Jagiellonian University Collegium Medicum JACEK PIETRASZEK
Cracow University of Technology
Summary
The biotransformation process is one of biotechnological processes utilized in laboratories and industry. It involves the use of plant tissues cultured in vitro cul-tures for processing substrates in the desired products. Efficiency of such a process is highly variable in time and one can usually determine the optimal duration of the process. The purpose of this article is to present how to use fuzzy spread regression to determine the optimal time of the process of biotransformation of hydroquinone to arbutin using callus tissue of purple coneflower (Echinacea purpurea L. Moench). Given the significant cost and long time of tissue growth, to determine the yield curve could not be used as many samples to obtain the appropriate narrow confi-dence intervals determined from probability theory. Therefore, samples taken in different moments of the process were described by triangular fuzzy numbers and then fuzzy spread regression was conducted. As the result, three regression curves were obtained describing respectively the left edge, right edge and center of the fuzzy triangle value. The value of maximum efficiency and its location were deter-mined separately for each of obtained curves. After combining all three maxims, the fuzzy value of maximum efficiency and fuzzy value of its time were determined. The approach should also be useful for similar studies, when probabilistic description of uncertainty is not possible for reasons of time, equipment or financial limits. The developed method will be useful in eventual transition of the process from laborato-ry scale to industrial scale.
Keywords: artificial intelligence method, fuzzy numbers, fuzzy regression, methodology of research, biotechnology
1. Introduction
Cells from in vitro plant cultures have the ability to enzymatic changes in many chemicals. Biotransformation reactions carried out in plant cultures are often a source of valuable secondary metabolites. Biotechnological solutions make crop production independent of the climatic condi-tions, soil condicondi-tions, seasonality of crops, yield variability, and enable a much higher content of the desired product in a very short production cycle. Price of substances produced by biotechno-logical methods ranges from a few to several thousand dollars per kilogram of pure product. The callus tissue culture is an intermediate stage in the development of industrial plant biotechnology
leading to a culture in a bioreactor. The most advanced plant biotechnological processes imple-mented in the production are used in Japan (Mitsui Petrochemicals, Nitto Denki Kyogo, Toyobo, Kanebo) and Germany (Natterman, Boehringer Mannheim, Diversa Ges).
The research object, considered in this article, is a purple coneflower (Echinacea purpurea (L.) Moench). This plant is of interest to physicians and the pharmaceutical industry for many years due to a number of valuable medicinal properties.
This paper shows the optimization of process conditions in the case of biotransformation of hydroquinone to arbutin performed on the callus tissue culture
1.1. Research object
Genus of Echinacea includes nine species according to recent taxonomic researches [7]. One of these species is the purple coneflower (Echinacea purpurea (L.) Moench), which has the best documented therapeutic effect. Echinacea purpurea is a perennial, which reaches a height of 40 to 180 cm. It is native to south-eastern North America. Its cone-shaped flowering heads are usually, but not always purple.
The Indians used it in folk medicine for treating difficult to heal wounds, burns, cough, tooth-ache, colds, and as an antidote to snake venom. European settlers adopted the Indian knowledge of the medicinal properties of Echinacea. The plant was brought to Europe at the beginning of the twentieth century. Echinacea is extracted from the crop in several European countries, including Poland.
Many years of research on the chemical composition of herbal raw materials of the genus Echinacea allowed researchers to isolate and identify several compounds with significant biologi-cal activity [2]. These compounds can be divided into two main groups: the lipophilic fraction and hydrophilic fraction. These compounds stimulate phagocytosis, anti-inflammatory and cause local anesthesia. Compound arousing strong interest is sour galactoarabans, which demonstrates the ability to activate macrophages against cancer cells and microorganisms.
1.2. Target product
Arbutin is hydroquinone--d-glucopyranoside with chemical formula C12H16O7 and compli-cated ring structure [8]. Visually, it is a white odorless crystalline powder. It has a molecular weight of 272.25. Its melting point is 192–202 ºC. Arbutin solubility in methanol is a good, low in the water and ethanol. Specific rotation is [α]20
D-64º. UV Spectrum (5% methanol) is character-ized by absorption maximum 230 and 285 nm and minimum absorption 250 nm.
The beginnings of the use of medicinal properties of this compound dates back to the eight-eenth century. Even then, from practice, there were known its anti-inflammatory, antibacterial and disinfectant.
Arbutin is used in cosmetics and dermatology due to the antioxidant effect and inhibition of tyrosinase. The chemical compound is used as a relatively safe and effective way of lightening the skin in the case of diseases associated with hyperactivity of melanocytes. Arbutin is a component used in cosmetics for the treatment of pigmentation disorders (age spots and freckles). Arbutin can also be used for prophylaxis in the treatment of melanoma and sunburn.
1.3. Biotransformation
Arbutin may occur naturally in some plant species. It can also be produced from exogenous precursors by biotransformation in tissue cultures of many species. In recent years, research is designed to optimize the production of arbutin by biotransformation. The main precursors used in these studies are as follows: tyrosine, 4-hydroxybenzoic acid and hydroquinone.
Reasons for the use of hydroquinone to production of arbutin are: one-step process, substrate specificity of plant enzymes, and no need for products cleaning (no side reactions).
2. Description of the approach
Study subject was quantitative content of arbutin in the dry weight of Echinacea purpurea cal-lus tissue. The specificity of the biotransformation process is the strong variability of the content of the product in time. You can usually approximately determine the moment when the content of the product in the dry weight reaches a maximum.
Unfortunately, the samples are small physical size, because the tissue cultures are very time-consuming, costly, and worse, are exposed to many bacterial infections leading to destruction of the culture. As a result, the data are scarce and irregular. On the one hand, probabilistic method of estimation uncertainty is not very effective because it leads to very large confidence intervals, much larger than the variation observed in reality. On the second hand, any repetition are strongly at risk of systematic errors due to the variability of the raw plant material. Under these conditions, the conducting of regression to determine the optimal time of collection of material for further processing is very difficult and the obtained results may be unreliable.
The authors propose to use fuzzy regression, in which the probabilistic uncertainty will be re-placed by fuzzy uncertainty determined by researcher from irregular data.
2.1. Raw material
The Echinacea purpurea callus tissue, grown in vitro in the Department of Pharmaceutical Botany, Jagiellonian University, was used to carry out biotransformation reactions [5].
The tissue was grown on the Murashige and Skoog’s medium, solidified by agar, supplement-ed growth regulators: benzylaminopurine, auxins and gibberellins. Such msupplement-edium variant has previously been selected as optimal for multiplication of callus tissue. Culture was conducted in a breeding room at 25±2 ºC with continuous illumination of 900 lux intensity.
After nineteen days of in vitro culture, 25 ml of an aqueous solution of hydroquinone at a con-centration of 1 mg / ml and 100 ml of fresh medium was added to the flasks. The precursor was not added to two flasks of each series. The flasks were only supplemented with medium, and then they were used as control sample. Flasks were placed on the reciprocal shaker and then the in vitro culture were gradually eliminated (two flasks at time) at the right moment: in the first run after 0,5h, 1h, 2h, 3h, 6h, 24h, 48h, 72h, 96h, 168h; in the second run after 1h, 2h, 3h, 6h, 9h, 12h, 24h, 36h, 48h, 72h and 168h. The control samples were eliminated after 168h.
The resulting material was weighed, dried in a dryer, then re-weighed and pulverized in a mortar. Filtered medium was frozen, lyophilized and allowed for analysis.
Analysis of extracts produced from tissue and medium was carried out using thin layer chro-matography (TLC) and high performance liquid chrochro-matography (HPLC). The content of arbutin was determined.
2.2. Fuzzy spread polynomials regression
Unfortunately, the fuzzy numbers arithmetic [3] has numerous differences in relation to real numbers arithmetic. Particularly: there are not inverse elements for addition and multiplication. only positive fuzzy numbers subset has a regular algebraic structure. This subset is recognized as a semi-ring with zero and unity. The calculations on FN are very ineffective and time consuming. Due to this inconvenience, a lot of simplified subsets of FN were introduced: LR numbers, inter-vals approximations, alpha-cuts, triangle FN, trapezoid approximations [9, 10]. The calculation difficulties caused a practical reduction of fuzzy numbers expressions to a class of linear combina-tions of fuzzy numbers with real (crisp) coefficients. Generally, only such systems of fuzzy equations are resolved [11].
There are propositions of identification for those models, which are linear in relation to fuzzy parameters. A modified least squares criterion is proposed as method for the problem resolving [1]. A variety of approaches are applied: three coupled real (crisp) polynomials describing centre and both spreads of fuzzy outcome [4] a polynomial with fuzzy coefficients [6] and others. Apart of a polynomial form, difference measures of a fuzzy distance are applied. The approaches men-tioned above involve very complicated non-linear programming as a method for resolving: minimization of the least square criterion is coupled with additional conditions assuming e.g. non-negativity of both spreads. Typically, Karush-Kuhn-Tucker conditions are involved to test if a tested solution is optimal.
In this paper, the author applies analogous approach: a fuzzy polynomial regression model with three coupled real polynomials is applied for describing arbutin content in the dry weigh as a function of biotechnological process time, but logarithmic transformation of dependent variable is applied.
As a start point, a model proposed by D’Urso and Gostaldi [6] in the year 2002 was assumed. This model contains three coupled polynomials describing a center of a fuzzy outcome and its both spreads: left and right. The specific feature of this approach is that spreads are proportional to the center: p(x) d b c(x) q(x) h g c(x) = + ⋅ = + ⋅ (1) where:
c(x) – fuzzy center outcome regression model, p(x) – left spread regression model,
q(x) – right spread regression model.
Such coupling guarantees that magnitudes of spreads will be proportional to the magnitude of the center outcome.
In the original paper of D’Urso and Gostaldi [4] only polynomials were involved. Author modified that model and replaced the polynomials with general linear model based on arbitrary selected functions. The model appears as:
1. the centre model
0 1 c a f (x , a ) e m i k i k i k= = +
+ (2)2. the left spread model
0 1 p d b (a f (x , a )) m i k i k i k= = + ⋅ +
+ λ (3)3. the right spread model
0 1 q h g (a f (x ,a )) m i k i k i k= = + ⋅ +
+ ρ , (4) where: m – terms in a series,xi – observed values of independent variable,
aj, b, d, h, g – regression model parameters,
ci – mean of i-th outcome,
pi – minimum of i-th outcome,
qi – maximum of i-th outcome,
ei, λi, ρi – residuals of outcomes.
At last, the fuzzy approximated outcome may be written in the form of (ci-pi, ci, ci+qi).
2.3. Model identification
Identification of the model (2)…(4) is conducted by the least square method but the mini-mized criterion is modified and additional conditions are assumed. There are identified parameters aj, b, d, h, g. The minimized error criterion is modified to the form (5) containing weighted sum of
all errors, from center and from both spreads:
(
)
N 2 2 2 2 0 1 1 2 3 1 (a ,a , ,a ,d, b, h,g) w w w min s m i i i i D = = ε + λ + ρ → , (5)where: w1, w2, w3 – arbitrary set weights, typical values are 1/3. Additional conditions (6) are assumed:
0 1 d b (a f (x ,a )) 0 m k i k k= + ⋅ +
≥ , (6a) 0 1 h g (a f (x , a )) 0 m k i k k= + ⋅ + ≥ , (6b)which guarantee that solution will comply with relations (7) between elements of the model (1): c(x) p(x)− ≤ c(x) ≤ c(x) q(x)+ . (7)
The minimizing of (5) given subject (6) is possible by a generalization of Lagrange multipliers known as Karush-Kuhn-Tucker conditions. The minimal value of Ds2 obtained is known as the fuzzy least square distance. Due to non-linearity of the above optimisation problem, the solution may be obtained only by recursive numerical procedure, typically Levenberg-Marquardt approach. 3. Description of achieved results
In this chapter, there are presented source raw data obtained from TLC and HPLC analysis, then processed fuzzified data and – at last – identified models and optimum times found.
3.1. Results of TLC and HPLC analysis
In the Table 1, the results achieved from TLC and HPLC analysis [4] are presented. The con-tent of arbutin in tissue is related to dry mass of tissue. The average yield of biotransformation process describes the percent of hydroquinone transformed into arbutin by biotechnological process.
Table 1. The content of arbutin in tissue and yield of hydroquinone to arbutin biotransformation process
t [h]
The contents of arbutin in tissue [% of d.m.]
average yield of biotransformation [%]
run = 1 run =2 run = 1 run = 2
0,5 0,376 0,393 – – 5,34 6,41 – – 1 0,230* 0,556 0,421* 0,423* 1,57 6,30 3,05 3,02 2 0,414 0,526 0,378 0,445 5,17 5,68 7,75 9,10 3 0,458 0,490 0,419 0,551 5,10 4,05 6,00 7,40 6 1,410 2,283 0,471 0,502 14,26 28,73 7,86 8,54 9 – – 0,479 0,562 – – 3,23 4,85 12 – – 2,196 2,283 – – 21,18 27,66 24 3,229 4,066 4,046 4,699 39,36 39,47 44,57 54,91 36 – – 3,504 4,200 – – 52,37 63,84 48 2,928* 4,016 2,896 2,898 20,18 60,72 32,98 30,30 72 2,727 3,359 1,892 2,363 23,04 59,34 19,88 27,45 96 1,670 2,297 – – 30,67 37,83 – – 168 1,486 1,493 1,495 1,602 16,42 21,02 13,59 17,57
The contents of arbutin in tissue dry mass is presented graphically in the Fig. 1. As may be observed, the measures are rather stable and equal in the initial phase of the process and more scattered in the most efficient phase of the process. In the final phase of the process values are again similar.
3.2. Fuzzified measures
The obtained measures, presented in Table 1, were fuzzified into triangle fuzzy numbers FN(lbs, cs, rbs) by the following method. The left boundary lbs of the support was determined as the minimum of measures:
lbs min xi
i
= , (8)
where xi – i-th measure.
0.1 1 10 100 1000 Time [h] 0 1 2 3 4 5 a rb u ti n in d ry m a s s [% ]
Figure 1. The contents of arbutin in tissue as a percent of dry mass (time axis in logarithmic scale)
0.1 1 10 100 1000 Time [h] 0 20 40 60 80 Y ie ld o f h y d ro q u in o n e to a rb u ti n b io tr a n s fo rm a ti o n p ro c e s s [% ]
Figure 2. The yield of hydroquinone to arbutin biotransformation process (time axis in logarithmic scale)
Source: Own study.
The core cs of the support was determined as the median of measures: cs median xi
i
= , (9)
where xi – i-th measure. The median is a better description for low amount samples with
non-symmetric data.
The right boundary rbs of the support was determined as the maximum of measures: rbs max xi
i
= (10)
where xi – i-th measure.
Table 2. Fuzzified content of arbutin in tissue and fuzzified yield of hydroquinone to arbutin biotransformation process
t [h]
The contents of arbutin in tissue
[% of d.m.]
average yield of biotransfor-mation [%] lbs cs rbs lbs cs rbs 0,5 0,376 0,3845 0,393 5,34 5,875 6,41 1 0,23 0,422 0,556 1,57 3,035 6,3 2 0,378 0,4295 0,526 5,17 6,715 9,1 3 0,419 0,474 0,551 4,05 5,55 7,4 6 0,471 0,956 2,283 7,86 11,4 28,73 9 0,479 0,5205 0,562 3,23 4,04 4,85 12 2,196 2,2395 2,283 21,18 24,42 27,66 24 3,229 4,056 4,699 39,36 42,02 54,91 36 3,504 3,852 4,2 52,37 58,105 63,84 48 2,896 2,913 4,016 20,18 31,64 60,72 72 1,892 2,545 3,359 19,88 25,245 59,34 96 1,67 1,9835 2,297 30,67 34,25 37,83 168 1,486 1,494 1,602 13,59 16,995 21,02
Source: Own study. 3.3. Identified models
Both dependencies have the similar shapes: the quasi-gaussian peak with right end higher than the left almost asymptotic start. The authors propose a description of the functions of the form with seven parameters:
(
)
2 50 1 2 3 4
6
log(x) a c(x) a a tanh(a log(x) a ) a exp
a − = + − + − . (11)
It appears good enough to approximate but leaves enough degree of freedom to avoid an in-terpolation.
For the contents of arbutin the following parameters’ values were found: a0 = 1.078, a1 = 0.611, a2 = 116.748, a3 = 125.27, a4 = 2.355, a5 = 1.445, a6 = 0.122.
The related coefficients for the left spread are: d = 0.063, b = 0.1. The related coefficients for the right spread are: h = 0.197, g = 0.112.
The maximum is found at time equal to tc = 27.9 h. Estimated maximum value of the arbutin contents is described by the triangle value (3.58, 4.05, 4.70).
For the yield of biotransformation process the following parameters’ values were found: a0 = 5.602, a1 = 0, a2 = 0, a3 = 0, a4 = 40.506, a5 = 1.555, a6 = 0.243.
The related coefficients for the left spread are: d = 0.640, b = 0.136. The related coefficients for the right spread are: h = 0.891, g = 0.398.
The maximum of yield is found at time equal to tc = 35.9 h. Estimated maximum value of the yield of the process is described by the triangle value (39.2, 46.1, 65.4).
4. Conclusions
In this paper the application of fuzzy spread regression to analysis of biotechnological process efficiency is presented. A detailed description is presented, how to use fuzzy spread regression to determine the optimal time of the process of biotransformation of hydroquinone to arbutin using callus tissue of purple coneflower (Echinacea purpurea (L.) Moench). The optimum time of the process is determined as the fuzzy triangle number, separately for the maximum arbutin contents and for the maximum yield of the biotechnological transformation process.
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ZASTOSOWANIE PASMOWEJ REGRESJI ROZMYTEJ DO ANALIZY WYDAJNOĝCI PROCESU BIOTECHNOLOGICZNEGO
Streszczenie
Proces biotransformacji jest jednym z procesów biotechnologicznych stosowa-nych w laboratoriach i przemyle. Polega on na wykorzystaniu tkanek rolinstosowa-nych hodowanych w kulturach in vitro do przetwarzania substratów w podane produk-ty. Wydajno procesu jest bardzo zmienna w czasie i mona zazwyczaj okreli optymalny czas trwania procesu. Celem niniejszego artykułu jest pokazanie zasto-sowania pasmowej regresji rozmytej do wyznaczenia optymalnego czasu trwania procesu biotransformacji hydrochinonu do arbutyny przy wykorzystaniu tkanki kalu-sowej jeówki purpurowej (Echinacea purpurea (L.) Moench). Z uwagi na wysoki koszt prowadzenia hodowli i długi czas wzrostu tkanki,nie było moliwe wykorzysta-nie takiej liczby próbek, aby przedział ufnoci wyników wyznaczany na podstawie teorii prawdopodobiestwa był dostatecznie wski. Z tego powodu próbki pobierane w rónych chwilach trwania procesu były opisywane za pomoc trójktnych liczb rozmytych a nastpnie poddawane rozmytej regresji pasmowej. Rezultatem były trzy krzywe regresji opisujce odpowiednio lew krawd , praw krawd i rodek trój-ktnej wartoci rozmytej. Maksymalna wydajno i chwila jej osignicia były wyznaczane osobno dla kadej krzywej. Po połczeniu wszystkich trzech maksimów wyznaczana była maksymalna rozmyta wydajno i rozmyty czas jej uzyskania. Pro-ponowane podejcie powinno by uyteczne dla podobnych zagadnie, w których probabilistyczny opis niepewnoci nie jest moliwy do zastosowania z uwagi na ograniczenia czasowe, sprztowe lub finansowe. Opracowana metoda powinna by uyteczna przy ewentualnym przenoszeniu procesu z warunków laboratoryjnych do skali przemysłowej.
Słowa kluczowe: metody sztucznej inteligencji, liczby rozmyte, metodyka bada, biotechnologia
Ewa Skrzypczak-Pietraszek
Katedra i Zakład Botaniki Farmaceutycznej Collegium Medicum
Uniwersytet Jagielloski 30-688 Kraków, ul. Medyczna 9
e-mail: ewa.skrzypczakpietraszek@gmail.com Jacek Pietraszek
Instytut Informatyki Stosowanej Wydział Mechaniczny
Politechnika Krakowska
Al. Jana Pawła II 37, 31-864 Kraków e-mail: pmpietra@mech.pk.edu.pl
