ASSESSING PROTOPECTIN TRANSFORMATION POTENTIAL OF PLANT TISSUE USING A ZONED CRITERION SPACE Текст научной статьи по специальности «Биологические науки»

Assessing protopectin transformation potential of plant tissue using a zoned criterion space

Vladimir V. Kondratenko1* , Tatyana Yu. Kondratenko1 , Andrey N. Petrov1 ,

Georgy A. Belozerov2

1 Russian Research Institute of Canning Technology - branch of Gorbatov Federal Research Center for Food Systems at Russian Academy of Sciences, Vidnoye, Russia

2 Russian Scientific Research Institute of Refrigeration Industry - branch of Gorbatov Federal Research Center for Food Systems at Russian Academy of Sciences, Moscow, Russia

* e-mail: [email protected]

Received April 15, 2020; Accepted in revised form May 14, 2020; Published August 25, 2020

Abstract:

Introduction. The existing diversity of plant raw materials and products predetermine the prospects of studying their potential as sources of pectin substances. However all current classifications are either fragmented or inconsistent.

Study objects and methods. Our theoretical ivestigation aimed to develop an adequate classification for all taxa of plant origin, as well as their tissues and derivatives as pectin-containing materials. We developed criteria for assessing transformation potential of the protopectin complex based on the mass fractions of biologically active non-uronide components, native water-soluble pectin, the protopectin complex, and pectin substances. Individual boundary conditions were based on individual pectin potential, protopectin fragmentation potential, and pectin isolation potential.

Results and discussion. Based on the boundary conditions, we defined an universal criterion space that included a set of points M in the coordinates expressed by three main criteria. According to individual boundary conditions, the criterion space was divided, or zoned, into four domains corresponding to protopectin fragmentation potential. They were characterized by: 1) lack of pectin potential,

2) ineffective protopectin fragmentation, 3) ineffective isolation of fragmentation products, and 4) effective isolation. Finally, we developed a generalized algorithm to determine the location of points M [^, /u2, in the zoned criterion space, characterizing the plant tissue.

Conclusion. Our approach can be used to assess any plant tissue for its protopectin transformation potential, which determines the technological influence on its pectin potential. This approach is universal, i.e., applicable to both plant tissue and its derivatives.

Keywords: Protopectin complex, potential, transformation, evaluation system, criterion space

Funding: The materials were prepared as part of the government assignment to Gorbatov Federal Scientific Center for Food Systems at Russian Academy of Sciences.

Please cite this article in press as: Kondratenko VV, Kondratenko TYu, Petrov AN, Belozerov GA. Assessing protopectin transformation potential of plant tissue using a zoned criterion space. Foods and Raw Materials. 2020;8(2):348-361. DOI: http://doi. org/10.21603/2308-4057-2020-2-348-361.

E-ISSN 2310-9599 ISSN 2308-4057

Research Article Open Access

Check for updates

DOI: http://doi.org/10.21603/2308-4057-2020-2-348-361 Available online at http://jfrm.ru/en

INTRODUCTION

Food technology is currently striving to maximize the potential of raw materials and use new, non-traditional sources of essential nutraceuticals and food components with biological (antioxidants, enterosorbents, etc.) and/or technological (thickeners, stabilizers, etc.) functional activity [1, 2]. The most promising way to achieve that is a biotechnological approach that makes use of both living cultures of microorganisms and isolated enzyme systems. When

using isolated enzyme systems, this approach involves a multiple stage fragmentation of a native supramolecular complex of plant and/or animal cell walls into target components with a wide range of physicochemical and/ or technological properties [3-5].

One of the methods within this approach is to activate the potential of a multicomponent polymer matrix of cell walls and intercellular spaces. This method has a limited use in processing agricultural raw materials. It mainly consists in partial or complete

Copyright © 2020, Kondratenko et al. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), allowing third parties to copy and redistribute the material in any medium or format and to remix, transform, and build upon the material for any purpose, even commercially, provided the original work is properly cited and states its license.

degradation (depolymerization) of its individual components to change the consistency or transparency of the final product, or to clear it of degradation products and improve its sensory characteristics. Most certainly, a targeted use of this polymer matrix is complicated by its highly heterogeneous components, a system of bonds between them, and highly entangled polymer chains [6]. Moreover, the heterogeneity of individual matrix components is a serious obstacle to controlling their properties during extraction [7, 8].

Pectin substances are among major carbohydrate biopolymers that have a wide variety of functional and technological characteristics [9, 10]. In a plant cell, they are represented by two main fractions - native water-soluble pectin and a native water-insoluble protopectin complex. The last one is the most valuable for transformation due to its molecular structure and composition [9].

The structure of cell walls in almost all terrestrial plants makes them a potentially good resource for the industrial production of pectin [6, 11, 12]. However, it is difficult to implement. Since the protopectin complex is a branched supramolecular structure incorporated into the cell wall, its transformation is mainly fragmentation into water-soluble polymers (soluble pectin). In addition, mass fractions of pectin substances and the protopectin complex may depend on the type, grade, and purpose of raw materials, their structure and phase of development, soil and weather conditions for their vegetation, as well as localization, duration and storage conditions, processing intensity, etc. [10, 13]. In this regard, the choice of a plant as a pectin-containing material should be determined by the purpose of its use.

Raw materials can be classified according to the size of their pectin potential - "high", "medium," and "small" ("low", "insignificant") [9, 10, 14]. The only fundamental approach to pectin production was offered by Donchenko in [15] and supplemented by Rodionova et al. in [19, 20] (works [16-18] are actualy based on [15]). Although this approach is rather fragmented, it can be used as a basis for developing a universal system that takes into account the native pectin potential of plant tissue.

The protopectin complex is a key object whose fragmentation enables us to use the biomass of a plant material as a source of pectin substances. Due to the presence of certain plant organisms, mainly a natively soluble fraction of pectin, biomass can be attributed to potential sources of pectin. On the other hand, the biomass of certain taxonomic elements may contain a small amount of pectin, which makes its use ineffective.

Therefore, we found it relevant to develop a clear-cut classification of plant bio-resources into groups to determine the prospects of their use as pectin-containing raw materials.

In this regard, we aimed to develop a system of criteria for assessing the transformation potential of native complexes of plant carbohydrate biopolymers

exemplified by pectin. To achieve this aim, we set the following objectives:

- working out criteria to assess the transformation potential of native plant biopolymers and the concept of their applicability, and

- developing a system of boundary conditions and an universal algorithm for classifying plant materials according to the transformation potential of their native pectin components.

STUDY OBJECTS AND METHODS

According to existing data, all plant materials can be classified into four main groups, namely:

- bio-resources with sufficient potential for protopectin fragmentation and subsequent isolation of its products as independent substances;

- bio-resources with sufficient potential for protopectin fragmentation, but with insufficient potential for isolation of its products;

- bio-resources with insufficient potential for protopectin fragmentation, but with sufficient potential for natively soluble pectin;

- bio-resources with no pectin potential.

On the one hand, this differentiation involves unifying plant characteristics and reducing them to certain generalized values. On the other hand, it involves dividing the domain of generalized values into four fixed zones. As we know, a universal tool for unifying an arbitrary set of source factors is a range of anonymized criteria reducible to a certain system with the use of boundary conditions [21, 22]. Thus, we can apply a criteria-based approach to fulfilling our objectives.

To be able to scale the criteria to determine clear boundary conditions, we used Harrington's individual desirability function in its canonical form [23]:

_e-(P,0+b,1-K) /IX

di = e e (1)

where d is the dimensionless value of Harrington's individual desirability function; b m is the constant; b a is the coefficient; and 9. is the dimensionless operator of Harrington's individual desirability function.

We introduced the first and second individual criteria for protopectin fragmentation potential among the main criteria to assess the native pectin potential.

Let us begin with the first criterion. According to [7, 8], the presence of pectin in the tissue or a certain amount of protopectin in the cell wall matrix is not sufficient for assessing the native pectin potential of plant tissue. The tissues of many plant organisms also contain a significant amount of organic and mineral components with valuable vitamins and antioxidant activity, pronounced aroma, micro- and macronutrient values, etc. [17]. They are also highly sensitive to active technological impact factors. During protopectin fragmentation, organic and mineral components can enter into uncontrolled interactions, resulting in a partial or complete loss of their biological potential. Therefore,

when assessing the native pectin potential, we should take into account the presence of these biologically active components among other significant factors.

Thus, we decided a complex operator as an independent variable, taking into account mass fractions of protopectin and biologically active components in the tissue:

^ =

pp

Li

w, + w

(2)

pp

where app is the mass fraction of protopectin, mg in 100 g; a>i is the mass fraction of the i-th biologically active component, mg/100 g; and X is the number of biologically active components in the tissue (1 e N).

To apply this operator in practice, we transformed it as follows:

1 1

p =-

z:,

wt A +1 —+1

where

pp

A =

z;=i<

(3)

(4)

W

Thus m1 is the first dimensionless individual criterion of protopectin fragmentation potential.

As we can see, with all possible values of a

pp

i=1a)i, this criterion has the following range of definition:

M, e [0; œ)

(5)

In this case, Harrington's individual desirability function can be expressed as:

_Abio+biv<n.) _

d1 = e = e

-\ ¿10+-

M. 1

M1+1)

(6)

where d1 is the dependent dimensionless variable; b10 is the empirical dimensionless constant; and b11 is the empirical dimensionless coefficient.

To determine the numerical values of b10 and b11, we had to set the primary relations between the pairs {Mn;d11} and M2;d12}, for which we proceeded from the following considerations.

If an i-th biologically active component has a specific measure of value pi, the total measure of value for all biologically active components under consideration is:

bac

Z; m ;

mi • pi = — Z Wi • p i=i 1 ri 100 1 i=i

(7)

where vbac is the total measure of value for all biologically active components, units; mi is the mass of the i-th component, mg/100 g of plant tissue; m is the tissue mass, mg; pi is the specific measure of value of the i-th component, units/mg; and i is the mass fraction of the i-th component in the plant tissue, %.

If specific measures of value for the components are expressed through some average specific measure of value

Fav =:

lit,

mi • fi

z

;

;

i=1

then formula (7) looks as follows:

bac

Z;

i=l W'Pav =

100 ^ i=1

m ■ pa 100

Ji=1

w

from which

z;=1

; W vbaC -100

Wi =-

pav ■m

(9)

(10)

If we apply similar considerations to protopectin, then:

v = m ■ p = -

pp pp ^ pp

100 ■ppp

(11)

where vpp is the total measure of protopectin value, units; mpp if the mass of protopectin in the tissue, mg; ppp is the specific measure of protopectin value, units/mg; and app is the mass fraction of the i-th component in the plant tissue, %.

From Eq. (11), it follows that

wpp =

vpp -100

ppp ■m

Thus, formula (4) can be presented as:

vbac P pp

A =■

V pp Pa

(12)

(13)

Grouping similar values on its sides, formula (13) can be transformed as:

Vbac _ Mi ' pav

(14)

pp

pp

bac > i

Respectively, if vpp , protopectin fragmentation makes no sense, even with its significant amount in the tissue. Therefore, a prerequisite for protopectin fragmentation is:

^ppp Mi ^ —

Pav

(15)

If pCK, is expressed as Pav - in fractions of ppp, - then condition (15) looks as follows:

a ^ pa

(16)

When calculating pav, it is advisable to use pt rather than p, its value reduced to ppp:

pav =-

Z; _

i=1 mi • pi

Z;

i=1 mi

(17)

Theoretically, pi can be determined using several approaches. However, we believe that the most appropriate approach is based on a daily human need for individual nutrients. This approach is least opportunistic (compared to the financial approach) and subjective (compared to direct expert assessments). Naturally, daily

av

Table 1 Specific measures of value for biologically active components and pectin in 100 g of plant tissue

Component Recommended daily requirement, units Estimated daily requirement Specific measure of value, mg-1

mg mg/kg Pi Pi

1 2 3 4 5 6

Protein, g 800.00m

Amino acids, mg/kgm

- essential amino acids:

histidine 14 0.071428571 2.198

isoleucine 19 0.052631579 1.619

leucine 42 0.023809524 0.733

lysine 38 0.026315789 0.81

methionine 13.16I 0.075987842 2.338

phenylalanine + tyrosine 27 0.037037037 1.14

threonine 16 0.0625 1.923

tryptophan 4 0.25 7.692

valine 19 0.052631579 1.619

cysteine 5.84I 0.171232877 5.269

- non-essential amino acids 514.15" 0.001944958 0.06

- other amino acids 87.85IV 0.011383039 0.35

Lipids, gV 69.9 69 900 1 075.38

- saturated fatty acids 21.2 21 200 326.15 0.003066074 0.094

- monounsaturated fatty acids 25.4 25 400 390.77 0.00255905 0.079

- polyunsaturated fatty acids 23.3 23 300 358.46 0.002789712 0.086

Digestible carbohydrates, gVI 275 275 000 4 230.77 0.000236364 0.007

Pectin, gVII 2 2 000 30.77 0.0325 X 1

MineralsVm

- Ca, mg 1 000 1 000 15.38462 0.064999981 2

- Mg, mg 400 400 6.15385 0.162499898 5

- K, mg 2 500 2 500 38.46154 0.025999999 0.8

- Na, mg 1 300 1 300 20 0.05 1.538

- P, mg 800 800 12.30769 0.081250015 2.5

- Cl, mg 2 300 2 300 35.38462 0.028260866 0.87

- Fe, mg 14.4 14.4 0.22154 4.513857543 138.888

- Zn, mg 12 12 0.18462 5.416531253 166.663

- J Mg 150 0.15 0.00231 432.9004329 13 320.013

- Cu, mg 1 1 0.01538 65.01950585 2 000.6

- Mn, mg 2 2 0.03077 32.49918752 999.975

- Se, Mg 63 0.063 0.00097 1 030.927835 31 720.856

- Cr Mg 50 0.05 0.00077 1 298.701299 39 960.04

- Mo, Mg 70 0.07 0.00108 925.9259259 28 490.028

- Co Mg 10 0.01 0.00015 6 666.666667 205 128.205

- Si, mg 30 30 0.46154 2.166659444 66.666

- F, mg 4 4 0.06154 16.24959376 499.988

Vitamins and provitamin IX

- water soluble

ascorbic acid (vitamin C), mg 90 90 1.38462 0.722219815 22.222

thiamine (vitamin B1), mg 1.5 1.5 0.02308 43.32755633 1 333.156

riboflavin (vitamin B2), mg 1.8 1.8 0.02769 36.11412062 1 111.204

vitamin B6, mg 2 2 0.03077 32.49918752 999.975

vitamin B12, Mg 3 0.003 0.00005 20000 615 384.615

niacin, mg 20 20 0.30769 3.250024375 100.001

pantothenic acid, mg 5 5 0.07692 13.00052002 400.016

biotin, Mg 50 0.05 0.00077 1298.701299 39 960.04

folic acid and folates, Mg 400 0.4 0.00615 162.601626 5 003.127

- fat soluble

carotenoids, mg 5 5 0.07692 13.00052002 400.016

vitamin D, Mg 10 0.01 0.00015 6 666.666667 205 128.205

351

Continuation of the table 1

1 2 3 4 5 6

vitamin E, mg 15 15 0.23077 4.333318889 133.333

vitamin K, ^g 120 0.12 0.00185 540.5405405 16 632.017

- pseudo-vitamins

inositol, mg 500 500 7.69231 0.129999961 4

L-carnitine, mg 300 300 4.61538 0.216666883 6.667

coenzyme Q10 (ubiquinone), mg 30 30 0.46154 2.166659444 66.666

lipoic acid, mg 30 30 0.46154 2.166659444 66.666

vitamin U, mg 20 20 0.30769 3.250024375 100.001

orotic acid (B13), mg 30 30 0.46154 2.166659444 66.666

paraminobenzoic acid, mg 100 100 1.53846 0.65000065 20

choline, mg 500 500 7.69231 0.129999961 4

Flavonoids, mgVm 250 250 3.84615 0.26000026 8

I - according to [24] and the ratio in [25]

II - according to the ratio between essential and non-essential amino acids in [25]

III - according to the recommended dietary allowance in [24]

IV - the value is a difference between the daily requirement for protein and the sum of essential and non-essential amino acids

V - according to [24] and [26], based on a daily energy requirement of 2000 kcal

VI - according to [27] and [28]

VII - according to [18]

VIII - according to [28]

IX - according to [28] and [29, 30]

X - the value corresponds to p

requirements for certain components depend on our knowledge of biochemical processes in the human body, as well as on the constantly changing environmental situation in the world [24]. However, these factors should not significantly affect pav.

The value of pav was calculated in several stages.

At the first stage, we determined daily requirements for each of the biologically active components (u) and pectin (u ps) based on a daily energy requirement of 2000 kcal and an average body weight of 65 kg. The differences in daily requirements for men and women were averaged. For comparability, all the values were presented in mg/kg of body weight.

At the second stage, we calculated specific measures of value for biologically active components ( p ) and pectin (Pps):

-1 (18)

Pi = U i

P ps = U ps

(19)

The specific measures of value for pectin p ps and protopectin p pp were numerically identical since protopectin is only valuable for the human body in the form of its fragmentation products. To simplify, we assumed that processing resulted in all protopectin fragmented in a targeted manner (i.e., into fragments that could be identified as pectin).

At the third stage, we determined specific measures of value in the fractions of the specific measure of pectin values pi.

The calculation results are shown in Table 1.

At the fourth stage, we calculated the value of p-(Table 2). Based on the data in [31], we determined the content of biologically active components in 100 g of tissue for 21 types of plant materials from the classification presented in [16]. For each type of raw

material, formula (17) was used to calculate the values of Pay (j) and pav1( j), where j e N.

Some assumptions were made in the calculations. For example, the mass fractions of the components which were not available in the database were assumed as equal to zero [31]. The amount of carotenoids was calculated based on the biological potential of each type of raw material as mcar = mp-car + - ■XI^m, is the mass fraction

where m

ß-car

ȧ-car

of

P-carotene,

mg/100 g; Xn= mt (o c) is the sum of mass fractions of other carotenoids, mg/100 g [24]. The amount of tocopherols was also calculated taking into account the biological potential of each type of raw material as mtok = ma-toc +110 ■ mr-,oc, where ma-tac and my-toc are the mass fractions of a- and y-tocopherols, respectively; mg/100 g [24]. To determine the sum of the remaining amino acids, we subtracted the mass fractions of essential and non-essential amino acids from the mass fraction of protein.

The calculation results are shown in Table 2.

Since pav1(j) values were significantly different for different types of raw materials, we calculated the average p-1^ and the margin of error A to determine boundary values (pu and ^12):

—i

__1 = X j=1 Pav (j) (20)

pav ( av) =

£

A = t

X./=l( Pav ( j) - P-i )2 rav (av) J

-1)

(21)

V; Z-1)'^

where Ç is the number of raw material types; t(a. is Student's t-test; and a is the probability of error (0.05). Based on the above, the value of Mn for the first pair ; djj} was calculated as:

Table 2 Weighted average reduced measures of raw materials value in non-uronide biologically active components

Raw materials Pavij) Pal{j) Raw materials Pavij) Pal{j)

Carrot 0.8282 1.207 Persimmon 0.0887 11.274

Beetroot 0.4156 2.406 Grapefruit 0.2355 4.246

Watermelon 0.2860 3.497 Lemon with skin 0.6618 1,511

Pumpkin 0.6578 1.520 without skin 0.3057 3,271

Melon 0.1749 5.718 Orange 0.2729 3.664

Apples 0.0783 12.771 Tangerine 0.1691 5.914

Quince 0.0993 10.070 Currants red 0.2654 3,768

Pears 0.0889 11.249 black 0.4389 2,278

Figs 0.1137 8.795 Cranberry 0.3147 3.178

Pomegranate 0.1671 5.984 Gooseberry 0.2935 3.407

Grapes 0.1057 9.461 Feijoa 0.2074 4.822

—-1

Mil ~ Pav(av)

-A

(22)

The value of Mi 2 for the second pair {¿ul2;dl2} was calculated as the second order of //,

Ml2 =(p^(aV)-A)'

(23)

The critical (boundary) values of Mi were based on the analysis of Harrington's desirability function, using Mu and Mi 2 as reference values. Since they are preset, the calculated values were rounded to the nearest whole number.

Despite the rigor of expression (16), its right-hand side is an empirical value based on the chemical composition of a finite number of plant raw materials and, therefore, it cannot be considered a priori. To make up for this feature, we further determined the critical values of //, on the basis of Harrington's desirability function, using /¿n and M12 as reference values.

Since a smaller reference value corresponded to a larger value of Harrington's individual desirability function, we defined a condition Cond^ that determined the individual form of the function as:

Condr^ =

dn M11 3

0.60 du 0.40

M12 10

(24)

Based on Cnndrj. we calculated the values of the constant and the coefficient: bw = -0.246; />,, = 3.673.

The critical values of the first criterion for the protopectin fragmentation potential at the points with standard critical values of the desirability function can be calculated using Eq. (6) with the variable Mi:

MIP,] = -1"

6io+ln["lnK)]

(25)

where //, | /.), ] is the value of the criterion //, at the critical

Figure 1 Graphic interpretation of Harrington's individual desirability function given condition Condj and variable /¿j

point D, of Harrington's individual desirability function determined by Eq. (6) and corresponding to dv: and du is the standard Mh critical (canonical) value dl of Harrington's individual desirability function.

The graphic interpretation of Harrington's individual desirability function corresponding to the condition Condj is given in Fig. 1. For each value of dir we determined the corresponding values of //,1/), |.

As we can see, the //, range of definition includes four domains separated by the critical values of //, [Di ], where / = 1, 2, 3. By definition, domain IV includes those //, values at which the fragmentation of the protopectin complex makes no sense due to a low value of the individual function of desirability.

Domain III covers those //, values at which the individual desirability function is large enough for protopectin fragmentation to make sense, but insufficiently large to neglect non-uronide bioactive components and isolate the products of fragmentation.

In domains I and II, the individual desirability function is so large that the content of non-uronide bioactive components in plant tissue can be completely ignored.

Based on the physical meaning of the boundary conditions for //,. we established two individual boundary conditions that partially determined the native pectin potential of plant tissue.

Boundary condition I:

- //, > /J-,1 means the absence of the first individual potential for protopectin fragmentation;

- //, < //, | IX, | means the presence of the first individual potential for protopectin fragmentation.

Boundary condition II:

- | / x, | > > //||/>21 means the absence of the first individual potential for isolation of protopectin fragmentation products;

- //, < //, 11>21 means the presence of the first individual potential for isolation of protopectin fragmentation products.

Next, we determined the structure and properties of the second dimensionless individual criterion for the protopectin fragmentation potential.

The second independent variable was a complex operator based on the mass fraction of protopectin in the tissue:

pp

<,p-> =-= P-,

" 100 "

(26)

where <p2 is the dimensionless operator of Harrington's individual desirability function; and f2 is the second dimensionless individual criterion for the protopectin fragmentation potential.

Harrington's individual desirability function was expressed as:

.-(ho+hrvi)

d 2

Thus, the condition Condd individual function was set as:

_e-C'20+'>2r.«2> (27)

that determined the

Condj^ =

^21 ß 21

0.35 d,

22

0.65

0.001 ' 0.05

(28)

Based on Condwe calculated the values of the constant and the coefficient: b20 = -6.68 10 2 and 621 =18.179. The critical values of the //2 criterion were

calculated as:

M2[D,] = -

è20+ln[-ln(A,)]

21

(29)

where 1I is the value of ;i2 at the critical point /.), of Harrington's individual desirability function calculated by Eq. (6) and corresponding to d2i: d2j is the standard Mh critical (canonical) value d2 of Harrington's individual desirability function.

Figure 2 Graphic interpretation of Harrington's individual desirability function given condition Condd and variable ju2

The graphic interpretation of Harrington's individual desirability function corresponding to the condition Condd is presented in Fig. 2. For each value of d2i, we calculated the corresponding values of i2[ Dt ].

Just like with i1, the |2 range of definition includes four domains separated by the critical values of |[ Di ], where i = 1, 2, 3.

By definition, domain IV covers those values of l2 at which the fragmentation of the protopectin complex makes no sense. This led us to formulate the third individual boundary condition:

- i < i2 [D3 ] means the absence of the second individual potential for protopectin fragmentation;

- i2 >i2[D3] means the presence of the second individual potential for protopectin fragmentation.

We should note that fragmentation potentials I and II are categorical, i.e., if one of them is absent, the total fragmentation potential is absent as well.

Domains I, II, and III include such values of | that ensure not only protopectin fragmentation, but also the isolation of fragmentation products. Based on the canonical reference values of the individual desirability function, we formulated the fourth boundary condition:

- |2 [D3 ] < |2 < |2 [Dj ] means the absence of the second individual potential for isolation of protopectin fragmentation products;

- i2 >i2[Dj] means the presence of the second individual potential for isolation of protopectin fragmentation products.

Similar to the first and the second fragmentation potentials, the individual isolation potentials are categorical.

The third independent variable was a complex operator based on the mass fraction of pectin substances in the tissue:

Figure 3 shows the graphic interpretation of Harrington's individual desirability function given Condd. For each value of d3i, we calculated the corresponding values of | [ Di ].

Here, we can clearly see domain IV with no pectin potential in the plant tissue.

As a result, we formulated the fifth individual boundary condition:

- i3 < i3[D3] means the absence of pectin potential;

- |3 > |3[D3] means the presence of pectin potential.

Thus, the pectin potential is categorical. The fourth independent variable was a complex operator based on the ratio of the mass fractions of protopectin and pectin substances in the tissue:

a

Pa =■

pp

1

(33)

j}ps | +1

where p4 is the dimensionless operator of Harrington's individual desirability function; asp is the mass fraction of natively soluble pectin substances, %; and i4 is the third dimensionless individual criterion for the protopectin fragmentation potential calculated as:

a„

Ma =■

(34)

pp

Then, the condition CondA, which determined the

individual function, was calculated as:

Condj =

d.

» -

0.65 d.

- » -

0.80

(35)

2.50 jU42 1.25 Based on expression (35), we calculated the constant and the coefficient (b40 = -0.3419, b41 = 4.1441).

Based on Condd , the critical boundaries of nA were calculated as:

Ma[ D ] = -1 -

b

b40 + ln [-ln (d4i )]

(36)

(p, =-= M

3 100 ^

(30)

where i4[Di ] is the value of i4 at the critical point Di of Harrington's individual desirability function

where cp, is the dimensionless operator of Harrington's calculated bY (6) and corresponding to d4l; and d4, is the

individual desirability function; a)ps is the total amount of pectin substances, %; and i is the third dimensionless individual criterion for the protopectin fragmentation potential.

In this case, the condition Condd that determined the individual function was calculated as:

0.65" 0.07

Based on expression (31), we calculated the constant and the coefficient as b30 =-3.8367xjo-2 and b3j = 12.5788, respectively, and the critical boundaries of

Condd =

di» 040. d32 M31 0.01 'm32

» -

(31)

M3, as:

M[ Di ] = -

b30 + In [-In ( d3i )]

b

(32)

31

where |3[Di ] is the value of | at the critical point Di of Harrington's individual desirability function calculated by (6) and corresponding to d3i; and d3i is the standard i-th critical (canonical) value d3 of Harrington's individual desirability function.

standard i-th critical (canonical) value d4 of Harrington's individual desirability function.

Figure 4 shows the graphic interpretation of Harrington's individual desirability function given Condd , with d4i values corresponding to i4 [Di ] values.

Based on the logical content of d4i and the numerical values of i4[ Dt ], the range of definition can be divided into four domains that determine the fragmentation potential of the protopectin complex and the isolation potential of fragmentation products.

According to Fig. 4, domain IV covers those values I4 at which the mass fraction of water-soluble pectin exceeds that of the protopectin complex so much that there is practically no reason for its individual fragmentation. Thus, we determined the sixth boundary condition as follows:

- I4 > I4[D3] means the absence of the third individual potential for protopectin fragmentation;

- 1 <|[D3] means the presence of the third individual potential for protopectin fragmentation.

Hi

Figure 3 Graphic interpretation of Harrington's individual desirability function given condition Condd and variable /i3

f4

Figure 4 Graphic interpretation of Harrington's individual desirability function given condition Condi and variable

Following the same pattern, we determined the seventh boundary condition (VII), namely:

- /'41A I < /'4 - /'41I means the absence of the third individual potential for isolation of protopectin fragmentation products;

- /'4 - /'4 [A ] means the presence of the third individual potential for isolation of protopectin fragmentation products.

In addition, boundary conditions VI and VII are based on:

Ma^MA [A] (37)

where /' = 3 for condition VI and, /' = 2 for condition VII.

However, ju4 can be expressed as:

_ asp _ avs ~app (38)

avv avv

Then, given the presence of the third individual fragmentation potential:

] + l) (39)

Thus, the third individual potentials of fragmentation and isolation are relative since they are involved in the formation of respective total potentials indirectly.

through expressions in which they act as one of the variables.

If we assume that there is a certain criterion space with coordinates M\, Mi and mb, the pectin potential of any plant material can be clearly determined as a geometrical location of the point MM, Mi, Mb] corresponding to the material under analysis.

Based on the a priori assumption that

aps +

Zx

a, < 100

i=1 1

(40)

we can establish the eighth boundary condition (VIII): the top boundary of the range of definition for all possible values of MM, m2, m3] is determined by the following basic proposition:

M3(top) =1 Mi 'Mi

(41)

In addition, since a part cannot be larger than a whole, it is also true that:

a pp < a ps

which leads to the following condition:

Mi ^ Mi

(42)

(43)

i.e., the bottom boundary of the range of definition for all possible values of M [m1, m2, m3] is determined by the second basic proposition:

M3(bot ) = Mi

(44)

The last formula is an expression of boundary condition IX.

RESULTS AND DISCUSSION

Thus, according to boundary conditions VIII and IX, a set (A) of all points MM, Hn, M3] can be defined as

M[MM Mn, Mb] 6 [M3(bot^ M3(top)] M1 >0; Mi > 0;m3 > 0

(45)

graphically presented in Fig. 5.

The logic of assessing plant bioresources for the presence of pectin substances determines general boundary conditions for defining a set of points M[mj, Hn, Mb] as the following hierarchy: "individual pectin potential ^ individual fragmentation potential of the protopectin complex ^ individual isolation potential of protopectin fragmentation products". Thus, the entire set of points M[mj, Hn, H3] can be divided into four subsets:

- subset Aj characterized by the absence of a common pectin potential in all the elements;

- subset A2 where An n A1 = 0 and all the elements have a common pectin potential, but lack a common potential for protopectin fragmentation;

- subset A3 where A3 n An =0 and all the elements have common pectin and protopectin fragmentation potentials, but lack a common isolation potential for fragmentation products; and

- subset A, where

A4 o A3 = 0

and all elements

potentials, as well as isolation potential for fragmentation products.

By definition, the following is true for all the subsets:

A1 n An n A3 n A4 =0 (46)

Based on the above, the existence of A} corresponds to:1

Hi ^ Mb <Mb[^b] (47)

The area of definition for all A1 elements is partially presented in Fig. 6.

The existence of subset A2 correspond! to:

1 -mj "hi > mb > Ohn " (m4 [D3] +1), hi > hi [d <imb[db], mi < mi[d3]

> <j

oomi, mi >mb[db] [mb[dв], mi < mb[db]

Mi <Mi[)]

(48)

Mi >Mi[ D3]

Figure 7 shows a partial area of definition for all A2 elements.

The existence of A3 corresponds to:

1 (mi 'mi

Mi ' (m4 [D3] +1)

mi <mi[D3]

Mi >mi[D3 Mi <mi[ di Mi >Mi[Di mi [d3 ] >mi > mi [di ] Mi [d3 ] <mi < Mi [Di ]

> m3 >

mi '(m4[di] +1)

Mi

(49)

Figure 8 presents the area of definition for all A3 elements.

The existence of subset A4 corresponds to:

1 -mi 'mi mi '(m4[Di] +1)

> m3 > mi

mi <mi[di] mi >mi[di]

(50)

The area of definition for all A4 elements is presented in Fig. 9.

Thus, the specific value M[m1, Mi, H3] that shows its belonging to one of the subsets A. (where i = 1,i,3,4) in the zoned criterion space clearly determines the plant tissue's overall potential for protopectin fragmentation.

Our approach to classifying plants as pectin-containing materials, which is based on a system of criteria and a zoned criterion space, has clear advantages over existing methods due to its objectivity determined by the boundary conditions.

However, when analyzing this approach, we can easily see that the Mj-i and Mji values corresponding to d- and dji in the conditions Cond^ |j=i,B,4 were set a priori, based on general assumptions regarding the degree of acceptability of certain Mj values within Harrington's individual desirability functions in accordance with the boundary (canonical) values of d .

Yet, the conditions Cond

dj \j=i,3,4

determine the coefficients

have common pectin and protopectin fragmentation and constants, and, consequently, individual desirability

Figure 5 Definition area of the criterion space

Figure 6 Partial definition area for subset A;

Figure 7 Partial definition area for subset A

Figure 8 Partial definition area for subset A

functions, as well as numerical values of / [Dt ]. Therefore, at this stage, our approach has a general, conceptual form requiring further research.

Based on the results, we developed a generalized algorithm to determine the geometric location of plant tissue in the zoned criterion space, or M[/, /2, /] belonging to one of the subsets (Fig. 10). We can use this algorithm to assess any plant tissue's potential for transformation of the protopectin complex, which determines the influence of any technological impact on its pectin potential.

The approach that we used to determine the criterion space and boundary conditions for its zoning explicitly suggests that this algorithm is universal for classifying plant tissue or its derivatives as pectin-containing materials. Thus, the algorithm is applicable to any type of plant material for which the /2 and / criteria can be numerically expressed.

Figure 9 Partial definition area for subset A

CONCLUSION

To sum up, our investigation showed the following results.

1. We developed a system of criteria to assess the transformation potential of the protopectin complex in plant tissue. This system is based on the geometrical

Q Start ^

/ v1 7

ßi. ßs; ß4

ßi[Di]I¿=2,3;№>[Di]|¡=i,3. ß3[Di]\i=3. ß4[Di]|¡=2

protopectin complex' fragmentation without product isolation

protopectin complex' fragmentation with product isolation

^ Finish ^

Figure 10 Algorithm for plant tissue classification according to protopectin fragmentation potential based on the geometric location in the zoned criterion space

location of M[m1 , m2 , M3 ] - the point that corresponds to the material under analysis - in a zoned criterion space with coordinates in the form of dimensionless individual criteria for protopectin fragmentation potential.

i. The dimensionless individual criteria for protopectin fragmentation potential included the ratio between the mass fractions of biologically active components and protopectin in plant tissue, the mass fraction of the protopectin complex expressed in

unit fractions, and the mass fraction of total pectin substances expressed in unit fractions.

3. We established nine individual boundary conditions, individual pectin potential, two individual fragmentation potentials, and three individual isolation potentials for pectin substances, which altogether determine a system of zoning the criterion space.

4. The boundary conditions in the definition area for a set of points M[m1 , m2 , M3] had the following hierarchy: individual pectin potential ^ individual

fragmentation potential of the protopectin complex ^ individual isolation potential of protopectin fragmentation products.

CONTRIBUTION

All the authors were equally involved in writing the manuscript and are equally responsible for plagiarism.

5. We developed an algorithm to classify plant tissues according to protopectin fragmentation potential based on the geometric location in the zoned criterion space.

CONFLICT OF INTEREST

The authors state that there is no conflict of interest.

REFERENCES

1. Galstyan AG, Aksyonova LM, Lisitsyn AB, Oganesyants LA, Petrov AN. Modern approaches to storage and effective processing of agricultural products for obtaining high quality food products. Herald of the Russian Academy of Sciences. 2019;89(2):211-213. DOI: https://doi.org/10.1134/S1019331619020059.

2. Galstyan AG, Turovskaya SN, Ryabova AE, Illarionova EE, Semipyatnyi VK, Radaeva IA, et al. Technological additives as an element of dry milk properties directed formation. News of the National Academy of Sciences of the Republic of Kazakhstan. Series of Geology and Technical Sciences. 2019;4(436):95-102. DOI: https://doi. org/10.32014/2019.2518-170X.102.

3. Lee BH. Fundamentals of food biotechnology. Wiley-Blackwell; 2015. 544 p. DOI: https://doi. org/10.1002/9781118384947.

4. Bhatia SC. Food biotechnology. CRC Press; 2017. 412 p.

5. Holban AM, Grumezescu AM. Preface for volume 14: Advances in biotechnology for food industry. In: Holban AM, Grumezescu AM, editors. Advances in biotechnology for food industry. Elsevier; 2018. pp. 23-26. DOI: https://doi. org/10.1016/B978-0-12-811443-8.00022-0.

6. Caffall KH, Mohnen D. The structure, function, and biosynthesis of plant cell wall pectic polysaccharides. Carbohydrate Research. 2009;344(14):1879-1900. DOI: https://doi.org/10.1016/j.carres.2009.05.021.

7. Thakur BR, Singh RK, Handa AK, Chemistry and uses of pectin - A review. Critical Reviews in Food Science and Nutrition. 1997;37(1):47-73.

8. Srivastava P, Malviya R. Sources of pectin, extraction and its applications in pharmaceutical industry - an overview. Indian Journal of Natural Products and Resources. 2011;2(1):10-18.

9. May CD. Industrial pectins: Sources, production and applications. Carbohydrate Polymers. 1990;12(1):79-99. DOI: https://doi.org/10.1016/0144-8617(90)90105-2.

10. Muller-Maatsch J, Bencivenni M, Caligiani A, Tedeschi T, Bruggeman G, Bosch M, et al. Pectin content and composition from different food waste streams in memory of Anna Surribas, scientist and friend. Food Chemistry. 2016;201:37-45. DOI: https://doi.org/10.1016/jibodchem.2016.01.012.

11. Ovodov YuS. Current views on pectin substances. Russian Journal of Bioorganic Chemistry. 2009;35(3):269-284. DOI: https://doi.org/10.1134/S1068162009030017.

12. Pectin [Internet]. [cited 2020 Mar 04]. Available from: https://en.wikipedia.org/w/index.php?title=Pectin&oldid= 940586485.

13. Sato MF, Rigoni DC, Canteri MHG, Petkowicz CLO, Nogueira A, Wosiacki G. Chemical and instrumental characterization of pectin from dried pomace of eleven apple cultivars. Acta Scientiarum - Agronomy. 2011;33(3):383-389. DOI: https://doi.org/10.4025/actasciagron.v33i3.7125.

14. Baker RA. Reassessment of some fruit and vegetable pectin levels. Journal of Food Science. 1997;62(2):225-229. DOI: https://doi.org/10.1111/j.1365-2621.1997.tb03973.x.

15. Donchenko LV. Razrabotka i intensifikatsiya tekhnologicheskikh protsessov polucheniya pektina iz sveklovichnogo i drugikh vidov syr'ya [Development and intensification of technological processes for the production of pectin from beet and other raw materials]. Dr. eng. sci. diss. Kiev, 1990. 360 p.

16. Donchenko LV, Karpovich NS, Simkhovich EG. Proizvodstvo pektina [Pectin production]. Kishinev: Shtiintsa; 1994. 181 p. (In Russ.).

17. Donchenko LV Tekhnologiya pektina i pektinoproduktov [Technology of pectin and pectin products]. Moscow: DeLi; 2000. 256 p. (In Russ.).

18. Donchenko LV, Firsov GG. Pektin: osnovnye svoystva, proizvodstvo i primenenie [Pectin: basic properties, production and application]. Moscow: DeLi print; 2007. 275 p. (In Russ.).

19. Rodionova LYa. Teoreticheskoe i ehksperimental'noe obosnovanie tekhnologii pektinosoderzhashchikh izdeliy funktsional'nogo naznacheniya [Theoretical and experimental substantiation of the technology of pectin-containing functional products]. Dr. eng. sci. diss. Krasnodar: Kuban State Technological University; i004. 48 p.

10. Rodionova LYa, Donchenko LV, Sobol IV, Stepovoy AB. Pectin containing raw materials classification extension. Proceedings of the Kuban State Agrarian University. n015;(5n):199-n06. (In Russ.).

11. Galstyan AG, Semipyatnyy VK. K voprosu o rasshirenii oblasti otsenochnykh kriteriev kachestva pishchevykh produktov [On the issue of expanding the field of evaluation criteria for food quality]. Aktual'nye voprosy industrii napitkov [Current issues in the beverage industry]. n017;(1):n7-n9. (In Russ.).

ii. Oganesyants LA, Khurshudyan SA, Galstyan AG, Semipyatny VK, Ryabova AE, Vafin RR, et al. Base matrices -Invariant digital identifiers of food products. News of the National Academy of Sciences of the Republic of Kazakhstan. Series of Geology and Technical Sciences. i018;6(43i):6-15. DOI: https://doi.org/10.Bi014/i018.i518-170X.B0.

13. Harrington EC. The desirability function. Industrial Quality Control. 1965;i1(10):494-498.

14. Dietary reference intakes for energy, carbohydrate, fiber, fat, fatty acids, cholesterol, protein, and amino acids. Washington: National Academies Press; i005. 1B58 p. DOI: https://doi.org/10.17ii6/10490

15. Protein and amino acid requirements in human nutrition: report of a joint FAO/WHO/UNU expert consultation. Geneva: World Health Organization; i007. i65 p.

16. Fats and fatty acids in human nutrition: report of an expert consultation. Rome: FAO; i010. 166 p.

17. Carbohydrates in human nutrition. Report of a Joint FAO/WHO Expert Consultation. Rome: FAO; 1998. 140 p.

18. MR n.3.1.n43n-08 Normy fiziologicheskikh potrebnostey v ehnergii i pishchevykh veshchestvakh dlya razlichnykh grupp naseleniya Rossiyskoy Federatsii [Norms of physiological requirements for energy and nutrients for various population groups of the Russian Federation]. Moscow: Federal Center for Hygiene and Epidemiology of Rospotrebnadzor; i009. B6 p.

19. Vitamin and mineral requirements in human nutrition. ind ed. Rome: WHO and FAO; i004. B41 p. B0. Human vitamin and mineral requirements. Rome: FAO; i001. B0B p.

B1. U.S. Department of Agriculture [Internet]. [cited i0i0 Mar 04]. Available from: https://fdc.nal.usda.gov. ORCID IDs

Vladimir V. Kondratenko https://orcid.org/0000-0002-0913-5644 Tatyana Y. Kondratenko https://orcid.org/0000-0001-8237-0774 Andrey N. Petrov https://orcid.org/0000-0001-9879-482X Georgy A. Belozerov https://orcid.org/0000-0002-8152-146X