Introduction

Sesame (Sesamum indicum L.) is one the most important oil seed crops. It is known as a rich source of oil (44%), protein (19–25%) and other nutritional elements (Najeeb et al. 2012). Sesame seed was used as a cooking oil and or a primary source for the production of some industrial materials including paints, margarine and varnishes in the world (Tunde-Akintunde and Akintunde 2004). This plant is known as a drought-tolerant crop, but not at the early stage of the growth, particularly at germination stage (Bahrami et al. 2012). Sesame is grown well in tropical and subtropical areas in the world and also some areas of southern Iran such as Khozestan, Sistan–Baluchestan, Fars and Jiroft Provinces (Valiki et al. 2015). Annual production of this crop is 6.2 million tonnes with an average of 576 kg ha−1 grain yield in the world (FAO 2015). Seed germination (SG) is the main stage of plant’s life cycle, as well as for the establishment of most plants which is affected by many environmental signals such as temperature (T), water potential (ψ), oxygen, light, chemicals and abiotic regulators (Parmoon et al. 2015; Baskin and Baskin 2014; Atashi et al. 2014). T and ψ mainly effect on germination rate (GR) when other factors are not restrictive for nondormant seeds (Bradford 2002). However, it is important to identify three cardinal T s of SG including base (T b, where SG is equal zero), optimum (T o, where SG is maximum value) and maximum or ceiling (T c, where SG is equal zero) T s for determining the best plantinsg date for each crop (Parmoon et al. 2015; Bewley et al. 2013; Bakhshandeh et al. 2013). According to many published reports, T o may be only one point (based on segmented model) and or a range of T s which was limited between lower T o (T o1) and upper T o (T o2) (based on dent-like model) (Bewley et al. 2013; Bakhshandeh et al. 2013). To date, however, various mathematical models have been used to describe the relationship between GR and T (Bewley et al. 2013; Bakhshandeh et al. 2013; Atashi et al. 2014). Firstly researchers used thermal time (TT) models and or its derivative models to describe these relationships at sub- and supra-optimal T s, separately. The models can be written as:

$$ {\text{TT}}_{\text{sub}} = (T{-}T_{\text{b}} )t_{\text{g}} \quad {\text{at}}\;{\text{sub-optimal}}\,T, $$
(1)
$$ {\text{TT}}_{\text{supra}} = \left( {T_{{{\text{c}}\left( {\text{g}} \right)}} {-}T} \right)t_{\text{g}} \quad {\text{at}}\,{\text{supra-optimal}}\,T. $$
(2)

In these models, variation in the time to germination (t g) for each seed percentile (%) is quantified using varying at the TT constant for each percentile (Sharifiamina et al. 2016). However, a key weakness of these models is the inability to provide physiological explanations particularly at T s above T o. To prevent this problem and to improve the model prediction, Gummerson (1986) recommended hydrotime model (θ H), which describes the relationship between ψ and GR in the same manner to the TT models:

$$ \theta_{\text{H}} = \left( {\psi - \psi_{{{\text{b}}({\text{g}})}} } \right)t_{\text{g}} ,\quad {\text{or}} $$
(3)
$$ {\text{Probit}}\,\left( {\text{g}} \right)\, = \,\left[ {\psi {-}(\theta_{\text{H}} /t_{\text{g}} ){-}\psi_{{{\text{b}}( 50)}} } \right]/\sigma \psi_{\text{b}} , $$
(4)

where θ H, ψ, ψ b(g) and t g are the hydrotime constant (MPa h−1), the actual water potential (MPa), the base water potential (MPa, defined for a specific SG fraction) and the time to germination (h) for each seed percentile (%) in the seed population.

The TT and θ H models can be combined as a hydrothermal time (HTT) model (Gummerson 1986).

This model can describe germination time courses at all ψ s and T s in the sub-optimal T (from T b to T o):

$$ \theta_{\text{HTT}} = \left( {\psi - \psi_{{{\text{b}}({\text{g}})}} } \right)\left( {T - T_{\text{b}} } \right)t_{\text{g}} ,\quad {\text{or}} $$
(5)
$$ {\text{Probit}}\,\left( {\text{g}} \right) = [(\psi {-}(\theta_{\text{HTT}} /(T{-}T_{\text{b}} )t_{\text{g}} ){-}\psi_{{{\text{b}}(50)}} ]/\sigma \psi_{\text{b}} , $$
(6)

where ψ b(50) is the base ψ of the 50th percentile and σψ b is the standard deviation of ψ b within the seed lot population. The θ HTT and T b are assumed to be constant in this model and only the amount of ψ b(g) varied among seeds in the population (Gummerson 1986).

However, the model was unable to predict a decline in GR at T s > T o (Alvarado and Bradford 2002). At supra-optimal range of T, there were interactions between T and ψ which were documented in potato (Solanum tuberosum L.) (Alvarado and Bradford 2002), zucchini (Cucurbita pepo L.) (Atashi et al. 2015), lemon balm (Melissa officinalis L.) (Atashi et al. 2014) and watermelon (Citrullus vulgaris L.) (Bakhshandeh et al. 2015). In all these studies, the amount of ψ b(g) increased (i.e., became more positive) as T increased above T o. Furthermore, other studies indicate that at T s > T o, when T increases and approaches T c, the ψ b distribution shifts progressively toward and exceeds 0 MPa (Kebreab and Murdoch 1999). Bradford (2002) reported that these changes in ψ b(g) resulted in for delaying and inhibiting SG at T s exceeding T o. For supra-optimal T s, however, Bradford (2002) modified Eq. 5:

$$ \theta_{\text{HTT}} = \left[ {\psi - \psi_{{{\text{b}}({\text{g}})}} - \left( {k_{\text{T}} \left( {T - T_{\text{o}} } \right)} \right)} \right]\left( {T - T_{\text{b}} } \right)t_{\text{g}} ,\quad {\text{or}} $$
(7)
$$ {\text{Probit}}\,\left( {\text{g}} \right) = \left[ {(\psi {-}k_{\text{T}} (T{-}T_{\text{o}} )){-}\theta_{\text{H}} /((T{-}T_{\text{b}} )t_{\text{g}} )){-}\psi_{{{\text{b}}\left( { 50} \right)}} } \right]/\sigma \psi_{\text{b}} , $$
(8)

where k T is a constant (the slope of the relationship between ψ b(50) and T s > T o), the value of ψ b(50) is equal to ψ b(50) distribution at T o and T − T o is equal to T o − T b at supra-optimal range of T s (Alvarado and Bradford 2002).

The models (Eqs. 7 and 8) could be used when the shift in distribution of ψ b(g) with T is linear at T s > T o. Generally, using methods of the TTsub, TTsupra, θ H and HTT models (Eqs. 1–8) are fully described in Bewley et al. (2013) and Atashi et al. (2015).

As maintained above, a combination of HTT models (Eqs. 5 and 7) can then be used to describe and predict SG response at all T s and ψ s which germination could occur. The models have been widely applied to quantify the effects of environmental conditions (e.g., the thermal and hydric environment) on SG, seed dormancy and also to estimate the cardinal T s in various crops such as potato (Alvarado and Bradford 2002), zucchini (Atashi et al. 2015), watermelon (Bakhshandeh et al. 2015), safflower (Carthamus tinctorius L.) (Torabi et al. 2016) and tall fescue (Festuca arundinacea) (Sharifiamina et al. 2016), as well as in weedy species such as Ambrosia trifida L. (Schutte et al. 2008), Bromus diandrus Roth (García et al. 2013) and, grass red brome (Bromus rubens L.) and cheatgrass (Bromus tectorum L.) (Horn et al. 2015), and or some pharmaceutical species such luobuma (Apocynum venetum) (Rong et al. 2015). Therefore, the objectives of this study were to predict the response of sesame SG at various T s and ψ s and also to determine the base water potential and the cardinal T s for this plant. To the best of our knowledge, this is the first study related to the application of HTT models for predicting of sesame SG under different T s and ψ s.

Materials and methods

Four sesame (Sesamum indicum L.) seed cultivars including ‘Asbomahalleh’, ‘Darab’, ‘Dashtestan’ and ‘Yellowhite’ were used in the study (with < 98% viability). Seeds were produced in Sari region, Iran, in May 2014. The seeds were stored in a black plastic bag in the dark at 4–5 °C before use. A wide range of constant T s (20, 25, 30, 35, 37, 39 and 43 °C) at each of the following ψ s (0, − 0.12, − 0.24 and − 0.36 MPa) was used in this study. The ψ s were made using aqueous solutions of polyethylene glycol (PEG8000, Merck, Germany) as followed by Michel and Radcliffe (1995) and a distilled water was used as control (0 MPa). To ensure that each solution had the targeted ψ at the beginning of the experiment, a vapor pressure osmometer (Model 5100C: Wescor Inc., Logan, UT, USA) was used and the amount of ψ was modified for the effect of T. Seeds were germinated in 9-cm Petri dishes as in Bakhshandeh et al. (2015). Briefly, each Petri dish contained 50 seeds which were placed on two layers of Whatman No. 1 filter paper along with 7 ml of distilled water (as control) or PEG solutions. Three replicates were made for each treatment at each T. Petri dishes were randomly incubated within germination incubator (Memmert Beschickung-Loading-Model 100–800, Germany) in the dark, except when recording germination. Seeds were observed several times daily (depending on the T and ψ), and were considered to have germinated when the radical was at least 2 mm long. At recording germination, to avoid errors, germinated seeds were removed from each Petri dish. At all T s, the experiment was finished when we have no new germinated seeds in each replicate of a treatment for three consecutive days. The HTT models, however, were fitted using the statistical analysis system version 9.4 (SAS Institute 2013) and Excel software, and figures were drawn by Sigma Plot version 11 software. The parameters for the HTT models were determined according to the methods that are fully described in Alvarado and Bradford (2002) and Bewley et al. (2013). Briefly, the time taken to reach 50% germination (t 50) in each replicate was calculated using the Bakhshandeh et al. (2015) method. GR50 (h) was calculated as the inverse of the time to radicle emergence (GR50 = 1/t 50) for the 50th percentile which was as the median of the seed population.

Results

The results of this study indicated that ψ, T and their interactions significantly affected on the GR and germination percentage (GP) of sesame (P ≤ 0.01). Furthermore, the amount of GR and GP decreased when ψ declined at each T (data not shown). The experimental data at each T and under different ψ s were effectively analyzed using θ H (Eq. 3) with R 2 higher than 0.80 for all fits (Table 1). The θ H was constant 15 MPa h−1 for all cultivars (except for Yellowhite which was 13 MPa h−1), when T s increased above T o, but not at the sub-optimal range of T (Table 1), resulting in that water relations have become changed at low T s. On the other hand, the θ H values increased as T decreased at sub-optimal T s. At T o also the amount of θ H was approximately similar (17 MPa h−1, averaged for all cultivars) (Table 1).

Table 1 Estimated parameter values using the hydrotime (θ H, Eq. 3) model to describe sesame seed germination under different T s and ψ s. R 2 is the coefficient determination
Full size table

The ψ b(50) values of sesame cultivars were various with T, namely they were remained constant at T s < T o (~ − 1.23 MPa, averaged for all cultivars which was calculated using Eq. 8) and then increased linearly with T when T s increased above T o (Fig. 1e–h). Of course, there was an exception for Yellowhite (ψ b(50) = −1.13 MPa, calculated using Eq. 8), which was higher (more positive) than all others. The amount of σψ b was varied in all cultivars and ranged from 0.139 to 0.326 MPa (depending on the T).

Fig. 1
figure 1

a–d The effect of temperature (T) and water potential (ψ) on the germination rate (GR = 1/t 50) of sesame seeds and calculated cardinal T s for this plant. The actual data are shown by the symbols and the line drawn through these points are based upon the parameters presented in Table 2. e–h The effect of T on ψ b(50) for seed germination of sesame. The ψ b(50) value was the lowest at T o (~ − 1.23 MPa) and increased linearly (k T = 0.1041 MPa  °C −1) as T increased above T o and also remained constant below T o. The predicted line is for the 50th percentile intercepts ψ b(g) = 0 MPa axis at T c. a–d are showing sesame cultivars names including ‘Darab’, ‘Dashtestan’, ‘Asbomahalleh’ and ‘Yellowhite’, respectively

Full size image

Based on our results ψ b(50) values increased from ~ − 1.23 MPa at ~ 35.4 °C (T o) to − 0.31, − 0.49, − 0.35 and − 0.46 MPa for Darab, Dashtestan, Asbomahalleh and Yellowhite cultivars, respectively, at 43 °C, when T increased above T o (Table 1 and Fig. 1a–d). Therefore, to describe the relationship between ψ b(50) and T at supra-optimal T s, a linear model proposed by Alvarado and Bradford (2002) was fitted (Fig. 1e–h). The intercept point of the model ψ = 0 MPa at the T c value, which was extrapolated from the GR data (Fig. 1a–d) and or calculated by fitting of Eq. 8 (the slope of the model at T s > T o (k T)) (Table 2). After fitting the model, there was no significant difference, based on the confidence intervals (CIs) of the model coefficients, between cultivars so an average value of T c and k T was estimated as ~ 47.2 °C and 0.1041 MPa °C h−1 for all cultivars, respectively (Table 2). On the other hand, this indicates that for each °C increased at T > T o, seed ψ was increased (became more positive) by 0.1041 MPa as the effect on germination. According to the model coefficients, SG of sesame was prevented, even in water, when T was equal to T c or when the amount of ψ b(g) was equal to 0 MPa (Fig. 1e–h). Generally, there was variation in the amount of T c and various ψ s could be observed at T s > T o in all cultivars (Fig. 1). The T c value decreased from 47.2 to 43.5 °C as ψ decreased (became more negative) from zero to − 0.36 MPa, and the pattern was the same for all cultivars (Fig. 1a–d). In addition, a similar response was observed when T s at which ψ b(g) for the particular ψ was equal to 0 MPa, as a result of decreasing the amount of GR at T above T o. In fact, this is explaining how the amount of T c varied among different ψ s in a normal distribution.

Table 2 Estimated parameter values using the hydrothermal time model (HTT) for describing seed germination of sesame at seven-constant T s (20, 25, 30, 35, 37, 39 and 43 °C) at each of the following four different ψ s (0, − 0.12, − 0.24 and − 0.36 MPa)
Full size table
Fig. 2
figure 2

Linear regression of probit (g) plotted against base water potentials (Psib (g), MPa) and adjusted base water potentials (Psib (g) − k T(T − T o)). Points are the observed values of germination fraction for each set of T and the lines represent the predicted values by the models. a–d are showing sesame cultivars names including ‘Darab’, ‘Dashtestan’, ‘Asbomahalleh’ and ‘Yellowhite’, respectively

Full size image

To quantify the response of sesame SG to T at different ψ s, HTT models (Eqs. 5 and 7) were fitted for all cultivars, separately. Our results indicate that the model could describe well these relationships with R2 higher than 0.80 for all fits (Fig. 1 and Table 2). There was a linear relationship between GR and T s to T o, at all ψ s, which could be limited to a single T, i.e., T b (Fig. 1a–d) and then at T s above T o, at all ψ s, GR declined linearly until T c. The pattern was the same for all cultivars. However, there was no significant difference, based on the CIs of the model parameters, between cultivars in terms of the estimated cardinal T s, so an average value was 14.7 °C for T b, 35.4 °C for T o and 47.2 °C for T c in the control condition (0 MPa) for this plant (Fig. 1a–d and Table 2).

Our results also show that there was a strong correlation (R 2 > 0.80) between data at sub-optimal T s and reduced ψ, which share a common set of HTT parameters for each cultivar (Table 2 and Fig. 2). As noted previously, ψ b(50) increased (i.e., became more positive) linearly at T s > T o (Fig. 1e–h). Therefore, Eq. 8 is fitted to estimate the germination time courses at T s > T o. In this model, the value of T o, k T and θ H was systematically changing until ψ b(50) was equal to the ψ b(50) which was calculated by the HTT model (Eq. 5) at T s < T o. The best values of the model parameters are presented in Table 2. Based on our results, the models could predict well the germination time courses and accurately normalize all data from T s and ψ s to a single common TT scale (Fig. 3). However, the poor fit of the model at 43 °C occurs because the model was fitted to all data in each cultivar (all T s and ψ s) to describe well the full data set (Fig. 3).

Fig. 3
figure 3

Germination time courses across T s and ψ s are plotted on a single normalized TT scale showing the predicted time courses in water, based upon the parameters present in Tables 1 and 2. The normalized values from the supra-optimal T s (Fig. 1e–h) were multiplied by (T o − T b) for each cultivar to convert to TT units (°C h). a–d are showing sesame cultivars names including ‘Darab’, ‘Dashtestan’, ‘Asbomahalleh’ and ‘Yellowhite’, respectively

Full size image

Discussion

Knowledge of SG prediction is useful in agronomic management programs. Mathematical models can help to describe and quantify the effect of environmental factors on SG, particularly the variation that occurs in germination time among individual seeds in a seed lot (Bradford 2002). However, the TT models are successfully used in many studies to describe the germination time course at sub-optimal T s. But, at supra-optimal T s, there was an error in these models. In other words, TT models could not predict the decrease in GR when T s exceeded T o (Bradford 2002). Consequently, the θ H and HTT models were developed by others such as Gummerson (1986) and Bradford and Still (2004) to eliminate this problem. This study, therefore, was conducted to describe the response of sesame SG under different T s and ψ s and also to estimate the germination time course and the cardinal T s of sesame using HTT models (Eqs. 5 and 7) known as a seed population model.

HTT model is a robust method to understand how environmental factors (e.g., T and ψ) interact on SG in a seed lot (Bradford 2002). Consequently, the estimated parameters by the model can be used as an input for SG prediction models (e.g., in sesame) in the field condition. According to the results obtained in this study, at each T, a decrease (became more negative) in ψ resulted in lower GR and GP in sesame as a result of the seed dried from fully hydrated state and then it will be unable to initiate embryo growth and complete SG (Bradford 2002). Similar results were reported by others such as Alvarado and Bradford (2002) in potato, Atashi et al. (2015) in zucchini and Bakhshandeh et al. (2015) in watermelon. The amount of θ H increased and also GR decreased largely with the decreasing T, particularly at sub-optimal T s. Because, at T s < T o, the model calculated only a constant ψ b(50) (~ − 1.23 MPa, averaged for all cultivars) which was the main reason for the decreasing in GR, and after that (at T s > T o), the θ H was constant (~ 15 MPa h−1) and only ψ b(50) increased linearly (more positive) with the increasing T, which resulted in an increase in germination times and a decrease in GR. Similarly, Alvarado and Bradford (2002) in potato and Bakhshandeh et al. (2015) in watermelon reported an increase in θ H value at sub-optimal T s. Dahal and Bradford (1990) also reported that θ H value can be used as an indicator of the seed quality in a seed lot. For example, in winterfat (Krascheninnikovia lanata (Pursh) A.D.J. Meeuse & Smit) Wang (2005) indicates that the large seeds required a lower value of θ H than the small seeds, particularly at low T s. On the other hand, the large seeds can be germinated sooner than the small seeds at low T s. In other studies, θ H was used to classify barely (Hordeum vulgare L.) and sorghum (Sorghum bicolor (L.) Moench) cultivars in term of their seeds sensitivity to ψ which can be used in breeding programs.

We also observed that the amount of ψ b(50) was at a minimum at T s ≤ T o (~ − 1.23 MPa, averaged for all cultivars) and then increased linearly at supra-optimal Ts as a result of thermoinhibition of sesame SG. Many reports show that the ψ b(g) values were minimal at T o and increased linearly (e.g., became more positive) at supra-optimal T s such as Dahal and Bradford (1990) in tomato, Alvarado and Bradford (2002) in potato, Rowse and Finch-Savage (2003) in both carrot and onion, Atashi et al. (2015) in zucchini and Bakhshandeh et al. (2015) in watermelon. As mentioned above, this has the same effect as decreasing ψ, thus GR declined at T s > T o. Generally, within a seed lot, if the difference between ψ and ψ b(50) is small, then SG will be slow and germination times will be large (Bradford 2002). This can be related to a decrease in both activity of enzymes and oxygen availability during SG period, particularly at T s > T o (Bewley and Black 1994). In addition, at T o, ψ s higher than ψ b(50) (more positive) resulted in an increase in enzyme’s activity, water uptake rate and accelerates radical emergence (Kebreab and Murdoch 1999). The range of σψ b was varied from 0.140 to 0.326 MPa (depending on the cultivars) in this study. This parameter is defined as an indicator to show uniformity in SG among individual seeds in a seed lot (Bradford 1995). However, based on the estimated parameters (e.g., θ H, ψ b(50) and σψ b) we easily can predict complete sesame SG time courses at any ψ at a constant T.

The amount of T b (14.7 °C) estimated in this study was also lower than the T b reported by Angus et al. (1980) (16 °C) in sesame. In opposite, Carvalho et al. (2001), Mohamed et al. (2000) and Bakhshandeh et al. (2013) reported that T b for sesame ranged from 12.8 to 13.5 °C. The T o value (35.4 °C) also calculated to be closer to that reported by Carvalho et al. (2001) and Bakhshandeh et al. (2013) who showed the T o for sesame SG ranged from 31.9 to 36.8 °C. The T c value (47.2 °C) estimated in this study was almost equal to the T c value that reported by Carvalho et al. (2001) (45.5–46.0 °C), Mohamed et al. (2000) (44.5–46.0 °C) and Bakhshandeh et al. (2013) (47.0–48.5 °C) (depending on cultivars). Bradford (2002) proposed that using the HTT model (Eqs. 5 and 7) along with a normalization factor ([1 − (ψ/ψ b(g))]t g), all germination time courses at all T s and ψ s could be calculated on a single common normalized TT scale, which is supporting similar results in potato (Alvarado and Bradford 2002) and in watermelon (Bakhshandeh et al. 2015). We used this factor in the presence study, the results indicated that the factor could accurately describe the germination time courses of sesame, based on a TT scale but there was a poor fit at 43 °C which can be due to the model fitting to whole set data to provide a good description for all T s and ψ s. A similar result was reported by Rowse and Finch-Savage (2003) who fitted HTT model to describe SG of onion and carrot. They showed that the model was unable to predict well the germination time courses in both plants at supra-optimal range of T s.

Conclusion

Based on our findings, GR and GP significantly influenced by ψ, T and their interactions. The HTT model could describe well the response of sesame SG at all ψ s and T s. There was no significant difference, based on the CIs of the model parameters, between cultivars, so an average value of 339.7 MPa  °C h−1 for θ HTT, − 1.23 MPa for ψ b(50), 0.1041 MPa  °C h−1 for k T, 14.7 °C for T b, 35.4 °C for T o and 47.2 °C for T c was estimated for this plant. This model (as a predictive tool) or the estimated parameter values in this study can easily be used in sesame SG simulation models to quantitatively characterize the physiological status of sesame seed populations.

Author contribution statement

EB, MJ, EA and MGH conceived the experiments and experimental design. EB conducted the modeling and interpreted the data. EB, MJ, EA and MGH co-wrote all drafts of the paper, including all edits and revisions, and also approved the final draft for submission and took full public responsibility for the content.