants. The samples were quickly packed in airtight polybags. The fresh weight of leaf discs assessed and then samples were separately submerged in distilled water (DW, 6 h) under low light intensity to saturate the water uptake process. The surplus water was gently removed from the leaf discs using tissue paper before observing the turgid weight. The dry mass of these leaf discs determined after keeping them at 65 ± 2 °C (72 h).⁹¹ The quantification of the chlorophyll content made as per the procedure of ref 92⁹² using dimethyl sulphoxide (DMSO). The absorbance of pigment extract was recorded at 663 and 646 nm using a spectrophotometer, DMSO was used as a blank followed by the assessment of chlorophyll.⁹³ The SPAD value was monitored using a chlorophyll meter (SPAD-502, Konica Minolta Inc., Japan).

4.4. Photosynthetic Efficiency and Chlorophyll Fluorescence

Photosynthetic responses, that is, photosynthesis (P_N), stomatal conductance (g_s), transpiration rate (E), and Chl a fluorescence (F_v/F_m), were observed after a specific time duration of soil irrigation of Si subjected to water stress using an Li-6800 portable photosynthesis system with an integrated modulated chlorophyll fluorometer (Li-COR Biosciences, Lincoln, NE, US). A dark-adapted (30 min) leaf was used for Chl a fluorescence. All measurements were made from 09:30 to 11:30 h using photosynthetically mature leaves without changing the leaf angle. Photosynthetic photon flux density, ambient air temperature, and CO₂ level were fixed (1200 μmol m^–2 s^–1, 25 °C, and 400 ppm, respectively) inside the leaf chamber. The middle portion of the leaf was chosen for all measurements to obtain optimal photosynthetic efficiency. Leaf blades (without midrib) were quickly frozen in liquid N₂ and stored in −80 °C for quantification of enzyme activities.

4.5. Estimation of Antioxidant Enzymes

The plant leaf (each sample 0.5 g) was homogenized in phosphate buffer solution (0.1 M, pH 7.5) having EDTA (0.5 mM) and centrifuged (12,000g, 10 min, 4 °C), and the supernatant was chosen for the quantification of catalase (CAT), superoxide dismutase (SOD), and APx enzyme activities. CAT activity was assayed by the procedure of ref 94⁹⁴ with slight changes spectrophotometrically at 240 nm using enzyme unit (EU) mg^–1 protein. SOD activity was examined by the method of ref 95⁹⁵ spectrophotometrically (560 nm). One unit of SOD is the volume of protein regulating 50% photoreduction of NBT. The SOD activity is expressed as EU min^–1 protein.

The quantification of APx activity in plant leaf samples was performed individually by grinding them in a homogenizing medium containing phosphate buffer (0.1 M, pH 7.5), 0.5 mM EDTA, and 2 mM ascorbic acid. The APx activity was quantified as per the procedure of ref 96⁹⁶ with minor changes spectrophotometrically (290 nm). One unit of APx is the volume of protein used to decompose 1 mM of substrate min^–1 (25 °C).

4.6. Hypothesis for Model Development

The rate of reduction of associated physiological and enzymatic activities with respect to silicon application under water-deficit conditions is directly proportional to the appropriated Si concentration.

Mathematically, it can be expressed as below

1

where P_{enz_r} = reduction in associated physiological and enzymatic responses rate due to Si application, (Si + λ) = appropriate Si concentration, and λ = constant for the appropriation of the physiological and enzymatic response rate.

Equation 1 can be written in the form of the following governing equation by introducing a proportionality constant (μ).

2

4.7. Solution

Separating variables and integrating eq 2, one will arrive at

3

4

5

where I_c = integration constant which can be determined by substituting the initial condition (Si = 0, P_{enz_r} = P_{enz_r_max})

6

7

Substituting the value of I_c in eq 5, one will arrive at the following general solution

8

which can be finally written as below

9

where ξ = μ/2.

Author Contributions

K.K.V. and X.-P.S. equally contributed to this work. K.K.V.: conceptualization, methodology, investigation, data processing, and writing—original draft. X.-P.S.: conceptualization, methodology, investigation, writing—review and editing, project administration, and funding acquisition. D.-D.T.: resources and software and data processing. M.S.: writing—review and editing. C.L.V.: statistical and hypothesis analysis and data processing. V.D.R.: software and writing—review and editing. R.K.S., A.S., P.S., and M.K.M.: formal analysis and data processing. Y.-R. L: conceptualization, methodology, investigation, writing—review and editing, project administration, and funding acquisition. All authors read and approved the manuscript for publication.

The authors declare no competing financial interest.