INTRODUCTIONIntestinal microbiota affects human health andvitality. Microbial community is a powerful andmultifunctional metabolic system that modulatesimmunity, suppresses pathogens, and produces variousvitamins [1, 2]. A disturbed qualitative and quantitativemicrobial composition leads to various alimentaryand chronic diseases. For instance, low countsof Bacteroides and Firmicutes, if accompanied byexcessive proteobacteria, fusobacteria, and the mucindecomposingRuminococcus gnavus, can trigger Crohn’sdisease, ulcerative colitis, obesity, and diabetes [3].However, some intestinal microbes inhibitpathogens and food contaminants by producingsuch antimicrobial substances as organic acidsand bacteriocins or competing for nutrients andadhesion sites [4–7]. If it were not for them, unwantedmicroorganisms would cause constant harm tohuman health by producing various toxins orenzymes. For instance, Bacillus cereus is a common366Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376food contaminant that produces two types of toxinsand causes vomiting and diarrhea intoxication [8].B. cereus spores are resistant to heat treatment andchemical preservation [9].Non-typhoid Salmonella is another wide-spreadcause of foodborne diseases [10]. Salmonella entericas. Typhimurium is often resistant to antibiotics and candevelop biofilms, thus causing gastroenteritis, vomiting,and diarrhea [11]. Antibiotic-resistant bacteria are themost dangerous causes of intestinal infections [12].Therefore, novel non-antibiotic ways to suppressthese pathogens and food contaminants for therapyand prevention are one of the most urgent tasks of themodern medicine. Synbiotic compositions offer apotential solution to this problem because they areextremely effective in inhibiting the growth, activity,and pathogenesis of specific undesirable microorganisms.Probiotics, prebiotics, and synbiotics are partsof functional foods that inhibit unwanted membersof intestinal microbiota [13]. These food additivesare known to increase α-diversity, combat obesity,improve immunity, and counteract pathogens [13–16].Synbiotics are the most effective type because theypossess synergistically enhanced beneficial properties ofprobiotics and prebiotics [17].For synbiotics, the most important criteria are theirinhibiting properties, adhesion to intestinal epithelialcells, and pathogen toxicity. Antagonistic researchof synbiotic combinations is a promising strategyfor developing new synbiotics. Ruiz et al. studiedthe combined antimicrobial activity of a synbioticbased on Bifidobacterium longum subsp. infantis andgalactooligosaccharides against such enteric pathogensas Escherichia coli, Cronobacter sakazakii, Listeriamonocytogenes, and Clostridium difficile. C. sakazakiiand C. difficile proved to be the most effectivepathogen inhibitors [18]. Co-cultivation of B. longumor Bifidobacterium breve with C. difficile in a mediumwith commercial fructooligosaccharides reducedthe pathogen growth, as well as the toxicity of itsmetabolites [19].Śliżewska and Chlebicz-Wójcik focused on the effectof various prebiotics co-cultivated with lactobacillion pathogenic S. enterica of various serovars andL. monocytogenes. Inulin demonstrated the greatestantagonistic activity, although the effect depended onthe test strain [20]. Obviously, the effectiveness of oneand the same composition depends on the pathogen.The inhibitory effect can be measured by the inhibitorymetabolites produced by probiotics. This effect canbe expressed in terms of inhibition constants (Ki) orminimal inhibitory concentrations. The synbioticfactor is another quantitative criterion for evaluatingthe effectiveness of synbiotic compositions. It showshow many times the specific growth rate of a pathogenor microbial contaminant decreases under the actionof acids produced by a probiotic when they are cocultivatedin the same medium with this prebiotic [21].Plant extracts are common sources of prebioticsubstances. In addition to polysaccharides of variousmolecular weights, they may contain non-carbohydratesubstances with a potential beneficialeffect, e.g., polyphenols [22, 23]. Precipitation withdifferent concentrations of ethanol can separate plantcarbohydrates into fractions with different degrees ofpolymerization. Polysaccharides with a higher degree ofpolymerization require a lower concentration of ethanol.As the alcohol concentration increases, the averagedegree of polymerization of the precipitated fractiondecreases [24, 25]. Polysaccharides with a high degreeof polymerization are not metabolized by pathogenswithout extracellular hydrolases. However, they canbe metabolized by many types of probiotics, e.g.,bifidobacteria and some lactobacilli, which determinestheir significant prebiotic potential [26]. In our previousresearch, we evaluated the effectiveness of a synbioticcomposition in vitro by the degree of its antagonismagainst staphylococci. It depended on the fractionalcomposition of Arctium lappa fructans, as well as on theratio of the initial probiotic and pathogen counts [27].The response surface methodology was developedby Box and Wilson [28]. It is a powerful toolfor establishing quantitative relationships betweenvarious factors and the response function, also bytaking into account the mutual effect of factors inmultiparameter equations. Shuhaimi et al. used thismethod to optimize the composition of a synbiotic thatconsisted of Bifidobacterium pseudocatenulatum andseveral prebiotics, while Pandey and Mishra tested thismethod on a soy drink with lactic acid bacteria andorganophosphates [29, 30].Few researchers venture beyond simple optimizationto look for the patterns between various factorsand the response function. This approach provedquite effective in studying the change patterns inmicrobial communities under various environmentalfactors [31, 32]. Antagonism is a type of relationships inmicrobial communities. Our research objective was touse the response surface method to evaluate the effectof fructan fractional composition, the initial counts ofprobiotics and the pathogen test strain on the antagonismof the synbiotic against B. cereus and S. enterica.STUDY OBJECTS AND METHODSPlant raw materials and obtaining fructanfractions. To isolate fructans, we used burdockroot powder (Arctium lappa L.) in accordance withpharmacopeial monograph 2.5.0025.15 of the RussianPharmacopoeia. The powder was diluted with distilledwater in a ratio of 1:12 (g dry solids per 1 mL extractant)and extracted twice at 75°C and pH 6.5 for 30 min withconstant stirring. The pulp was separated by vacuumfiltration. To separate high-molecular impurities, theextract was ultrafiltered at 45°C through a hollow fibermodule (AR-0.5-20PS, NPO Biotest, Kirishi, Russia)with a retention threshold of 20 kDa. The permeatewas stirred with active clarifying carbon at a rate of367Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–37615 g/L for 30 min until the extract became colorless.The activated charcoal was separated by vacuumfiltration [33].The extract was evaporated using a rotary filmevaporator (model 561-01110-00 with glass set G1,Heidolph, Germany) at 45°C until the carbohydrateconcentration reached 170–200 g/L. To separate thecarbohydrates into fractions with different degreesof polymerization, the extract was precipitated withvarying ethanol concentrations (20.0, 32.2, 50.0, 67.8,and 80.0%) at 4°C for 4 days [24].The precipitates were separated by centrifugation at5000 rpm for 15 min and dried in a ScanVac Coolsafe100-9 freeze-dryer under the following temperatureand time conditions: 0°С – 8 h, 5°С – 8 h, 10°С – 6 h,15°С – 6 h, and 20°С – 6 h. The samples were diluted1:1 with a 10% solution of trichloroacetic acid andhydrolized for 40 min in a boiling water bath. After that,the content of fructans was determined by the modifiedBertrand method.Microbial objects and cultivation conditions. Allthe bacterial cultures were obtained from the NationalBioresource Center of the All-Russian Collection ofIndustrial Microorganisms in the National ResearchCenter of Kurchatov Institute (VKPM). Bifidobacteriumbifidum (AS-1666, ATCC 29521T) served as a probioticculture. Bacillus cereus (B-8076, ATCC 9634) wasused as a model food contaminant. Salmonella enterica(B-5300) was a model intestinal pathogen. The mediumdescribed in [34] was modified to obtain inoculums andco-cultivate the probiotic and test strains.The composition of the carbohydrate-freemedium was as follows (g/L): casein trypton (DifcoLaboratories) – 10; yeast extract (Springer) – 7.6; meatextract (Panreac) – 5; ascorbic acid (AppliChem) – 1;sodium acetate – 1; (NH4)2SO4, – 5; urea – 2;MgSO4·7H2O – 0.2; FeSO4·7H2O – 0.01; MnSO4·7H2O –0.007; NaCl – 0.01; Tween-80 – 1, and L-cysteine –0.5 (pH 7.0). All the components were dissolvedin 80% of the required amount of distilled water andautoclaved at 115°C for 30 min. The fructan precipitateswere dissolved in distilled water (20% of the requiredmedium volume) and sterilized separately under thesame conditions. Prior to inoculation, carbohydrateswere added to the medium aseptically until theirconcentration was 8 g/L.Inoculums were cultivated at 37°C and stirred at180 rpm under anaerobic conditions (2% CO2, 98% N2)in a CB-210 CO2 incubator (Binder, Germany) for 12 hwithout maintaining a constant pH. After that, theinoculums were centrifuged at 6000 rpm and 4°C for2 min and washed twice in sterile saline (9 g/L NaCl).Then the precipitate was resuspended in a carbohydratefreemedium to obtain suspensions with an opticaldensity depending on the bacterial count. To achieve theselected initial count of the probiotic and the test strain,0.5 mL of the obtained solution was added to the mediawith pre-added fructans. To determine the synbioticfactor, co-cultivation lasted during 10 h under the sameconditions. Sampling took place at the beginning andend of fermentation.Microbial count. Microbial count was conductedin triplicate by seeding tenfold dilutions in Petri disheswith the media. Colonies of B. cereus and S. entericawere counted after 24 h of aerobic growth at 37°C inMRS medium [35]. B. bifidum colonies were countedafter 48 h of growth in BFM medium with thefollowing composition (g/L): peptone – 10, NaCl – 5.0,lactulose – 5.0, L-cysteine – 0.5, riboflavin – 0.01,yeast extract – 7, meat extract – 5, starch – 2, thiaminechloride – 0.01, and lithium citrate – 3.3 [36]. The pHwas adjusted to 5.5 by adding propionic acid (5 mL/L).The dishes were incubated under anaerobic conditions at37°C using a BD GasPak™ Anaerobic Container System.Determining the content of organic acids. Theconcentration of organic lactic and acetic acids wasdetermined by high-performance liquid chromatography(HPLC) according to a slightly modified standardprocedure by the refractometric signal [37]. Theexperiment involved an Agilent 1220 Infinity chromatograph(Santa Clara, CA, USA) with an Agilent Hi-Plex H column (250×4.6 mm). The supernatant wascentrifuged at 12 000 rpm for 15 min, then filteredthrough 0.45-μm cellulose acetate membranes (HAWP,MF-Millipore, St. Louis, MO, USA). Other parametersincluded: sample volume – 3 μL, temperature – 50°C,mobile phase flow rate (0.002 M H2SO4) – 0.3 mL/min.To prepare calibration solutions, the concentratedorganic acids were diluted in their mobile phase toconcentrations of 1, 5, and 10 g/L.Determining the structure of fructans. Thestructure of the isolated fructans was analyzed usingcarbon-13 nuclear magnetic resonance (13C-NMR)spectrometry following the procedure described byMariano et al. [38]. One-dimensional spectra wereobtained at 298 K on a BRUKER CXP-200 NMRspectrometer (50.3 MHz) (Bruker, Germany) in anaqueous solution of D2O. Inulin (Orafti ® HSI, BENEOORAFTI,Belgium) and oligofructose (Orafti ® P95,BENEO-ORAFTI, Belgium) served as standard.Calculating the synbiotic factor. The synbioticfactor was calculated in accordance with thepreviously approach proposed by Karetkin et al. andEvdokimiova et al. [21, 27]. The microbial count, pH,and the concentration of organic acids were determinedat the initial and final stages of co-cultivation. Based onthe data obtained, the synbiotic factor was calculated asfollows:(1)where SF is the synbiotic factor; pHopt is pH optimalfor test strain growth; pHmin is pH the minimal for teststrain growth; [LA] is the concentration of undissociatedlactic acid, (mg/mL); [AA] is the concentration ofundissociated acetic acid, mg/mL; MICLA is the minimalinhibiting concentration of lactic acid, mg/mL; MICAAis the minimal inhibiting concentration of acetic acid,( ) 2 2 21 2 3 0 1 1 2 2 3 3 12 1 2 23 2 3 13 1 3 123 1 2 3 11 1 22 2 33 3 , , kYx x x b bx = + + b x + b x + b x x + b x x + b x x + b x x x + b x + b x + b x[ ] [ ] 1 1minopt min LA AApH pH LA AA SFpH pH MIC MIC−   α    β = ×  −    ×  −    −        368Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376mg/mL; α and β are constants for B. cereus orS. enterica, which we defined in [39] (Table 1).Design of experiment and statistical analysis.The central composition rotatable design was appliedto study the effect of the following parameters on theco-cultivation: the precipitant concentration x1, thefractional composition of A. lappa fructans, the initialcount (decimal logarithm) of bifidobacteria (x2), andtest strain cells (x3). Synbiotic factor (Y1) and final teststrain count (Y2) were chosen as response functions. Thevariation levels were determined based on data obtainedfrom [21, 27] (Tables 3 and 4). The response functionwas presented as follows:The significance test of the coefficients for Eq. (2)was based on the t-test. The adequacy of the equationwas assessed by the Fisher criterion at P = 0.05.Response surfaces were calculated and constructedusing the MathLab software. The scanning methodwith a variable step as in [40] was applied to determinethe extreme values of the factors. The method consistsin a sequential search for points in the parametricspace using the GeoGebra Classic software 6.0.694.0(University of Salzburg, Salzburg, Salzburg state,Austria).RESULTS AND DISCUSSION13C-NMR specters of Arctium lappa L. rootfructan fractions. Figure 1 illustrates 13C-NMRspecters of standard inulin and oligofructose, purifiedfrom A. lappa L. fructan fractions and precipitated bydifferent concentrations of ethanol.The analysis was based on the difference betweenthe chemical shifts of the carbon atoms of the monomerslocated inside the chain of oligo- and polysaccharidesand the atoms of the terminal monomers [24]. Thechemical shifts of carbon atoms in the standard and testsamples are typical of inulin-type fructans (Table 2).The obtained spectra of fructan fractions were closerto those of commercial oligofructose in terms of thenumber and location of peaks. In terms of signalintensity, they were between standard oligofructoseand highly purified inulin. None of the test samplesdemonstrated peaks at the terminal C-2 atom ofD-fructofuranose. However, the test samples showed anincrease in the relative areas of the peaks, as well as anincrease in the precipitant concentration for all carbonTable 1 Minimal inhibitory concentrations, constants, and optimal and minimal pH during the process of Bacillus cereus orSalmonella enterica inhibition by lactic and acetic acidsTest strain pHopt pHmin MICLA, mg/mL MICAA, mg/mL α βBacillus cereus 7.0 4.9 3.48 3.20 0.25 0.40Salmonella enterica 7.0 5.0 2.25 1.77 1.70 0.90Figure 1 13C-NMR specters in distilled water with D2Oand (a) HSI inulin, (b) oligofructose and Arctium lappa L.fructan fractions precipitated by ethanol with concentrations,(c) 20.0% (Burd-20), (d) 32.2% (Burd-32), (e) 50.0% (Burd-50),(f) 67.8% (Burd-68), and (g) 80.0% (Burd-80)efgabcd100ppm90 80 70 60atoms of the D-fructofuranose residues within the chain(forming a 2→1 bond).All the peak areas for the corresponding carbonatoms were smaller than for inulin, and the valuesobtained for Burd-50 and Burd-68 were closest to2 2 23 3 12 1 2 23 2 3 13 1 3 123 1 2 3 11 1 22 2 33 3 b x + b x x + b x x + b x x + b x x x + b x + b x + b x[ ] [ ] 1LA AALA AA MIC MIC α    β −    ×  −          ( ) 2 2 21 2 3 0 1 1 2 2 3 3 12 1 2 23 2 3 13 1 3 123 1 2 3 11 1 22 2 33 3 , , k Yx x x = b + b x + b x + b x + b x x + b x x + b x x + b x x x + b x + b x + b x[ ] [ ] 1 1minopt min LA AApH pH LA AA SFpH pH MIC MIC−   α    β = ×  −    ×  −    −        (2)369Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376oligofructose. The differences in the relative proportionsof peak areas for Burd-20 and Burd-32 were smalland manifested as unidentified peaks in the Burd-20.Probably, carbohydrates of similar molecular weightwere precipitated at these ethanol concentrations.No correlation was observed between the relativeproportions of the peak areas for the terminal atoms ofglucopyranose and fructofuranose.Synbiotic antagonism to Bacillus cereus andresponse surface analysis. To assess the effect ofvarious factors on the anti-B. cereus activity of thesynbiotic composition, the experiment was carried outaccording to a central composition rotatable design. Thelimiting values of ethanol concentration were chosenas 20 and 80% as in [27]. The average polymerizationdegree of the precipitated carbohydrate fraction was atits highest at 20% of ethanol.Zeaiter et al. used 33% ethanol to obtain a fractionof inulin-type artichoke fructans with an average degreeof 32–42 [26]. Table 3 demonstrates the planning matrix,as well as the experimental and calculated values ofresponse functions, i.e., the synbiotic factor and the finaltest strain cell count.The coefficients of the response function equationwere determined from the values of the synbiotic factorand the final bacterial count. The response surface wasconstructed according to Eq. (2) (Fig. 2). The adequacyof the equations was confirmed by Fisher’s criterionF = 1.681 and 1.66: it was below the tabulated F = 4.704at P = 0.05.The synbiotic factor reduced of the specificgrowth rate of the test strain. It showed how manytimes the specific growth rate decreased relativeto the optimal value under the effect of inhibitorsproduced by the probiotic and the prebiotic. Themaximal inhibition corresponded to the lowest valueof the synbiotic factor [21]. The synbiotic factor of thecomposition of Bifidobacterium bifidum and A. lapparoot fructans had a positive linear dependence onthe precipitant concentration (x1). Therefore, thecomposition with fructans precipitated by the lowestalcohol concentration had the greatest inhibitory effecton B. cereus because it had the highest average degree ofpolymerization. This result confirms the data obtainedby us before [27]. The dependence of the synbioticfactor on the initial probiotic count (x2) was parabolicand reached its minimum at +1.156, which correspondedTable 2 13C-NMR chemical shifts of β-D-fructofuranose and α-D-glucopyranose of HSI inulin standard samples, oligofructose, andexperimental samples of Arctium lappa L. root fructan fractions precipitated with various concentrations of ethanol: 20% (Burd-20),32.2% (Burd-32), 50% (Burd-50), 67.8% (Burd-68), and 80% (Burd-80)Carbon atom Chemical shift, ppmInulin Oligofuctose Burd-20 Burd-32 Burd-50 Burd-68 Burd-80C-2 f (terminal) – 103.88 – – – – –C-2 f (2→1 bond) 103.4262 103.2645 104.26 104.29 103.40 103.43 103.43– 97.98 99.31 99.25 – – –C-1 g (terminal) – 92.7261 93.41 – – – –– 88.76 – – – – –C-5 f (terminal) – – – – – – –C-5 f (2→1 bond) 81.3253 81.3253 82.40 82.30 81.44 81.50 81.44– 77.71 – – – – –C-3 f (2→1 bond) 77.2824 77.1477 78.31 78.06 77.32 77.48 77.54C-3 f (terminal) – 76.77 77.16 77.00 76.07 – 77.32– – – – – – –C-4 f (2→1 bond) 74.5872 74.70 75.85 75.76 74.83 74.96 74.86C-4 f (terminal) – – – 75.44 – – –C-3 g (terminal) – 72.8892 73.75 73.75 – 72.79 73.04C-5 g (terminal) – 72.6736 – – – – –C-2 g (terminal) – 71.4337 72.53 72.41 – 71.58 71.54C-4 g (terminal) 69.4 69.3045 71.06 70.94 70.11 70.17 70.46– 68.39 69.09 68.83 68.13 68.19 68.13C-6 f (2→1 bond) – 64.1566 65.38 64.49 64.30 64.30 64.43C-6 f (terminal) – 63.67 64.65 63.47 63.69 63.79 63.69– – 64.36 – – – –C-1 f (2→1 bond) 62.3777 62.4858 63.53 62.06 62.61 62.61 62.57C-1 f (terminal) 61.16 60.84 62.06 61.78 61.04 61.20 61.27C-6 g (terminal) – 60.49 58.78 58.71 57.88 – 57.852Y1 = 0.0211+ 0.008x1 − 0.0074x2 + 0.0032x27 7 7 6 6 2 2 3 2 3 Y = 4.9 ×10 −1.6×10 x −1.2 ×10 x − 7.1×10 x x − 7.4 ×10 x21 1 2 2 Y = 0.0211+ 0.008x − 0.0074x + 0.0032x7 7 7 6 6 2 2 3 2 3 Y = 4.9 ×10 −1.6×10 x −1.2 ×10 x − 7.1×10 x x − 7.4 ×10 x21 1 2 2 Y = 0.0211+ 0.008x − 0.0074x + 0.0032x7 7 7 6 6 22 2 3 2 3 3 Y = 4.9 ×10 −1.6×10 x −1.2 ×10 x − 7.1×10 x x − 7.4 ×10 x (4)(3)370Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376probiotic count of 7.69 lg(CFU/ml) and the A. lappafructan fraction precipitated with 20% ethanol.As the initial bifidobacterial count (x2) increased,the final bacterial count decreased (Fig. 2b). Thedependence of the final test strain count (Y2) on theinitial one (x3) was parabolic. The maximal value ofthe response function was reached when the bifidobacterialcount was minimal, i.e., 6.0 lg(CFU/mL), andthe initial test strain count in the design center was5.5 lg(CFU/mL). At these values, the inhibition wasleast effective. The minimal final test strain count wasaround the highest seed doses of both the probiotic andto 7.69 lg(CFU/mL). As x2 rose (> +1.156), the synbioticfactor also increased.All experimental values appeared to be much higherthan those obtained by calculation, both at the minimalpoint and at high values of x2. Apparently, the observeddecrease in the antagonistic activity could be ignored.All the coefficients at x3 proved insignificant, and theinitial test strain count did not affect the synbiotic factor.Within the range of the variables, the minimal value ofthe synbiotic factor (maximal suppression of the teststrain) was 0.0033 and lied at the point with coordinates–1.682 and 1.156, which corresponded to the initialFigure 2 Synbiotic factor response surface (a) and final bacterial count (b), CFU/mLTable 3 Range of variation and encoding of variables: experimental and calculated values of response functions for Bacillus cereusTestNo.Factors Synbiotic factor Final bacterial count,Precipitant concentration lg(CFU/mL)*(EtOH), %Initial prebiotic count,lg(CFU/mL)Initial bacterial count,lg(CFU/mL)z1 x1 z2 x2 z3 x3 SFobs SFpred Xbac obs Xbac pred1 67.8 +1 7.6 +1 6.4 +1 0.0267 0.0249 5.72 6.772 67.8 +1 7.6 +1 4.6 –1 0.0310 0.0249 7.48 7.653 67.8 +1 6.4 –1 6.4 +1 0.0420 0.0397 7.80 7.724 67.8 +1 6.4 –1 4.6 –1 0.0433 0.0397 7.77 7.805 32.2 –1 7.6 +1 6.4 +1 0.0136 0.0089 5.43 6.776 32.2 –1 7.6 +1 4.6 –1 0.0092 0.0089 7.58 7.657 32.2 –1 6.4 –1 6.4 +1 0.0224 0.0236 7.66 7.728 32.2 –1 6.4 –1 4.6 –1 0.0244 0.0236 7.79 7.809 20.0 –1.682 7.0 0 5.5 0 0.0188 0.0076 7.77 7.6910 80.0 +1.682 7.0 0 5.5 0 0.0404 0.0346 7.63 7.6911 50.0 0 6.0 –1.682 5.5 0 0.0471 0.0425 7.82 7.8812 50.0 0 8.0 +1.682 5.5 0 0.0179 0.0177 7.51 7.3413 50.0 0 7.0 0 4.0 –1.682 0.0268 0.0211 7.77 7.6914 50.0 0 7.0 0 7.0 +1.682 0.0301 0.0211 6.63 6.8415 50.0 0 7.0 0 5.5 0 0.0213 0.0211 7.74 7.6916 50.0 0 7.0 0 5.5 0 0.0122 0.0211 7.68 7.6917 50.0 0 7.0 0 5.5 0 0.0239 0.0211 7.76 7.6918 50.0 0 7.0 0 5.5 0 0.0241 0.0211 7.70 7.6919 50.0 0 7.0 0 5.5 0 0.0205 0.0211 7.56 7.6920 50.0 0 7.0 0 5.5 0 0.0237 0.0211 7.66 7.69* the response function was calculated as CFU/mL; the results are given on a logarithmic scalea b% EtOHX0 BifX0 BacX0 Bif371Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376surface was parabolic, and its analytical minimum wasoutside the variation range. These surfaces demonstratedan increase in the initial bifidobacterial count, whichfollowed the increase in the initial Salmonella count.The larger bifidobacterial count resulted inthe greatest suppression, which varied from x3 = – 1.682to x3 = 0. Thus, the response surface method made itpossible to define the critical value of the Salmonellacount (6.5 lg(CFU/mL)). When this value was exceeded,only the maximal count of viable bifidobacterial cellscould inhibit the pathogen. If the initial pathogen countexceeded 6.91 lg(CFU/mL), the response surfaces had asaddle shape.The global minimum of the response function withinthe variation range was determined by the variablestep scanning method. Initially, all variables for eachcoordinate had an interval with two equal subintervals.The values of the function were calculated at the nodesof the resulting grid to select the optimal point withthe lowest synbiotic factor. Subsequently, the intervalwas cut in two. The calculation cycles continued untilthe interval along one of the coordinates fell below0.001. The minimum was determined at the border ofthe region in coordinates –1.682, +1.682, and +1.682.Therefore, the greatest antagonistic effect was expectedat the lowest alcohol concentration of 20% and the2 2Y1 = 0.029 + 0.012x1 − 0.007x3 + 0.006x1x2 − 0.006x1x3 + 0.007x1x2x3 + 0.004x1 + 0.003x28 7 7 7 2 7 2 7 22 2 3 1 2 3 Y = 4.14 ×10 − 4.58×10 x + 3.95×10 x − 3.61×10 x − 2.08×10 x + 2.63×10 x2 23 1 2 1 3 1 2 3 1 2 0.007x + 0.006x x − 0.006x x + 0.007x x x + 0.004x + 0.003x7 7 2 7 2 7 22 3 1 2 3 x + 3.95×10 x − 3.61×10 x − 2.08×10 x + 2.63×10 xFigure 3 Synbiotic factor response surface as a function of ethanol concentration (x1) and initial probiotic count (x2) at fixed initialSalmonella count (x3)x3 = +1.682 x3 = 0.46x3 = 0 x3 = – 0.86 x3 = – 1.682the test strain. As the initial probiotic and test strainconcentrations increased, the final bacterial countplummeted. Probably, bacilli inhibited their own growthby their own metabolites, i.e., lactic acid.Antagonism of synbiotic compositions againstSalmonella enterica and response surface analysis.Table 4 shows the design matrix with experimentaland calculated values of the response functions forS. enterica. The variation range of variables in naturalcoordinates did not differ from that of bacilli, except forthe shift in the initial test strain count by +1 lg(CFU/mL).The response surface analysis for synbiotic factor (Y1)was represented as the following equation confirmed byFisher’s criterion (F = 3.99 < 4.87, P = 0.05):The coefficients for all factors and their pairwiseinteractions turned out to be significant. The responsesurfaces were calculated for fixed (Fig. 3). For all thesurfaces obtained, the smallest value of the responsefunction within the variation range was obtained whenthe precipitant concentration was minimal. Whenwas below 0.46, which corresponded to the initialSalmonella count (6.91 lg(CFU/mL)), the response(5)X0 Bif% EtOHX0 Bif% EtOHX0 Bif% EtOHX0 Bif% EtOHX0 Bif% EtOH372Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376highest initial bifidobacterial count of 8.0 lg(CFU/mL).Unlike the bacilli, the metabolism of the test strainaffected the synbiotic factor and reduced its value.Probably, the reduction happened because of extra acidproduction.The final Salmonella count equation (F = 2.20 < 4.74,Р = 0.05) looked as follows:As for the synbiotic factor, all factors had asignificant impact on target function Y2. The responsesurfaces were calculated for fixed x3 values (Fig. 4).The surface was parabolic in coordinates x1 and x2.The maximal value of the final test strain count was8.68 lg(CFU/mL) in coordinates 0, –1.101, and +1.685.Thus, the synbiotic composition of fructans precipitatedby 50% ethanol and bifidobacteria with the initial countof 6.34 lg(CFU/mL) had the lowest antagonistic effectagainst Salmonella. As the initial Salmonella countincreased, the efficiency weakened.The effect of the initial test strain count on theresponse function was not symmetrical to the designcenter because the minimum of the function for thisvariable was at the point – 0.749, 5.83 lg(CFU/mL). Thedependence had a quadratic nature. As a result, thefinal Salmonella count remained almost the same whenthe initial count was below 6.5 lg(CFU/mL). When thevalues were large, the value of the response functionrose sharply. Therefore, the initial Salmonella count of6.5 lg(CFU/mL) was critical from the standpoint ofmicrobiology.The response paraboloid was symmetrical to thedesign center of variable. Thus, both fructan fractionsprecipitated by the highest and the lowest alcoholconcentrations possessed the same inhibition effects.However, as the initial probiotic count exceeded 6.34lg(CFU/mL), the inhibition of the pathogen increased.The lowest values of the final S. enterica count (and thegreatest antagonistic effect) within the variation rangewere achieved at the maximal initial bifidobacterialcount of 8.0 lg(CFU/mL) in the medium with A. lapparoot fructan fractions precipitated with 20 or 80%ethanol.Previously, we considered Staphylococcus aureusas the test strain and also found out that the effect ofA. lappa fructans precipitated with 40 and 60% ethanolwas weaker than those precipitated with 20 or 80%ethanol [27]. Apparently, the highest average degree ofpolymerization was effective because the carbohydratesubstrate was less available. The lowest degree ofpolymerization was effective because the bifidobacteriaconsumed the substrate faster and thus produced moremetabolites. This issue, however, requires furtherresearch.Table 4 Range of variation and encoding of variables: experimental and calculated values of response functions for SalmonellaentericaTestNo.Factors Synbiotic factor Final bacterial count,Precipitant concentration lg(CFU/mL)*(EtOH), %Initial prebiotic count,lg(CFU/mL)Initial bacterial count,lg(CFU/mL)z1 x1 z2 x2 z3 x3 SFobs SFpred Xsal obs Xsal pred1 67.8 +1 7.6 +1 7.4 +1 0.0544 0.0477 8.55 8.582 67.8 +1 7.6 +1 5.6 –1 0.0636 0.0596 8.53 8.473 67.8 +1 6.4 –1 7.4 +1 0.0233 0.0214 8.71 8.674 67.8 +1 6.4 –1 5.6 –1 0.0689 0.0616 8.64 8.595 32.2 –1 7.6 +1 7.4 +1 0.0114 0.0088 8.58 8.586 32.2 –1 7.6 +1 5.6 –1 0.0265 0.0267 8.41 8.477 32.2 –1 6.4 –1 7.4 +1 0.0328 0.0351 8.60 8.678 32.2 –1 6.4 –1 5.6 –1 0.0278 0.0247 8.60 8.599 20.0 –1.682 7.0 0 6.5 0 0.0225 0.0202 8.51 8.4910 80.0 +1.682 7.0 0 6.5 0 0.0525 0.0602 8.47 8.4911 50.0 0 6.0 –1.682 6.5 0 0.0468 0.0371 8.61 8.6412 50.0 0 8.0 +1.682 6.5 0 0.0221 0.0371 8.46 8.4413 50.0 0 7.0 0 5.0 –1.682 0.0399 0.0413 8.59 8.6314 50.0 0 7.0 0 8.0 +1.682 0.0179 0.0162 8.77 8.7415 50.0 0 7.0 0 6.5 0 0.0328 0.0287 8.61 8.6216 50.0 0 7.0 0 6.5 0 0.0289 0.0287 8.61 8.6217 50.0 0 7.0 0 6.5 0 0.0334 0.0287 8.65 8.6218 50.0 0 7.0 0 6.5 0 0.0244 0.0287 8.63 8.6219 50.0 0 7.0 0 6.5 0 0.0230 0.0287 8.63 8.6220 50.0 0 7.0 0 6.5 0 0.0308 0.0287 8.57 8.62* the response function was calculated as CFU/mL; the results are given on a logarithmic scale(6)8 7 7 7 2 7 2 7 22 2 3 1 2 3 Y = 4.14 ×10 − 4.58×10 x + 3.95×10 x − 3.61×10 x − 2.08×10 x + 2.63×10 x7 7 7 2 7 2 7 22 3 1 2 3 4.58×10 x + 3.95×10 x − 3.61×10 x − 2.08×10 x + 2.63×10 x373Evdokimova S.A. et al. Foods and Raw Materials. 2022;10(2):365–376In this study, we considered lactic and acetic acidsas inhibitors. As proved by Prosekov et al., manybifidobacteria can produce antimicrobial peptides(bacteriocins), and some representatives of B. bifidumare among them [41]. However, their synthesis usuallybecomes active at the stationary phase, and by that timethe bifidobacterial count in the co-culture of bacilliand Salmonella stop growing. Therefore, the synbioticfactor calculations did not take into account the effect ofbacteriocins. Further research is required to study theseinhibitors under conditions close to real, e.g., intestinalsimulators with a continuous slow medium flow.The approach proposed in this paper can also beapplied to non-plant prebiotics. Lactulose is one ofthe best prebiotics [42]. It is often combined withother prebiotics, such as fructooligosaccharides, tomake up functional foods. Scientists also turn tooligosaccharides of goat’s milk, which are a mix of triandtetrasaccharides that consist of glucose, fructose,galactose, and their acylated derivatives [43]. Obviously,the qualitative and quantitative composition affects theaction of the prebiotic both separately and as part of asynbiotic composition. Our approach can be applied tosimilar studies in vitro.CONCLUSIONIn this research, the highest synbiotic efficiencybelonged to the fraction of fructans with a higher degreeof polymerization precipitated by the lowest ethanolconcentration and the highest bifidobacterial count. Thestudy established a quantitative relationship between thebifidobacteria and the parameters of fructan productionand the antagonistic activity of their synbioticcomposition. We also determined the effect of the ratioof probiotic and pathogen counts on antagonism. Theproposed approach can substantiate the compositionof new synbiotics. In the future, we plan to study othercompositions of probiotics and prebiotics in vivo to findtheir optimal ratio.CONTRIBUTIONS. Evdokimova and B. Karetkin developed theresearch concept. E. Guseva and I. Shakir wereresponsible for data curation and formal analysis.B. Karetkin acquired the funding. S. Evdokimova andN. Khabibulina performed the experiments. B. Karetkinand E. Guseva developed the methodology. B. Karetkinsupervised the project. E. Guseva and M. Zhurikovworked with the Software. I. Shakir validated theobtained data. S. Evdokimova and M. Zhurikov developedthe infographics. S. Evdokimova wrote the originaldraft. B. Karetkin and V. Panfilov edited themanuscript. All the authors discussed the results andcontributed to the final manuscript. All the authorshave read and agreed to the published version of themanuscript.CONFLICT OF INTERESTThe authors declare that there is no conflict ofinterests regarding the publication of this article.ACKNOWLEDGEMENTSNMR spectrometry was performed on the equipmentof the Mendeleev Center for Collective Use.The authors would like to express their gratitude toAndrey B. Polyakov.