Assessing the effects of in vitro imposed water stress on pineapple growth in relation to biochemical stress indicators using polynomial regression analysis

Knowing the mechanisms that operate under water stress in commercial crops, particularly those that can affect productivity, such as phenolic or cell wall metabolism, is becoming increasingly important in a scenario of global climate change. However, our understanding of how to analyse statistically the relationships between these commonly used biochemical markers of water stress and growth in crops like pineapple, needs to be improved. In the present work, we have addressed the question of whether polynomial regression analysis can be used to describe the influence of selected plant metabolites (chlorophylls, carotenoids, phenolics and aldehydes) on shoot biomass, in response to a mannitol-induced water stress in temporary immersion bioreactors (TIBs). Polynomial regression analysis has been applied to investigate plant stress responses in many species but is very seldom used in in vitro screening studies. Here, the relationship between biochemical indicators ( x ; independent variable) and shoot growth ( y ; dependent variable) has been characterised, with y modelled as an n th degree polynomial in x . This statistical approach accommodated for the non-linear (curvilinear) relationships between variables, and the results showed that shoot biomass was negatively, and significantly correlated with soluble phenolics, cell wall-linked phenolics and other aldehydes (characterised by “ High ” R 2 values).


Introduction
Statistical tools can outline trends in biological data sets.Regression analysis is used as a predictive tool to investigate the relationship between a dependent and an independent variable, with linear regressions being the most common type of analysis.However, when the collected data are non-linear (or curvilinear), polynomial regressions are performed.This is often the case for many biological processes in plants (see references below).For polynomial regressions, the relationship between the independent variable x and the dependent variable y is modelled as an n th degree polynomial in x.In order to validate the strength of the model, the coefficient of determination is calculated.The coefficient of determination is the square of the correlation coefficient, also known as "R".The R 2 values range from 0 (indicating a poor fit) to 1 (indicative of the best fit, or relationship, between the two factors) (Ivanov, 1989).
Polynomial regression models have a wide range of applications and have been used in engineering, computer science, human resource management, urban planning, health sciences, and many other fields (Ivanov, 1989).In the context of plant sciences, polynomial regression analysis has been extensively applied in studies investigating the response of plants to varied stress conditions.Fernández et al. (2002) used polynomial adjustment of log-transformed data to show that water stress altered the developmental response of two desert grass species, with leaf area ratio being the most prominent factor affected.Similarly, Vieira et al. (2019) used polynomial regression analysis in modelling the gas exchange behaviour of melon exposed to water stress.Wijewardana et al. (2019) showed that polynomial regressions could be employed to model the germination of soybean seeds exposed to water stress.A novel application was described by Runeckles (1982), where polynomial regressions were applied to define the relative death rate of plants exposed to stresses.Polynomial regressions were also used to investigate the effect of sub-acute high temperature on ovule and pollen development in tomato (Peet et al., 1997), the effect of high temperature on photosynthetic processes in a forest ecosystem (Peet et al., 1997;Hüve et al., 2019), or to model the effect of excess ammonium fertiliser in tomato (Barker, 1999).However, to the best of our knowledge, there are no published reports on the use of polynomial regression analysis to identify suitable biochemical indicators of stress tolerance in in vitro screen systems such as Temporary Immersion Bioreactors (TIBs).Hence, the current study reports on the characterisation of pineapple plants responses to mannitol (to mimic water stress) in TIBs, in relation to established stress biomarkers, such as the levels of chlorophyll a and b, carotenoids, phenolics (soluble, cell walllinked and exuded into the medium) and aldehydes, and the fresh mass of the shoots produced.The empirical data used for the analyses emanates from a previously published study by our group (Gómez et al., 2017).

Materials and Methods
Plant material and in vitro culture conditions Pineapple crowns were collected from plants grown in the field (cv.'MD2') as per Daquinta and Benegas (1997).Upon receipt in the laboratory, the crown leaves were removed, and the stem was washed with detergent and tap water to remove soil and other particles.The crown stem was then decontaminated by immersion in 1% (w/v) calcium hypochlorite for 10 min.Axillary buds, including a portion of basal tissue, were excised and placed onto initiation medium.Explants were cultured in 300 ml glass containers containing 5 ml of liquid culture medium per explant.The culture medium was comprised of MS (Murashige and Skoog, 1962) salts, 100 mg l -1 myo-inositol, 0.1 mg l -1 thiamine-HCl, 30 g l -1 sucrose, 4.4 μM 6-benzyladenine (BA), and 5.3 μM naphthaleneacetic acid (NAA).After 45 d of growth, shoots were subcultured to promote multiplication of explants, in the same medium described above, except that it contained 9.3 μM BA and 1.6 μM NAA.Shoots were multiplied for six months, with plants being transferred to fresh medium every 45 d.Once a sufficient number of shoots were obtained, they were placed in TIBs according to Escalona et al. (1999), supplemented with 3.0 μM paclobutrazol.The TIBs were programmed to allow for immersion of plantlets into the culture medium for 2 min every 3 h for 30 d.Each TIB contained 200 ml of liquid medium with five explants per bioreactor.

Measurement of stress indicators
Following 30 days of culture, shoot cluster fresh weight, and the levels of different biochemical stress markers were determined in the plant material.Total chlorophylls and carotenoids were extracted from plants with 5 ml acetone (80%, v/v).The samples were then centrifuged (12,000 rpm at 4 °C for 15 min).The absorbance of the supernatant was measured at 646.6 and 663.6 nm, and chlorophyll a and b contents were calculated as described in Porra (2002), whereas total carotenoid concentrations were determined from the absorbance of the samples at 470 nm, according to the method of Lichtenthaler (1987).A colourimetric method based on the Folin Ciocalteu reagent was used for extraction and quantification of phenolics (Gurr et al., 1992), and the results were expressed as mg chlorogenic acid equivalents per g fresh weight.Malondialdehyde (MDA) and other aldehydes were quantified based on the reaction with thiobarbituric acid (Heath and Packer, 1968).Phenolics excreted into the medium were also determined, using a modification of the Hoagland (1990) procedure: 0.5 ml of culture medium was mixed with 4.5 ml of distilled water and 0.5 ml of Folin Ciocalteau reagent (50% v/v).The mixture was stirred, the reaction was allowed to proceed for 5 min and 1 ml of a saturated sodium carbonate solution was added.The mixture was stirred again, left for 60 min, and the optical density was measured at 725 nm.The concentration of phenolics was determined using a calibration curve with chlorogenic acid as the standard.

Data analysis
Polynomial regression analyses were performed using Microsoft Excel.Each polynomial regression involved 15 (x, y) pairs (i.e. 5 mannitol concentrations; 3 TIBs per treatment).Determination coefficients (R 2 ) obtained for y = ax 2 + bx + c used the shoot fresh weight as the dependent variable (y), whereas biochemical indicators represented the independent variables (x).The R 2 values were classified as ¨Low¨ from 0.2184 to 0.3870; ¨Medium¨ from 0.3870 to 0.5556; and ¨High¨ from 0.5556 to 0.7243.The following formula was used to define the three R 2 categories: (Max R 2 value observed -Min R 2 value observed) / 3.

Results and Discussion
The current study investigated the application of polynomial regression analysis as a tool to define the response of pineapple plants to osmotic stress, applied in TIBs.The R 2 value represents a numerical statistical index that describes the goodness of fit of a regression model.In the present work, R 2 was used to indicate what fraction of y variations occurred as a consequence of x variations (Ivanov, 1989).Figure 1 shows the analysis and determination coefficient (R 2 ) values corresponding to the independent variables chlorophyll a (panel A), chlorophyll b (B), carotenoids (C), soluble phenolics (D), and Figure 2 shows cell wall-linked phenolics (A), soluble phenolics in the culture medium (B), MDA (C) and other aldehydes (D).The results indicated that the soluble and cell wall-linked phenolics, and other aldehydes affected the changes in shoot biomass observed in response to osmotic stress (Figure 1D, Figure 2A, D).In this regard, 72.11% of the variations of pineapple shoot cluster fresh weight under mannitol stress correlated with changes in soluble phenolic levels (R 2 = 0.7211; Figure 1D).The determination coefficient for this relationship was classified as "High".The results showed that as the soluble phenolic content of shoots increased, shoot weight declined, in agreement with the trend detected in the empirical data.A similar trend was observed for cell wall-linked phenolics and other aldehydes, i.e. as the levels of these two metabolites increased, shoot mass was adversely affected.These two factors also generated "High" R 2 values: 68.17% of shoot cluster weight variations were explained by modifications of cell wall-linked phenolic contents (Figure 2A), and 72.43% by increases in the levels of other aldehydes (Figure 2D).
"Medium" R 2 were recorded for carotenoid levels (R 2 = 50.95%,Figure 1C) and MDA contents (R 2 = 51.61%, Figure 2C).Changes in levels of chlorophylls a and b (Figure 1A, B), and soluble phenolics excreted into the culture medium (Figure 2B) did not appear to (mathematically) influence biomass of pineapple shoots in TIBs under osmotic stress, as the corresponding R 2 values were classified as "Low".
From our previous work (Gómez et al., 2017), it was established that exposure of pineapple shoots to mannitol above 50 mM for 30 days reduced the fresh weight of shoots with respect to the non-stressed controls; for example, the highest mannitol concentration tested (200 mM) decreased the multiplication rate by 59.7% and cluster fresh weight by 59.8%.From that study, several significant differences were found between the control and mannitol treatments using basic statistical analyses, namely one-way ANOVA and determination of 'overall coefficients of variation' (OCVs).
Figure 2. Determination coefficients (R 2 ) obtained in polynomial regressions analyses (Order 2: y = ax 2 + bx + c; Microsoft Excel).The fresh weight of shoot clusters was the dependent variable (y), and cell walllinked phenolics (A), soluble phenolics in the culture medium (B), MDA (C) and other aldehydes (D), the independent variables.R 2 were classified as "Low" from 0.2184 to 0.3870; "Medium" from 0.3870 to 0.5556; and "High" from 0.5556 to 0.7243.
Applying the more precise and robust polynomial regression analysis, those data have been reanalysed, which allowed refining the conclusions of the previous study.To give just some examples, both chlorophyll b and shoot soluble phenolics contents increased in response to the osmotic stress applied; comparing the controls with the 200 mM mannitol treatment, this increase amounted to 1.5-fold for chlorophyll b contents (from 36.93 to 54.29 μg g -1 fresh weight), and to 2.1-fold for soluble phenolics (from 430.15 to 904.03 μg g -1 fresh weight).In both cases, the increments were statistically significant (one-way ANOVA, Tukey, p > 0.05), with 'medium' OCVs (Gómez et al., 2017).However, polynomial regression analysis clearly distinguished the two putative stress indicators, ruling out the use of chlorophyll b (with a 'Low' R 2 value) as a reliable biochemical marker of osmotic stress in this specific experimental system, as compared to soluble phenolics, which showed a 'High' R 2 value.Similarly, the significant increase in cell wall-linked phenolics and 'other aldehydes' in response to mannitol-induced osmotic stress, showing 'low' OCVs (Gómez et al., 2017), were nevertheless strongly correlated ('High' determination coefficients, R 2 ) with the variations of pineapple shoot cluster fresh weight.
The impacts of climate change are already causing detrimental effects on agricultural productivity as well as in natural ecosystems.Warmer temperatures accompanied by longer dry spells and changing rainfall patterns affect all phases of plant development.Access to sufficient amounts of water (of good quality) at the appropriate developmental stage represents one of the most critical factors determining plant growth (Hernández et al., 2015;Naik and Al-Khayri, 2016).
From our previous work (Gómez et al., 2017) and the present analysis of pineapple plants micropropagated in TIBs, the levels of soluble phenolics and other aldehydes can be defined as the most precise biomarkers of mannitol-induced osmotic stress; these two groups of compounds are known to play a role in plant responses to stress conditions.These results are in agreement with other published reports of studies conducted in different culture systems and with different plant species (Winkel-Shirley, 2002;Haghighi et al., 2012;Rivelli et al., 2012;Selmar and Kleinwächter, 2013;Boestfleisch et al., 2014;Hernández et al., 2015;Boestfleisch and Papenbrock, 2017).This observation provides evidence indicating that TIBs, in combination with regression analyses of biochemical stress indicators, are suitable systems to investigate plant responses to stress conditions.

Conclusions
The current study supports the use of polynomial regression analysis for comparing the relative importance of biochemical indicators of stress tolerance in in vitro screening studies.We recommend that this statistical approach be applied to other species and stressors to validate its utility for screening varieties for stress tolerance in vitro.