ORIGINAL PAPER

Mathematical modelling of the accumulation of carbohydratesand organic acids throughout the ripening process of Hungariansour cherry cultivars

G. Ficzek • M. Ladanyi • G. Vegvari •

M. Toth

Received: 18 August 2014 / Revised: 24 November 2014 / Accepted: 19 January 2015 / Published online: 1 February 2015

� Springer-Verlag Berlin Heidelberg 2015

Abstract

Key message Changes in sugar and acid content of

Hungarian sour cherries during the ripening period can

be described by a mathematical model.

Abstract The Hungarian sour cherry cultivars can be

utilised not only as raw material for the food industry, but

also for fresh consumption. Changes in the main sugar and

organic acid components in the fruit of sour cherry culti-

vars bred in Hungary (‘Erdi jubileum’, ‘Erdi b}oterm}o’,

‘Maliga emleke’, ‘Kantorjanosi 3’ and IV-3/48) were

determined with the aid of HPLC analysis at nine sam-

pling dates during the ripening process. The main carbo-

hydrate components of the fruit of the Hungarian

cultivars tested were glucose (48.73–81.57 mg/g), fructose

(30.99–60.26 mg/g) and sucrose (11.67–50.37 mg/g). In

the course of ripening the changes in the glucose and

fructose contents could be described using a saturation

model, and changes in the sucrose content with an expo-

nential model. The main organic acid components were

malic acid (220.38–382.72 mg/g), succinic acid

(104.54–209.90 mg/g), tartaric acid (89.04–182.01 mg/g)

and ascorbic acid (4.60–17.49 mg/g). In general the

decrease in the organic acid components could be descri-

bed using a decreasing saturation model, while the vitamin

C content either increased in the course of ripening

according to a logistic model or exhibited a decline that

could be described with a quadratic function. Conse-

quently, there were substantial differences in the sugar and

acid profiles of the various Hungarian sour cherry cultivars,

some of which can be recommended for use as parents in

breeding for better chemical quality.

Keywords Prunus cerasus L. � Fruit development �HPLC � Regression model

Introduction

The consumption of sour cherries (Prunus cerasus L.) is of

considerable importance due to their suitability for pro-

cessing, their extremely favourable composition and par-

ticularly their beneficial effect on human health. Their

favourable dietary effect can be attributed not only to their

high content of polyphenols, flavonoids and anthocyanins

(Chaovanalikit and Wrolstad 2004; Kirakosyan et al. 2009;

Khoo et al. 2011), but also to the average or above-average

quantities of minerals (K, Ca, Mg, Fe, Cu, Zn, Mn)

(Mester-Ficzek et al. 2008).

The growing conditions in the Carpathian Basin are

ideally suited to the ecological requirements of sour cher-

ries, as is clear from the large number of landraces and the

wide variety of forms presented by the cultivars. Crossing

and regional selection have resulted in numerous Hungar-

ian sour cherry cultivars, which have also been tested in

Communicated by E. Priesack.

G. Ficzek (&) � M. Toth

Department of Pomology, Faculty of Horticultural Sciences,

Corvinus University of Budapest, Villanyi ut 29-43,

1118 Budapest, Hungary

e-mail: gitta.ficzek@uni-corvinus.hu

M. Ladanyi

Department of Mathematics and Informatics, Faculty of

Horticultural Sciences, Corvinus University of Budapest,

Villanyi ut 29-43, 1118 Budapest, Hungary

G. Vegvari

Department of Soil Science and Water Management, Faculty of

Horticultural Sciences, Corvinus University of Budapest,

Villanyi ut 29-43, 1118 Budapest, Hungary

123

Trees (2015) 29:797–807

DOI 10.1007/s00468-015-1159-6

other countries in Europe and America. In addition to a

number of advantageous cultivar traits (e.g. self-fertility),

the Hungarian cultivars also have outstanding anthocyanin

content, while their anthocyanin profile is completely dif-

ferent from that of West European and American cultivars

(Ficzek et al. 2011). An important aim of further breeding

is to improve the fruit quality and the beneficial health

effects, which will require an expansion of the basic

breeding materials. The breeding value of certain Hun-

garian sour cherry cultivars (‘Erdi b}oterm}o’, ‘Ujfehertoi

furtos’) has also been recognised in the USA (Wang et al.

2000; Iezzoni et al. 2005).

The quantity and ratio of carbohydrate and acid com-

ponents determine the flavour of the fruit and the nature of

the products manufactured from them. The chemical

components in the ripe fruit have been proved to differ

from one cultivar to another (Scalzo et al. 2005; Dragovic-

Uzelac et al. 2007), while the findings of Poll et al. (2003)

and Steger-Mate et al. (2010) have shown that they also

depend on the stage of maturity. Whether the end-use will

be fresh consumption or industrial processing, it is thus

important to monitor the accumulation of primary photo-

synthetic metabolites over the course of ripening. The

growth of stone fruits can be described by a double sigmoid

curve consisting of growth stages I–III (Tukey 1934). In

stage I intensive cell division results in a substantial rate of

growth, after which the hardening of the endocarp during

stage II is accompanied by slower growth. In stage III,

which is again characterised by intensive growth, carbo-

hydrates are accumulated and ripening processes begin.

The biological productivity of the cultivars is thus influ-

enced not only by the increase in fruit size, but also by the

accumulation of primary photosynthetic metabolites.

Information is available on the sugar and acid composition

of various fruit species and cultivars at harvest maturity

(Souci et al. 2008), but few data have been published on

how these parameters change in the course of ripening.

Changes in the sugar components during fruit development

were studied in ‘Golden Delicious’ apples by Beruter and

Kalberer (1983) and in ‘Suncrest’ peaches by Genard et al.

(1996). Walker et al. (2011) monitored changes in the

soluble carbohydrate components of the sweet cherry cul-

tivar ‘Durone Nero II’ during fruit development, while Gao

et al. (2003) determined the transport of sorbitol in

‘Montmorency’ as the fruit developed, but changes in the

sugar and acid components during the ripening process

have not yet been analysed in sour cherry.

The aim of the present research was to determine the

main carbohydrate and organic acid components and to

construct a mathematical model of their accumulation

throughout the ripening process in experiments involving

Hungarian sour cherry cultivars that have not previously

been analysed.

Materials and methods

Fruit materials

The fruit examined in 2008 were harvested from 10-

12-year-old trees of the cultivars ‘Erdi jubileum’, ‘Erdi

b}oterm}o’, ‘Maliga emleke’ and ‘Kantorjanosi 3’ and the

prospective cultivar IV-3/48, grown in the experimental

orchard of the Fruitculture Research Institute of the

National Agricultural Research and Innovation Centre in

Erd-Elvira (Table 1). Fruit samples were taken from the

north, south, east and west sides of four trees of each

genotype. Samples were taken on a total of nine occasions

from growth stage III, i.e. from the start of fruit colouring,

until the over-ripe stage (Table 2). The maturity optimum

was determined by fruit removal force and analytical

measurements in a parallel study carried out also in Erd-

Elvira by Kallay et al. (2010a, b). The 75–80 % maturity

was considered to be optimal for the processing industry,

and it was reached at the 7th sampling date.

Reagents and solutions

Glucose (CAS No. [50-99-7]), fructose (CAS No. [57-48-

7]) and sucrose (CAS No. [57-50-1]) of analytical purity,

and malic acid (CAS No. [97-67-6]), succinic acid (CAS

No. [110-15-6]), fumaric acid (CAS No. [110-17-8]),

ascorbic acid (CAS No. [50-81-7]) and tartaric acid (CAS

No. [526-83-0]) standards were obtained from the Sigma

Aldrich Chemical Co. The water used as solvent was pre-

pared using a MILLEX water purification system, with a

final Millipore filter size of 0.22 lm. The standards were

dissolved in water and injected into the HPLC equipment

after repeated filtration.

HPLC equipment

The WATERS (Milford, MA, 01757, USA) HPLC system

had the following components: a 1525 Binary HPLC pump,

a column thermostat, a 717plus autosampler (set to 5 �C)

and an in line degasser, and was powered by EMPOWER

TM2 software.

Sample preparation

The flesh of the fruit samples (1,000 g) was homogenised

in a food processor and stored at -25 �C until required. For

the measurements, 100 lg of each sample was placed in an

Eppendorf tube and diluted with water to 1 ml. In the

course of sugars and acids extraction the samples were kept

in the dark at 4 �C, and dissolving was assisted using an

ultrasonic bath for 4 min The samples were then centri-

fuged at 4 �C at 15,000 rpm in a Hettich Mikro 22R

798 Trees (2015) 29:797–807

123

ultracentrifuge, after which the supernatant was passed

through a 0.45 lm Millipore Syringe Filter Unit SLHN-13.

The samples thus obtained were injected into the HPLC

system.

Sugar analysis

A WATERS 2414 Refractive Index Detector was installed,

with the cell temperature set to 40 �C. Chromatographic

separation was performed on a WATERS Sugar-PakI col-

umn (300 mm 9 6.5 mm ID), tempered to 90 �C. The

sampling frequency was 10/s with a sensitivity of 256. The

mobile phase was water, in which 50 mg/l Ca-EDTA (cal-

cium disodium ethylene diamine tetraacetate) was dissolved.

The flow rate was 0.5 cm3/min, resulting in a pressure of

450 ± 20 psi on the column. The injected sample quantity

was 20 ll, with a running time of 30 min. The retention

times of the individual components were as follows: sucrose

8.6 min, glucose 10.3 min, fructose 12.2 min.

Organic acid determination

A WATERS 2487 Dual Absorbance UV/VIS Detector

was installed. The individual components were separated

using a Shodex RSpak KC-811 organic acid column and

a Shodex KG-G precolumn (tempered to 40 �C). The

mobile phase was water containing 0.1 % phosphoric

acid, purified prior to use with a Millipore filter (pore

size 0.45 lm). The flow rate was 1 ml/min, leading to a

pressure of 600 ± 25 psi on the column. The injected

sample quantity was 20 ll and the running time 15 min.

Detection took place at a wavelength of 220 nm, with

the exception of vitamin C, which was detected at

260 nm. The sampling frequency was 10/s. The retention

times of the standards were as follows: malic acid

7.6 min, succinic acid 8.7 min, tartaric acid 7.2 min,

ascorbic acid 7.9 min.

Statistical analysis

Changes in the sugar and acid components of sour cherry

cultivars during ripening were modelled using non-linear

regression with the least squares method. The explained

variances (R2) were calculated, and the models and their

parameters were tested using ANOVA and Student’s t test,

respectively. The normality of the residuals was verified

using the Kolmogorov–Smirnov test with Lillieford cor-

rection at the p[ 0.1 level (Table 3).

Table 1 Origin and ripening

order of the cultivars tested

(Apostol 2003)

Cultivars Origin Ripening time in Hungary

IV-3/48 Erdi b}oterm}o 9 Meteor korai 22–25th May

Erdi jubileum Pandy 9 Eugenia 10–15th June

Erdi b}oterm}o Pandy 9 Nagy angol 16–18th June

Maliga emleke Pandy 9 Eugenia 20–25th June

Kantorjanosi 3 Local selection 28th June–2nd July

Table 2 Picking dates for the

sour cherry cultivars tested, in

order of maturity

Picking date Picking order

IV-3/48 Erdi jubileum Erdi b}oterm}o Maliga emleke Kantor-janosi 3

20th May 1

23rd May 2

26th May 3 1 1 1

30th May 4 2 2 2

2nd June 5 3 3 3

6th June 6 4 4 4

9th June – 5 5 5 1

13th June 7 6 6 6 2

16th June 8 7 7 7 3

20th June 9 8 8 8 4

23rd June 9 9 9 5

26th June 6

30th June 7

4th July 8

8th July 9

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123

Table 3 Regression models and their parameters

Model Parameters

Increasing or decreasing saturation model Y = p0 ? p1(1 - exp

(-p2 9 X)) ? eWhere p0 = Y(0),

p0 ? p1 = limX???Y(X), i.e. the saturation value

p1p2 = slope at point X = 0,

(p2[ 0 in increasing model while p2\ 0 in decreasing model)

X—picking as independent variable

e—normally distributed error term with zero expectation

Quadratic model: Y = p0 ? p1 9 X ? p2 9 X2 ? e Where pi are the coefficients of Xi (i = 1, 2, 3)

Exponential model: Y = p0 9 exp (p1 9 X) ? e Where p0 = Y(0)

p0p1 = slope at point X = 0

Inverse model: Y = p0 ? (p1/X) ? e Where p0 = limX???Y(X)

-p1 = slope at point X = 1

p0 ? p1 = Y(1)

Logistic model: Y = p0 ? (p1 - p0)/(1 ? exp (-p2 9 (x - p3))) ? e Where p0 = limX?-?Y(X)

p1 = limX???Y(X), i.e. the saturation value

The model has an inflexion point at X = p3 with slope value

(p1 - p0)p2

Table 4 The content of the

sugar components in sour cherry

cultivars throughout the

ripening period (picking dates

1–9)

Different letters are for

significantly different cultivars

groups within the same picking

time, according to Tukey’s post

hoc test (p\ 0.05)

Picking IV-3/48 Erdi jubileum Erdi b}oterm}o Maliga emleke Kantor-janosi 3

Glucose (mg/g)

1 26.86 a 46.72 cd 41.80 b 42.41 bc 48.34 d

2 38.22 a 56.64 c 54.53 c 43.83 ab 48.54 b

3 55.11 b 68.27 c 53.19 b 44.55 a 48.78 ab

4 64.47 c 67.16 c 53.73 b 41.6 ab 43.14 ab

5 66.16 b 64.27 b 55.21 a 47.83 a 50.96 a

6 66.71 c 72.02 c 56.42 b 49.80 ab 48.94 a

7 65.08 c 81.57 d 57.21 b 48.73 a 54.69 ab

8 68.26 b 82.99 c 67.86 b 49.73 a 52.94 a

9 68.60 bc 75.93 c 67.76 b 57.71 a 57.34 a

Fructose (mg/g)

1 13.60 a 41.66 c 21.69 b 20.12 b 37.99 c

2 23.95 a 52.09 c 35.46 b 25.12 a 37.72 b

3 38.46 b 44.45 c 37.76 b 23.02 a 37.69 b

4 45.58 c 53.35 d 41.38 c 28.65 a 34.18 b

5 46.93 bc 50.78 c 41.85 b 25.83 a 44.73 bc

6 46.44 c 55.69 d 44.26 c 31.12 a 37.25 b

7 44.74 b 60.26 c 44.28 b 30.99 a 40.26 b

8 48.69 b 61.84 d 48.80 c 32.99 a 39.85 b

9 48.69 b 56.79 c 48.80 b 38.27 a 34.55 c

Sucrose (mg/g)

1 2.83 a 17.83 d 6.84 b 7.66 b 14.59 c

2 4.32 a 29.46 d 12.71 c 7.66 b 14.58 c

3 7.71 a 24.56 d 12.03 b 6.55 a 14.56 c

4 12.56 ab 33.45 c 14.00 b 10.25 a 10.77 a

5 14.45 b 33.88 c 14.10 b 8.14 a 15.01 b

6 15.42 b 39.82 c 15.53 b 11.46 a 13.25 ab

7 15.64 b 50.16 c 16.54 b 11.67 a 14.96 ab

8 17.64 b 50.37 c 20.12 b 12.70 a 16.94 b

9 17.98 a 48.05 c 20.20 b 16.97 a 17.63 a

800 Trees (2015) 29:797–807

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Since the amount of carbohydrates and organic acids

(expressed by seven indices) are dependent variables, it

was reasonable to run a two-way multivariate ANOVA

(MANOVA) model with factors ‘species’ (5 levels) and

‘picking time’ (9 levels). Normality of the residuals was

accepted by their skewness and kurtosis (Tabachnick and

Fidell 2007). Homogeneity of variances was checked by

Levene’s test (p[ 0.05). Given the significance of the

overall test, the univariate main effects were examined and

the treatment means were separated by Tukey’s post hoc

test. All statistical procedures were conducted using the

software IBM SPSS 21.

Results

Two-way MANOVA revealed a significant multivariate

main effect both for species and picking time (Wilk’s

k\ 0.001, p\ 0.001 in both cases). Significant univariate

main effects were obtained for each (sugar and acid)

variables and for both factors [Fspecies (4, 90) = 270,

p\ 0.001; Fpicking (8, 90) = 9.6, p\ 0.001]. Significant

pairwise differences according to Tukey’s post hoc test are

represented in Tables 4 and 6 (p\ 0.05).

Sugar composition and accumulation in the fruit

Changes in the main sugar components, glucose, fructose and

sucrose with the regarding homogenous groups throughout the

ripening process are illustrated in Table 4. Of the nine sam-

pling dates, the 7th, equivalent to 75–80 % maturity, meets the

requirements of the most important processing end-use (bot-

tled fruit). The results indicated that the quantity of the indi-

vidual carbohydrate components increased in the course of

ripening, though the rate of increase differed both for the

cultivars and the individual sugar components.

Table 5 Estimated model

parameters for the saturation of

the sugar components during

ripening, their significance level

and the F values of the ANOVA

tests for the models with their

significance level and the

explained variance (R2)

Models, estimated values of the

parameters, t values belonging

to each parameter, ANOVA

F values for each model, and the

value of the coefficient of

determination (R2)

* Significant at the p\ 0.001

level

Cultivar Model Parameters t F R2

Glucose

IV-3/48 Increasing saturation p0 24.96 12.76 2,548.23 0.95*

p1 44.63 20.52

p2 0.54 7.99

Erdi jubileum Increasing saturation p0 47.95 18.99 1,847.90 0.83*

p1 35.87 7.60

p2 0.27 2.91

Kantorjanosi 3 Increasing saturation p0 46.03 29.47 2,094.99 0.54

p1 11,216.66 0.00

p2 9.81E-05 0.00

Fructose

IV-3/48 Increasing saturation p0 12.16 7.84 1,983.18 0.95*

p1 36.84 21.57

p2 0.57 8.57

Erdi jubileum Increasing saturation p0 43.30 21.25 1,535.83 0.66*

p1 25.10 1.82

p2 0.14 1.03

Erdi b}oterm}o Increasing saturation p0 23.10 17.95 2,771.46 0.92*

p1 24.58 16.64

p2 0.47 6.27

Sucrose

IV-3/48 Increasing saturation p0 1.84 3.27 1,304.09 0.96*

p1 19.96 13.21

p2 0.22 5.74

Erdi jubileum Exponential p0 21.42 21.46

p1 0.12 12.22 149.41 0.86*

Erdi b}oterm}o Exponential p0 9.14 19.84

p1 0.01 10.16 103.26 0.81*

Maliga emleke Exponential p0 6.66 20.12

p1 0.01 9.52 90.57 0.78*

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123

The main sugar component in the fruit tested was glu-

cose, which was detected in the largest quantities in ‘Erdi

jubileum’ at all the harvest dates. At the 7th sampling date

the glucose quantity was 20 % lower in IV-3/48 than in

‘Erdi jubileum’, followed in decreasing order by ‘Erdi

b}oterm}o’, ‘Kantorjanosi 3’ and ‘Maliga emleke’. The

changes in the glucose content during ripening were

characterised by an initial intensive rise, which was close

to saturation point by the 7th sampling date, after which

little change was observed. Of the five cultivars tested, the

changes in three could be described using a saturation

model, with extremely high R2 values for IV-3/48 and ‘Erdi

jubileum’ (Table 5). The data recorded for the latter cul-

tivar are illustrated in Fig. 1.

In the case of sour cherry the sweet taste of the fruit can

be attributed not only to glucose, but also to fructose. At all

the picking dates the highest fructose content was mea-

sured in the fruit of ‘Erdi jubileum’. At the 7th sampling

date the fructose content was approx. 30 % lower in ‘Erdi

b}oterm}o’ and ‘Kantorjanosi 3’ and 50 % lower in ‘Maliga

emleke’ than in ‘Erdi jubileum’. An intensive increase in

the fructose level was observed in the latter cultivar even in

the over-ripe stage (Table 4). The changes over the rip-

ening period could be described with a saturation curve for

three cultivars (IV-3/48, ‘Erdi jubileum’, ‘Erdi b}oterm}o’),

two of which had R2 values in excess of 0.9 at the

p\ 0.001 level (Table 5). The fructose content of the fruit

was shown by the model to approach the saturation point

by the 7th sampling date. The model fitted for genotype IV-

3/48 is presented as an example in Fig. 2.

The highest sucrose content was observed in ‘Erdi ju-

bileum’, while the fruit of the other cultivars only con-

tained small quantities of this sugar component (Table 4).

For three cultivars the changes in sucrose content during

ripening could be described with an exponential model,

with very high R2 values significant at the p\ 0.001 level

(Table 5). The data recorded for ‘Erdi b}oterm}o’ are illus-

trated in Fig. 3.

Acid composition and accumulation of sour cherries

Changes in the four organic acid components measured

(malic acid, succinic acid, tartaric acid, ascorbic acid) with

regard to the homogenous groups are presented in Table 6.

In general the quantity of the acid fractions in the fruit of

all the cultivars exhibited a decline throughout the ripening

period, but the intensity of the decrease varied as a function

of the acid component and the cultivar.

The main acid component was malic acid. At the 7th

sampling date the highest, very similar malic acid con-

tents were recorded in the fruit of ‘Kantorjanosi 3’ and

‘Erdi jubileum’, with 20 and 30 % lower values in ‘Ma-

liga emleke’ and ‘Erdi b}oterm}o’, respectively. The lowest

malic acid content was recorded for genotype IV-3/48

(Table 6). Changes in the malic acid content of three

cultivars could be described using a saturation model.

Fig. 1 Glucose content in the fruit of ‘Erdi jubileum’ and the

saturation model fitted to the data

Fig. 2 Fructose content in the fruit of IV-3/48 and the saturation

model fitted to the data

Fig. 3 Sucrose content in the fruit of ‘Erdi b}oterm}o’ and the

exponential model fitted to the data

802 Trees (2015) 29:797–807

123

Unusually, in the case of IV-3/48 intensive malic acid

biosynthesis was only detected until the 5th sampling

date, when the level approached the saturation value, after

which little change was observed (R2 = 0.896). In the

fruit of ‘Erdi b}oterm}o’ and ‘Kantorjanosi 3’ a decreasing

saturation model could be fitted to the malic acid data,

which declined gradually until the saturation value was

approached (Table 7). Figure 4 illustrates the model

found for ‘Kantorjanosi 3’.

Succinic acid was found in the largest quantities in

‘Kantorjanosi 3’ and ‘Erdi jubileum’ and in the smallest

amounts in ‘Maliga emleke’, ‘Erdi b}oterm}o’ and IV-3/48 at

the 7th picking date (Table 6). In ‘Erdi b}oterm}o’ (Fig. 5)

and ‘Kantorjanosi 3’ the changes during the ripening pro-

cess could be described by an inverse function, with an

initial rapid decline that gradually slowed, while a

decreasing saturation model could be used to describe the

changes in ‘Maliga emleke’ (Table 7).

Table 6 The content of the

acid components in sour cherry

cultivars throughout the

ripening period (picking dates

1–9)

Different letters are for

significantly different cultivars

groups within the same picking

time, according to Tukey’s post

hoc test (p\ 0.05)

Picking IV-3/48 Erdi jubileum Erdi b}oterm}o Maliga emleke Kantor-janosi 3

Malic acid (mg/100 g)

1 108.06 a 369.65 c 357.62 c 283.43 b 351.92 c

2 120.67 a 370.89 c 356.98 c 282.43 b 451.81 d

3 181.83 a 386.96 d 337.42 c 272.62 b 442.27 e

4 199.97 a 328.67 b 307.67 b 335.97 b 422.37 c

5 229.12 a 350.40 c 301.26 b 321.40 bc 381.72 d

6 218.88 a 352.07 c 287.72 b 328.11 c 393.58 d

7 220.38 a 365.64 c 252.07 a 317.01 b 382.72 c

8 218.64 a 352.79 c 288.13 b 290.48 b 357.36 c

9 217.97 a 278.78 b 287.47 b 233.43 a 376.99 c

Succinic acid (mg/100 g)

1 103.49 a 189.49 b 257.03 c 194.86 b 241.74 c

2 101.49 a 172.03 b 206.18 c 197.86 c 308.94 d

3 128.67 a 181.65 b 182.80 b 186.59 b 292.89 c

4 115.91 a 142.55 b 160.38 b 215.74 c 244.30 d

5 121.37 a 127.48 ab 143.43 b 195.25 c 206.75 c

6 117.82 a 204.43 d 151.41 b 175.99 c 208.79 d

7 104.54 a 192.39 d 128.00 b 168.37 c 209.90 e

8 117.14 a 197.01 c 136.47 b 137.53 b 183.57 c

9 118.47 a 131.16 b 135.81 b 160.69 c 181.21 d

Tartaric acid (mg/100 g)

1 27.10 a 231.95 c 177.62 b 162.68 b 173.46 b

2 36.03 a 212.59 c 195.07 c 163.04 b 213.23 c

3 71.88 a 218.48 c 159.05 d 128.00 b 179.07 c

4 73.52 a 170.57 c 163.02 c 134.23 b 172.39 c

5 88.55 a 186.13 c 172.05 c 133.54 b 141.83 b

6 99.65 a 195.54 d 170.94 c 137.41 b 143.61 b

7 89.04 a 182.01 c 126.00 b 135.00 b 134.21 b

8 81.63 a 186.89 c 136.66 b 132.47 b 123.87 b

9 77.97 a 167.65 d 123.36 b 139.54 c 143.93 c

Ascorbic acid (mg/100 g)

1 6.41 a 12.70 b 7.16 a 19.67 c 24.42 d

2 7.07 a 11.12 b 12.86 c 10.44 b 25.56 d

3 11.39 b 13.58 c 13.39 c 9.62 a 23.03 d

4 12.76 b 14.59 c 10.17 a 9.50 a 21.41 d

5 12.72 b 16.60 c 7.89 a 8.50 a 17.57 c

6 15.99 c 16.70 c 9.76 b 4.22 a 17.26 c

7 17.49 d 16.41 c 8.75 b 4.60 a 16.46 d

8 15.77 c 19.81 d 10.02 b 5.20 a 16.20 c

9 16.07 c 19.21 d 9.96 b 5.92 a 17.46 cd

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Table 7 Estimated model

parameters for changes in acid

components during ripening,

their significance level and the

F values of the ANOVA tests

for the models with their

significance level and the

explained variance (R2)

Models, estimated values of the

parameters, t values belonging

to each parameter, ANOVA

F values for each model, and the

value of the coefficient of

determination (R2)

* Significant at the p\ 0.001

level

Cultivar Model Parameters t F R2

Malic acid

IV-3/48 Increasing saturation p0 97.36 11.97

p1 132.25 14.13

p2 0.46 5.33 1,553.23 0.90*

Erdi b}oterm}o Decreasing saturation p0 366.28 46.68

p1 -97.71 -5.69

p2 0.25 2.33 3,530.04 0.79*

Kantorjanosi 3 Decreasing saturation p0 488.99 21.60

p1 -141.59 -6.92

p2 0.25 1.77 3,642.45 0.74*

Succinic acid

Maliga emleke Decreasing saturation p0 146.6 18.81

p1 65.93 3.51

p2 0.23 1.45 1,315.85 0.61*

Erdi b}oterm}o Inverse p0 121.64 13,575.00

p1 143.78 18.24 332.55 0.93*

Kantorjanosi 3 Inverse p0 149.54 21.77

p1 349.94 13.23 175.05 0.89*

Tartaric acid

IV-3/48 Quadratic model p0 0

p1 28.34 30.64

p2 -2.2 30.65 1,688.47 0.99*

Erdi jubileum Decreasing saturation p0 232.49 30.66

p1 -57.751 30.67

p2 0.373 30.68 1,638.86 0.62*

Erdi b}oterm}o Exponential p0 188.23 30.69

p2 -29,304.18 41,850.00 49.53 0.66*

Maliga emleke Decreasing saturation p0 166.09 30.71

p1 -32.12 30.72

p2 0.76 30.73 2,059.04 0.57*

Kantorjanosi 3 Decreasing saturation p0 264.96 30.74

p1 -135.69 30.75

p2 0.47 30.76 2,027.03 0.89*

Ascorbic acid

IV-3/48 Logistic p0 3.49 1.12

p1 16.66 27.17

p2 0.73 2.90

p3 2.89 41,730.00 954.05 0.93*

Erdi jubileum Logistic p0 10.45 41,712.00

p1 20.73 6.44

p2 0.47 1.17

p3 4.95 4.42 935.16 0.81*

Erdi b}oterm}o Inverse p0 7.87 13.34

p1 10.84 4.77 22.78 0.51*

Maliga emleke Inverse p0 3.59 8.81

p1 16.03 16.26 264.49 0.91*

Kantorjanosi 3 Inverse p0 13.56 13.85

p1 25.40 28.46 191.70 0.90*

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Great variability was detected for the changes in tartaric

acid content (Table 6). Of the five cultivars investigated,

three (‘Erdi jubileum’, ‘Maliga emleke’, ‘Kantorjanosi 3’)

could be described using a decreasing saturation model,

while those of IV-3/48 and ‘Erdi b}oterm}o’ followed a qua-

dratic and an exponential model, respectively (Table 7). The

model fitted to ‘Erdi jubileum’ is illustrated in Fig. 6.

The vitamin C content of the fruit exhibited an increase

during ripening in two cultivars (IV-3/48, ‘Erdi jubileum’)

and a decrease in three (‘Erdi b}oterm}o’, ‘Maliga emleke’,

‘Kantorjanosi 3’). At the 7th sampling date very similar

quantities of vitamin C were measured in the fruit of IV-3/

48, ‘Erdi jubileum’ and ‘Kantorjanosi 3’, while consider-

ably lower values were recorded for ‘Erdi b}oterm}o’ and

‘Maliga emleke’ (Table 6). The cultivars could be divided

into two groups on the basis of changes in the vitamin C

content. The increase could be described with a logistic

model for two cultivars (IV-3/48, ‘Erdi jubileum’), while

the decrease in the other three cultivars (Erdi b}oterm}o’,

‘Maliga emleke’, ‘Kantorjanosi 3’), which was significant

at the p\ 0.001 level, followed an inverse model

(Table 7). The models fitted to IV-3/48 and ‘Maliga em-

leke’ are illustrated in Figs. 7 and 8.

Discussion

Previous studies have dealt mainly with the sugar and acid

components of sour cherries in the harvest maturity stage.

The present results confirm those of Souci et al. (2008),

Fig. 4 Malic acid content in the fruit of ‘Kantorjanosi 3’ and the

decreasing saturation model fitted to the data

Fig. 5 Succinic acid content in the fruit of ‘Erdi b}oterm}o’ and the

inverse model fitted to the data

Fig. 6 Tartaric acid content in the fruit of ‘Erdi jubileum’ and the

decreasing saturation model fitted to the data

Fig. 7 Vitamin C content in the fruit of IV-3/48 and the logistic

model fitted to the data

Fig. 8 Vitamin C content in the fruit of ‘Maliga emleke’ and the

inverse model fitted to the data

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123

Bonerz et al. (2007) and Gao et al. (2003), who found that the

sugar content of the fruit consisted mainly of glucose.

However, the glucose content of the Hungarian cultivars

(49–82 mg/g) exhibited greater diversity than that reported

by Bonerz et al. (2007) and Souci et al. (2008) in the case of

German cultivars (49–52 mg/g). The same was true of the

fructose content, which ranged from 31–60 mg/g in the

present work. The sweet taste of the fruit of ‘Erdi jubileum’

could be attributed not only to its high glucose and fructose

content, but also to the substantial quantity of sucrose. It was

also clear that some of the Hungarian cultivars were superior

to the German and American cultivars in terms of glucose

and fructose content. It can thus be stated that Hungarian sour

cherries have a very varied sugar profile. With respect to the

main sugar components the Hungarian cultivars resemble the

German cultivars, as both contain primarily glucose, fructose

and sucrose, while the main sugar components of the

American cultivar ‘Montmorency’ are glucose, fructose and

sorbitol (Gao et al. 2003). The differences in sugar compo-

sition, the variable sugar profile and the diversity in the fla-

vour balance all confirm the different genetic origin of the

Hungarian sour cherry genotypes.

Functions describing the accumulation of sugar compo-

nents in sour cherries have not previously been determined.

During the characterisation of the sorbitol transporter gene,

Gao et al. (2003) recorded the glucose, fructose and sorbitol

contents of ‘Montmorency’ cherries on eight sampling dates

covering the whole of fruit development (stages I–III). As

the accumulation of photosynthetic pigments is concen-

trated in stage III, the modelling of quantitative changes in

these compounds is only possible if a large number of

samples are taken during this stage. The mathematical

models constructed on the basis of the present work can thus

be regarded as novel results.

The main acid component of the Hungarian sour cher-

ries was malic acid. This is in agreement with the findings

of Poll et al. (2003) and Bonerz et al. (2007), but consid-

erable differences in the quantities were detected between

the cultivars, and this was also true for the other acid

components. The cultivars tested contained similar quan-

tities of succinic and tartaric acid. The majority of the

Hungarian cultivars contained approx. 40 % more vitamin

C than the 12 mg/g value reported by Souci et al. (2008).

The present work therefore identified the special value of

certain Hungarian cultivars in terms of acid content, as well

as being the first to present a mathematical model of

changes in the acid components in the course of ripening.

Conclusions

Hungarian sour cherry cultivars have an extremely varied

sugar and acid profile. Some of these cultivars (e.g. ‘Erdi

jubileum’, ‘Erdi b}oterm}o’, IV-3/48) are not only ideal for

fresh consumption and processing purposes, but can also

be recommended as parental partners in breeding for

improved chemical quality. The fresh fruit of cultivars

with low carbohydrate content (‘Maliga emleke’,

‘Kantorjanosi 3’) can also be included in the diet of dia-

betics. In the present study, changes occurring in the main

carbohydrates and organic acids in the course of ripening

have been described using mathematical models for the

first time. The data obtained in this work will form the

basis for further investigations on the optimum picking

date for processing.

Author contribution statement Sugar and acid composition were

measured with HPLC by G. Vegvari and G. Ficzek. The large part of

the text was written by G. Ficzek, who also prepared the figures.

Statistical analysis and the related part of the text were made by M.

Ladanyi. M. Toth gave useful advices, corrected the text and she was

the supervisor of the research. All authors made a statement to accept

the manuscript.

Acknowledgements Thanks are due to the Fruitculture Research

Institute of the National Agricultural Research and Innovation Centre,

and especially to Dr. Geza Bujdoso and Sandor Szugyi, for providing

the samples. This research was funded by the Regional University

Knowledge Centre—Research and Development in Foodstuff Chain

(Project No. RET-04/2006) and by the TAMOP 4.2.1./B-09/01/KMR/

2010-0005 project. The authors would also like to thank the staff of

WATERS Ltd., Budapest, for their technical advice with the HPLC

analysis.

Conflict of interest The authors declare that they have no com-

peting interests.

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