Population-based analyses of single-seed oxygen consumption rates

While seed oxygen consumption data from the Q2 instrument can be analysed by focusing on the shapes of the individual oxygen depletion time courses (Bradford et al., Reference Bradford, Bello, Fu and Barros2013), we introduce here a novel approach to visualize the variation in respiratory patterns among seeds (see subsequent sections for evidence that respiratory activity accounts for most seed oxygen consumption). We convert the oxygen depletion time courses of the individual seeds in the measured population into a cumulative curve based on the time required for each seed to reduce the oxygen in the Q2 well to a specific percentage of the initial value. This initial oxygen concentration (21% in the air) is normalized to 100% based on the first measurement for each individual well or vial. The time at which each seed reduces the oxygen concentration to that percentage can be plotted as a cumulative percentage curve versus the time of imbibition (Fig. 1). The resulting time course of respiratory activity is analogous to a germination time course, which is a cumulative plot over time of when each seed achieves the end point of radicle emergence. These population oxygen depletion (POD) curves provide a simple and convenient way to compare the effects of various treatments on the distribution of respiration rates in the measured seed population. A spreadsheet accepting data exported from the Q2 instrument and converting it to POD curves is available from the supplementary file Spreadsheet S1. This approach takes advantage of the ability of the Q2 instrument to collect data for each individual seed and utilizes all of the data for analyses, rather than only means or medians of the population (Fig. 1). Unlike other derived parameters based on the shapes of the original oxygen depletion time courses (Bradford et al., Reference Bradford, Bello, Fu and Barros2013), the POD curves are visually similar to germination time courses and are therefore familiar to seed biologists and technologists.

Varying the percentage of the oxygen depletion selected results in somewhat different shapes of these cumulative curves (Fig. 1). For convenience and illustrative purposes, we use 75% (R75), 50% (R50) and 25% (R25) of the initial oxygen remaining, but the percentage of oxygen depletion used can be varied as long as it is applied consistently across all seeds. Of course, greater oxygen depletions mean lower oxygen percentages remaining in the vials, which itself can reduce respiration rates and delay or prevent germination. As this is a closed-system test, essentially all of the oxygen is eventually consumed. However, for many species, germination was not affected greatly until the percentage of oxygen in air was less than ~5% (Bradford et al., Reference Bradford, Côme and Corbineau2007), corresponding to approximately 25% of the initial oxygen concentration (21%) remaining. In general, the R50 level of oxygen depletion provides the median response of the population, while less or greater depletion levels can be used to reduce the duration of the test (R75) or to better match germination time courses in some cases (R25; see below). By selecting the appropriate oxygen depletion percentage value, time courses and treatment differences that closely resemble those among germination time courses can be generated. In addition, as we show below, the POD curves can be analysed using the same PBT models that have been applied to germination time courses.

Germination and respiration responses to temperature (thermal time model)

Temperature has a primary influence on both the capacity for germination in dormant seeds and the rate or speed of germination in non-dormant seeds (Bewley et al., Reference Bewley, Bradford, Hilhorst and Nonogaki2013; Batlla and Benech-Arnold, Reference Batlla and Benech-Arnold2015). Three cardinal temperatures (minimum, optimum and maximum) describe the range of temperatures over which seeds of a particular species can germinate (Alvarado and Bradford, Reference Alvarado and Bradford2002). Germination rates (the inverse of time to a specific percentage germination in the total population, i.e. 1/t ₅₀ for 50% germination) generally increase linearly between the minimum or base temperature (T _b) and the optimum temperature (T _o), as in the degree-days or thermal time model, θ _T (g) = (T – T _b) t _g , where θ _T (g) is the thermal time required from imbibition until radicle emergence of fraction or percentage g and T is the temperature at which the seeds are imbibed. The thermal time model has been applied extensively to describe seed germination timing in response to temperature (Bierhuizen and Wagenvoort, Reference Bierhuizen and Wagenvoort1974; Garcia-Huidobro et al., Reference Garcia-Huidobro, Monteith and Squire1982; Covell et al., Reference Covell, Ellis, Roberts and Summerfield1986; Dahal et al., Reference Dahal, Bradford and Jones1990; Alvarado and Bradford, Reference Alvarado and Bradford2002). Since all seeds in a population do not germinate simultaneously, germination rates of seed populations (rather than of specific percentages) can be analysed by transforming the cumulative germination percentages to probits and plotting versus a log time scale (Covell et al., Reference Covell, Ellis, Roberts and Summerfield1986; Dahal et al., Reference Dahal, Bradford and Jones1990). This can be described according to equation (1):

(1) $${\rm probit} \left( g \right){\rm} = {\rm} \left\{ {{\rm log} \left[ {\left( {T{\rm} - {\rm} T_{\rm b}} \right)t_g} \right]{\rm} - {\rm log}\theta _T\left( {50} \right)} \right\}/\sigma _{\theta T}$$

where probit (g) is the germination fraction transformed into probits and σ _θT  is the standard deviation of thermal times to germination among seeds in the population. Germination time courses at different temperatures will be linearized when probit (g) is plotted versus log t _g . Log θ _T (50) is where the resulting line crosses 50% germination (probit (50) = 0), and the inverse of the slope is σ _θT , the standard deviation of log thermal time requirements among seeds. Repeated regressions using different T _b values are used to optimize the best fit between probit (g) and the log of θ _T (g), which is generally normally distributed within the population (Dahal et al., Reference Dahal, Bradford and Jones1990). The model can also be fit using programs that optimize the variables in equation (1) (Chantre et al., Reference Chantre, Batlla, Sabbatini and Orioli2009) or by other statistical methods (Hay et al., Reference Hay, Mead and Bloomberg2014; Hardegree et al., Reference Hardegree, Walters, Boehm, Olsoy, Clark and Pierson2015).

To compare respiration and germination rates across temperatures, tomato (S. lycopersicum) seeds were imbibed on agar in sealed wells in the Q2 instrument at constant 15, 20 and 25°C. At each temperature tested, the seeds exhibited an initial relatively slow rate of respiration, followed by a transition to a phase of more rapid of respiration until it again slowed as oxygen concentrations became limiting, as illustrated for 25°C (Fig. 1). Overall shapes of oxygen depletion curves were similar for all germinating seeds, with the differences among seeds due primarily to the times at which oxygen consumption transitioned from the slow initial respiration rate to the more rapid second phase (Fig. 1). In the case of tomato seeds, this transition coincides closely with the time of radicle emergence (Bradford et al., Reference Bradford, Bello, Fu and Barros2013). Dead seeds did not exhibit significant oxygen consumption, with final oxygen levels after 150 h remaining above 90% of the initial value (e.g. top grey line in Fig. 1), and dormant seeds have lower and often declining rates of oxygen consumption (see the hormone section below). These characteristics of the individual seed and population respiratory patterns have been analysed previously using ASTEC values that focus on the shapes of the individual oxygen depletion time courses (Zhao and Zhong, Reference Zhao and Zhong2012; Bradford et al., Reference Bradford, Bello, Fu and Barros2013; Zhao et al., Reference Zhao, Cao, Chen, Ruan and Yang2013).

When median oxygen depletion patterns of tomato seed populations were compared at different temperatures, oxygen consumption was delayed as temperature decreased (Fig. 2A). Temperature affected both initial and secondary respiration rates similarly, slowing both phases of respiration at lower temperatures and increasing them at warmer temperatures (Fig. 2A). This is reflected in increasing median slopes [starting metabolism rate (SMR) and oxygen metabolism rate (OMR) values] of oxygen depletion curves and earlier transitions between initial and secondary respiration rates [increasing metabolism time (IMT) values] as temperatures increased (see supplementary Table S1). Times to radicle emergence in the Q2 wells were observed at intervals (Fig. 3A) and POD curves were developed based on the times required for individual seeds to deplete the oxygen in their wells to 75, 50 and 25% of the initial amount at the different temperatures (Fig. 3B, C and D, respectively). Times to germination increased as temperature decreased, but 93% of seeds completed germination even at the lowest temperature (Fig. 3A, supplementary Table S1). POD curves at 75, 50 and 25% oxygen remaining exhibited relationships across temperatures very similar to those for radicle emergence (Fig. 3A–D). As respiration data are available for every seed rather than only being registered at periodic observations, the greater density of data points is evident for the POD curves compared to the germination time courses.

Figure 2. Median oxygen depletion curves of: (A) tomato seeds imbibed at temperatures of 25°C (orange), 20°C (green) or 15°C (blue) at 0 MPa; (B) tomato seeds imbibed at water potentials of 0 MPa (orange), −0.2 MPa (green), −0.4 MPa (blue), −1.0 MPa (purple), −1.5 MPa (red) or −2.0 MPa (brown) at 25°C; (C) tomato seeds imbibed in concentrations of the respiratory inhibitor KCN of 0 mM (control; orange), 0.1 mM (green), 0.2 mM (blue) or 0.3 mM (red) at 25°C; (D) tomato seeds imbibed in concentrations of the respiratory inhibitor SHAM of 0 mM (control; orange), 0.05 mM (green), 1 mM (blue), 2 mM (purple) or 3 mM (red) at 25°C. All seeds in the test populations were used to calculate median curves, regardless of their germination status.

Figure 3. Germination time courses (A, E, I and M) and R75, R50 and R25 population oxygen depletion (POD) time courses (B–D, F–H, J–L and N–P) of tomato seeds imbibed under different conditions. Cumulative germination (A) and POD time courses (B, C, D) are shown for seeds imbibed on agar at 25°C (orange circles), 20°C (green triangles) or 15°C (blue squares). Cumulative germination (E) and POD time courses (F, G, H) are shown for seeds imbibed at 25°C on agar at 0 MPa (open orange circles), −0.2 MPa (open green triangles), −0.4 MPa (open blue squares), −1 MPa (filled purple circles), −1.5 MPa (filled red circles) or −2 MPa (filled brown circles). Cumulative germination (I) and POD time courses (J, K, L) of seeds imbibed at 25°C on agar containing 0 (control, open orange circles), 0.1 mM (open green triangles), 0.2 mM (open blue squares) or 0.3 mM (filled purple circles) KCN. Cumulative germination (M) and POD time courses (N, O, P) of seeds imbibed at 25°C on agar containing 0 (control, open orange circles), 0.5 mM (open green triangles), 1 mM (open blue squares), 2 mM (filled purple circles) or 3 mM (filled red triangles) SHAM. Continuous curves are predicted by fitting the appropriate population-based threshold model to the data across the temperature, water potential, KCN or SHAM ranges (Table 1). Solid and dashed curves indicate where two different models were fit to sub-components of the data (see text).

The thermal time model for suboptimal temperatures was used to calculate the T _b values for both germination and respiration (R75, R50 and R25 POD curves; Table 1) and time courses were predicted from the model using the resulting parameter values (solid lines in Fig. 3A–D). The thermal time model fitted both germination and respiration time courses extremely well, with r ² values of 0.916 for germination and from 0.974 to 0.944 for POD curves (Table 1; supplementary Fig. S1A–D). Similarly, the times to 50% germination (t ₅₀) were highly correlated to the times required for 50% of seeds to deplete oxygen in the wells to specific levels at each temperature (Fig. 4A, open symbols). The T _b values estimated from the thermal time model were slightly higher for germination (6.6°C) than for respiration (2.2–4°C) (Table 1), as might be expected if respiration could continue at slow rates even at low temperatures at which germination would not be completed. As values from the thermal time model based on the R75 POD curves were highly correlated with actual germination timing (r ² = 0.93; Fig. 4A), seed respiration rates even quite early in the oxygen consumption time course are highly predictive of the effects of temperature on rates of radicle emergence.

Figure 4. Relationships between median times to radicle emergence (t ₅₀) and the median times for seeds to reduce the oxygen in their wells to 75% (blue squares), 50% (green triangles) or 25% (orange circles) of the initial value for: (A) tomato seeds imbibed at different temperatures (open symbols) or water potentials (closed symbols); (B) tomato seeds imbibed in different concentrations of KCN, SHAM or KCN + SHAM (closed symbols), of ABA (open symbols) or of GA (half-closed symbols) (ABA and GA data not included in linear regressions); (C) lettuce seeds subjected to accelerated ageing (open symbols represent primed seeds, not included in the linear regressions); and (D) radish seeds subjected to controlled deterioration. Significance levels of the regression values are indicated as: ns, non-significant; **, P < 0.01; ***, P < 0.001.

Table 1. Model parameters and probit regressions for the PBT models describing germination and respiration

Significance of regressions: * = P < 0.05; ** = P < 0.01; *** = P < 0.001.

Germination and respiration responses to water potential (hydrotime model)

Seed germination rates are very sensitive to water potential (Ψ), exhibiting a linear decline (i.e. delay) with even small decreases in Ψ (Gummerson, Reference Gummerson1986; Bradford, Reference Bradford1990). Unlike the T _b, which in the simplest case is assumed to be constant among all seeds in a population, the Ψ _b values differ among seeds, such that some can germinate to lower Ψ than others (Gummerson, Reference Gummerson1986). The Ψ that just prevents germination of a specific fraction of the seed population (g) is termed the base water potential for that fraction, or Ψ _b(g). The Ψ _b(g) values are generally normally distributed within the population and inversely related to t _g , resulting in a hydrotime model of the form θ _H = (Ψ − Ψ _b(g))t _g , indicating that all seeds in the population require the same accumulated hydrotime (θ _H) to complete germination but vary in their thresholds for responding to Ψ. Germination rates of seed populations imbibed at different Ψ (at a constant single temperature) can be analysed by repeated regression by plotting probit (g) versus Ψ − (θ _H/t _g ), according to equation (2):

(2) $${\rm probit} \left( g \right){\rm} = {\rm} \left[ {\Psi - {\rm} \left( {\theta _{\rm H}/t_g} \right){\rm} - \Psi_{\rm b} \big( {50} \big)} \right]/\sigma _\Psi{_{\rm b}} $$

where σ _Ψb is the standard deviation of the distribution of Ψ _b(g), which is assumed to be normally distributed (Bradford, Reference Bradford1990). The model parameters are optimized by varying θ _H values until the highest r ² for the regression is obtained. Ψ _b(50) is determined as the value at which the probit regression line crosses zero, and σ _Ψb is the inverse of the slope (Bradford, Reference Bradford1990, Reference Bradford2002; Bradford and Still, Reference Bradford and Still2004).

It was shown previously that average respiration rates of pooled tomato seed samples fell as Ψ decreased (Dahal et al., Reference Dahal, Kim and Bradford1996). We re-examined this relationship using single-seed respiration measurements of tomato seeds in the Q2. At the higher Ψ range (0 to −0.4 MPa), germination speed was delayed, as expected, although final germination percentages remained above 80% (Fig. 3E). Median oxygen depletion rates were also slower and the sharp transition to a more rapid rate disappeared as Ψ was reduced (Fig. 2B). At low Ψ, oxygen depletion rates remained essentially linear at the initial rate, which, in contrast to results obtained with temperature, were less affected by increasing water stress in this higher Ψ range (see supplementary Table S1). At lower water potentials at which radicle emergence was prevented (Ψ ≤ −1.0 MPa) (Fig. 3E), initial respiration rates were slower and remained linear for up to 150 h (Fig. 2B, supplementary Table S1), consistent with previous reports (Dahal et al., Reference Dahal, Kim and Bradford1996). This pattern is also consistent with the transition to a more rapid respiration rate in tomato seeds being associated with radicle emergence (Bradford et al., Reference Bradford, Bello, Fu and Barros2013), although radicle emergence still occurred at −0.4 MPa (Fig. 3E) without such a change in median oxygen depletion rate (Fig. 2B).

When expressed as POD curves, delays in respiration between 0 and −0.4 MPa were small but detectable at the higher R75 oxygen threshold level and became clearly evident at the R50 and R25 depletion levels (Figs 3F–H). Initial respiration rates (indicated by R75) declined further at lower Ψ at which germination was prevented, and responded quantitatively as Ψ was decreased (Fig. 3F). At R50 and R25 levels of oxygen depletion, decreasing respiration rates were more evident, such that only a few seeds attained the R25 depletion level at −1 MPa and lower (Fig. 3G, H; see also Fig. 2B). The hydrotime model accounted well for the effects of increasing water stress between 0 and −0.4 MPa on both germination and respiration (Fig. 3E–H, solid curves; Table 1). There was a close linear correlation between germination t ₅₀ values and median times to R75, R50 or R25 based on POD curves across these Ψ values (Fig. 4A, closed symbols); this relationship was essentially identical to that for temperature, as noted previously (Dahal et al., Reference Dahal, Kim and Bradford1996). While respiration proceeded at and below −1.0 MPa with POD curves similar to those at higher Ψ (Fig. 3F, G), data across the entire Ψ range from 0 to −2.0 MPa could not be fit satisfactorily using a single hydrotime model. This was also reported for germination rates of tomato seeds across a wide range of Ψ (Dahal et al., Reference Dahal, Bradford and Jones1990; Ni and Bradford, Reference Ni and Bradford1992; Dahal and Bradford, Reference Dahal and Bradford1994) and has been addressed by separating the data into high and low Ψ ranges and fitting the hydrotime model separately to data for each group of Ψ values. That approach demonstrated that seeds initially imbibed at inhibitory Ψ levels adjusted by lowering their Ψ _b values and then progressed toward completion of germination in accordance with that new Ψ _b(g) distribution. When we fit the hydrotime model to the POD curves separately for data from 0 to −0.4 MPa and from −1.0 to −2.0 MPa, the models fit each dataset well (Table 1; supplementary Fig. S1F, G) and predicted time courses closely matched the individual seed data in both Ψ ranges (Fig. 3F, G). As had been found for germination (Dahal and Bradford, Reference Dahal and Bradford1994), incubation at lower Ψ also resulted in a shift in the Ψ _b distribution for respiration to lower values, but once this had occurred, the effects of further reductions in Ψ were consistent with that new distribution. The Ψ _b(50) value for R75 at high Ψ is −3.0 MPa but increases to −1.1 and −0.83 for R50 and R25, respectively (Table 1), reflecting the greater sensitivity of the second phase of respiration compared to the initial phase in this Ψ range (Fig. 2B). At the lower Ψ range at which germination was inhibited, respiration continued, but now in relation to lower Ψ _b(50) values of −4.9 and −3.8 MPa for R75 and R50, respectively (Table 1; experiments were terminated before oxygen was depleted to 25% for most seeds). Thus, the negative adjustment of Ψ _b(50) values for germination reported previously is also reflected in adjustment to lower Ψ _b thresholds for respiration. Taking this physiological adjustment into account, the models were able to predict quite accurately the effects of increasing water stress not only on germination but also on respiration time courses at high and low ranges of water stress, including those at which germination was completely prevented (Fig. 3E–H). In addition, the Ψ _b(50) values for germination and for R50 were similar (−1.2 MPa and −1.1 MPa, respectively) (Table 1; supplementary Fig. S1E, G). Thus, there is a close relationship between the effects of Ψ on respiration and on germination in the range of Ψ at which germination can be completed (Fig. 4A).

Germination and respiration responses across combined temperatures and water potentials (hydrothermal time model)

The effects of T and Ψ can be combined to generate the hydrothermal time model that can predict the effects of the combination of those factors (Gummerson, Reference Gummerson1986; Dahal and Bradford, Reference Dahal and Bradford1994). The values of the hydrothermal time constant (θ _HT) and T _b are obtained by repeated probit regressions, as described above, to optimize both values, using equation (3):

(3) $${\rm probit} \left( g \right){\rm} = {\rm} \left\{ {\left[ {\Psi - \theta _{{\rm HT}}/\left( {\big( {T{\rm} - {\rm} T_{\rm b}} \big)t_g} \right)} \right]{\rm} - \Psi _{\rm b}\big( {50} \big)} \right\}/\sigma _\Psi{_{\rm b}}. $$

In cases where the thermal and hydrotime models describe the data well and there is limited interaction between their effects (Kebreab and Murdoch, Reference Kebreab and Murdoch1999; Bloomberg et al., Reference Bloomberg, Sedcole, Mason and Buchan2009), the hydrothermal time (HTT) model can be applied (Gummerson, Reference Gummerson1986; Dahal and Bradford, Reference Dahal and Bradford1994; Alvarado and Bradford, Reference Alvarado and Bradford2002). Our results indicate that the HTT model accurately described the germination and respiration behaviour of tomato seeds across all T and Ψ conditions tested (Table 1; supplementary Fig. S2). This allowed all the time-course data across temperatures and at the high and low Ψ ranges to be normalized into single curves for germination and for respiration at each oxygen depletion level (Fig. 5A–C). This normalization based on the model parameters accounts for the effect of Ψ and adjusts each curve to what it would be expected to be in water, in a similar way that plotting on a thermal time scale normalizes time courses across temperatures (Bradford, Reference Bradford1990). As noted above, T and Ψ conditions that had similar effects on germination rates (t ₅₀) also had very similar effects on respiration (Fig. 4A). This was also apparent in the similar parameter values for germination and R50 POD time courses in the HTT model (supplementary Table S1). The model also revealed interesting comparisons of various conditions in their effects on respiration. For example, R50 time courses for conditions that differed by 5°C or ~ −0.25 to −0.4 MPa coincided almost exactly: POD curves at −0.2 MPa and 25°C coincided with those at 0 MPa and 20°C; curves for –0.4 MPa at 25°C coincided with those for –0.25 MPa at 20°C; curves for –0.4 MPa at 20°C coincided with ones for 0 MPa at 15°C, etc. (supplementary Fig. S2). This indicates that, as far as seed respiration and germination rates are concerned, the influences of T and Ψ are essentially interchangeable and additive, consistent with prior work on seed priming that demonstrated interchangeable and additive effects of T and Ψ on physiological advancement toward radicle emergence (Bradford and Haigh, Reference Bradford and Haigh1994).

Figure 5. Normalized germination time courses (A, D, G) and POD time courses (B, C, E, F, H, I) for tomato seeds for R75 (blue squares), R50 (green triangles) and R25 (orange circles) oxygen depletion levels when imbibed at different temperatures and water potentials based upon the (HTT) model (A–C), or at different KCN or SHAM concentrations based on the dosage model (D–I) (see Fig. 3). Different data (symbols) and modelled responses (solid curves) are shown for higher and lower Ψ, KCN or SHAM concentrations (see Fig. 3 and text), except for germination at low water potentials (A), where no germination occurred. The normalization procedure for Ψ or inhibitor dosage adjusts all time courses under different conditions back to their expected time courses in water (Bradford, Reference Bradford1990; Ni and Bradford, Reference Ni and Bradford1993).

Abscisic acid and gibberellin (hormone model)

A variation of the hydrotime model was developed to describe the effects of different concentrations of abscisic acid (ABA) or gibberellin (GA) on seed germination rates (Ni and Bradford, Reference Ni and Bradford1992, Reference Ni and Bradford1993). Because ABA is an inhibitor of germination, the analysis of ABA responses assumes that there is a base concentration or dosage (ABA_b) that will just prevent germination of a specific fraction g of the seed population, and that these ABA_b(g) values are normally distributed among the seed population. When a logarithmic ABA concentration scale was used, as hormonal responses are generally logarithmic with concentration (Bradford and Trewavas, Reference Bradford and Trewavas1994), times to germination were found to be inversely proportional to the difference between the ABA concentration applied in the test [ABA] and the ABA_b(g) value for the specific fraction g. Based on that relationship, an ABA-time constant, θ _ABA could be defined as:

(4) $$\theta _{{\rm ABA}} = \left\{{{\rm log}\left[ {{\rm ABA}} \right]{\rm} - {\rm log}\left[ {{\rm AB}{\rm A}_{\rm b}\left( g \right)} \right]} \right\}t_g\; = {\rm} \left\{ {{\rm log}\left[ {{\rm ABA/AB}{\rm A}_{\rm b}\left( g \right)} \right]} \right\}t_{g}$$

and the model parameters can be calculated as described previously according to:

(5) $${\rm log}\left[ {{\rm AB}{\rm A}_{\rm b}\left( g \right)} \right]{\rm} = {\rm log}\left[ {{\rm ABA}} \right]{\rm} - \theta _{{\rm ABA}}/t_g.$$

An analogous model was developed for the promotion of germination by GA (Ni and Bradford, Reference Ni and Bradford1993), according to:

(6) $$\theta _{{\rm GA}} = {\rm} \left\{ {{\rm log}\left[ {{\rm GA}} \right]{\rm} - {\rm log}\left[ {{\rm G}{\rm A}_{\rm b}\left( g \right)} \right]} \right\}t_g\; = {\rm} \left\{ {{\rm log}\left[ {{\rm GA/G}{\rm A}_{\rm b}\left( g \right)} \right]} \right\}t_{g}. $$

To test the effects of ABA on seed respiration, we used seeds of the ABA-deficient sitiens (sit^w ) tomato mutant, which germinate rapidly and are highly responsive to inhibition by ABA (Groot and Karssen, Reference Groot and Karssen1992; Ni and Bradford, Reference Ni and Bradford1993). Germination was delayed and reduced by imbibition in 1 and 3.3 μM ABA and was almost completely inhibited by 10 μM ABA (Fig. 6A). The median base ABA concentration required to inhibit germination by 50% according to the dosage PBT model was 4.8 μM (log ABA_b(50) = 0.68) (Table 1). The PBT model fitted the respiration data well across ABA concentrations (see supplemental Fig. S3), showing a quantitative effect of increasing ABA concentration in decreasing seed respiration rates (Fig. 6B–D, Table 1). Initial rates of oxygen consumption (R75 POD curves) were reduced by ABA, but the concentration dependence was relatively small (Fig. 6B), while R50 and R25 POD curves more closely reflected the hormone concentration dependence for germination (Figs 6C, D). As discussed previously (Ni and Bradford, Reference Ni and Bradford1992), it is not possible to use a value of 0 ABA concentration in a logarithmic model; instead, we estimated the minimum ABA concentrations that would be expected to have any effect on germination or respiration and used those values in the model to predict time courses in the absence of added ABA. For germination, this predicted minimum threshold value for an effect of ABA was 0.08 μM, compared to estimated values of 0.08 μM for R50 and 0.10 μM for R25 POD curves. Interestingly, respiration rates at high ABA concentrations at which germination is inhibited declined continuously over time to very slow rates (see supplementary Fig. S4), suggesting that a feedback mechanism exists to reduce the respiration rates of seeds that will not complete germination due to low Ψ (Fig. 2B) or high ABA (Fig. 6A), in order to conserve seed reserves.

Figure 6. Germination time courses (A, E) and R75, R50 and R25 POD time courses (B–D, F–H) of ABA-deficient sit^w (A–D) and gibberellin-deficient gib1 (E–H) mutant tomato seeds imbibed on agar with different concentrations of ABA (A–D) or GA (E–H) at 25°C. As no seeds reached the 75% oxygen depletion level at GA concentrations less than 10 μM, no data are shown, but the predicted time course for 1 μM is plotted (see supplementary Fig. S4 for actual respiration time courses for these conditions).

This was also evident in the respiratory patterns of GA-deficient gib1 mutant tomato seeds, which are dependent upon exogenous GA to germinate (Groot and Karssen, Reference Groot and Karssen1987; Ni and Bradford, Reference Ni and Bradford1993). Respiration and germination increased in concert with GA concentration and were described well by the dosage PBT model (Fig. 6E–H; supplementary Fig. S3E–H). For both GA and ABA, there was a linear relationship between times to 50% germination (at concentrations where this percentage was attained) and median respiration rates derived from the POD curves (Fig. 4B). However, at lower GA concentrations that did not result in germination, initial oxygen consumption rates quickly declined to essentially zero (see supplementary Fig. S4F–H) and did not even reach R75 (Fig. 6F–H). This indicates that seeds that are not progressing toward germination (i.e. are dormant or lack other conditions permitting germination) can essentially stop oxidative respiration even though they are fully imbibed. The lack of oxygen consumption in these imbibed viable but dormant seeds also indicates that other reactions that could utilize oxygen [e.g. phenol oxidation or other chemical reactions; Lenoir et al. (Reference Lenoir, Corbineau and Côme1986)] must be negligible in these seeds.

Germination and respiration responses to respiratory inhibitors (dosage model)

Given the close relationships between oxygen consumption and germination rates, we asked whether directly inhibiting respiration rates would have corresponding effects on germination rates. We developed a model to account for changes in germination when respiration is artificially inhibited by addition of different concentrations (dosages) of KCN or SHAM:

(7) $${\rm probit} \left(g \right) = \left\{\log \left( D \right) - (\theta _D/t_g) - \log \left[D_{\rm b}\left( 50 \right) \right] \right\} /\sigma_{D_{\rm b}} $$

where D is the tested dosage of KCN or SHAM, θ _D is the dosage time constant, D _b(50) is the median base dosage that reduces germination to 50%, and the distribution of D _b(g) among seeds in the population is characterized by σ _Db, or the standard deviation of D _b(g). This is a general PBT model for effects of chemicals on germination rates and can be used in either logarithmic or linear mode, depending upon the seed responses to the dosage levels.

At high concentrations of KCN, germination of lettuce (L. sativa) seeds was reported to be completely inhibited (Khan and Zeng, Reference Khan and Zeng1985), and KCN-sensitive respiration accounted for about 80% of the total oxygen consumption in cocklebur (Xanthium strumarium) seeds (Esashi et al., Reference Esashi, Sakai and Ushizawa1981). However, in prior work with tomato seeds (Dahal et al., Reference Dahal, Kim and Bradford1996), inhibiting or enhancing respiration rates by reducing or elevating oxygen concentrations had relatively little effect on the time of initiation of germination. In the Q2, increasing concentrations of KCN progressively delayed germination and reduced oxygen consumption rates of tomato seeds (Figs 3I and 2C, respectively). In general, seed oxygen consumption was much more sensitive to KCN than was final germination percentage, which was only reduced at higher KCN concentrations. The inhibitor delayed germination and increased the spread of radicle emergence, although 90% of seeds eventually completed germination. KCN affected primarily the duration (not the rate) of the initial phase of oxygen uptake before the transition to a more rapid rate (Fig. 2C), which coincided with radicle emergence. Times to 50% germination (t ₅₀) were highly correlated with median times for POD curves (Fig. 4B). As for T and Ψ, germination and respiration time courses at a range of KCN concentrations can be modelled by the dosage-based PBT model (equation 7; Fig. 3I–L; Table 1). As the response was logarithmic, the minimum threshold for a response was estimated to be 0.05 mM KCN, which was used for plotting the predicted curves for control seeds (Fig. 3I–L). Resembling the situation encountered with lower Ψ, seeds at higher KCN dosages adjusted their sensitivity thresholds and the populations became more uniform (σ decreased) (Table 1), and therefore responded differently than would be predicted by the model based on their responses to lower concentrations (Fig. 3I–L). Separating the dosages of KCN into high and low categories enabled each model to fit the individual seed data for both germination and respiration with high precision (see supplementary Fig. S1I–L; Table 1), as shown by the ability to normalize the data from each concentration range to single time courses using the dosage model (Fig. 5D–F) (Ni and Bradford, Reference Ni and Bradford1993).

The inhibition of respiration and the eventual recovery of germination in the presence of KCN suggested that tomato seeds might be capable of respiration via the alternative metabolic pathway that is sensitive to the inhibitor SHAM (Esashi et al., Reference Esashi, Sakai and Ushizawa1981). As for KCN, oxygen consumption rates were reduced in a dosage-dependent manner when tomato seeds were treated with SHAM (Fig. 2D), with a minimum response threshold estimated to be 0.4 mM for germination or 0.1–0.2 mM for respiration. This dosage dependence in response to SHAM was also complex, and showed two distinct response threshold regions, as occurred for KCN (Fig. 3M, O, P; Fig. 5G–I), except that increasing SHAM concentration above 2 mM had no further effect on R75 (Fig. 2D). Thus, only a single model was applied to the R75 data from 0 to 2 mM (Figs 3N, 5H). The differences in respiratory behaviour (R50 and R25) at low and high SHAM concentrations were accounted for by changes in all three parameters of the dosage model (Table 1). These sensitivity shifts could be due to metabolism of the inhibitors over time or shifts to alternative respiratory pathways. The different responses to inhibitor dosages provides evidence that metabolic adjustments can occur when respiration is inhibited, with possible relevance to the shift in Ψ _b(g) thresholds following incubation at low Ψ (Fig. 3F, G).

Given the presence of both cyanide-sensitive and cyanide-insensitive respiratory pathways in tomato seeds, we also tested the effects of combined exposure to both KCN and SHAM. As might be expected, when both respiratory pathways were blocked, both oxygen consumption and germination were strongly inhibited (supplementary Table S1). When the relationships between t ₅₀ for germination and median values for POD curves were plotted across all KCN and SHAM concentrations in which germination reached 50%, all points for a given oxygen depletion level fell on a similar linear trend (Fig. 4B). Thus, regardless of which respiratory pathway was inhibited, a given reduction in oxygen consumption rates was associated with a corresponding delay in germination rates. These results further support the conclusion that respiration, rather than other oxygen-consuming reactions, is primarily responsible for the oxygen depletion measured in the Q2. Interestingly, the relationships between germination rates and respiration rates in response to ABA and GA were similar to those for KCN and SHAM (Fig. 4B).

Germination and respiration responses to accelerated ageing and controlled deterioration (ageing model)

One of the earliest indications of seed ageing and deterioration is a slowing of the rate of germination, well before total viability is affected (Dell'Aquila, Reference Dell'Aquila1987; Tarquis and Bradford, Reference Tarquis and Bradford1992). We therefore asked whether such delays were also evident in respiration rates as seeds age. A PBT model has been developed specifically to analyse the germination time courses of seeds during ageing (Bradford et al., Reference Bradford, Tarquis and Duran1993). This model estimates the predicted maximum longevity of seeds under the storage conditions tested based upon changes in germination rates over storage times. The model assumes that seeds in the population exhibit a distribution of maximum potential lifetimes under the storage conditions (p _max(g)), and that the delay in germination with increasing ageing period is proportional to the fraction of that potential maximum storage lifetime that has already passed for each seed. That is, as the accumulated ageing period (p) approaches the maximum potential lifetime (p _max), the time to germination increases proportionately until germination does not occur at all (i.e. time to germination is infinite or germination rate is zero), which can be described as θ _age = [p − p _max(g)]t _g , where θ _age is the ageing time constant. The model can be fit as described previously (Bradford et al., Reference Bradford, Tarquis and Duran1993):

(8) $${\rm probit} \left( g \right) = \left[ {\,p - \left( {\theta _{{\rm age}}/t_g} \right) - p_{{\rm max}}\left( {50} \right)} \right]/\sigma _p{{\rm max}} $$

where p _max(50) is determined from the midpoint of the regression line and refers to the ageing period at which germination is reduced to 50% and σ _pmax is the standard deviation of p _max values among seeds in the population. We call this the ‘metronome model’ of seed ageing, as it implies that each seed has a maximum potential number of ‘ticks’ before losing viability (p _max), and the storage conditions (primarily moisture content and temperature) speed up or slow down the rate (in standard clock time) at which these ticks are used up, just as a metronome can run faster or slower depending upon the musical tempo.

Two types of rapid ageing treatments were tested: (1) controlled deterioration (33% RH equilibration followed by incubation at 50°C) for radish (R. sativus) seeds; and (2) more severe accelerated ageing (75% RH equilibration followed by incubation at 50°C) for lettuce seeds. We evaluated the effects of ageing on respiration and germination simultaneously by observing the radicle emergence times of individual seeds in the vials during Q2 measurements, so that individual oxygen depletion curves could be colour-coded based on the times of completion of germination of that same seed (see supplementary Fig. S5). In both cases, ageing conditions and time periods were selected that affected germination rates but viability remained high (Fig. 7A, E). The effects of both types of ageing conditions were readily apparent in delayed germination and slower oxygen depletion rates following imbibition (Fig. 7; supplementary Fig. S5). The PBT ageing model fitted well to both germination and respiration (i.e. POD curve) data for both species and ageing conditions (Table 1), as can be seen from comparison of the predicted and actual values (Fig. 7A–H, solid lines and symbols, respectively) and from the regression plots used to fit the models using equation (8) (see supplementary Fig. S6). This is also evident in the linear correlations between t ₅₀ values for germination and median times of the POD curves (Fig. 4C, D). The lack of a significant slope at the higher oxygen threshold level (R75) for radish seeds is due to the relatively small effect of ageing on the initial respiration rate of radish seeds compared to the delays in transition to higher respiration rates (supplementary Fig. S5A–D). In contrast to radish, respiratory patterns for individual lettuce seeds were quite heterogeneous within the population (supplementary Fig. S5E–H). Due to the presence of both sigmoid and linear respiratory patterns, average curves across the seed population resulted in patterns that did not match those of any individual seed (supplementary Fig. S5E–H, dashed black lines). Median curves somewhat more closely matched the actual shapes of the individual seed patterns, but again were a compromise among the different respiratory patterns exhibited (supplementary Fig. S5E–H, solid black lines). Germination of most control seeds was completed within 16 h, well before the large differences in subsequent respiration patterns occurred, which apparently reflect variation in respiration rates of lettuce seedlings. Q2 data for individual lettuce seeds/seedlings illustrate the wide physiological variation that can exist within apparently uniform seed lots (Still and Bradford, Reference Still and Bradford1997).

Figure 7. Germination time courses (A) and R75, R50 and R25 POD time courses (B–D) for untreated (control) radish seeds (open orange circles) or after 45 (green triangles), 66 (blue boxes) or 80 (dark blue circles) days of controlled deterioration at 33% RH and 50°C. Similarly, germination time courses (E and I) and R75, R50 and R25 POD time courses (F–H and J–L) for untreated (control) lettuce seeds (open orange circles), primed seeds (open red triangles) or seeds after 2 (green triangles), 4 (blue boxes) or 6 (purple circles) days of controlled deterioration at 75% RH and 50°C. The time courses predicted by the ageing time model for germination or respiration data are represented for all treatments on panels A–H as solid lines of the corresponding colour. Primed seeds were modelled using −1 day of ‘ageing’ time. Additionally, solid lines in panels I–L illustrate predicted time courses based upon summing the contributions of two distinct subpopulations in the seed lot (for details see supplementary Fig. S7).

Although the PBT model matched the overall respiratory pattern of ageing lettuce seeds relatively well (Fig. 7F–H), the double-sigmoid shape of the POD curves suggested that the seed lot was composed of two subfractions with different respiratory behaviours (particularly evident in Fig. 7G). The presence of subpopulations in the lettuce seed lot is also evident from the ‘bend’ (non-linearity) in the probit regressions of the lettuce ageing data, as compared to the linear probit plots (normal distribution) for the radish data (see supplementary Fig. S6F–H). We further analysed the lettuce data by assuming that the seed lot contained two different subpopulations with distinct respiratory threshold distribution parameters and responses to ageing. We then modelled the complete population time courses by summing the predicted time courses of each subpopulation across the time course (supplementary Fig. S7B–D; supplementary Table S2; modelling approach described in supplementary Fig. S7). This greatly improved the match between the modelled and actual respiratory behaviour of the complete population (Fig. 7J–L; supplementary Fig. S7J–L). We note that while subpopulations are quite obvious in the POD curves, the lower frequency of sampling for germination time-course data would not in itself justify a two-population model (Fig. 7E). However, applying the same approach to the germination data also improved the match of the model to the data across ageing periods (Fig. 7I; supplementary Fig. S7A, I). This modelling approach could theoretically be extended to include as many subpopulations as are justified by the data. In this way, complex germination or POD time courses can be ‘deconvoluted’ into multiple subpopulations, each with its own distribution and response to environmental, hormonal or chemical factors.

Germination and respiration responses to seed priming (ageing model)

Seed priming is a technique for accelerating germination by prehydrating seeds under controlled conditions to initiate germinative metabolism but prevent radicle emergence, which is then followed by seed drying (Bewley et al., Reference Bewley, Bradford, Hilhorst and Nonogaki2013). When primed seeds are subsequently imbibed, they exhibit accelerated germination rates. We therefore asked whether primed seeds also exhibit correspondingly accelerated respiration rates during imbibition. The same lettuce seed lot that was used for the ageing study was also primed and assayed for germination and respiration rates. Times to germination of lettuce seeds were slightly shortened by priming compared to control (untreated) seeds (Fig. 7E, I; supplementary Fig. S5E, I), but initial respiration rates were relatively unaffected, with the exception that slower germinating seeds now exhibited more rapid rates of oxygen depletion and shifted to more sigmoid patterns (supplementary Fig. S5I). This was also evident as a greater effect of priming on median R25 values than on R75 or R50 values (Fig. 4C, open symbols). Germination and respiration time courses of primed lettuce seeds were modelled using the same ageing model parameters developed for the accelerated ageing data, but using a ‘negative ageing’ time of −1 d under those ageing conditions and slightly adjusting the fraction of seeds in each subpopulation (see legend of supplementary Fig. S7). Priming may not actually ‘negatively age’ or ‘rejuvenate’ seeds, but its effect in advancing germination and accelerating respiration was equivalent to a negative ageing time in this model (Fig. 7E–H), and this worked particularly well when the subpopulation model was applied (Fig. 7I–L).