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Application forms and mode of action of biocontroller in the management of Meloidogyne incognita in tomato

Mixture of antagonist agents and form of application may influence in the control of root-knot nematodes. Thus, the aim of this work was to study the action of a biological product based on enzyme mixtures, Bacillus sp. and Trichoderma sp., at different concentrations on hatching, motility, mortality and reproduction of Meloidogyne incognita in tomato, considering two ways of application of the product. Eggs and second-stage juveniles (J2) of M. incognita were placed in biological product solutions at concentrations: 0, 1.25, 2.5, 5, 10, 20 and 40 g L-1. The same concentrations were applied to planting pits or to the soil surface. Afterwards, 3,692 eggs of M. incognita were inoculated in tomato crop. A significant reduction in J2 hatching of M. incognita J2 was observed in the highest concentrations and higher mortality of J2 from concentration of 5 g L-1. The interaction between concentrations and form of application of the product significantly influenced the infectivity and reproduction of M. incognita. Greater root system mass was obtained by applying the biological product to the surface, regardless of concentration.

Research
Horticultura Brasileira 38 (3) July -September, 2020 R oot-knot nematode species are considered limiting factors and of great economic importance in horticulture sector in tropical and subtropical countries (Hallmann & Meressa, 2018). Among these species, M. incognita stands out for high dissemination, due to its wide range of hosts, estimating yield losses of 37.4% in tomato crop (Solanum lycopersicum) (Hema & Khanna, 2018).
A p p l i c a t i o n o f c h e m i c a l nematicides, as a control measure, has been increasingly restricted because of the high risks of environmental contamination and damage to human health. Thus, developing non-chemical as well as more ecologically acceptable or less aggressive methods for nematode control is essential (Zhang et al., 2017). Considering this, the use of biological control agents has shown to be a promising method to control phytonematodes. Bacillus and Trichoderma species produce metabolites which inhibit from the hatching and penetration process until the nematode reproduction, besides promoting plant growth (Rocha & Souza, 2015;Zhang et al., 2017). In addition to the production mechanisms of toxins and enzymes (proteases, lipases, collagenases) in the degradation of the cuticle and eggshell of the nematode, some species / isolates can also cause changes in attractive substances, produce volatile organic compounds and induction of systemic resistance in plants (Rocha & Souza, 2015).
Palavras chave: Bacillus spp., Trichoderma longibrachiatum, nematoides-das-galhas, enzimas, controle biológico. observed a reduction in M. incognita population in tomato crop. However, more studies are necessary in order to elucidate the mechanism of action of this product on nematode as well as if the concentration and form of application can increase the efficiency of nematode control in tomato crop. Thus, the aim of this study was to observe the action of different concentrations of commercial biocontroller product composed of a mixture of enzymes and antagonistic agents on hatching, motility, mortality and infectivity and reproduction of M. incognita in tomato crop, applied to planting pits or to the soil surface.

MATERIAL AND METHODS
The researches were carried out at the Federal University of Minas Gerais (UFMG), Campus Montes Claros-MG.
In vitro experiments were performed in Phytopathology Research Laboratory, in February and March, 2018. In vivo trial was performed in a greenhouse, from May to July, 2018. In both trials, the commercial product Nem-Out TM was used, obtained from Alltech Crop Science, approved to be used as additive for composting, according to standards NOP-EUA, IBD/IFOAM, CE 889/08, JAS and the Brazilian Law No. 10.831/2003, which is the base of enzymes (protease, cellulase, xylanase), and Bacillus subtilis, B. licheniformes and Trichoderma longibrachiatum at the concentration 3.75 x 10 8 CFU/g. Inoculum of M. incognita previously identified on the basis of perineal configuration and esterase phenotype was used in the trials. The suspension of M. incognita eggs was obtained from the roots of infected tomato crops, cv. Kada, grown in a greenhouse, using Hussey & Barker's technique (1973), modified by Boneti & Ferraz (1981). The suspension was cleaned according to Coolen & D'Herde's technique (1972). The J2 were obtained from incubated eggs in a hatching chamber at room temperature. Only J2 hatched on the third day were used.
In vitro trials -hatching, motility and mortality In a hatching chamber formed with mesh, non-woven fabric (TNT) and Petri dish were placed 6 mL of suspension containing 5,985 eggs mL -1 of M. incognita and 24 mL of solutions of biological product at concentrations of 1.25; 2.5; 5; 10; 20 and 40 g L -1 . The chambers were incubated at room temperature (25±3 o C) for 14 days. The eggs incubated in water were considered control. Hatched J2 were first counted 48 hours after trial installation and 14 days after incubation, with 24-hour intervals. After collecting hatched J2, new solution of the biological product studied was put in the hatching chamber, corresponding to each treatment, in order to evaluate the effect of the product on J2 hatching.
In order to evaluate motility and mortality, 4 mL of biological product solutions and 1 mL of suspension containing 1,848 J2 of M. incognita were placed in glass test tubes (10 mL). The same concentrations used in the previous trial were evaluated. The tubes were sealed with transparent PVC film and incubation was done at room temperature for 24 hours. Then, J2 were poured into an 11 µm-sieve and rinsed with distilled water. The quantification of the J2 motility and mortality was carried out according to the methodology described by Rocha et al. (2005a).
In both trials, a completely randomized design, with seven treatments and six replicates, was used.

In vivo trial -infectivity and reproduction
In plastic pots filled with 800 cm 3 substrate in a ratio 2:1 (sand:soil), 40 mL of biological product solution were applied to the planting pit. Afterwards, a 35-day-old tomato seedling (cv. Kada) was transplanted into each pot. Inoculation was done applying 2 mL of suspension containing 1,848 eggs of M. incognita, distributed in two ±3-cm-deep holes around the seedlings. For treatments with application of the product on soil surface, the seedlings were transplanted to pots and irrigated with the same volume and concentrations of solutions evaluated by application to open pit. Then, the seedlings were inoculated with eggs of M. incognita, as previously described. The seedlings which were inoculated only with eggs of M. incognita were considered control. Pots were kept in the greenhouse and, thirty days after inoculation, the tomato root systems were collected, weighed and egg masses were colored according the technique described by Rocha et al. (2005b). Number of egg mass, galls and eggs per root system were quantified. Using the data obtained, the same variables were estimated for each gram of root. Reproduction factor (Rf) was calculated by dividing the final and initial population densities for each treatment (Rf= Pf/Pi), according to Seinhorst (1967).
The experimental design was completely randomized, with seven replicates, in factorial scheme 6x2+1, considering six concentrations of biological product (1,25; 2,5; 5; 10; 20 and 40 g L-1 ), applied to planting pits or to the soil surface, an additional treatment, without the product (control). Each plot consisted of one pot with one plant, totalizing 91 plots.
Hatching, motility and mortality were submitted to non-parametric analysis, since they had not presented normal distribution and homogenous variances. The treatments were compared using Kruskal-Wallis test (p≤0.05). Infectivity and reproduction data were submitted to analysis of variance and regression. The averages of qualitative factor (application mode) were compared using F test, at 5% probability. For quantitative factor (concentrations), equations were adjusted, being the coefficients tested using t-test. In order to compare the averages of the control with the averages of each treatment (concentrations x application mode), Dunnett's test at 5% significance level was applied.

In vitro trials
Only the concentrations of 20 and 40 g L -1 of biocontroller product caused a significant reduction in hatching of M. incognita J2, comparing with the control ( Figure 1A). Motility inferior to 0.17% was observed in J2 exposed to concentrations starting from 5.0 g L -1 ( Figure 1B). J2 mortality above 90% also occurred from this concentration ( Figure 1C).
During the hatching process, J2 perforates the egg shell and / or can modify its structure by chitinase (Cotton et al., 2014), which can allow the entry of substances with nematicidal action, causing death or nematostatic activity in J2 still inside the egg, and consequently, inhibiting the hatching process. As in this study egg suspension was used at different stages of embryonic development, this may partly explain why an inhibition in the hatching of 79.5% in the highest concentration (40 g L -1 ) was observed during the 14-day incubation period (Figure 1 A). On the other hand, the eggshell of phytonematodes is formed by a vitelline, chitinous and lipid layer (Ferraz & Brown, 2016) which protect the nematode against nematicidal substances and antagonistic agents. Thus, to provoke the death of J2 still inside the egg, it is necessary that the enzymes degrade the egg shell. Several researches have reported the action of enzymes as proteases produced by different species of Bacillus with nematicidal activity on eggs and juveniles of Globodera rostochiensis and M. incognita (Huang et al., 2010;Margino et al., 2012;Rocha & Souza, 2015). Therefore, the greater immobility of J2 already in the first 24 hours of exposure to the biocontroller product and mortality above 80% at concentration of 2.5 g L -1 ( Figure 1C) reinforces the hypothesis that the main cause in the reduction of hatching is due to the entry of substances inside the egg which acted on J2.
The production of extracellular enzymes by the antagonist agent in the degradation of the cuticle and eggshell of the nematode constitutes an important stage of parasitism and as a virulence factor. Bacillus nematocida produces the extracellular enzyme serine protease Bace16 which can degrade the juvenile cuticle and the eggshell of Panagrellus redivivus (Niu et al., 2007). Niu et al. (2006) observed that P. redivirus exposure to crude extracellular protease extract, produced by Bacillus sp. B16 for 48 hours, caused 95% mortality of nematodes. The same authors also verified that all the nematodes exposed to purified protease at a concentration of 1.79 μg mL -1 were killed and degraded after 48 hours. Consequently, these facts probably mean that proteases in the commercial biological product studied, act by reducing the motility of J2, degrading cuticle and eggshell, leading nematode to death. In this study, as the eggs remained in the solutions of the biocontoller product for a longer time and, as the eggshell to be degraded needs proteases and chitinases, whereas J2 cuticle needs only the action of proteases, explains why a greater action of proteases on J2 at the concentration of 5 g L -1 was noticed, even causing 100% immobilization and mortality at the highest concentration (40 g L -1 ). As a matter of fact, in previous studies, mortality of M. incognita J2 in 24 hours after the exposure to the biocontroller product used was due to nematode cuticle degradation process (unpublished data).
Another relevant factor is the quality and concentration of enzymes produced by antagonistic agents. Bacillus licheniformis MH48 produces protease which can cause 80% mortality of Bursaphelenchus xylophilus, at 20% concentration of crude extract, and cuticle degradation after two-day exposure (Jeong et al., 2015). Al-Shammari et al. (2013) verified that T. longibrachiatum caused reduction of 8.9% in hatching and mortality of 64.5% of M. javanica J2 after 72-hour exposure to fungal filtrate.

In vivo trials
The infectivity and reproduction of M. incognita were significantly influenced by the interaction between concentrations and application of the biological product (Table 1). Whereas the non-treated control showed an average of 20.9 galls/g of roots, average values were observed between 5.3 and 11.0 at concentrations of 5.0 and 1.25 g L -1 applied to the surface and 13.4 at the concentration of 1.25 g L -1 applied to the pit. Comparing with the control, the concentrations from 1.25 to 10 g L -1 , applied to the surface resulted in the lowest number of galls. When the product was applied to the pit at a concentration of 1.25 g L -1 , the number of galls was also low. However, at concentrations from 5 to 40 g L -1 , the number of galls was higher than the control. Comparing the forms of application, the number of egg masses at the concentration of 1.25 g L -1 was higher than the applied to the surface. At concentration of 40 g L -1 , highest average value was verified when applied to the pit. At other concentrations, no significant difference between forms of application was observed (Table 1). There was also no significant difference when comparing the average of each concentration with the average of the untreated control (10.7).
Comparing the number of eggs per gram of roots between the application forms of the product, the authors observed that at concentrations of 2.50 and 40 g L -1 , concerning the application to the surface, the values were superior (Table 1). However, at concentrations of 5 and 10 g L -1 , the number of eggs/g of roots was superior for application to the pit. At other concentrations, there were no significant differences. In relation to the control (740.4), application to the surface, at concentrations from 1.25 to 2.5 g L -1 provided lower average values for number of eggs/g roots, whereas concentrations from 20 to 40 g L -1 provided values higher than the control. At intermediate concentrations there was no significant difference. For application to the pits, only at concentration of 2.5 g L -1 no significant difference was noticed. At higher concentrations (10, 20 and 40 g L -1 ), the averages observed were superior to the control. Comparing Rf, concerning forms of application, at concentrations of 2.5, 20 and 40 g L -1 , we observed that application to the surface showed average values superior in comparison to the ones applied to the pit (Table 1). Only at concentration of 10 g L -1 we observed a higher average of Rf for application to the pit. Comparing to the control (7.5), all averages (of each concentration and for each form of application) were superior, except for dose 2.5 g L -1 , applied to the pit, which did not differ statistically.
Except for infectivity, expressed in egg masses/g of root, the product applied to the soil surface presented no significant effect of concentrations, whereas the number of galls and egg masses/g of root resulted in linear increasing with increasing concentrations of biological product (Figures 2A and 2B). The same was verified about reproduction, expressed by the number of eggs/g of root and Rf, when the product was applied to the surface; however, the application to the pit showed quadratic effect with an increase of the product concentrations ( Figures 2C and 2D). An increase in Rf was observed up to the calculated concentration of 22.64 g L -1 , reaching the value of 44.94, and decreasing to 18.43 at concentration of 40 g L -1 .
In addition to the significant reduction in the mass of the root system by the form of application of the biological product, we also observed that applying the product to the soil surface, regardless of concentration, the mass of the root system of tomatoes was higher than that found in the treatment with application to the planting pit (Table 2). However, only using the concentration of 10 g L -1 , applied to the surface, significant difference was observed, with Dunnett's test, at 5% probability. Apparently, this form of application of the biological product promotes a greater distribution of antagonistic agents and / or of their compounds in the root system of tomatoes in relation to the application to planting pits, providing a greater mass of fresh matter in the root system. The increase in infectivity and reproduction observed in some concentrations versus forms of application and, mainly, at higher concentrations (20 and 40 g L -1 ) of the biological product applied to the surface and to the pit is related to the increase in the root system, which increases the chances of J2 finding the root, penetrate and induce the feeding site, which reflects a greater number of Table 1. Average values of number of galls, egg masses, eggs and reproduction factor (Rf) of Meloidogyne incognita per gram of root of tomatoes in relation to different concentrations of biocontroller product and application forms. Montes Claros, UFMG, 2018.

Concentrations
(g L -1 ) Averages followed by uppercase letters in line do not differ significantly (Tukey test, 5%). *and** different from the control at 5% and 1% probability using Dunnett's test, respectively. Data were transformed by the formula . Values presented in parentheses refer to the original data.
Application forms and mode of action of biocontroller in the management of Meloidogyne incognita in tomato galls, egg masses, eggs and Rf. Bacillus and Trichoderma present in the mix of the studied biological product are reported with activity in the control of nematodes, interfering in the parasitism process through the production of enzymes, volatile organic compounds and the promotion of plant growth (Araújo & Marchesi, 2009;Chen et al., 2009;Yang et al., 2010;Rocha & Souza, 2015). However, according to the results obtained in this study, we observed only nematicidal activity of the biological product in in vitro studies, but not in a greenhouse. Although the same concentrations were used in both trials, the results of lack of control in the greenhouse can be explained by the effect of dilution and leaching of the product in the soil because of irrigation during tomato cultivation. This fact may have favored the directed migration behavior of the nematode to the roots due to the low action of the biological product on the nematode, but with the action of promoting the root system, increasing the parasitism of the root system by the nematode.
In this study, higher concentrations used (20 to 40 g L -1 ) represent the use of 6 and 12 kg/ha of the evaluated commercial product, and at this dose of applications, technical professionals and producers have reported that, in field conditions, it is possible to observe an increase in productivity and growing of the root system of the plants, promoted by the biological product, even in the presence of root-knot nematodes. At concentration of 20 and 40 g L -1 , applying the product to the surface, Rf value was 54.8 and 69.8, respectively, whereas the control showed a value of 7.5. Although an increase in infectivity and nematode reproduction in tomatoes were noticed, when applying the product to the surface, an increase in fresh mass of the root system between 6.5 and 63.4%, compared to the control was also verified, which allows greater tolerance of the plant to nematode attack. Root system masses of tomatoes which received the application in the pit were lower and a reduction in the reproduction factor was noticed, when compared to those with application to the soil surface, which explains the results previously mentioned. Silva et al. (2017) found an increasing reduction in population density and Rf of M. incognita in tomatoes with dosages of 6, 8 and 10 kg/ha of the biocontroller product at 45 days after inoculation, but there was no growing promotion of the root and shoot system. Nevertheless, in the same study, these authors verified that, in control, Rf was 157.54 and at concentrations of 8 and 10 kg/ha, was 10.11 and 7.48, respectively, at 45 days. At 65 days, the authors observed an increase in nematode reproduction in tomato crop. This means that despite M. incognita population reduction, Rf still remained above 1.0, and, according to Seinhorst's criteria (1967), the plants were classified as good hosts of nematodes.
Organic matter content in the substrate, the form of treatment and the time of colonization of the roots may have negatively interfered with the performance and effectiveness of the biocontrol agents. Actually, the best results of isolates of Trichoderma and Bacillus in M. incognita and M. javanica control in tomato and okra crops have been reported with a previous application to soil or with seed treatment (Javeed & AL-Hazmi, 2015;Eltayeb, 2017;Uday et al., 2019). These factors, added to just one application of the product, may explain the low performance of antagonists in in vivo control compared to in vitro control, which resulted in more promising values.
In summary, in this study it can be concluded that the evaluated biocontroller product, although showing a deleterious effect on M. incognita in vitro, did not provide consistency in nematode control in tomatoes, at any concentration or form of application, when the variables number of galls, number of egg masses, number of eggs and reproduction factor in a greenhouse were calculated. by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brasil (CAPES), Finance Code 001. To CAPES, for the scholarship to the first author. The authors also thank to Alltech Crop Science for providing the commercial product studied and partnership.


extfieldsofstudy: Chemistry Medicine

provenance: AgriculturalAndFoodSciences,2019-2020-Agricultural And Food Sciences-2020.jsonl.gz.gz

text:
In vitro prebiotic activities of oligosaccharides from the by-products in Ganoderma lucidum spore polysaccharide extraction

Until recently, a variety of oligosaccharides from fruits, vegetables and mushrooms have demonstrated positive prebiotic effects. Ganoderma lucidum, a well-known traditional medicine and tonic in East Asia, has been utilized in the prevention and treatment of a broad range of illnesses. In this study, each of three oligosaccharides was obtained from the polysaccharide extraction by-products of sporoderm: the unbroken and broken spores of Ganoderma lucidum (UB-GLS, B-GLS). Their molecular weight distribution, monosaccharide composition and preliminary structures were analyzed using gel permeation chromatography (GPC), GC-MS, UV and FTIR, respectively. All of the oligosaccharides were found to exhibit prebiotic activities, evaluated by detecting growth stimulation on Lactobacillus in vitro. Among these, UB-O80 and B-O80 displayed the most significant effects (p < 0.05) in these groups, and UB-O80 showed higher resistance to hydrolysis by artificial human gastric juice compared with inulin, giving a maximum hydrolysis rate of 1.65%. Compared with inulin media, Lactobacillus also revealed high tolerance to lower pH levels and simulated gastric juices in UB-O80 and B-O80 media. Compared with a control in gut microbiota fermentation, the abundance of some beneficial bacteria increased and some harmful bacteria declined in the groups of UB-O80 and B-O80. In conclusion, the results suggest that GLS oligosaccharides could be exploited as promising prebiotics for the enhancement of human health.

Introduction
Nowadays, the gut microbiota is regarded as a "new organ" of the human body, 1 whose cells are approximately tenfold greater in number than human cells. This biome colonizes in the intestinal tract, forms a mutual symbiotic relationship with the host, and plays an important role in the metabolism and immune systems. For instance, the intestinal ora of patients suffering from diabetes, hypertension and other metabolic diseases is quite different from that of healthy people. 2 Intestinal microorganisms are normally divided into benecial, harmful and neutral bacteria. Bidobacterium and Lactobacillus are the two principal benecial/probiotic bacteria of the intestinal microora due to their health promoting properties; they make up about 25% of the total number of gut bacteria. 3 Organic acids including lactic acids are produced by Lactobacilli fermentation, and acid-induced environment in the colon inhibit the growth of pathogens. These also include boosting immune function, improving digestion and eliminating fecal, and reducing the likelihood of irresistible bowel syndrome (IBS). 4 Many studies conrm that the selective addition of certain substances to the diet is a valid approach to the dietary manipulation of the colonic microbiota, and substances are referred to as prebiotics. 4 To date, some carbohydrates extracted from fruits, vegetables, mushrooms have been reported as being potential sources of natural prebiotics. 5,6 Ganoderma lucidum (G. lucidum), a species belonging to the macro-fungi, has a long history of application as traditional medicine and tonic with its healthpromoting properties in East Asia. 7 Modern pharmacological studies have veried that G. lucidum is involved in anti-tumor, hypoglycemic, immunomodulation, liver protection, and other activities. 8,9 It contains a variety of functional components, including polysaccharides, fatty acids, peptides, triterpenoids, organic germanium, adenosines and inorganic elements. 10 The polysaccharides of G. lucidum can promote the growth of probiotics and alleviate colorectal cancer by altering of special gut bacteria. 8,11 It helps reduce the abundance of potential pathogenic bacteria; additionally, G. lucidum polysaccharides have been found to signicantly increase the numbers of several benecial bacteria for anti-obesity SCFA-production in mice. 12 The Ganoderma lucidum spores (GLS) contains all the genetic material and health-care effects of G. lucidum. They are the essential parts of G. lucidum and have been widely used for medicinal and functional food products in China. Nevertheless, their broken spores have been found to provide better absorption and therapeutic effects than unbroken spores, as the genetic material and biological composition were wrapped in two outer layer walls mainly consisting of chitin, which is extremely difficult for the alimentary tract to digest. 13,14 In the alcohol precipitation process of edible fungus polysaccharide extraction, the resulting supernatant is rich in oligosaccharides components. It is generally directly discharged as waste, which not only affects the environment, but also produces waste resources. Studies conrmed that different soluble glucans extracted from oyster mushrooms can stimulate the growth of colon microorganisms. 15 The fermentable ber as well as oligosaccharides from mushrooms act as the prebiotics. 16 However, there are still few studies on the prebiotics of GLS oligosaccharides, which do exist in the resulting supernatant of polysaccharide extractions.
In this study, each of the three GLS oligosaccharides were individually obtained from the supernatants of UB-GLS and B-GLS polysaccharide extraction by different ethanol concentration precipitation methods. The basic structure of the oligosaccharides was characterized, and the in vitro effects of GLS oligosaccharides on the proliferation of probiotics (Lactobacillus) were assessed by determination the changes in optical density (OD), articial human gastric juice hydrolysis and their tolerance to lower pH levels in simulated gastric juice, the effects on gut microbiota were assessed by fermentation in vitro. This investigation might provide a promising way to avoid the vast production of by-products by the polysaccharide industry.

Samples and chemicals
UB-GLS and B-GLS were provided by Shouxiangu Pharmaceutical Co. Ltd (Zhejiang, China). Inulin was purchased from Inbo Biotechnology Co. Ltd. Lactobacillus (Lactobacillus acidophilus) was purchased from the China Centre of Industrial Culture Collection (CICC, 6095) and was preserved by Microbiology Laboratory, Zhejiang University of Technology. It was cultured on MRS media and preserved for further use at 4 C. Dialysis membranes (M w cutoff ¼ 100-500 Da) were obtained from Shanghai Yuanye Biotechnology Co. Ltd. Monosaccharide standards, TFA, NaBH 4 and pepsin were purchased from Aladdin Chemistry Co. Ltd. Takara Ex Taq were purchased from Takara Bio Technology Co. Ltd. Other reagents were of analytical grade.

Extraction
Briey, 200 g of GLS (UB-GLS, B-GLS) was soaked in 95% ethanol for 24 h, followed by forced air-drying at room temperature. They were then extracted by hot water bath at 90 C for 3 h and centrifuged at 8000 Â g for 15 min at 4 C (CR21N; Hitachikoki, Japan). The supernatant was subsequently concentrated to a volume of one-fourth of its initial value, under reduced pressure and with a rotary evaporator at 50 C, and then precipitated in sequence by 10-fold (v/v) 80%, 50%, 30% ethanol (nal concentration v/v) at 4 C for 24 h. The supernatant, UB-GLS and B-GLS oligosaccharides (UB-O30, UB-O50, UB-O80, B-O30, B-O50, B-O80) were collected by centrifuge at 8000 Â g for 15 min and subjected to dialysis for 48 h at 16 C. Finally, the retentate was concentrated and lyophilized with a freeze-dryer (Virtis BTP; Genevac, Britain) and stored in a desiccator until use. The sugar content was analyzed by the phenol-sulfuric method using glucose as the reference standard. 17 The protein content was determined by using bovine serum albumin (BSA) as the standard to check its level of purity. 18 The phenol content was quantied by the Folin-Ciocalteu method. 19

Determination of molecular weight
The molecular weights (M w ) of the GLS oligosaccharides were determined by GPC (2695; Waters, USA) with an Agilent 1260 differential detector. 6 The analytical system consisted of Ultra hydrogel 500 columns (7.8 Â 300 mm; Waters, USA), Ultra hydrogel 250 columns (7.8 Â 300 mm; Waters, USA), and Ultra hydrogel 120 columns (7.8 Â 300 mm; Waters, USA), and connected in series by decreasing pore sizes. The mobile phase was 0.1 M in potassium nitrate and the ow rate was 1.0 mL min À1 . The column temperature was xed at 40 C. Standards and samples were ltered through a 0.22 mm syringe lter and the injection volume was 40 mL. The molecular weight was calibrated with a series of polyethylene glycol standards. The M w s of the samples was determined by comparing the retention time with the standard curves.

Determination of monosaccharide composition
The monosaccharide composition was analyzed by GC-MS (Trace 1300-ISQ; Thermo, USA) with TG-5 chromatographic column. [20][21][22] The sample (2 mg) was dissolved in 2 M TFA (6 mL), and hydrolyzed at 110 C for 2 h. The TFA was completely removed by vaporizing it with methanol under reduced pressure. The residue was dissolved in distilled water (3 mL), and NaBH 4 (25 mg) was added. Aer 3 h, the pH of solution was adjusted to 4.5 AE 0.2 either with 0.5 M hydrochloric acid or sodium hydroxide. The solution was evaporated to dryness by the addition of methanol. Acetic anhydride (4 mL) was added to the evaporation residue for acetylation at 100 C for 1 h, and then the residue was evaporated to dryness level by the addition of toluene. It was dissolved in chloroform and added to distilled water to remove the water. The chloroform solution was ltered using an organic phase microltration membrane (0.22 mm) and analyzed by GC-MS. The carrier gas (helium) ow rate was at 1.0 mL min À1 . The column was kept at 120 C for 1 min, and then increased from 120 C to 165 C at 10 C min À1 , 1 min at 165 C, from 165 C to 169 C at 1 C min À1 and 0.5 min at 169 C, 169 C to 196 C at 10 C min À1 and 0.5 min at 196 C, 196 C to 200 C at 1 C min À1 and 1 min at 200 C, from 200 C to 240 C at 10 C min À1 and 5 min at 240 C. The temperature of injector and detector were both set at 250 C and the injection volume was 1.0 mL. Rhamnose, fucose, arabinose, xylose, mannose, glucose and galactose were used as monosaccharide standards. The qualitative analysis of sugar in the sample was determined by comparison to the retention time of standard sugar. The concentration of sugar in the sample was calculated by a comparison with the peak area of the standard curve of the respective sugar.

Fourier transform infrared (FTIR) and ultraviolet (UV) characterization of oligosaccharides
The structures of the GLS oligosaccharides were assayed by FTIR (Nicolet iS50; Thermo, USA). The samples were mixed with KBr (1 : 100 v/v), and pressed into tablets. The spectra were recorded from 400-4000 cm À1 with a resolution of 4 cm À1 at room temperature. 1 For UV analysis, the sample was dissolved in distilled water and scanned from 200-500 nm using a UV-visible spectrophotometer (TU-1900; Pgeneral, China).

Prebiotic activity
The pH of the fermentation broth was measured with a pH meter, which was calibrated using buffers of pH 4.01, pH 6.86 and pH 9.18.
GLS oligosaccharides and positive prebiotic control (inulin) were used as the individual carbon sources for the growth of Lactobacillus in MRS medium, and the total sugar content was added to different mediums from extracts of the same level (1%, w/v). The fermentation broth was adjusted to pH 6.8 AE 0.1, either with 0.5 M hydrochloric acid or sodium hydroxide. The media were dispensed as 10 mL aliquots into test tubes with stoppers and then sterilized by autoclaving them at 121 C for 30 min. Aer subculturing them twice in MRS medium at 37 C for 24 h, the logarithmic phase culture of Lactobacillus was obtained by inoculating the MRS medium at 37 C for 12 h. Then, 0.1 mL logarithmic culture of Lactobacillus was added to the sample liquid for fermentation. The growth of the probiotics was evaluated by increased turbidity aer 0, 6, 12, 18, 24 and 48 h at 37 C and measured by OD at 600 nm. 23 The change of sugar concentration was analyzed by the phenol-sulfuric method aer 0, 6, 12, 18, 24 and 48 h. 18

The effects of articial human gastric juice hydrolysis
Prebiotics must be able to withstand the digestive process before reaching the colon, and it is preferable for them to persist throughout the large intestine to also benet its distal end. Therefore, the tolerance of prebiotics to gastric acid, mammalian enzymatic hydrolysis and gastrointestinal absorption were tested. 24 The non-digestibility of the carbohydrates does not mean that they are completely indigestible. The digestibility of the GLS oligosaccharides were studied for gastric juice in comparison with inulin. Human gastric juice was simulated with a hydrochloric acid buffer containing (g L À1 ): NaCl, 8 The pH of the buffer was adjusted to 1.0, 2.0, 3.0, 4.0 and 5.0 using 5 M hydrochloric acid. The GLS oligosaccharides were dissolved in distilled water to give a 1.0% (the content of sugar, w/v) solution. Aerwards, 5 mL of buffer was added to the 5 mL of oligosaccharides solution at each different pH, and incubated in a water bath at 37 AE 1 C for 6 h. Sampling were done periodically at 0, 0.5, 1, 2, 4 and 6 h. Reducing sugar concentration was determined by DNS 25 and the total sugar content was determined by the phenol-sulphuric acid method. 17 The hydrolysis rate of the sample was calculated according to the liberated amount of reducing sugar and the total sugar content, and presented as the following formula.

Tolerance tests of lower pH and simulated gastric juice
The composition of the gastroenteric environment tolerance test medium was similar to that of the fermentation medium. Acid buffers and simulated gastric juice were prepared according to the method reported by Huang. 26 In the acid tolerance test, the pH of fermentation medium was adjusted to 1.5, 2.0, 2.5 and 3.0. Lactobacillus was incubated in different pH mediums. The growth rate of Lactobacillus was measured by changes in the OD value following anaerobic culture for 0, 2 and 4 h. In the simulated gastric juice tolerance test, Lactobacillus was incubated in mediums with 0.5% pepsin at pH 3.0. 27 The growth of Lactobacillus was monitored by OD following anaerobic culture for 0, 1, 2, 4 and 6 h.

Fermentation in vitro
Fecal samples were collected from ten healthy human (ve women, ve men). All experiments were performed in accordance with the Guidelines of Biomedical Research Ethics Review Method Involving People (China), and approved by the Ethics Committee at Zhejiang University of Technology. Informed consents were obtained from human participants of this study. The basic medium contained the followings: 0.45 g per L KH 2 PO 4 ; 0.45 g per L K 2 HPO 4 ; 0.05 g per L NaCl; 0.064 g per L CaCl 2 $2H 2 O; 0.09 g per L MgSO 4 $7H 2 O; 10 g per L tryptone; 2.5 g per L yeast extract; 1.0 g per L l-cysteine; 2.0 mL per L heme; 200 mL per L vitamin. In order to assess the utilization of GLS oligosaccharides by the human fecal microbiome, 8.0 g L À1 each of UB-O80 and B-O80 were added into the growth medium as the sole carbon source. The pH value of fermentation medium was adjusted to 6.5, 5.0 mL of test medium was dispensed into a 10 mL-bottle under anaerobic conditions. 28 Fecal samples (0.8 g) were homogenized with 8.0 mL of 0.1 M anaerobic phosphate-buffered saline (pH 7.0) using an automatic fecal homogenizer (Halo Biotechnology Co. LTD., Jiangsu, China) to make a 10% (w/v) slurries. Then 500 mL of slurries was added to the blank (control), UB-O80 and B-O80 medium, and incubated at 37 AE 1 C for 24 h. Immediately aerward, 1.0 mL aliquots were removed for further analysis.
The removed aliquots were centrifuged, and the pellet was stored at À80 C. The DNA of samples was extracted by DNA extraction kit (Q328520, Thermo, USA), and then the purity and concentration of the DNA was detected by agarose gel electrophoresis (HE-120, Tanon, China). Then an appropriate amount of sample was taken into the centrifuge tube, and the diluted genomic DNA was used as the template, the specic primers with Barcode and Takara Ex Taq high-delity enzyme were used for PCR amplication (580BR10905, Bio-Rad, USA) and sequencing according to the selection of sequencing area. 12

Statistical analysis
All graphs were plotted using Graphpad Prism 6. The statistical analysis was performed with SPSS 20.0. One-way analysis of variance and Duncan's multiple range tests were used to determine the differences of diverse samples, and p < 0.05 was considered statistically signicant.

The preparation results of oligosaccharides
GLS oligosaccharides (UB-O30, UB-O50, UB-O80, B-O30, B-O50 and B-O80) were obtained from the by-products of the polysaccharide extracts from UB-GLS and B-GLS. The yields of the investigated oligosaccharides were shown in Table 1. It was found that the yields of the oligosaccharides decreased as the alcohol concentration increased (30% > 50% > 80%). Compared with different groups, under equal conditions, the results of B-GLS was signicantly higher (p < 0.05) than that of UB-GLS, which is attributed to the higher carbohydrate dissolution rates of the species' broken as opposed to unbroken walls. The oligosaccharides possessed moisture levels of about 8.2-11.5%, a minor percentage of protein (2.6-5.2%) and polyphenol (1.8-3.4%); the total sugar content of the extracts was 67.3-75.7%.

The molecular weight distribution of oligosaccharides
The M w distribution of the GLS oligosaccharides was analyzed by GPC as shown in Fig. 1. The results revealed that the degree of GLS oligosaccharides polymerization was about 2-7, which was in nearly the same range as some fructooligosaccharides, xylooligosaccharide, mannan and galactan. 6 Some prebiotic oligosaccharides from plants, such as honeysuckle, dragon fruit, dahlia, oat and onion, also contain oligosaccharides of comparable M w range to those in our study. 29 The results revealed that some the values of 30% alcohol extraction were  greater than 50% and 80% in alcohol precipitation, which was attributed to the observation that the higher the alcohol concentration, the more easily the carbohydrates with larger molecular weight were precipitated by the alcohol. As a result, the lower molecular weight remain in the supernatants and the M w of the extracts were more homogeneous.

The monosaccharide composition of oligosaccharides
Monosaccharide composition and molar ratio play an important role in oligosaccharide biological activity. The monosaccharide composition of the GLS oligosaccharides is shown in Table 2. Standard monosaccharide peaks in sequence were determined as being rhamnose, fucose, arabinose, xylose, mannose, glucose and galactose. The monosaccharide composition of the oligosaccharides was determined by comparison to the retention time of standard sugar. The results revealed that the monosaccharide composition of UB-GLS oligosaccharides was similar to that of B-GLS oligosaccharides, but the molar ratio of the UB-GLS oligosaccharides differs. Both UB-GLS and B-GLS oligosaccharides contained the monosaccharides of arabinose, mannose, glucose and galactose, where glucose was the most abundant. The monosaccharide composition of UB-O80 was arabinose, mannose, glucose and galactose in a molar ratio of 0.9 : 5.1 : 11.9 : 0.01, whereas the monosaccharide composition of B-O80 was arabinose, mannose, glucose and galactose in a molar ratio of 4.5 : 11.1 : 21.6 : 0.1. These were different from that the main monosaccharide composition and its molar ratio of GLS as reported in other literature. The polysaccharides of both broken and unbroken spores prepared by ultrasonic vibration or reux consisted of rhamnose, arabinose, mannose, glucose, and galactose, although there was a small difference in their relative content. 30 This difference was possibly attributed to variations in the growth environments of G. lucidum and the oligosaccharide preparation methods.

FTIR and UV spectrum analysis
FTIR is a non-destructive and rapid technique that can recognize different functional groups and is very sensitive to dissimilarities occurring in molecular structures. FTIR spectrum was used to identify the preliminary structures in the functional groups of the oligosaccharides based on peak vibration values in the regions of inferred radiation. The FTIR spectra ( Fig. 2a and b) demonstrated that the graphs of the GLS oligosaccharides were basically consistent with typical carbohydrate vibrational bands. 31 Peaks at around 3400 cm À1 were due to the hydroxyl tensile vibration modes, and the peaks at around 2936 cm À1 indicated the C-H stretch absorption of sugars. Bands between 1200-1500 cm À1 were mainly caused by C-OH bending and C-H deformation vibrations. 32 The peaks at 950-1200 cm À1 were attributed to the stretching vibrations of heavy atoms C-C and C-O in the pyran ring. 33,34 The band at 1040 cm À1 corresponded to the stretching vibration of C-O-C.
The absorption peak at 540 cm À1 was characteristic of a pyrantype sugar ring. The occurrence of amide-based vibrations at 1640 cm À1 (due to Amide I) also indicated the presence of binding peptides in these oligosaccharides. 35 The peaks at 1408 cm À1 might refer to phenols. 36 Table   2 Monosaccharide composition of different GLS oligosaccharides In carbohydrate analysis using FTIR spectra, a and b conformers can be clearly distinguished within the anomeric region vibrational bands since the aand b-congurations are well separated in the 950 to 750 cm À1 regions, where 870-840 cm À1 corresponds to a conformers, while the b conformers lie at around 890 cm À1 . 31 As compared to UB-GLS, there is a signicant change in bands of the (B-GLS) spectra. The weaker band found near this region (896 cm À1 in BSCP) was believed to indicate the presence of b-glucan, therefore, the band adjacent to 894 cm À1 was reported as being a b-glucosidic bond. 31 UV spectra for GLS oligosaccharides (UB-O30, UB-O50, UB-O80, B-O30, B-O50 and B-O80) were shown in Fig. 2c. The absorption in 260-280 nm indicated that the crude oligosaccharides might contain some nucleic acids or protein, which was in coincidence with the results of FTIR. And the contents of the B-GLS oligosaccharides were higher than that of the UB-GLS oligosaccharides, which was attributed to the higher dissolution of genetic material and biological composition in B-GLS as compared to UB-GLS.

The growth of Lactobacillus
Lactobacillus is a probiotic microorganism that is benecial to the functional food industry. 37 As our previous work 38 indicated that the trend of OD value seemed very consistent with that of viable cell count. So GLS oligosaccharides were used as the individual carbon source for the cultivation of Lactobacillus, and the growth of Lactobacillus ( Fig. 3a and b) was recorded by changes of optical density (OD). It was found that all of the oligosaccharides, as comparable to inulin, had a signicant effect on the genus' growth of Lactobacillus. Lactobacillus showed an outstanding growth rate of following 6 h of fermentation using UB-O30, UB-O50, UB-O80, B-O30, B-O50 and B-O80 as its carbon source, as opposed to inulin, which gave slower growth rates. The growth of Lactobacillus in UB-O30 and B-O30 mediums was slower aer 24 h than that of inulin, and groups 80 was signicantly higher (P < 0.05) than that of groups 50 and 30. Statistical signicance was observed between the groups UB-GLS and B-GLS. Regarding growth rates, rapid increases were observed at approximately 6 h post-inoculation aer which the groups entered a logarithmic growth period. They achieved a balance aer 24 h post-inoculation. The change of sugar content  This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 14794-14802 | 14799 during culture was shown in Fig. 3c and d, which was identical to the trend for Lactobacillus. It achieved a balance within 24 h. Our results were similar to those with low molecular weight carbohydrates extracted from fruits and vegetables, which could stimulate the growth of Lactobacilli and Bidobacterium. 39 Jackfruit seed oligosaccharides had been reported as stimulating the growth of Lactobacilli and Bidobacterium. A similar result was observed on gluco-oligosaccharides produced by G. oxydans, this being an indicator that GLS oligosaccharides, the by-products of GLS polysaccharide extraction, possess good potential for exploitation as a prebiotic.

Resistant to articial human gastric juice hydrolysis
The non-digestibility characteristic of prebiotics ensure that they can reach the colon and persist throughout the large intestine, so that they can effectively stimulate certain native bacterial species (including probiotics) in the gut. The resistance of UB-O80 to hydrolysis in articial human gastric juice was evaluated. As shown in Fig. 4, UB-O80 showed higher resistance to articial human gastric juice. The percentage of hydrolysis increased with the decreased pH of the gastric juice. The degree of hydrolysis for UB-O80 at pH 1.0, 2.0, 3.0, 4.0 and 5.0 was 1.65%, 1.14%, 0.56%, 0.26% and 0.06%, respectively. It showed high acid resistance abilities compared to the reference prebiotic (inulin) at the same conditions, which gave maximum hydrolysis of 31.78%, 23.52%, 13.43%, 5.92% and 1.45% at pH 1, 2, 3, 4 and 5. Normally, food remains in the human stomach for about 3 h. Thus, when GLS oligosaccharides are ingested, more than 98% of them would reach the intestine. From the data point of view, UB-O80 was not sensitive to gastric juice, regardless of the incubation time. The data of UB-O80 were comparable to that for other oligosaccharides such as those from pitaya esh, which were 96% resistant to articial human gastric juice. 5 Kojio-oligosaccharide displayed 100% resistance. 40 3.7. The effects of GLS oligosaccharides on probiotic growth at lower pH and in simulated gastric juice The pH of the stomach can be as low as pH 1.5, but generally ranges from pH 2.5-3.5. 41 While GLS oligosaccharides have benecial effects on the proliferation rate of Lactobacillus, the growth of these bacteria can be affected by gastrointestinal conditions. This study aims to assess the transit tolerance of Lactobacillus in human gastric juice in vitro, and evaluate the effects of GLS oligosaccharides on the viability of Lactobacillus at lower pH and in simulated gastric juice.
The effect of GLS oligosaccharides (UB-O80, B-O80) on the tolerance of Lactobacillus to lower pH is revealed in Table 3. Lactobacillus showed a better growth rate following 2 h of fermentation at lower pH when using UB-O80 and B-O80 as their carbon source than with inulin, which indicates a slower growth rate with the latter. When simulated media were at pH 3.0, the viability of Lactobacillus remained at the highest level; the viability of Lactobacillus varied with pH (3.0 > 2.5 > 2.0 > 1.5), indicating that lower pH has a seriously inhibitory effect on the growth of Lactobacillus, such that UB-O80 and B-O80 offers a certain degree of protection against Lactobacillus' lower the pH intolerance.
The effect of GLS oligosaccharides (UB-O80, B-O80) on Lactobacillus' tolerance to simulated gastric juice (medium with pepsin) was shown in Fig. 5. It was found that the growth of Lactobacillus in simulated gastric juice containing the oligosaccharide of UB-O80 or B-O80 was higher than that inulin. However, the tolerance ability of Lactobacillus to the simulated gastric juice was not signicantly different among UB-O80 and B-O80. When pH values were <3, inhibition of the action of   This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 14794-14802 | 14801


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Effects of cadmium toxicity on sesame seed germination explained by various nonlinear growth models

– This experiment was conducted to evaluate the effects of cadmium toxicity on the seed germination properties of sesame cultivars (Halil, Nazok Shakhei, Oltan, and Yellow White) using nonlinear growth models. Seeds were germinated in petri dishes (90 mm diameter), with a double layered of ﬁ lter paper soaked in distilled water as control treatment or cadmium (CdSO4) solutions in concentrations of 0, 100, 200, 400, 600, 800 and 1000 ppm. Each treatment was replicated four times and included 50 seeds in each petri dishes. Hyperbolastic growth models for the description of seed germination data were compared to Richards, Weibull, Logistic and Gompertz models. Our results revealed that all studied cultivars were germinated at the cadmium-polluted germination medium to a maximum of 200 ppm without reduction in germination fraction, while seed germination rate was decreased at this concentration compared to 0 and 100 ppm. Increasing cadmium concentration resulted in the germination fraction reduction from 1 to 0.4 at the 400 ppm. The recommended hyperbolastic growth model was type III or (H3) as it provided the best model with the lowest Corrected Akaike Information Criterion for cv. Halil (AICc = (cid:1) 14.6) and cv. Nazok Shakhei, (AICc = (cid:1) 14.2).

Introduction
Industrialization and human activities caused serious environmental pollution by heavy metals. This not only causes direct hazardous effects to both human and ecosystems, but has also influenced food safety and security in agriculture lands (Das et al., 1997;Benavides et al., 2005). Cadmium is a heavy metal that does not have any known nutritious function for plants (Hanc et al., 2009;Gallego et al., 2012). However, due to the increase of mine production, industrial activities and urbanization, its concentrations in the environment has increased drastically. Cadmium is considered a highly significant pollutant due to its high toxicity and large water solubility (Benavides et al., 2005). It has been accepted that cadmium can interfere with water uptake and reduce root growth and development of plants (DalCorso et al., 2008). Exploring the interaction of cadmium and seed germination is important for the safety of crop production. It is also worth to study the risks of good and uniform seed germination in the soils with various levels of cadmium contaminations.
Modeling biological data conveniently summarizes information into small sets of parameters that can be interpreted biologically. Growth models are mainly empirical and they rely on physiological or biochemical mechanisms (Eby et al., 2017). Generally, growth models are expressed as the rate function of an independent variable over time. It is very important to consider that each growth function must be biologically meaningful. The benefits of nonlinear regression analysis in seed biology is due to their interpretability, parsimony and prediction possibility for biologically related phenomena, especially outside the range of actual experimental data (Archontoulis and Miguez, 2015). Many nonlinear growth models have been successfully applied in biological science. Gompertz, Richards, Weibull, Logistic and Hill are the most applied nonlinear functions to describe cumulative seed germination (Dumur et al., 1990;Shafii et al., 1991;Tjørve and Tjørve, 2017). The number of parameters in each model varies from three to five depending on the mathematical bases of the model construction method, to provide the best curve fit for experimental data. In the logistic model, the period to reach the maximum growth rate is equal to the inflection point, thus, this model is symmetric around the maximum growth rate. In contrast, Richards and Gompertz models have different durations for short and fast growth rates and they are considered asymmetric models (Shafii et al., 1991). Recent reports suggested that hyperbolastic nonlinear growth models in some cases provide a better fit for complex growth patterns in biological studies, over more traditional models such as generalized Gompertz or logistic functions (Tabatabai et al., 2005;Ahmadi and Golian, 2008;Eby et al., 2017;Barrera et al., 2018). Hyperbolastic models were introduced by Tabatabai et al. to study tumor and stem cells growth rates (Tabatabai et al., 2005). The term Hyperbolastic for this type of nonlinear models comes from the model function equation showing that these models are a function of the inverse hyperbolic sine (Ahmadi and Golian, 2008). Hyperbolastic growth models are classified into three types: H1, H2 and H3, according to their function. Hyperbolastic growth models are developed to provide higher accuracy and more flexibility, compared to other growth models such as Gompertz, Weibull, and others (Eby et al., 2017).
The purpose of our study was to evaluate the possible application of Hyperbolastic models to fit empirical data obtained from an experiment exploring the influence of various concentrations of heavy metals on sesame genotypes.

Material and methods
Seeds of sesame (Sesame indicum L.) cultivars were obtained from the oil seed division at the Seed and Plant Improvement Institute in Karaj, Iran in 2018. Seeds of five sesame cultivars (Halil, Nazok Shakhei, Oltan, and Yellow White) were used in this experiment, and generally followed the ISTA rules for standard seed germination test (ISTA, 2017). The seeds were germinated in petri dishes (90 mm diameter), with a double layered of filter paper soaked in distilled water as control treatment or cadmium (CdSO 4 ) solutions in concentrations of 0, 100, 200, 400, 600, 800 and 1000 ppm. Each treatment was replicated four times and included 50 seeds in each petri dishes. Seeds were subjected to standard seed germination tests using top of paper method and at alternate temperature regime (20/30°C) under dark conditions (ISTA, 2013). The number of germinated seeds were recorded every 12 h until day six after test initiation. Germination test was ended when seed germination was reached to the maximum and no seeds have germinated for three subsequent counts.

Statistical analyses
Two-way ANOVA with Tukey's post-hoc analysis (Seal et al., 2018) was used to analyze the effects of cultivar, concentrations of cadmium, and their interaction on seed germination and the germination index of sesame. Analysis of variance and comparison of means were conducted using the Minitab ® 18 statistical software. The Software SigmaPlot (SigmaPlot 14, Systat Software, Inc.) was used for non-linear regression analyses and model fit on seed germination data.
Seed germination index was calculated according to (Fenner and Edwards, 1991). In this study various nonlinear growth models were applied on the cumulative seed germination data, in order to make an appropriate comparison between hyberbolastic models and other models generally applied in seed biology. The applied hyperbolastic models have been previously explained using three different models of H1 to H3, and are presented in equations (1) to (3) below (Tabatabai et al., 2005;Ahmadi and Golian, 2008;Eby et al., 2017). The hyperbolastic growth rate of type I (H1) (Tabatabai et al., 2005) is: Where: Where P(t) is the number of germinated seeds at time t, the constant Ymax is the parameter representing carrying capacity, and b and u are constants. It is worth noting that both b and u are parameters that describe growth (germination) rate. The arcsinh(t) is the inverse hyperbolic sine function of t. The hyperbolastic growth rate of type II (H2) (Tabatabai et al., 2005) is: With the initial condition P(t 0 ) = P 0 ; and Ymax, b, and g as parameters. The growth rate is determined using b (intrinsic growth rate) and g (allometric constant). The hyperbolastic growth rate of type III (H3) (Tabatabai et al., 2005) is: With the initial condition P(t 0 ) = P 0 ; and Ymax, b (by the time prescribed for the, final count), g (allometric constant) and the distance from symmetric sigmoidal growth is determined by the value of |u|. In hyperbolastic models H1, H2 and H3 the parameter Ymax will represent the maximum fraction of germination percentage, while the parameter b will represent the rate of increase of seed germination with respect to time. In H1 the additional parameter u helps determine variation in the intrinsic rate. In H2 the additional parameter g is an allometric parameter that also provides departure from logistic symmetry by rescaling, and the effective rate is determined by both b and g. Finally, the parameter g in H3 is an allometric parameter as in H2, while u is a shape parameter, and its role is comparable to the role in H1 and H2; and b, g, and u collectively determine the effective growth rate.
A three parameter logistic function is fitted on our experimental data using equation (4) (Verhulst, 1838;Tanveer et al., 2017;Soler-Guilhen et al., 2020). An additional parameter, d, has the effect of shifting the graph vertically (the lower asymptote), and it turns the three-parameter logistic to a four-parameter logistic function (Eq. (5)).
Y is the cumulative percentage of germination at time t, Ymax is the maximum rate of seed germination (the upper asymptote), K is the increasing rate of germination, L is time scale constant, and d is the lower asymptote.
Gompertz is a sigmoid model which has been widely used to curve fitting of growth data. The three-and four-parameter Gompertz functions were fitted on data using the following equations (Gompertz, 1825;Tjørve and Tjørve, 2017): Richards' function is a modified to a four-parameter sigmoid function having an especial shape parameter to provide a flexible curve fitting our experimental data. This model was fitted to our experimental data using equation (8) (Richards, 1959).
Y is the cumulative percentage of germination at time t, Ymax is the maximum rate of seed germination (the upper asymptote), K is the increasing rate of germination, L is time scale constant, and c is the shape parameter to provide a flexible curve fitting our experimental data. Weibull function has also been successfully applied in seed germination studies by many researchers. This model not only have biologically interpretable parameters, but also have unique properties when the exponential distribution is not well explained for experimental data due to the limitations of randomization (Shafii et al., 1991). A Weibull model was fitted to our experimental data using the following equation (Weibull, 1951): These models were applied to a cumulative fraction dataset of sesame cultivars seed germination, using nonlinear regression to estimate the parameters for each model. The statistical calculations for the determination coefficient (R 2 ) was used to assess the accuracy of each model. However, it should be noted that R 2 may not always represent the most appropriate metric because it does not account for the number of parameters in the model (Archontoulis and Miguez, 2015). To increase the precision of the model selection criterion, the Corrected Akaike Information Criterion (AICc) was calculated for all applied models. Data with a probability index resulted in a lower AICc and better fit to the data (Bullied et al., 2012).
AICc ¼ nln residual sum of squares n þ 2k Where n is the number of observations, and k is the number of model parameters (Burnham and Anderson, 2002).

Results and discussion
Seed germination of all sesame cultivars declined as the cadmium concentration increased. Our results revealed that sesame seeds are tolerated to 200 ppm of cadmium. However, the germination rate declined as the cadmium contamination increased. At cadmium concentrations over 400 ppm, there was a drastic reduction of final seed germination for all the sesame cultivars (Tab. 1). Among all studied cultivars, cv. Halil exhibited the highest tolerance to cadmium toxicity up to 400 ppm, at which seed germination was 43%, 27%, 31% and 27% for cv. Halil, cv. Nazok Shakhei, Oltan and Yellow wWhite respectively (Tab. 1). The fastest seed germination was observed when there was no cadmium pollution for cv. Halil.
However, at a cadmium concentration of 600 ppm, the fastest seed germination was observed in cv. Oltan (Tab. 1). The germination index for the control treatment was 1003 for cv. Yellow White. However, the index was reduced to 117 by increasing the cadmium concentration up to 600 ppm. Similar findings regarding the reduction of seed germination due to heavy metals toxicity have been previously reported with (Akpofure, 2012;Asgher et al., 2015;Fattahi et al., 2019). It has been shown that cadmium pollution may increase seeds' indigenous abscisic acid levels and inhibit seed germination (Munzuro glu et al., 2008). Cadmium toxicity can damage normal seed respiration during imbibition (Deswal and Laura, 2018). It has also been shown that antioxidants and amylase enzyme functionality is reduced when cadmium concentrations increase in the seed environment, causing a decrease in the seed germination rate index (Afzal et al., 2019;Chugh and Sawhney, 1996;Zhang et al., 2009). In our case, cumulative germination fraction of cv. Halil was reduced from 1 to 0.4 at a 400 ppm cadmium concentration and to lower than 0.2 at 600 ppm. The seed germination pattern of cv. Halil was well fitted by the sigmoid models while hyperbolastic functions were capable of describing the data with reasonable fit at cadmium concentrations of 200 ppm (Fig. 1). For instance, the estimated AICc of three-parameter logistic for cv. Halil at cadmium concentrations of 100, 200, 400 ppm were À23.1, À16.1, and À29.0 respectively, which were the lowerst estimated AICc among other studied models. Hyperbolastic models I, II and III poorly fit the germination data above 200 ppm cadmium concentration. In cv. Oltan for instance, the estimated AICc were 12.8, À13.8 and À16.4 for hyperbolastic models I, II and III; while the AICc of Gompertz 3p was estimated at À21.1, showing better fit compared to the hyperbolastic models.
In cv. Yellow White, the estimated AICc at cadmium concetrations of 200 ppm was À18.8, À15.1, À16.0, À15.6, À8.2, À15.8, À13.7, À14.1 and À10.9 for three-parameter logistic, four-parameter logistic, three-paramter Gompertz, four-parameter Gompertz, Richards, Weibull and hyperbolastic Ithrough III respectively (Tab. 2). The cv. Nazok Shakhei was sensitive to cadmium toxicity and it did not germinate at the 800 ppm concentration. The seed germination fraction reduced from 1 to 0.2 at the 400 ppm concentration . Hyperbolastic type III was the only hyperbolic function that provided a good fit for the cadmium concentrations of 0 to 400 ppm (Fig. 2). The seed germination rate was considerably reduced at the 200 ppm cadmium concentration, while seeds could still germinate at the 800 ppm cadmium concentration. Our results show that without cadmium contaminations, the best fit for the haperbolastic models were obtained from hyperbolastic II for cv. Halil (AICc = À18.4), hyperbolastic III for cv. Oltan (AICc = À16.5), hyperbolastic I for cv. Nazok Shakhei (AICc = À16.5) and hyperbolastic II for cv. Yellow White (AICc = À16.2). Increase in the cadmium concentration from 200 to 400 ppm caused drastical reduction of the seed germination potential in all investigated cultivars. In cv. Hali and cv. Yellow White, the best model fit for all cadmium concentrations above 100 ppm were obtained from the threeparameter logistic function.
Hyperbolastic curves fitted for the seed germination data of cv. Oltan did not satisfactoraly cover data points at high cadmium concentrations (600 to 800 ppm) (Fig. 3). For instance, AICc values of Hyperbolastic I and II were À9.3 and À10.3 at the 600 ppm cadmium concentations, while the AICc values for Weibull and Logistic 3p at the same cadmium concentration were À27.5 and À25 respectively (Tab. 2). Since cv. Yellow White did germinate or survive at the 800 ppm cadmium concentration, it is considered the most sensitive cultivar to cadmium toxicity among the studied sesame cultivars. There was no seed germination at the 800 ppm cadmium concentration for cv. Yellow White. The total seed germination fraction declined from 1 at no cadmium treatment to approximately 0.15 at the 600 ppm cadmium concentration (Fig. 4).
Application of mathematical and empirical models allowed us to describe the seed germination patterns of sesame cultivars without the common limitations of single-value germination indices. For instance, in the studied sigmoid models, the outcome is either binary or dichotomous. The binary outcome in our study is either germinated (survived) or non-germinated seeds. The probability of seed germination as our outcome of interest is investigated under various levels of cadmium toxicity. Using natural logarithm (ln), the odd ratio of seed germination (probability/1-probability) was used to model the probability of seed germination at various levels of cadmium toxicity. In sigmoid models, every unit increase in the x variable (cadmium concentrations) doesn't have the same decrease in the probability of seed germination. Thus, there isn't a consistent slope or changes in probability of seed germination versus increases of cadmium concentrations, instead the slope varies at different points across the cadmium concentrations. To interpret the relationship between seed germination and cadmium concentration, logic transformation is applied in our logistic regression analysis. This allows us to fit a line with a constant slope. In fact, this slope shows how the logodds of seed germination change with each increase in cadmium concentration. In other words, it tells us that for every 100 ppm increase in cadmium concentration, the log-odds of seed germination decreased by the value of the estimated slope. The critical point of the sigmoid models as their important parameter, also shows us that the amount of cadmium concentrations inhibits completion of seed germination by half of its maximum potential. The maximum seed germination potential for each of the studied sesame cultivars under various levels of cadmium concentrations (carrying capacity) is also estimated as a parameter of Ymax in the applied mathematical models.
Fitted models provided a great result for describing the time course of seed germination. The predicted seed germination values, and our models' goodness of fit and residuals are presented in Table 2. The best model fit among studied empirical models was varied in each genotype under no stress conditions. The lowest AICc value À which is the best goodness of fit À was found for the Weibull model of the cv. Halil seed germination (AICc = À35.3), However, in the case of Oltan (AICc = À22.4) and YellowWhite (AICc = À28.5), the three-parameter Logistic model performs better. The three-parameter Gompertz (AICc = À29.4) provide the best fit for Nazok Shakhei. Increase in cadmium concentrations, significantly influenced the best model fit for each individual genotype except for Yellow White. The three-parameter logistic model was always the best fitted model to describe germination of Yellow White (Tab. 2). At concentrations of 600 ppm cadmium, the best data fit of seed germination for Oltan and Nazok Shakhei was obtained from the Weibull model with AICc of À27.5 and À51.2 respectively. Estimated parameters of all studied growth models are presented in Table 3. It is clear that hyperbolastic growth models are well suited to describe seed germination data; however, when data get close to the lower limits of germination fraction, the goodness of fit is drastically decreased for all studied cultivars. This was evident at cadmium concentrations above 400 ppm. Tabatabai et al. (2005) developed Hyperbolastic models to resolve this issue. These models have mobile inflection points, which provide them with special properties to fit the biological data. Of all the sigmoidal models tested, the Richardshas the least flexibility and in general has the poorest fit to the data. Our results suggest that hyperbolastic models perform well in modeling time-coarse seed germination, compared with competing  Â 10 À11 ± 0.00 0.00 ± 0.00 3.96 ± 4.10 2.7 Â 10 À6  ± 0.00 0.00 ± 0.00 3.65 ± 0.0 Gompertz, Richards, Weibull, and other commonly used models as shown in Table 2.
Our study results suggest that the shape flexibility of the investigated hyperbolastic models I to III leads to a good fit, and thus, these models could be considered when describing seed germination data. For our dataset, we observed that the Weibull function gave a reasonable representation of the data, followed closely by the hyperbolastic models type-I to type-III.
Estimated parameters for the rate of seed germination in the Weibull function (k) declined as the concentration of cadmium exceeded 400 ppm for all cultivars. In addition, due to an increase in cadmium toxicity, there was a higher lag time for germination to be completed (Tabs. 3-6). The reasons for the lower values for R 2 and high values for AICc at the 800 ppm cadmium concentrations, appear to be due to high toxicity and rapid morality rate in seeds that can be observed within the data. The estimated Ymax using hyperbolastic type III was very similar to the Weibull function. Results are in agreement with Tabatabai et al. (2011) regarding the similarity of hyperbolistic models to other growth models such as Logistic, Weibull and Gompertz. We suggest that the hyperbolastic growth model type-II (H2) is more flexible to fit the data than the other model types (H1 and H2), with the lowest AICc value in most of the cadmium concentrations (Tab. 2). As germination reduces when cadmium toxicity increases, the goodness of model fit also decreases. Our findings show that in many cases the best fitting model was not hyperbolastic growth models type-I (H1), type-II (H2), or type-III (H3), although they provided reasonable goodness of fit. It is also important to note that the Richards model provided less accuracy than all other models. The goodness of fit by hyperbolastic models can be attributed to their flexibility in shape. The cumulative seed germination time course of sesame genotypes was successfully fitted using nonlinear regression models including hyperbolastic growth models (Figs. 1-4). Therefore, we recommend that hyperbolastic growth models type-I (H1), type-II (H2), and type-III (H3), be considered among the available nonlinear models in seed biology. Results of model outputs predicting seed germination fraction using Weibull and hyperbolastic models are presented in (Fig. 5).

Conclusion
As germination reduces when cadmium toxicity increases, the goodness of model fit also decreases. Increasing cadmium concentration resulted in the germination fraction reduction from 1 to 0.4 at the 400 ppm. The recommended hyperbolastic growth model was type III or (H3) as it provided the best model with the lowest Corrected Akaike Information Criterion for cv. Halil (AICc = À14.6) and cv. Nazok Shakhei, (AICc = À14.2).