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Biological variance in the colour of Granny Smith apples
Postharvest Biology and Technology 50 (2008) 153–163
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Biological variance in the colour of Granny Smith apples Modelling the effect of senescence and chilling injury L.M.M. Tijskens a,∗ , P.J. Konopacki b , R.E. Schouten a , J. Hribar c , M. Simˇciˇc c a
Horticultural Supply Chains, Wageningen University, Marijkeweg 22, 6709 PG Wageningen, The Netherlands Institute of Pomology and Floriculture, Skierniewice, Poland c University of Ljubljana, Biotechnical Faculty, Slovenia b
a r t i c l e
i n f o
Article history: Received 3 January 2008 Accepted 17 May 2008 Keywords: Biological variance Modelling Maturity at harvest Growing conditions
a b s t r a c t The colour of ‘Granny Smith’ apples, harvested from three orchards at two stages of maturity, was measured individually using the CIE L*a*b* system during storage in regular atmosphere at three temperatures: 1, 4 and 10 ◦ C. A model was developed based on a simplified mechanism to describe the development of the apple colour during storage as affected by senescence (aging) and chilling injury. Monitoring of individual apples made it possible to include and to describe the biological variance of colour in batches of apples and to correct the colour of each apple individually for its own biological shift factor (biological age; random effect). The biological shift factor is related to the initial condition and range of colour change. The rate of the colour development was estimated in common (fixed effects) for all batches using non-linear mixed effects regression analysis. The variance accounted for by the developed model, including effects of temperature, harvest maturity and orchard location, was more than 95% on 3211 observations. The overall reaction rate constant of decolouration, combining the effects of senescence and chilling injury, was found to depend on temperature. The temperature that showed the lowest overall reaction rate of decolouration is 8 ◦ C, which is in contrast with the currently recommended storage temperature for ‘Granny Smith’ apples. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Colour of fruit and vegetables is one of the most important quality factors for consumers and buyers. It provides a simple and elegant way of assessing or estimating the maturity and stage of development of the commodity, without the need of destroying or even touching the product. The intensity of the deep green colour is one of the most important quality indicators for ‘Granny Smith’ apples. The preservation of the green colour of apples during storage and transport is therefore important for consumer acceptance. Understanding the development of colour is of utmost importance to achieve a quality, desired or asked for by the end-user, with respect to harvest date, storage conditions and facilities and the optimisation of the complete fruit supply chain. Modelling the development of colour during storage and related to harvest conditions and growing regions provides a systematic way to acquire that understanding and make predictions of colour and quality possible. The colour of apple skin is caused by chlorophyll and carotenoid pigments located in plastids and coloured phenolic pigments
∗ Corresponding author. E-mail address: [email protected] (L.M.M. Tijskens). 0925-5214/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.postharvbio.2008.05.008
(anthocyanins) and their uncoloured precursors (flavonols, and proanthocyanidins) located in the vacuole (Lancaster et al., 1994). For green apples like ‘Granny Smith’, changes in colour during storage are the result of loss of chlorophyll in the peel plastids. The green colour of chlorophyll normally masks the yellow pigments that are not appreciably affected by storage (Hung et al., 1995). Therefore, the loss of chlorophyll results in green apples turning yellow. The chlorophyll catabolism is affected by the increase of chlorophyllase activity during ripening of the fruit on the tree and during prolonged storage (Ihl et al., 1994). Preharvest conditions and actions that affect skin greenness are climatic conditions, high N-levels, dips in diphenylamine emulsion (Lurie et al., 1989) and heat treatments (Lurie et al., 1996; Mignani and Zocchi, 1998). Foliar sprays with urea are more effective in promoting greenness in green apples than the application of high levels of N fertilisation (Meheriuk et al., 1996). High levels of N fertilisation, however, reduce the fruit firmness and increase the incidence of postharvest disorders. With respect to postharvest conditions, CO2 shock treatment and controlled atmosphere storage reduce the chlorophyll degradation of apples (Hribar et al., 1994). In any batch of agricultural produce, variation will exist in all properties and quality attributes. Dealing with biological variation has become a major topic in recent literature, on theoretical
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Nomenclature bt chl col Eac Enz kc Nobs p R S.E.E. t t T
biological time (day) level of green compound (chlorophyll) (arbitrary) physical colour in the CIE L*a*b* system (arbitrary) energy of activation of colouring reaction (kJ mol−1 ) enzyme activity (arbitrary) rate constant of colouring reaction (mol−1 day−1 ) number of observations (–) probability (–) gas constant (8.3143 J K−1 mol−1 ) standard error of estimate (–) time of storage (day) biological shift factor (day) temperature (◦ C or K)
Subscripts 0 initial at time 0 max maximal value min minimal value ref at reference temperature (283 K (10 ◦ C)) stan standardised with respect to colmin Codes AS BL CM EH KK
Orchard at Arnovo Selo Orchard at Blanca commercial harvest early harvest Orchard at Krˇsko
(Tijskens et al., 2003; Schouten et al., 2004) and practical issues (Hertog, 2002; Lammertyn et al., 2003; Schouten et al., 2004; Hertog et al., 2004; De Ketelaere et al., 2006). During growth, small local differences in growing conditions (position of fruit on the tree, microclimate especially light and temperature, hormonal and nutritional effects) integrate into a considerable variation in maturity at the moment of harvest. When this occurs to a noticeable level in quality attributes, problems may arise when deciding what the best handling strategy will be. Sorting and grading on external attributes, like colour, size and defects, have successfully been applied for almost a century. With internal quality attributes (taste, flavour, vitamins, antioxidants, etc.) becoming increasingly important to consumers, the strategy of sorting and grading no longer functions properly in absence of rapid and non-destructive measuring techniques (Tijskens et al., 2003). Together with global sourcing of fruit and vegetables gaining in importance (Tijskens et al., 2006a), which generates even higher variation between batches, the lack of suitable techniques for sorting will make it necessary for horticulture and agriculture to understand biological variance, its origins and its behaviour in order to keep on complying with the changing demands of consumers. In this paper, colour data, expressed as a*value, from different orchards and harvest times are analysed over time (using a deterministic model) and per batch (by including biological variance in the deterministic model) to describe degreening of ‘Granny Smith’ apples. 2. Materials and methods 2.1. Materials Apples (Malus domesticus, Borkh. cv. Granny Smith) were grown at three different orchards in Slovenia in 1997. All orchards were in the south of Slovenia, near the border with Croatia. One orchard
with a clay soil was at Arnovo Selo (code AS). The orchard was 13 years old and M9 rootstock was used, planted in three rows. The second orchard with also a clay soil was at Blanca (code BL). The orchard was 12 years old and M9 rootstock was used, planted in one row. The third orchard was at Krˇsko (code KK), where the soil consists of pebble-porous river clay. The orchard was 22 years old and M9 rootstock was used, planted in one row. Apples were harvested at two stages of maturity, at commercial maturity (code CM) and 10 d earlier (code EH). Apples with a weight of about 200 g were divided into batches of 30 apples each and individually numbered. Apples with a marked blush (red on green) were excluded. Each apple was numbered in the upper quadrant and labelled at the equator using a water-resistant marker. Two arrows at a 90◦ angle were used to assign a measurement area to enable repeated colour measurements at exactly the same spot. 2.2. Methods The batches of individually marked apples were stored at three constant temperatures (1, 4 and 10 ◦ C) for up to 142 d in normal atmosphere. The relative humidity was not controlled but was roughly constant between 88% and 92% for all three temperatures. At regular intervals during storage (day 0, 28, 49, 79, 111, 142), the background colour was measured at the marked site at the equator of the apple. Colour measurements are carried out using the tristimulus colour analyser (Minolta CR-200, Minolta Co., Japan) expressing colour in the Commission Internationale d’Eclairage L*a*b* colour-space coordinates. The colour of the apples was measured and recorded for each apple individually. Previously developed models (Thai et al., 1990; Tijskens and Evelo, 1994; Shewfelt et al., 1988; Schouten et al., 2002; Hertog et al., 2004; Tijskens et al., 2007) were used as starting points to develop a model using Maple 10 (MapleSoft, Waterloo Maple Inc., Waterloo, Canada), a computer program capable of handling and solving algebraic and differential equations. 2.3. Model development The colour development depends on many factors. Some of them are obvious (e.g. cultivar and exposure of fruit to sun) while others could only be guessed (e.g. mineral content of the fruit skin). Some of those factors affect batches as a whole (e.g. cultivar, temperature, rate of reaction) while other factors are strictly individual for each fruit (e.g. amount of chlorophyll and of colouration decay products present). However, as colour formation and decay are chemical processes they certainly depend on time and temperature. 3. General function The pattern of colour change generally observed is a sigmoidal pattern that frequently is modelled and described by the logistic function (e.g. Thai et al., 1990; Tijskens and Evelo, 1994; Schouten et al., 1997; Hertog, 2002; Hertog et al., 2004; Tijskens et al., 2007). The raw data gathered in this multiple harvest and multiple location experiment do indicate that the sigmoidal is indeed the basic pattern. The apparently exponential decay observed represents then the lower half of the sigmoidal pattern for mature green fruit. In mathematical terms, the logistic equation is shown in Eq. (1): col=
colmax −colmin + colmin 1+(colmax −col0 )/(col0 − colmin ) · e−kc ·(colmax −colmin )·t (1)
with col the measured colour (here a*-value), colmax the maximum and colmin the minimum colour the apples can possibly reach and
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col0 the initial colour of each apple, t is the time (days) and kc the reaction rate constant (mol−1 day−1 ). 3.1. Mechanistic background The colouration process is very complex, even in simply green apples. The decolouration process of apples is probably caused by chlorophyll degradation into (yellow) pheophytin and colourless products (Heaton and Marangoni, 1996; Van Boekel, 2000) by action of some enzyme, probably chlorophyllase (Ihl et al., 1994). At the same time more enzyme is generated autocatalytically (Ihl et al., 1994). This indicates that the parallel reactions of decay of colouring compounds and of formation of enzyme, as described in the physiological models (Heaton and Marangoni, 1996; Van Boekel, 2000; Schouten et al., 2002) are somehow coupled and not independent of one another. In analogy to the colouration of tomatoes (Tijskens and Evelo, 1994) and of cucumbers (Schouten et al., 1997) the model of decolouration of apples can be represented in a simplified fashion by one autocatalytic reaction: kc
chl + Enz→2Enz
(2)
where chl is the level of substrate (chlorophyll) Enz is the molar amount of active enzyme (presumably chlorophyllase) and kc is the reaction rate constant of the decolouring process. The mechanism can be converted into a set of differential equations, using the rules of chemical kinetics: ∂ chl = −kc · chl · Enz ∂t ∂ Enz = kc · chl · Enz ∂t
(3)
At constant external conditions, e.g. temperature as in these experiments, Eq. (3) can be solved analytically. By converting the compound oriented expression in chl into the physical (colour) variable col using linear transformation, one arrives at the logistic function as shown in Eq. (1). 3.2. Biological shift factor and the variation between individuals The pre-exponential factor in Eq. (1) contains all the information on the initial condition (col0 ) of individual fruits and is converted into the biological shift factor (Tijskens et al., 2005) t* by an exponential transformation (Eq. (4)). colmax − col0 ∗ = et col0 − colmin
(4)
t* is a stochastic variable that contains all the information concerning maturity at harvest for each individual fruit in the whole batch, but now expressed in standardised dimensionless time relative to the midpoint of the logistic function. Standardised means that the variable time is expressed at a certain temperature, dimensionless means that it contains the information on range and rate. To express t* in the time dimension, this variable has to be divided by the rate constant at the desired temperature (kc,T ) and by the range in colour (Eq. (5)). t =
t ∗ (colmax − colmin )kc,T
(5)
3.3. Final equation used The factor colmax − colmin in the exponent of Eq. (1) and in the denominator of Eq. (5) is necessary to accommodate for the same relative change in time in case the total range of change in colour
Fig. 1. Measured (symbols dark gray = CM, light gray = EH) and simulated data (lines) plotted against time for all individual apples of orchard Arnovo Selo, both stages of harvest maturity stored at 1 ◦ C (top) and Blanca at 10 ◦ C (bottom). The few deviating lines are indeed outliers (high colmin value, high t value) compared to the other individuals, but were fully included in the analyses.
can vary with seasons and with different growing conditions. Substituting Eqs. (4) and (5) into Eq. (1), the final equation used in the analyses is obtained: col =
colmax − colmin + colmin 1 + e−kc ·(colmax −colmin )·(t+t)
(6)
To improve the representation of measured data, and to get rid of the disturbing effects of the potential greenness (colmin ), the data can be converted into a standardised form as shown in Eq. (7). a∗stan =
a∗ − colmin colmax − colmin
(7)
3.4. Density function Considering the behaviour of colour during storage, as shown in Fig. 1, one can readily see that the distribution of the a*-value (or better the standardised a*-value) will have a distribution that does depend on all the variables in the model, including time and reaction rate constant. That means that the shape of the distribution of measured data differs depending on the time and temperature of storage. This distribution function can be derived for the standardised values (a∗stan ) from the analytical solution assuming that the
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distribution of the biological shift factor is normal (Gaussian). Up to now an increasing number of analyses of measured data has not falsified this assumption. The actual derivation of the density function is described in Schouten et al. (2004) and Hertog et al. (2004). For the model used in this study (Eq. (6)) the distribution function can be derived as:
1−astan
Table 1 Description of batch and kinetic parameters Parameters
Typea
Description
Kinetic k1,ref
FE
Reference reaction rate of the chilling sensitive colouration reaction at reference temperature Tref Reaction rate constant for the senescence decolouration process at Tref Activation energy of the autocatalytic chilling sensitive reaction. For chilling sensitive reactions this value has a negative value Activation energy for the senescence decolouration process
k2,ref
FE
Ea1
FE
Ea2
FE
Batch colmax
FE
3.5. Effect of temperature
colmin
RE
Eq. (6) describes the change of colour as a function of storage time (t) and the biological shift factor (t). The reaction rate constant kc is assumed to depend on temperature (T) according to Arrhenius’ law (Eq. (9)). However, the process of the colour development proved to be susceptible (see below) to cold temperatures (chilling injury). This behaviour was also reported for apples by Pai and Sastry (1990). A similar increase in rate constant for chlorophyll degradation in Granny Smith apples can be found in the data provided in Fig. 1 of Dixon and Hewett (1998). The reaction rate constant of the process was therefore split up in two reaction rate constants to account for two separate processes: one for the chilling process (k1 ) and one for the process that describes the decolouration due to senescence or aging (k2 ). Both reaction rate constants depend on temperature according to Arrhenius law:
col0
RE
t
RE
log −t−
e
astan
kc ·(colmax −colmin )
−
2 2
−t
p= √ 2 · · · kc · (colmax − colmin ) · as tan · (as tan − 1)
(8)
where p is the density of the data (closely related to the more commonly used frequency) and is the standard deviation of the biological shift factor t.
kc = k1 + k2 Eai ki = ki,ref e R
1 Tref
−
1 T
(9)
where ki,ref is reference reaction rate constant of the decolouration due to chilling (i = 1) or to senescence (i = 2) processes at the reference temperature Tref , chosen to be 10 ◦ C. Eai is the activation energy of the respective reactions (kJ mol−1 ). Kinetic parameters describe the kinetics of the colouring process and are anticipated to be common for all fruit from the same cultivar and orchard (fixed effects), since they describe a common chemical process irrespective of the initial conditions. Batch parameters represent those properties that may be different for each individual in a batch (random effect) and which contain information on biological variation of each fruit. It is the randomness of these parameters that make batches different. In Table 1 an overview of these parameters and their meaning is shown. 4. Results and discussion Green to yellow colour changes are characterised by an increase of chromametric parameters a* and b*. A linear correlation (not shown) between visually observed colour changes and the a* parameter was found. As a more complex correlation was found for the b* parameter, the a* parameter was used to describe the apple colour. The raw data gathered in this multiple harvest and multiple location experiment indicate that the sigmoidal is indeed the basic pattern, although in most cases only the lower half of the sigmoid pattern is observed. An example of colour data, expressed as a*-value, together with the simulated behaviour (see below) is presented in Fig. 1. Some of the lines in this graph (e.g., top lines in
The maximum colour the apples can possibly reach (fixed at 5) The minimum colour each apple can possibly have reached The initial colour of each apple individually Biological shift factor of each apple relative to the midpoint of the logistic function
Tref = reference temperature (fixed at 10 ◦ C). a FE = fixed effect, RE = random effect.
bottom graph) show already the beginning of the second part of the sigmoidal behaviour by the flattening of the curve at higher times. Colour data were analysed using the non-linear mixed effects package (nlme with the default method ML maximising the loglikelihood) of R (R Development Core Team, 2005), with storage time and temperature simultaneous as explaining variables, taking the variation over the individuals and between the orchards and the stages of harvest maturity into account. All data were used individually and in their entirety without calculation of mean values. This means that all data were used and analysed without any further change, using colour, time, temperature, harvest maturity and orchard in a series of separate analyses. Kinetic parameters were estimated in common (fixed effects), the batch parameters were estimated individually (random effect). This means that the kinetic parameters (ki , ki,ref and Eai ) were forced to have the same value for all apples of each orchard and maturity stage, the batch parameters (t and colmin ) were estimated separately for each apple. 4.1. Analysis for the series separate To get a feeling of the behaviour of the data and to indicate where the major variation is in the data, first a preliminary analysis is done on series separate for harvest maturity, orchard and storage temperature. For each series, the analysis is based on Eq. (6), estimating t and colmin per individual (random effect), and the rate constant in common (fixed effects) maximised for log-likelihood (method ML). Despite the monitoring of colour development up to 142 d of storage at regular atmosphere, the a*-values did not reach the top half of model’s curve (see Fig. 1). As a consequence, the values of colmax could not be estimated. colmax was therefore fixed at a plausible value of 5 for all apples. The results of the analysis of the data for each orchard, harvest maturity and temperature separately, are shown in Table 2 (upper half). The percentages variance accounted 2 ) ranged from 94% to more than 98% for the 18 combinations for (Radj of orchard location and maturity at harvest and temperature. The reliability of the estimated parameters is high since the standard errors of estimate (lower half Table 2) are mostly below 10%. Occasionally an individual apple appears to be an outlier (see e.g. the uppermost lines in Fig. 1 top). The behaviour is, however,
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Table 2 Results of non-linear mixed effects regression analysis for each combination of harvest orchard and temperature separately Estimated parameter value Harvest
Orchard
Temperature
colmin
t
kc
Nobs
2 Radj
CM CM CM EH EH EH CM CM CM EH EH EH CM CM CM EH EH EH
AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK
1 1 1 1 1 1 4 4 4 4 4 4 10 10 10 10 10 10
−20.106 −20.711 −20.921 −20.052 −20.620 −20.953 −20.757 −20.880 −21.991 −20.711 −20.897 −22.825 −21.524 −23.868 −32.102 −21.287 −23.105 −27.626
−219.953 −175.759 −197.356 −226.484 −197.380 −213.252 −221.489 −190.292 −184.289 −240.897 −198.675 −205.328 −188.685 −135.027 −89.945 −186.221 −142.127 −106.146
0.001022 0.001195 0.000749 0.001076 0.001198 0.000771 0.000662 0.000831 0.000584 0.000634 0.000753 0.000437 0.000600 0.000560 0.000268 0.000705 0.000579 0.000398
27.820 27.203 30.041 21.867 25.048 28.997 12.852 12.780 31.967 10.438 24.584 26.669 22.234 27.479 31.193 28.912 15.623 17.317
180 178 179 180 180 180 180 178 180 180 180 180 174 179 176 171 178 178
0.944 0.961 0.954 0.956 0.954 0.962 0.976 0.909 0.973 0.963 0.959 0.983 0.967 0.980 0.980 0.972 0.979 0.979
Standard error of estimates Harvest
Orchard
Temperature
colmin
t
kc
CM CM CM EH EH EH CM CM CM EH EH EH CM CM CM EH EH EH
AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK
1 1 1 1 1 1 4 4 4 4 4 4 10 10 10 10 10 10
0.2160 0.1564 0.2433 0.2092 0.1473 0.1765 0.1607 0.2243 0.3313 0.2027 0.2470 0.3203 0.2759 0.4193 0.8411 0.2395 0.3634 0.8492
7.0317 5.5150 6.4687 6.7422 5.6498 6.4895 3.9188 4.2370 6.2419 5.6758 5.4648 5.2728 4.6574 5.3377 7.2477 5.7139 3.3138 5.3129
0.0000648 0.0000559 0.0000464 0.0000700 0.0000641 0.0000432 0.0000325 0.0000662 0.0000340 0.0000429 0.0000445 0.0000249 0.0000356 0.0000277 0.0000132 0.0000359 0.0000293 0.0000272
colmin and t are the mean values estimated separately (random effect each with 30 apples as Ngroups ), kc is estimated in common (fixed effects), is the standard deviation over all individual values of t. Top: estimated values, bottom: standard error of estimates.
fully represented in the model. The difference here is the high value for colmin and the high value for t for these apples. This indicates that those particular apples were less mature and had a less green appearance to start with. In Table 2, colmin represents the mean value of all the individually estimated colmin values. The differences between these mean values are rather large. That would indicate a major effect
of the growing conditions (like temperature, light, rain) during fruit growth. t reflects the mean value of all individually estimated biological shift factors. reflects the standard deviation of the t values. Together, both parameters describe the biological variation in the batches of apples. The behaviour and properties of these batch parameters will be covered in more detail below.
Table 3 Results of non-linear mixed effects regression analysis per temperature series for both harvest periods and orchard locations combined Estimates Harvest
Orchard
Temperature
colmin
t
kc
Nobs
2 Radj
All All All
All All All
1 4 10
−20.483 −21.168 −23.889
−203.989 −206.697 −149.866
0.001002 0.000654 0.000503
30.297 26.754 38.005
1077 1078 1056
0.955 0.962 0.976
Standard error estimates Harvest
Orchard
Temperature
colmin
t
kc
All All All
All All All
1 4 10
0.080 0.102 0.187
2.780 2.458 2.978
0.000024 0.000017 0.000011
colmin and t are the mean values estimated separately (random effect each with 180 apples as Ngroups ), kc is estimated in common (fixed effects), is the standard deviation over all individual values of t. Top: estimated values, bottom: standard error of estimates.
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L.M.M. Tijskens et al. / Postharvest Biology and Technology 50 (2008) 153–163 Table 4 Results of the final analysis combining all series over harvest maturity, orchard location and temperature according to Eqs. (6) and (9)
Fig. 2. Rate constants (day−1 ) (averaged over the harvest types) as function of temperature (◦ C). Symbols are estimated values for the three orchards (Table 2), lines simulated based on estimated values shown in Table 3.
The values for the rate constant kc for the different series at the same temperature in Table 2 are not significantly different and an effect of harvest time is not apparent. 4.2. Analysis combined per temperature Since the reaction rate constant kc is specific for the colour degradation process it is unlikely that it depends on orchard or maturity at harvest. Table 2 shows that kc values are indeed similar for each temperature series. The data of all the series are therefore used in a new non-linear mixed effects regression analysis per temperature of storage. In Table 3, the results of the analysis combining both harvest periods and all three orchard locations are shown. 2 ) are very high Again, the percentages variance accounted for (Radj (well over 95%) and the standard errors of estimates are small. Apparently, the reliability of the analysis has not been affected by combining orchards and harvest periods. 4.3. Including the effect of temperature Surprisingly the temperature has an unexpected effect on kc (Tables 2 and 3): with increasing temperatures the rate constant first decreases then increases (Fig. 2). This would indicate a chilling injury effect for this apple cultivar (Watkins et al., 1995; Burmeister and Dilley, 1995; Erkan and Pekmezcü, 2004). Decolouration in other fruit due to chilling injury is linked to ethylene exposure for avocado (Pesis et al., 2002) and stopped when applying 1-MCP for persimmon fruit (Salvador et al., 2004). Ethylene suppression through an antisense ACC oxidase gene considerably reduced the sensitivity to chilling injury of Charentais cantaloupe melons (BenAmor et al., 1999). So, it is plausible that, for ‘Granny Smith’ apples, ethylene is not only involved in the decolouration due to senescence, but also due in chilling injury. The effect of chilling injury on the rate constant has been modelled (Tijskens et al., 1994) as the sum of two separate rate constants of degradation, (see Eq. (9)) one for the chilling injury process (k1 ) and one for the senescence process (k2 ) occurring at higher temperatures. Both reaction rates depend on temperature according to Arrhenius’ law, one with a negative activation energy for k1 (Ea1 ) and one with a positive activation energy for k2 (Ea2 ). This approach is also applied here, although estimation of the activation energy for the colour degradation due to senescence was not possible due to the small temperature range (1–10 ◦ C) present in the experimental dataset. Based on the data provided by Ibarz et al. (1999) the activation energy for the colour degradation of pear puree was of 110 kJ/mol was estimated. Based on the report of Dixon and Hewett (1998) an activation energy for the colour degradation
colmin t k1,ref Ea1 k2,ref Ea2 Tref Nobs Ngroups 2 Radj
Value
S.E.E.
−21.498 −189.692 0.000210 −93.46 0.000390 80 41.007 283 (10 ◦ C) 3211 540 0.972
0.075 1.942 0.000024 8.07 0.000025 Fixed
colmin and t are the mean values estimated separately (random effect each with 540 apples as Ngroups ), k1,ref , k2,ref and Ea1 are estimated in common (fixed effects), is the standard deviation over all individual values of t.
for the hue angle of 46 kJ/mol and for chlorophyll decay in ‘Granny Smith’ apples of 43 kJ/mol was estimated. The activation energy for colour degradation at higher temperatures (k2 ) was therefore fixed at a plausible value of 80 kJ/mol. Table 4 shows the results of the final analysis, over all series of orchards, harvest dates and storage temperature. The percentage variance accounted for is 97% and all standard error of estimates are low: 1% or less for colmin and t, around 10% for the kinetic parameters k1,ref , k2,ref and Ea1 , which indicates that this pooling of data is allowed. In Fig. 3, the scatter plot is shown to indicate the overall goodness of fit. The choice of the fixed value of the activation energy Ea2 does of course affect the values estimated for the other kinetic constants (k1,ref , k2,ref , Ea1 ) in the subsequent analysis (Fig. 4, top). However, the overall rate constant, that is the sum of k1 and k2 at all three temperatures, was estimated the same independent of the choice of Ea2 (Fig. 4, bottom). As a consequence, fixing this activation energy neither affect the overall behaviour of colour, the estimated values for colmin , t nor the calculated standardised a*-value (see later). The determination of the proper values of the kinetic constants can be postponed until more appropriate data become available. To express the results of this analysis in a more comprehensive fashion, the a*-values were standardised according to Eq. (7), using the individual estimated value of colmin and the fixed value of 5 for colmax .
Fig. 3. Scatter plot for apples (all orchards and harvest dates) at the three storage temperatures.
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In Fig. 5 the measured data, converted according to Eq. (7), are shown as a function of the biological time (bt, which is the sum of the calendar time and the individually estimated t (Tijskens et al., 2007). A small difference in behaviour can be observed for the three storage temperatures (see Fig. 5 bottom right). Also one can observe a slight difference in range (both in biological time as in standardised a*-value) between the different orchards. All this information indicates that the degreening process in ‘Granny Smith’ apples is indeed independent of orchard and harvest maturity. Moreover, the values of the reaction rate constants at the different temperatures were highly similar as the ones reported by Dixon and Hewett (1998) for the hue angle in ‘Granny Smith’ apples and with the ones reported by Pai and Sastry (1990) for the a-values of ‘Red Delicious’ apples. From all this information, it is clear that the process of decolouration in apples is a generic process that can be modelled and analysed based on plausible mechanisms. Moreover, it is also clear that the decolouration is slightly susceptible to chilling injury at temperatures below 6–8 ◦ C.
4.4. Results on estimated batch parameters: the biological variance
Fig. 4. Top: Effect of choice in Ea2 value on the other three kinetic constants (k1,ref , k2,ref , Ea2 ). Activation energy Ea1 at the left axis, reference rate constants (k1,ref ,k2,ref ) at the right axis. Bottom: Overall rate constant at all temperatures independent of choice of Ea2 .
4.4.1. The biological shift factor t The biological shift factor represents the time difference of an individual fruit relative to the midpoint of the logistic curve (see e.g. Figs. 1 and 5) and is therefore indicative of its maturity. In most cases where the system of biological shift factor has been applied, the distribution of this parameter over all individuals in a batch
Fig. 5. Standardised measured a*-values versus biological time in days. Black () = Arnovo Selo, light gray () = Blanca, dark gray (+) = Krˇsko. Lines: simulated behaviour of standardised a*-value, based on parameters values from Table 4. Bottom right: simulated temperature effects combined.
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Table 5 Overview of variation in the estimated stochastic values of the different series L
H
a∗stan,max
btmin
btmax
tmean
AS AS BL BL KK KK AS BL KK
CM EH CM EH CM EH All All All
0.508 0.510 0.737 0.640 0.698 0.717 0.510 0.737 0.717
−0.484 −18.429 14.733 −8.765 23.653 −20.549 −0.484 14.733 23.653
192.138 187.532 260.784 201.260 234.715 239.014 187.532 260.784 239.014
−22.275 −30.731 14.660 2.979 20.422 14.945 −26.503 8.819 17.683
28.416 32.078 39.015 39.951 36.152 40.875 30.514 39.808 38.576
follows the normal or Gaussian distribution (Hertog et al., 2004; Schouten et al., 2004; Tijskens et al., 2006b, 2006c, 2007). In Table 5 an overview is shown for the minimum and maximum value of a∗stan and the biological time (bt), together with the average value and the standard deviation of t. Testing the distributions in t, relative to their own mean using the two sample Kolmogorov–Smirnov test, revealed no difference at all (p > .5) between the two harvest dates (commercial harvest CM and early harvest EH), except for their mean value. The difference in mean biological shift factor was about 8 d for the orchard at Arnovo Selo (AS), 12 d for the orchard Blanca (BL) and 5 d for the orchard Krˇsko (KK). That means that the apples of these orchards were 8, 12 or 5 d respectively less mature at the early harvest than
at the commercial harvest. That the difference between the two harvest dates is not exactly 10 d (the calendar difference between the harvests), reflects the variation in determining the commercial harvest date for each orchard, and the different circumstances of e.g. weather, during those last days in these orchards. Also can be taken from Table 5 (tmean ) that the three orchards differ considerably in maturity at harvest. This is probably also caused by the different weather conditions in these orchards during growth and ripening. Testing the distribution for the pooled biological shift factor t between the orchards using the two sample Kolmogorov–Smirnov test revealed that the distributions of the orchards at Blanca and Krˇsko were not distinguishable, while the one at Arnovo Selo had a smaller variation. That can also be observed from the difference in standard deviation () in Table 5. The number of rows the trees are planted in (one row at the Blanca and Krˇsko orchards, three rows at Arnovo Selo orchard), might be linked to this difference in . Trees planted in three rows will produce apples that have been grown more in the shade compared to those that are grown in one row. Less variation is expected for the apples from trees grown in three rows due to smaller variation in sunlight intensity.
4.4.2. The potential greenness of apples colmin From the examples shown in Fig. 1, especially the apparent outliers, it is clear that the potential greenness colmin will exhibit a large and asymmetrical distribution. The value of the parameter relates
Fig. 6. Distribution of potential greenness colmin per orchard showing the differences in mean values and standard deviation and pooled (right bottom).
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Fig. 7. Development in time of distribution in standardised colour during storage at 1 ◦ C for the orchard at Arnovo Selo.
to the amount of chlorophyll that has been accumulated in the skin during early development and represents the maximal greenness in very immature apples. Most probably it results from the actual situation in terms of shading and sun light of that apple during fruit set and growth. Although nothing much is known about the processes involved, the actual value of the potential greenness of apples seems to be of utmost importance. As long as data are represented in non-standardised a*-values, the development of colour appears to be erratic. As soon as the results are expressed in standardised values (a∗stan ) using the estimated values (Eq. (7)) for colmin , the development of colour becomes clear and can be interpreted in terms of temperature effects and individual differences. In Fig. 6 the distribution of colmin per orchard and combined is shown. For the orchard at Krˇsko, the distribution of colmin is much wider than for the orchards at Blanca and Arnovo Selo. At the same time the mean value is higher (less green) for the orchard at Arnovo Selo (see also Table 3). Both effects are apparently not related to the planting strategy in those orchards: one row at Blanca and Krˇsko and three rows at Arnovo Selo. The reason for the observed differences is not known. 4.4.3. The actual green colour of apples col The distribution in biological shift factor is more or less normal or Gaussian (as was assumed) and does not change shape during storage. Only the mean value shifts to higher times. For the colour variable itself, that does not hold. In Fig. 7, an example is shown for the development of the density of apple colour (Eq. (8)), expressed as standardised a*-value
(Eq. (7)) of the apples from the orchard at Arnovo Selo stored at 1 ◦ C. All other series show a similar behaviour. The density (bars) is based on the standardised a*-values, the lines are the simulated densities, calculated according to Eq. (8), using the parameters values as shown in Table 4. Differences in distribution pattern can clearly be observed. At the start of storage (time = 0 d), the distribution is sharp and skew, changing gradually to a wider and more bell shape curve with progressing time of storage (more mature and less green). That means that at the moment of harvest the perceived colour is quite homogeneous, but during storage the differences become more and more noticeable, resulting eventually in heterogeneous batches after storage. In Fig. 8, the simulated densities at the three storage temperatures of storage are shown for orchard Blanca. Clearly can be seen the broadening and flattening of the distribution during storage towards an intermediate state of maturity. The effect of the higher variation in biological shift factor for this orchard (and the one at Krˇsko) can be seen in the wider distribution at the start of storage compared to Fig. 7. One very evident observation can be made from this type of presentation: although the rate constants were estimated in common (fixed effects) for all individuals with the same actual value for any condition (random effects), the apparent rate of colour development (what is actually perceived) seems to be quite different for the immature, intermediate and mature individuals within a batch. The median value (at the maximum of the density curves in Fig. 8) develops at about half the rate of the mature individuals (to the right in the distribution), while the immature seem not to develop at all. As a consequence, the mean rate of development (not the rate
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constant) for a batch as a whole, will depend on the randomness of that batch at the start of the storage period. This is consistent with the theoretical observations made earlier (Tijskens and Wilkinson, 1996). It is also consistent with the many apparently erratic observations that batches with the same mean colour can develop quite differently. 5. Conclusions 2 ) obtained The high percentages variance accounted for (Radj confirm that even such a simple and maybe oversimplified model can effectively and efficiently represent the colour development of apples (or other fruit) including the existing variation between individual apples. The rate constants estimated are valid for all three orchards. For the narrow temperature range of 1–10 ◦ C studied, the rate of colour development was found to express a process of chilling injury. The high contribution of colmin parameter (representing the potential greenness) and t parameter (representing the biological age of each apple) to a reliable estimation confirms the importance of incorporating biological variance into models describing biological processes. Biological variance in a batch of products, and especially its development during subsequent storage, can be described and modelled in a deterministic way. The fundamental understanding of the processes involved, greatly increases the possibilities to deal with this apparently indestructible problem of perishable products. Monitoring quality attributes of individual items in a batch greatly enhances the possibilities to model, describe and predict batch behaviour of fruits and vegetables. When it is possible to develop an inexpensive device for colour monitoring of individual apples (Zude and Herold, 2002), managers of orchards and storage facilities will obtain a valuable tool to map the maturity differences in and between orchards. In that case labour allocation for harvesting and processing can be fine tuned to optimise the apple quality for consumers.
Acknowledgements This study was made financially possible by scholarships from cDLO, the Netherlands, and from the Ministry of Agriculture, Nature Management and Fisheries, the Netherlands. Further financial support from EU by means of a grant from COST 924 for a short term scientific mission is gratefully acknowledged. References
Fig. 8. Theoretical simulated density changes in standardised a*-value for the apples from orchard Blanco. Different lines are the storage times (lighter gray with increasing time).
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Postharvest Biology and Technology journal homepage: www.elsevier.com/locate/postharvbio
Biological variance in the colour of Granny Smith apples Modelling the effect of senescence and chilling injury L.M.M. Tijskens a,∗ , P.J. Konopacki b , R.E. Schouten a , J. Hribar c , M. Simˇciˇc c a
Horticultural Supply Chains, Wageningen University, Marijkeweg 22, 6709 PG Wageningen, The Netherlands Institute of Pomology and Floriculture, Skierniewice, Poland c University of Ljubljana, Biotechnical Faculty, Slovenia b
a r t i c l e
i n f o
Article history: Received 3 January 2008 Accepted 17 May 2008 Keywords: Biological variance Modelling Maturity at harvest Growing conditions
a b s t r a c t The colour of ‘Granny Smith’ apples, harvested from three orchards at two stages of maturity, was measured individually using the CIE L*a*b* system during storage in regular atmosphere at three temperatures: 1, 4 and 10 ◦ C. A model was developed based on a simplified mechanism to describe the development of the apple colour during storage as affected by senescence (aging) and chilling injury. Monitoring of individual apples made it possible to include and to describe the biological variance of colour in batches of apples and to correct the colour of each apple individually for its own biological shift factor (biological age; random effect). The biological shift factor is related to the initial condition and range of colour change. The rate of the colour development was estimated in common (fixed effects) for all batches using non-linear mixed effects regression analysis. The variance accounted for by the developed model, including effects of temperature, harvest maturity and orchard location, was more than 95% on 3211 observations. The overall reaction rate constant of decolouration, combining the effects of senescence and chilling injury, was found to depend on temperature. The temperature that showed the lowest overall reaction rate of decolouration is 8 ◦ C, which is in contrast with the currently recommended storage temperature for ‘Granny Smith’ apples. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Colour of fruit and vegetables is one of the most important quality factors for consumers and buyers. It provides a simple and elegant way of assessing or estimating the maturity and stage of development of the commodity, without the need of destroying or even touching the product. The intensity of the deep green colour is one of the most important quality indicators for ‘Granny Smith’ apples. The preservation of the green colour of apples during storage and transport is therefore important for consumer acceptance. Understanding the development of colour is of utmost importance to achieve a quality, desired or asked for by the end-user, with respect to harvest date, storage conditions and facilities and the optimisation of the complete fruit supply chain. Modelling the development of colour during storage and related to harvest conditions and growing regions provides a systematic way to acquire that understanding and make predictions of colour and quality possible. The colour of apple skin is caused by chlorophyll and carotenoid pigments located in plastids and coloured phenolic pigments
∗ Corresponding author. E-mail address: [email protected] (L.M.M. Tijskens). 0925-5214/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.postharvbio.2008.05.008
(anthocyanins) and their uncoloured precursors (flavonols, and proanthocyanidins) located in the vacuole (Lancaster et al., 1994). For green apples like ‘Granny Smith’, changes in colour during storage are the result of loss of chlorophyll in the peel plastids. The green colour of chlorophyll normally masks the yellow pigments that are not appreciably affected by storage (Hung et al., 1995). Therefore, the loss of chlorophyll results in green apples turning yellow. The chlorophyll catabolism is affected by the increase of chlorophyllase activity during ripening of the fruit on the tree and during prolonged storage (Ihl et al., 1994). Preharvest conditions and actions that affect skin greenness are climatic conditions, high N-levels, dips in diphenylamine emulsion (Lurie et al., 1989) and heat treatments (Lurie et al., 1996; Mignani and Zocchi, 1998). Foliar sprays with urea are more effective in promoting greenness in green apples than the application of high levels of N fertilisation (Meheriuk et al., 1996). High levels of N fertilisation, however, reduce the fruit firmness and increase the incidence of postharvest disorders. With respect to postharvest conditions, CO2 shock treatment and controlled atmosphere storage reduce the chlorophyll degradation of apples (Hribar et al., 1994). In any batch of agricultural produce, variation will exist in all properties and quality attributes. Dealing with biological variation has become a major topic in recent literature, on theoretical
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Nomenclature bt chl col Eac Enz kc Nobs p R S.E.E. t t T
biological time (day) level of green compound (chlorophyll) (arbitrary) physical colour in the CIE L*a*b* system (arbitrary) energy of activation of colouring reaction (kJ mol−1 ) enzyme activity (arbitrary) rate constant of colouring reaction (mol−1 day−1 ) number of observations (–) probability (–) gas constant (8.3143 J K−1 mol−1 ) standard error of estimate (–) time of storage (day) biological shift factor (day) temperature (◦ C or K)
Subscripts 0 initial at time 0 max maximal value min minimal value ref at reference temperature (283 K (10 ◦ C)) stan standardised with respect to colmin Codes AS BL CM EH KK
Orchard at Arnovo Selo Orchard at Blanca commercial harvest early harvest Orchard at Krˇsko
(Tijskens et al., 2003; Schouten et al., 2004) and practical issues (Hertog, 2002; Lammertyn et al., 2003; Schouten et al., 2004; Hertog et al., 2004; De Ketelaere et al., 2006). During growth, small local differences in growing conditions (position of fruit on the tree, microclimate especially light and temperature, hormonal and nutritional effects) integrate into a considerable variation in maturity at the moment of harvest. When this occurs to a noticeable level in quality attributes, problems may arise when deciding what the best handling strategy will be. Sorting and grading on external attributes, like colour, size and defects, have successfully been applied for almost a century. With internal quality attributes (taste, flavour, vitamins, antioxidants, etc.) becoming increasingly important to consumers, the strategy of sorting and grading no longer functions properly in absence of rapid and non-destructive measuring techniques (Tijskens et al., 2003). Together with global sourcing of fruit and vegetables gaining in importance (Tijskens et al., 2006a), which generates even higher variation between batches, the lack of suitable techniques for sorting will make it necessary for horticulture and agriculture to understand biological variance, its origins and its behaviour in order to keep on complying with the changing demands of consumers. In this paper, colour data, expressed as a*value, from different orchards and harvest times are analysed over time (using a deterministic model) and per batch (by including biological variance in the deterministic model) to describe degreening of ‘Granny Smith’ apples. 2. Materials and methods 2.1. Materials Apples (Malus domesticus, Borkh. cv. Granny Smith) were grown at three different orchards in Slovenia in 1997. All orchards were in the south of Slovenia, near the border with Croatia. One orchard
with a clay soil was at Arnovo Selo (code AS). The orchard was 13 years old and M9 rootstock was used, planted in three rows. The second orchard with also a clay soil was at Blanca (code BL). The orchard was 12 years old and M9 rootstock was used, planted in one row. The third orchard was at Krˇsko (code KK), where the soil consists of pebble-porous river clay. The orchard was 22 years old and M9 rootstock was used, planted in one row. Apples were harvested at two stages of maturity, at commercial maturity (code CM) and 10 d earlier (code EH). Apples with a weight of about 200 g were divided into batches of 30 apples each and individually numbered. Apples with a marked blush (red on green) were excluded. Each apple was numbered in the upper quadrant and labelled at the equator using a water-resistant marker. Two arrows at a 90◦ angle were used to assign a measurement area to enable repeated colour measurements at exactly the same spot. 2.2. Methods The batches of individually marked apples were stored at three constant temperatures (1, 4 and 10 ◦ C) for up to 142 d in normal atmosphere. The relative humidity was not controlled but was roughly constant between 88% and 92% for all three temperatures. At regular intervals during storage (day 0, 28, 49, 79, 111, 142), the background colour was measured at the marked site at the equator of the apple. Colour measurements are carried out using the tristimulus colour analyser (Minolta CR-200, Minolta Co., Japan) expressing colour in the Commission Internationale d’Eclairage L*a*b* colour-space coordinates. The colour of the apples was measured and recorded for each apple individually. Previously developed models (Thai et al., 1990; Tijskens and Evelo, 1994; Shewfelt et al., 1988; Schouten et al., 2002; Hertog et al., 2004; Tijskens et al., 2007) were used as starting points to develop a model using Maple 10 (MapleSoft, Waterloo Maple Inc., Waterloo, Canada), a computer program capable of handling and solving algebraic and differential equations. 2.3. Model development The colour development depends on many factors. Some of them are obvious (e.g. cultivar and exposure of fruit to sun) while others could only be guessed (e.g. mineral content of the fruit skin). Some of those factors affect batches as a whole (e.g. cultivar, temperature, rate of reaction) while other factors are strictly individual for each fruit (e.g. amount of chlorophyll and of colouration decay products present). However, as colour formation and decay are chemical processes they certainly depend on time and temperature. 3. General function The pattern of colour change generally observed is a sigmoidal pattern that frequently is modelled and described by the logistic function (e.g. Thai et al., 1990; Tijskens and Evelo, 1994; Schouten et al., 1997; Hertog, 2002; Hertog et al., 2004; Tijskens et al., 2007). The raw data gathered in this multiple harvest and multiple location experiment do indicate that the sigmoidal is indeed the basic pattern. The apparently exponential decay observed represents then the lower half of the sigmoidal pattern for mature green fruit. In mathematical terms, the logistic equation is shown in Eq. (1): col=
colmax −colmin + colmin 1+(colmax −col0 )/(col0 − colmin ) · e−kc ·(colmax −colmin )·t (1)
with col the measured colour (here a*-value), colmax the maximum and colmin the minimum colour the apples can possibly reach and
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col0 the initial colour of each apple, t is the time (days) and kc the reaction rate constant (mol−1 day−1 ). 3.1. Mechanistic background The colouration process is very complex, even in simply green apples. The decolouration process of apples is probably caused by chlorophyll degradation into (yellow) pheophytin and colourless products (Heaton and Marangoni, 1996; Van Boekel, 2000) by action of some enzyme, probably chlorophyllase (Ihl et al., 1994). At the same time more enzyme is generated autocatalytically (Ihl et al., 1994). This indicates that the parallel reactions of decay of colouring compounds and of formation of enzyme, as described in the physiological models (Heaton and Marangoni, 1996; Van Boekel, 2000; Schouten et al., 2002) are somehow coupled and not independent of one another. In analogy to the colouration of tomatoes (Tijskens and Evelo, 1994) and of cucumbers (Schouten et al., 1997) the model of decolouration of apples can be represented in a simplified fashion by one autocatalytic reaction: kc
chl + Enz→2Enz
(2)
where chl is the level of substrate (chlorophyll) Enz is the molar amount of active enzyme (presumably chlorophyllase) and kc is the reaction rate constant of the decolouring process. The mechanism can be converted into a set of differential equations, using the rules of chemical kinetics: ∂ chl = −kc · chl · Enz ∂t ∂ Enz = kc · chl · Enz ∂t
(3)
At constant external conditions, e.g. temperature as in these experiments, Eq. (3) can be solved analytically. By converting the compound oriented expression in chl into the physical (colour) variable col using linear transformation, one arrives at the logistic function as shown in Eq. (1). 3.2. Biological shift factor and the variation between individuals The pre-exponential factor in Eq. (1) contains all the information on the initial condition (col0 ) of individual fruits and is converted into the biological shift factor (Tijskens et al., 2005) t* by an exponential transformation (Eq. (4)). colmax − col0 ∗ = et col0 − colmin
(4)
t* is a stochastic variable that contains all the information concerning maturity at harvest for each individual fruit in the whole batch, but now expressed in standardised dimensionless time relative to the midpoint of the logistic function. Standardised means that the variable time is expressed at a certain temperature, dimensionless means that it contains the information on range and rate. To express t* in the time dimension, this variable has to be divided by the rate constant at the desired temperature (kc,T ) and by the range in colour (Eq. (5)). t =
t ∗ (colmax − colmin )kc,T
(5)
3.3. Final equation used The factor colmax − colmin in the exponent of Eq. (1) and in the denominator of Eq. (5) is necessary to accommodate for the same relative change in time in case the total range of change in colour
Fig. 1. Measured (symbols dark gray = CM, light gray = EH) and simulated data (lines) plotted against time for all individual apples of orchard Arnovo Selo, both stages of harvest maturity stored at 1 ◦ C (top) and Blanca at 10 ◦ C (bottom). The few deviating lines are indeed outliers (high colmin value, high t value) compared to the other individuals, but were fully included in the analyses.
can vary with seasons and with different growing conditions. Substituting Eqs. (4) and (5) into Eq. (1), the final equation used in the analyses is obtained: col =
colmax − colmin + colmin 1 + e−kc ·(colmax −colmin )·(t+t)
(6)
To improve the representation of measured data, and to get rid of the disturbing effects of the potential greenness (colmin ), the data can be converted into a standardised form as shown in Eq. (7). a∗stan =
a∗ − colmin colmax − colmin
(7)
3.4. Density function Considering the behaviour of colour during storage, as shown in Fig. 1, one can readily see that the distribution of the a*-value (or better the standardised a*-value) will have a distribution that does depend on all the variables in the model, including time and reaction rate constant. That means that the shape of the distribution of measured data differs depending on the time and temperature of storage. This distribution function can be derived for the standardised values (a∗stan ) from the analytical solution assuming that the
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distribution of the biological shift factor is normal (Gaussian). Up to now an increasing number of analyses of measured data has not falsified this assumption. The actual derivation of the density function is described in Schouten et al. (2004) and Hertog et al. (2004). For the model used in this study (Eq. (6)) the distribution function can be derived as:
1−astan
Table 1 Description of batch and kinetic parameters Parameters
Typea
Description
Kinetic k1,ref
FE
Reference reaction rate of the chilling sensitive colouration reaction at reference temperature Tref Reaction rate constant for the senescence decolouration process at Tref Activation energy of the autocatalytic chilling sensitive reaction. For chilling sensitive reactions this value has a negative value Activation energy for the senescence decolouration process
k2,ref
FE
Ea1
FE
Ea2
FE
Batch colmax
FE
3.5. Effect of temperature
colmin
RE
Eq. (6) describes the change of colour as a function of storage time (t) and the biological shift factor (t). The reaction rate constant kc is assumed to depend on temperature (T) according to Arrhenius’ law (Eq. (9)). However, the process of the colour development proved to be susceptible (see below) to cold temperatures (chilling injury). This behaviour was also reported for apples by Pai and Sastry (1990). A similar increase in rate constant for chlorophyll degradation in Granny Smith apples can be found in the data provided in Fig. 1 of Dixon and Hewett (1998). The reaction rate constant of the process was therefore split up in two reaction rate constants to account for two separate processes: one for the chilling process (k1 ) and one for the process that describes the decolouration due to senescence or aging (k2 ). Both reaction rate constants depend on temperature according to Arrhenius law:
col0
RE
t
RE
log −t−
e
astan
kc ·(colmax −colmin )
−
2 2
−t
p= √ 2 · · · kc · (colmax − colmin ) · as tan · (as tan − 1)
(8)
where p is the density of the data (closely related to the more commonly used frequency) and is the standard deviation of the biological shift factor t.
kc = k1 + k2 Eai ki = ki,ref e R
1 Tref
−
1 T
(9)
where ki,ref is reference reaction rate constant of the decolouration due to chilling (i = 1) or to senescence (i = 2) processes at the reference temperature Tref , chosen to be 10 ◦ C. Eai is the activation energy of the respective reactions (kJ mol−1 ). Kinetic parameters describe the kinetics of the colouring process and are anticipated to be common for all fruit from the same cultivar and orchard (fixed effects), since they describe a common chemical process irrespective of the initial conditions. Batch parameters represent those properties that may be different for each individual in a batch (random effect) and which contain information on biological variation of each fruit. It is the randomness of these parameters that make batches different. In Table 1 an overview of these parameters and their meaning is shown. 4. Results and discussion Green to yellow colour changes are characterised by an increase of chromametric parameters a* and b*. A linear correlation (not shown) between visually observed colour changes and the a* parameter was found. As a more complex correlation was found for the b* parameter, the a* parameter was used to describe the apple colour. The raw data gathered in this multiple harvest and multiple location experiment indicate that the sigmoidal is indeed the basic pattern, although in most cases only the lower half of the sigmoid pattern is observed. An example of colour data, expressed as a*-value, together with the simulated behaviour (see below) is presented in Fig. 1. Some of the lines in this graph (e.g., top lines in
The maximum colour the apples can possibly reach (fixed at 5) The minimum colour each apple can possibly have reached The initial colour of each apple individually Biological shift factor of each apple relative to the midpoint of the logistic function
Tref = reference temperature (fixed at 10 ◦ C). a FE = fixed effect, RE = random effect.
bottom graph) show already the beginning of the second part of the sigmoidal behaviour by the flattening of the curve at higher times. Colour data were analysed using the non-linear mixed effects package (nlme with the default method ML maximising the loglikelihood) of R (R Development Core Team, 2005), with storage time and temperature simultaneous as explaining variables, taking the variation over the individuals and between the orchards and the stages of harvest maturity into account. All data were used individually and in their entirety without calculation of mean values. This means that all data were used and analysed without any further change, using colour, time, temperature, harvest maturity and orchard in a series of separate analyses. Kinetic parameters were estimated in common (fixed effects), the batch parameters were estimated individually (random effect). This means that the kinetic parameters (ki , ki,ref and Eai ) were forced to have the same value for all apples of each orchard and maturity stage, the batch parameters (t and colmin ) were estimated separately for each apple. 4.1. Analysis for the series separate To get a feeling of the behaviour of the data and to indicate where the major variation is in the data, first a preliminary analysis is done on series separate for harvest maturity, orchard and storage temperature. For each series, the analysis is based on Eq. (6), estimating t and colmin per individual (random effect), and the rate constant in common (fixed effects) maximised for log-likelihood (method ML). Despite the monitoring of colour development up to 142 d of storage at regular atmosphere, the a*-values did not reach the top half of model’s curve (see Fig. 1). As a consequence, the values of colmax could not be estimated. colmax was therefore fixed at a plausible value of 5 for all apples. The results of the analysis of the data for each orchard, harvest maturity and temperature separately, are shown in Table 2 (upper half). The percentages variance accounted 2 ) ranged from 94% to more than 98% for the 18 combinations for (Radj of orchard location and maturity at harvest and temperature. The reliability of the estimated parameters is high since the standard errors of estimate (lower half Table 2) are mostly below 10%. Occasionally an individual apple appears to be an outlier (see e.g. the uppermost lines in Fig. 1 top). The behaviour is, however,
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Table 2 Results of non-linear mixed effects regression analysis for each combination of harvest orchard and temperature separately Estimated parameter value Harvest
Orchard
Temperature
colmin
t
kc
Nobs
2 Radj
CM CM CM EH EH EH CM CM CM EH EH EH CM CM CM EH EH EH
AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK
1 1 1 1 1 1 4 4 4 4 4 4 10 10 10 10 10 10
−20.106 −20.711 −20.921 −20.052 −20.620 −20.953 −20.757 −20.880 −21.991 −20.711 −20.897 −22.825 −21.524 −23.868 −32.102 −21.287 −23.105 −27.626
−219.953 −175.759 −197.356 −226.484 −197.380 −213.252 −221.489 −190.292 −184.289 −240.897 −198.675 −205.328 −188.685 −135.027 −89.945 −186.221 −142.127 −106.146
0.001022 0.001195 0.000749 0.001076 0.001198 0.000771 0.000662 0.000831 0.000584 0.000634 0.000753 0.000437 0.000600 0.000560 0.000268 0.000705 0.000579 0.000398
27.820 27.203 30.041 21.867 25.048 28.997 12.852 12.780 31.967 10.438 24.584 26.669 22.234 27.479 31.193 28.912 15.623 17.317
180 178 179 180 180 180 180 178 180 180 180 180 174 179 176 171 178 178
0.944 0.961 0.954 0.956 0.954 0.962 0.976 0.909 0.973 0.963 0.959 0.983 0.967 0.980 0.980 0.972 0.979 0.979
Standard error of estimates Harvest
Orchard
Temperature
colmin
t
kc
CM CM CM EH EH EH CM CM CM EH EH EH CM CM CM EH EH EH
AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK AS BL KK
1 1 1 1 1 1 4 4 4 4 4 4 10 10 10 10 10 10
0.2160 0.1564 0.2433 0.2092 0.1473 0.1765 0.1607 0.2243 0.3313 0.2027 0.2470 0.3203 0.2759 0.4193 0.8411 0.2395 0.3634 0.8492
7.0317 5.5150 6.4687 6.7422 5.6498 6.4895 3.9188 4.2370 6.2419 5.6758 5.4648 5.2728 4.6574 5.3377 7.2477 5.7139 3.3138 5.3129
0.0000648 0.0000559 0.0000464 0.0000700 0.0000641 0.0000432 0.0000325 0.0000662 0.0000340 0.0000429 0.0000445 0.0000249 0.0000356 0.0000277 0.0000132 0.0000359 0.0000293 0.0000272
colmin and t are the mean values estimated separately (random effect each with 30 apples as Ngroups ), kc is estimated in common (fixed effects), is the standard deviation over all individual values of t. Top: estimated values, bottom: standard error of estimates.
fully represented in the model. The difference here is the high value for colmin and the high value for t for these apples. This indicates that those particular apples were less mature and had a less green appearance to start with. In Table 2, colmin represents the mean value of all the individually estimated colmin values. The differences between these mean values are rather large. That would indicate a major effect
of the growing conditions (like temperature, light, rain) during fruit growth. t reflects the mean value of all individually estimated biological shift factors. reflects the standard deviation of the t values. Together, both parameters describe the biological variation in the batches of apples. The behaviour and properties of these batch parameters will be covered in more detail below.
Table 3 Results of non-linear mixed effects regression analysis per temperature series for both harvest periods and orchard locations combined Estimates Harvest
Orchard
Temperature
colmin
t
kc
Nobs
2 Radj
All All All
All All All
1 4 10
−20.483 −21.168 −23.889
−203.989 −206.697 −149.866
0.001002 0.000654 0.000503
30.297 26.754 38.005
1077 1078 1056
0.955 0.962 0.976
Standard error estimates Harvest
Orchard
Temperature
colmin
t
kc
All All All
All All All
1 4 10
0.080 0.102 0.187
2.780 2.458 2.978
0.000024 0.000017 0.000011
colmin and t are the mean values estimated separately (random effect each with 180 apples as Ngroups ), kc is estimated in common (fixed effects), is the standard deviation over all individual values of t. Top: estimated values, bottom: standard error of estimates.
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Fig. 2. Rate constants (day−1 ) (averaged over the harvest types) as function of temperature (◦ C). Symbols are estimated values for the three orchards (Table 2), lines simulated based on estimated values shown in Table 3.
The values for the rate constant kc for the different series at the same temperature in Table 2 are not significantly different and an effect of harvest time is not apparent. 4.2. Analysis combined per temperature Since the reaction rate constant kc is specific for the colour degradation process it is unlikely that it depends on orchard or maturity at harvest. Table 2 shows that kc values are indeed similar for each temperature series. The data of all the series are therefore used in a new non-linear mixed effects regression analysis per temperature of storage. In Table 3, the results of the analysis combining both harvest periods and all three orchard locations are shown. 2 ) are very high Again, the percentages variance accounted for (Radj (well over 95%) and the standard errors of estimates are small. Apparently, the reliability of the analysis has not been affected by combining orchards and harvest periods. 4.3. Including the effect of temperature Surprisingly the temperature has an unexpected effect on kc (Tables 2 and 3): with increasing temperatures the rate constant first decreases then increases (Fig. 2). This would indicate a chilling injury effect for this apple cultivar (Watkins et al., 1995; Burmeister and Dilley, 1995; Erkan and Pekmezcü, 2004). Decolouration in other fruit due to chilling injury is linked to ethylene exposure for avocado (Pesis et al., 2002) and stopped when applying 1-MCP for persimmon fruit (Salvador et al., 2004). Ethylene suppression through an antisense ACC oxidase gene considerably reduced the sensitivity to chilling injury of Charentais cantaloupe melons (BenAmor et al., 1999). So, it is plausible that, for ‘Granny Smith’ apples, ethylene is not only involved in the decolouration due to senescence, but also due in chilling injury. The effect of chilling injury on the rate constant has been modelled (Tijskens et al., 1994) as the sum of two separate rate constants of degradation, (see Eq. (9)) one for the chilling injury process (k1 ) and one for the senescence process (k2 ) occurring at higher temperatures. Both reaction rates depend on temperature according to Arrhenius’ law, one with a negative activation energy for k1 (Ea1 ) and one with a positive activation energy for k2 (Ea2 ). This approach is also applied here, although estimation of the activation energy for the colour degradation due to senescence was not possible due to the small temperature range (1–10 ◦ C) present in the experimental dataset. Based on the data provided by Ibarz et al. (1999) the activation energy for the colour degradation of pear puree was of 110 kJ/mol was estimated. Based on the report of Dixon and Hewett (1998) an activation energy for the colour degradation
colmin t k1,ref Ea1 k2,ref Ea2 Tref Nobs Ngroups 2 Radj
Value
S.E.E.
−21.498 −189.692 0.000210 −93.46 0.000390 80 41.007 283 (10 ◦ C) 3211 540 0.972
0.075 1.942 0.000024 8.07 0.000025 Fixed
colmin and t are the mean values estimated separately (random effect each with 540 apples as Ngroups ), k1,ref , k2,ref and Ea1 are estimated in common (fixed effects), is the standard deviation over all individual values of t.
for the hue angle of 46 kJ/mol and for chlorophyll decay in ‘Granny Smith’ apples of 43 kJ/mol was estimated. The activation energy for colour degradation at higher temperatures (k2 ) was therefore fixed at a plausible value of 80 kJ/mol. Table 4 shows the results of the final analysis, over all series of orchards, harvest dates and storage temperature. The percentage variance accounted for is 97% and all standard error of estimates are low: 1% or less for colmin and t, around 10% for the kinetic parameters k1,ref , k2,ref and Ea1 , which indicates that this pooling of data is allowed. In Fig. 3, the scatter plot is shown to indicate the overall goodness of fit. The choice of the fixed value of the activation energy Ea2 does of course affect the values estimated for the other kinetic constants (k1,ref , k2,ref , Ea1 ) in the subsequent analysis (Fig. 4, top). However, the overall rate constant, that is the sum of k1 and k2 at all three temperatures, was estimated the same independent of the choice of Ea2 (Fig. 4, bottom). As a consequence, fixing this activation energy neither affect the overall behaviour of colour, the estimated values for colmin , t nor the calculated standardised a*-value (see later). The determination of the proper values of the kinetic constants can be postponed until more appropriate data become available. To express the results of this analysis in a more comprehensive fashion, the a*-values were standardised according to Eq. (7), using the individual estimated value of colmin and the fixed value of 5 for colmax .
Fig. 3. Scatter plot for apples (all orchards and harvest dates) at the three storage temperatures.
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In Fig. 5 the measured data, converted according to Eq. (7), are shown as a function of the biological time (bt, which is the sum of the calendar time and the individually estimated t (Tijskens et al., 2007). A small difference in behaviour can be observed for the three storage temperatures (see Fig. 5 bottom right). Also one can observe a slight difference in range (both in biological time as in standardised a*-value) between the different orchards. All this information indicates that the degreening process in ‘Granny Smith’ apples is indeed independent of orchard and harvest maturity. Moreover, the values of the reaction rate constants at the different temperatures were highly similar as the ones reported by Dixon and Hewett (1998) for the hue angle in ‘Granny Smith’ apples and with the ones reported by Pai and Sastry (1990) for the a-values of ‘Red Delicious’ apples. From all this information, it is clear that the process of decolouration in apples is a generic process that can be modelled and analysed based on plausible mechanisms. Moreover, it is also clear that the decolouration is slightly susceptible to chilling injury at temperatures below 6–8 ◦ C.
4.4. Results on estimated batch parameters: the biological variance
Fig. 4. Top: Effect of choice in Ea2 value on the other three kinetic constants (k1,ref , k2,ref , Ea2 ). Activation energy Ea1 at the left axis, reference rate constants (k1,ref ,k2,ref ) at the right axis. Bottom: Overall rate constant at all temperatures independent of choice of Ea2 .
4.4.1. The biological shift factor t The biological shift factor represents the time difference of an individual fruit relative to the midpoint of the logistic curve (see e.g. Figs. 1 and 5) and is therefore indicative of its maturity. In most cases where the system of biological shift factor has been applied, the distribution of this parameter over all individuals in a batch
Fig. 5. Standardised measured a*-values versus biological time in days. Black () = Arnovo Selo, light gray () = Blanca, dark gray (+) = Krˇsko. Lines: simulated behaviour of standardised a*-value, based on parameters values from Table 4. Bottom right: simulated temperature effects combined.
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Table 5 Overview of variation in the estimated stochastic values of the different series L
H
a∗stan,max
btmin
btmax
tmean
AS AS BL BL KK KK AS BL KK
CM EH CM EH CM EH All All All
0.508 0.510 0.737 0.640 0.698 0.717 0.510 0.737 0.717
−0.484 −18.429 14.733 −8.765 23.653 −20.549 −0.484 14.733 23.653
192.138 187.532 260.784 201.260 234.715 239.014 187.532 260.784 239.014
−22.275 −30.731 14.660 2.979 20.422 14.945 −26.503 8.819 17.683
28.416 32.078 39.015 39.951 36.152 40.875 30.514 39.808 38.576
follows the normal or Gaussian distribution (Hertog et al., 2004; Schouten et al., 2004; Tijskens et al., 2006b, 2006c, 2007). In Table 5 an overview is shown for the minimum and maximum value of a∗stan and the biological time (bt), together with the average value and the standard deviation of t. Testing the distributions in t, relative to their own mean using the two sample Kolmogorov–Smirnov test, revealed no difference at all (p > .5) between the two harvest dates (commercial harvest CM and early harvest EH), except for their mean value. The difference in mean biological shift factor was about 8 d for the orchard at Arnovo Selo (AS), 12 d for the orchard Blanca (BL) and 5 d for the orchard Krˇsko (KK). That means that the apples of these orchards were 8, 12 or 5 d respectively less mature at the early harvest than
at the commercial harvest. That the difference between the two harvest dates is not exactly 10 d (the calendar difference between the harvests), reflects the variation in determining the commercial harvest date for each orchard, and the different circumstances of e.g. weather, during those last days in these orchards. Also can be taken from Table 5 (tmean ) that the three orchards differ considerably in maturity at harvest. This is probably also caused by the different weather conditions in these orchards during growth and ripening. Testing the distribution for the pooled biological shift factor t between the orchards using the two sample Kolmogorov–Smirnov test revealed that the distributions of the orchards at Blanca and Krˇsko were not distinguishable, while the one at Arnovo Selo had a smaller variation. That can also be observed from the difference in standard deviation () in Table 5. The number of rows the trees are planted in (one row at the Blanca and Krˇsko orchards, three rows at Arnovo Selo orchard), might be linked to this difference in . Trees planted in three rows will produce apples that have been grown more in the shade compared to those that are grown in one row. Less variation is expected for the apples from trees grown in three rows due to smaller variation in sunlight intensity.
4.4.2. The potential greenness of apples colmin From the examples shown in Fig. 1, especially the apparent outliers, it is clear that the potential greenness colmin will exhibit a large and asymmetrical distribution. The value of the parameter relates
Fig. 6. Distribution of potential greenness colmin per orchard showing the differences in mean values and standard deviation and pooled (right bottom).
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Fig. 7. Development in time of distribution in standardised colour during storage at 1 ◦ C for the orchard at Arnovo Selo.
to the amount of chlorophyll that has been accumulated in the skin during early development and represents the maximal greenness in very immature apples. Most probably it results from the actual situation in terms of shading and sun light of that apple during fruit set and growth. Although nothing much is known about the processes involved, the actual value of the potential greenness of apples seems to be of utmost importance. As long as data are represented in non-standardised a*-values, the development of colour appears to be erratic. As soon as the results are expressed in standardised values (a∗stan ) using the estimated values (Eq. (7)) for colmin , the development of colour becomes clear and can be interpreted in terms of temperature effects and individual differences. In Fig. 6 the distribution of colmin per orchard and combined is shown. For the orchard at Krˇsko, the distribution of colmin is much wider than for the orchards at Blanca and Arnovo Selo. At the same time the mean value is higher (less green) for the orchard at Arnovo Selo (see also Table 3). Both effects are apparently not related to the planting strategy in those orchards: one row at Blanca and Krˇsko and three rows at Arnovo Selo. The reason for the observed differences is not known. 4.4.3. The actual green colour of apples col The distribution in biological shift factor is more or less normal or Gaussian (as was assumed) and does not change shape during storage. Only the mean value shifts to higher times. For the colour variable itself, that does not hold. In Fig. 7, an example is shown for the development of the density of apple colour (Eq. (8)), expressed as standardised a*-value
(Eq. (7)) of the apples from the orchard at Arnovo Selo stored at 1 ◦ C. All other series show a similar behaviour. The density (bars) is based on the standardised a*-values, the lines are the simulated densities, calculated according to Eq. (8), using the parameters values as shown in Table 4. Differences in distribution pattern can clearly be observed. At the start of storage (time = 0 d), the distribution is sharp and skew, changing gradually to a wider and more bell shape curve with progressing time of storage (more mature and less green). That means that at the moment of harvest the perceived colour is quite homogeneous, but during storage the differences become more and more noticeable, resulting eventually in heterogeneous batches after storage. In Fig. 8, the simulated densities at the three storage temperatures of storage are shown for orchard Blanca. Clearly can be seen the broadening and flattening of the distribution during storage towards an intermediate state of maturity. The effect of the higher variation in biological shift factor for this orchard (and the one at Krˇsko) can be seen in the wider distribution at the start of storage compared to Fig. 7. One very evident observation can be made from this type of presentation: although the rate constants were estimated in common (fixed effects) for all individuals with the same actual value for any condition (random effects), the apparent rate of colour development (what is actually perceived) seems to be quite different for the immature, intermediate and mature individuals within a batch. The median value (at the maximum of the density curves in Fig. 8) develops at about half the rate of the mature individuals (to the right in the distribution), while the immature seem not to develop at all. As a consequence, the mean rate of development (not the rate
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constant) for a batch as a whole, will depend on the randomness of that batch at the start of the storage period. This is consistent with the theoretical observations made earlier (Tijskens and Wilkinson, 1996). It is also consistent with the many apparently erratic observations that batches with the same mean colour can develop quite differently. 5. Conclusions 2 ) obtained The high percentages variance accounted for (Radj confirm that even such a simple and maybe oversimplified model can effectively and efficiently represent the colour development of apples (or other fruit) including the existing variation between individual apples. The rate constants estimated are valid for all three orchards. For the narrow temperature range of 1–10 ◦ C studied, the rate of colour development was found to express a process of chilling injury. The high contribution of colmin parameter (representing the potential greenness) and t parameter (representing the biological age of each apple) to a reliable estimation confirms the importance of incorporating biological variance into models describing biological processes. Biological variance in a batch of products, and especially its development during subsequent storage, can be described and modelled in a deterministic way. The fundamental understanding of the processes involved, greatly increases the possibilities to deal with this apparently indestructible problem of perishable products. Monitoring quality attributes of individual items in a batch greatly enhances the possibilities to model, describe and predict batch behaviour of fruits and vegetables. When it is possible to develop an inexpensive device for colour monitoring of individual apples (Zude and Herold, 2002), managers of orchards and storage facilities will obtain a valuable tool to map the maturity differences in and between orchards. In that case labour allocation for harvesting and processing can be fine tuned to optimise the apple quality for consumers.
Acknowledgements This study was made financially possible by scholarships from cDLO, the Netherlands, and from the Ministry of Agriculture, Nature Management and Fisheries, the Netherlands. Further financial support from EU by means of a grant from COST 924 for a short term scientific mission is gratefully acknowledged. References
Fig. 8. Theoretical simulated density changes in standardised a*-value for the apples from orchard Blanco. Different lines are the storage times (lighter gray with increasing time).
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