Insaf Nachi
email: nachiinsaf@gmail.com

Imene Fhoula

Imen Smida

Imen Ben Taher

Moncef Chouaibi

Janis Jaunbergs

Vadims Bartkevics

Mnasser Hassouna

Assessment of lactic acid bacteria application for the reduction of acrylamide formation in bread

Keywords: Sourdough bread, Lactic acid bacteria, Acrylamide, Sensory evaluation

SS, spontaneous sourdough; SLb, sourdough inoculated with L.brevis S12; SLp, sourdough inoculated with L.plantarum S28; SPp, sourdough inoculated with P.pentoseus S14; Spa, sourdough inoculated with P.acidilactici S16; DSS, dough made with spontaneous sourdough; DLb, dough inoculated with L

Introduction

Bread is one of the staple foods for human nutrition. It supplies a considerable portion of the nutrients required for growth, maintenance of health and well-being. The baker's yeast bread is the most consumed type in Tunisian diet (EI, 2014). During bread baking, some hazardous byproducts can be formed, such as acrylamide. This compound has been recognized as a neurotoxic and potentially carcinogen substance for humans (IARC, 1994).

Acrylamide has been detected in a wide range of cooked and fried carbohydrate rich foods, particulary crisp bread, potato chips, breakfast cereals, and coffee [START_REF] Gökmen | Effects of dough formula and baking conditions on acrylamide and hydroxymethylfurfural formation in cookies[END_REF]. The most probable route of acrylamide formation is through Maillard reactions involving the amino acid asparagine and reducing sugars [START_REF] Mottram | Food chemistry: Acrylamide is formed in the Maillard reaction[END_REF]. It also can be formed through several other pathways, such as the reaction between aspartic acid and reducing sugars (Yaylayan & Stadler, 2005), thermal degradation of amino acids and proteins [START_REF] Keramat | Acrylamide in Foods: Chemistry and Analysis[END_REF], as well as decarboxylation and deamination of asparagine [START_REF] Granvogl | Thermally Generated 3-Aminopropionamide as a Transient Intermediate in the Formation of Acrylamide[END_REF].

A wide range of researchers representing national food safety authorities, academia, and food manufacturers have sought to better understand the mechanisms of acrylamide formation and to find ways to minimize its formation in foods (EFSA, 2011).

Previous studies have indicated that the occurrence of acrylamide in heat-processed foods may depend on specific factors, such as the initial concentrations of asparagine, reducing sugars, pH, water activity, time and temperature of the heating proces [START_REF] Gökmen | Effects of dough formula and baking conditions on acrylamide and hydroxymethylfurfural formation in cookies[END_REF].

Over the last decades, there have been many attempts to reduce acrylamide formation by the optimization of processing conditions. Indeed, the HEATOX report by [START_REF] Hellenäs | The HEATOX Project[END_REF] showed that acrylamide synthesis increased at higher baking temperature (200-260°C) and with time (10-25 min). Another strategy for reducing the acrylamide content depended on the choice of appropriate raw materials. Wang et al. (2017) suggested that the generation of acrylamide can be mitigated by reducing the presence of degraded starch in flour.

Several studies indicated that fermentation processes performed with lactic acid bacteria (LAB) and yeast could reduce the acrylamide content in bread. This effect is mainly related to a decrease of pH rather than to the consumption of precursor nutrients (asparagine and reducing sugars) by microorganisms growing in sourdough [START_REF] Fredriksson | Fermentation Reduces Free Asparagine in Dough and Acrylamide Content in Bread[END_REF][START_REF] Bartkiene | Study on the reduction of acrylamide in mixed rye bread by fermentation with bacteriocin-like inhibitory substances producing lactic acid bacteria in combination with Aspergillus niger glucoamylase[END_REF]Wang et al., 2017).

Moreover, the use of lactic acid bacteria in sourdough improved the properties of dough and enhanced the flavor and texture of bread (Saeed et al., 2014). It was also reported that the use of sourdough extended the microbiological shelf life of bread by controlling and inhibiting spoilage organisms during fermentation, due to the lower pH value and antimicrobial metabolites of LAB [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF]. Likewise, lactic acid

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ACCEPTED MANUSCRIPT 5 sourdough had a higher content of biogenic compounds, lower level of anti-nutritional factors and a better value of glycemic response, as well as improved the uptake of minerals [START_REF] Gobbetti | Lactic Acid Bacterium and Yeast Microbiotas of 19 Sourdoughs Used for Traditional/Typical Italian Breads: Interactions between Ingredients and Microbial Species Diversity[END_REF].

So, the challenge of this study was to find a way to reduce the acrylamide content in Tunisian bread without compromising its organoleptic properties. Thus, a lactic fermentation was conducted using four LAB strains, previously isolated from Tunisian flours and identified. They were tested to decrease the acrylamide concentration in bread. Up to our knowledge, no research has been conducted on acrylamide reduction in Tunisian food. For this purpose, the known acrylamide precursors (asparagine and reducing sugars) were measured in fermented dough. At the same time, the influence of lactic acid fermentation on sensory features of the final products was studied.

Materials and methods

Materials

The flour used (type PS-7 and moisture content 14.43%) was purchased from the mill SOTUMIS (Ennakhla) situated in Tunisia. Chemicals and analytical standards were mainly purchased from Sigma-Aldrich (Dublin, Ireland). All analytical standards had a purity of at least 95%.

Microorganisms

Fresh yeast was supplied by Rayen Food Industries. The strains of lactic acid bacteria (LAB) used in this study (Lactobacillus brevis strain S12 (MF458471), Lactobacillus plantarum strain S28 (MF458477), Pediococcus pentoseus strain S14 (MF4584872), and Pediococcus acidilactici strain S16 (MF458474) were previously isolated, identified by 16S ribosomal RNA (rRNA) gene from various Tunisian bakery flours and selected basing on their acidification activity according to the method described by [START_REF] Alfonzo | Diversity and technological potential of lactic acid bacteria of wheat flours[END_REF] where LAB cells were assessed to reduce pH of a flour extract after 24 h, 48 h and 72 h of inoculation (Data not shown).

Preparation of sourdough

Experimental sourdough bread was manufactured using the previously described selected strains of LAB (L.brevis S12, L.plantarum S28, P.pentoseus S14 and P.acidilactici S16) based on their acidification capacity.

The LAB strains were cultivated in MRS broth (1% maltose w/v, 1% lactose w/v, pH 5.6) at 30°C for 18 h. Bacterial cells were harvested by centrifugation (10,000 × g, 10 min, 4°C), washed twice with 50 mM sterile potassium phosphate buffer (pH 7.0) before being resuspended in tap water. Each strain was individually M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 6 characterized and inoculated into the dough. The sourdough was made according to [START_REF] Nionelli | Exploitation of Albanian wheat cultivars: Characterization of the flours and lactic acid bacteria microbiota, and selection of starters for sourdough fermentation[END_REF].

Briefly, for preparing 100 g of sourdough, 62.5 g of flour were mixed with 37.5 mL of tap water containing 10 9 CFU/g of LAB cells. The obtained sourdough was incubated at 30°C for 16 h. A spontaneous sourdough (SS) prepared without inoculation with the selected LAB strains was used as a control.

Making of bread

The dough was made according to the recipe of [START_REF] Nionelli | Exploitation of Albanian wheat cultivars: Characterization of the flours and lactic acid bacteria microbiota, and selection of starters for sourdough fermentation[END_REF]. In all of the experiments, 20% (w/w) of sourdough was added to dough. Baker's yeast was added at the amount of 2% (w/w). Dough yield (DY = (dough weight / flour weight) × 100) was fixed at 160. After that, dough samples were left to ferment for 1 h 30 min.

The control bread was made according to the same formulation, but without the addition of sourdough. All bread samples were prepared in triplicates. All breads were baked at 220°C for 20 min.

Analytical methods

Determination of pH and total titratable acidity

The values of pH and total titratable acidity (TTA) were determined after mixing 10 g of sourdough or dough with 90 mL of distilled water using a Stomacher mixer. The pH was measured using a pH meter and the acidification capacity (∆pH) was calculated as the difference between pH after fermentation and pH before fermentation. The mixture was used to measure the TTA expressed as the amount (mL) of 0.1 M NaOH solution needed to reach the pH value of 8.3.

Determination of reducing sugars

The sugar content (glucose, fructose, and sucrose) of freeze-dried doughs was determined by high-performance liquid chromatography (HPLC) system (Waters 2695 Separations Module) according to the method of [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF]. Five grams of each sample were mixed with 20 mL of deionized water. The filtrate was placed in a water bath for 1 h at 75°C, in order to inactivate the enzymes, before being centrifuged at 13500 × g for 10 min.

The obtained supernatants were analyzed by a HPLC system equipped with an AKTA purification system, an analytical column (Phenomenex Luna 5µm NH 2 , 150 × 4.6 mm (Torrance, CA, USA)) and a refractive index detector (Waters 2414). The compounds were quantified using a calibration curve of the corresponding standards ranging between 50 and 500 mg/mL. Sucrose, glucose, and D-fructose standards were obtained from Sigma-Aldrich.

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.3. Analysis of asparagine

Asparagine was extracted by the method reported by [START_REF] Rizzello | Use of sourdough fermented wheat germ for enhancing the nutritional, a for food preservation[END_REF]. Each sample (2 µL) was injected into HPLC coupled with a Shimadzu LC-20AD evaporative light scattering detector (ELSD). The mobile phase was composed of solvent A (0.1% formic acid in water) and solvent B (0.1% formic acid in 98% acetonitrile) with a flow rate of 0.7 mL/ min at 30°C, and the injection volume was 10 µL. The gradient starting from 0 % B for 5 min, 15 % B for 7 min, 30 % B for 5 min, and finally followed by a 18 min maintained at 0% B. Asparagine was quantified using a calibration curve made with L-asparagine (Sigma-Aldrich).

Determination of acrylamide by LC-MS/MS

The extraction of acrylamide was carried out on bread samples according to the method of [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF]. It was conducted with acetonitrile and QuEChERS salt mixture (4 g anhydrous MgSO 4 (Sigma Aldrich) and 0.5 g of NaCl (Analytika Ltd (Check Republic)). The extracts were then added to 50 mg of PCA-sorbent (SSELECTRA Bulk Sorbents) and 150 mg anhydrous MgSO 4 to obtain pure extracts. These latter were than analyzed with liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS). The quantitative analysis was performed by QTRAP 5500 LC-MS/MS instrument (AB SCIEX, Framingham, MA, USA) coupled to an Acquity UPLC system (Waters, Milford, MA, USA). The separation of acrylamide was obtained with Luna 3µm HILIC column (100 × 3.00 mm) (Phenomenex, Torrance, CA, USA). The solvent system was composed of 0.1% formic acid in water and 0.1% formic acid in methanol with a flow rate of 0.3 mL/min at 30°C, and the injection volume was 10 µL. The conditions selected for the MS/MS detection were as follows: curtain gas (Nitrogen): 30.0 psi; ion spray: 5500 V; temperature: 400°C, nebulizer gas (Nitrogen): 40 psi; nebulizer gas (Nitrogen): 50 psi. Acrylamide was quantified using a calibration curve made with internal standard (acrylamided 3 ) dissolved in acetonitrile and chromatograms were acquired and processed by using the Analyst software, version 1.5 (AB SCIEX).

The evaluation of bread quality

The hardness of bread samples was determined with TVT 6700 texture analyzer (Perten Instruments, North Ryde BC, NSW, Australia). All samples were prepared and baked on the day of test. Three slices of bread (20 mm thick) were compressed by using a cylindrical compression probe with 75 mm diameter. The following settings were selected: test speed 5 mm/s, 50% deformation of the sample and two compression cycles with a break of 12 The crumb features of breads were evaluated after 24 h of storage. Images of three slices were acquired using a Nikon D3100 digital camera (55 mm lens; level of sensitivity: ISO1600; shutter speed: 1/640 s). Two 20 mm × 20 mm square fields of view were evaluated in each image. Segmentation was performed manually, by binarization of 8-bit greyscale images into black-and-white images using the Otsu ImageJ thresholding algorithm implemented with Fiji 1.51 software package. After that, the void fraction (the fraction of the total area corresponding to the bread pores) and cell density (number of cells/mm 2 ) were extracted and calculated.

Sensory analysis of baked breads was accomplished after 1 hour of manufacturing by a semi-trained panel (38 panelists consisting of students (male and female) from the High School of Food Industries of Tunisia). The panelists evaluated the sensory properties of the bread samples based on their degree of acceptance (scale of 1-8, with 8 being the highest score). The sensory attributes were discussed with the panelists during the introductory sensory training sessions. Before the sensory evaluation, the loaves were cut into 1.5 cm thick slices and were then served in random order. The elasticity, crust and crumb colors, acidic and salty taste, appearance, volume and crumb aeration were considered as sensory attributes. All sensory evaluation tests were performed in accordance to the ethical and professional guidelines described in the document issued by the Institute of Food Science and Technology (IFST, 2015).

Statistical analysis

All experiments were repeated three times and illustrated as the mean values ± standard deviations. Statistical analyses were performed using the IBM SPSS Statistics software version 23.0. The data were analyzed using one-way analysis of variance (ANOVA), followed by the Duncan's test with the significance level set at p<0.05 to establish the significance of differences between the samples. Pearson correlation analysis was also performed.

Results and discussion

Physico-chemical analysis of sourdough

The values of pH, TTA, the content of sugars (glucose, fructose, and sucrose) and free asparagine in spontaneous and inoculated fermented sourdoughs were determined, as presented in Table 1.

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After 16 h of fermentation, the pH of all sourdough samples had decreased from 6.36 ± 0.06 to 4.03 ± 0.06 in SS -3.55 ± 0.04 in SLb. Moreover, the highest ∆pH (2.81) (p<0.05) was found in the sourdough prepared with L.brevis S12 (SLb), whereas the lowest ∆pH value (2.33) was measured in the spontaneous sourdough (SS). In fact, LAB are recognized to considerably decrease the pH values in sourdoughs, but the variation of pH depends on the LAB strain used (Elsanhoty et al., 2016). According to [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF], adding sourdough to bread could control and notably inhibit spoilage organisms through lowering the pH value during fermentation.

Besides, TTA was significantly (p<0.05) increased after fermentation, from 2.5 mL to 5.2-12.2 mL. The comparison of results highlighted that all sourdoughs inoculated with the selected LAB strains had significantly (p<0.05) higher TTA values than those observed for spontaneous sourdough (SS). Furthermore, a high negative correlation (r = -0.953) between the pH and TTA values was found after fermentation. These findings are in agreement with the results of [START_REF] Mamhoud | Selection of lactic acid bacteria isolated from Tunisian cereals and exploitation of the use as starters for sourdough fermentation[END_REF]. Concerning the analysis of reducing sugars, a significant (p<0.05) increase of their concentration (from 612 ± 38 to 966 ± 21 mg/100g dry weight (d.w.) and from 266 ± 48 to 563 ± 12 mg/100g d.w. for glucose and fructose, respectively) was shown after 16 h of fermentation.

Interestingly, P.pentoseus S14 was the key strain for the formation of reducing sugars at concentrations reaching 1529 mg/100g d.w. after fermentation (74.15%). The use of LAB caused a significant (p<0.05) increase of the glucose concentration (718-966 g/100g d.w.) compared to spontaneous sourdough (529 g/100g d.w.) after fermentation. This observed increase of glucose concentration in sourdough could be related to the degradation of sucrose and starch by cereal amylases and LAB [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF].

Before fermentation, the concentration of sucrose was estimated to be 460 ± 71 mg/100g d.w. After 16 h of fermentation, a significant (p<0.05) decrease of sucrose amount was noticed in sourdoughs, ranging from 413 ± 22 mg/100g d.w. in DSS to 173 ± 5 mg/100g d.w. in SLp). The sharpest decrease of sucrose concentration was recorded in the sourdough inoculated with L.plantarum S28 (62.39%), compared to the results for spontaneous sourdough, which showed only a very weak decrease (9.78%).

The fermentation of dough plays a major role in the control of the acrylamide formation rate related to the presence of asparagine [START_REF] Dastmalchi | The Impact of Lactobacillus plantarum, Paracasei, Casei-Casei, and Sanfranciscensis on Reducing Acrylamide in Wheat Bread[END_REF]. In this context, the content of free asparagine was determined in all sourdough samples before and after fermentation (Table 1) in order to investigate whether the quantity of this amino acid was reduced by fermentation.

Before fermentation, the content of free asparagine was found to be 16.1 ±0.6 mg/100g d.w. Nevertheless, all LAB strains were significantly (p<0.05) able to increase the asparagine content after 16h of fermentation. That

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10 could be explained by the proteolytic activity of the selected starters [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF][START_REF] Mamhoud | Selection of lactic acid bacteria isolated from Tunisian cereals and exploitation of the use as starters for sourdough fermentation[END_REF].

Physico-chemical analysis of dough

The variation of pH, the concentrations of reducing sugars and asparagine in the dough samples were measured after fermentation and are presented in Table 2. The Baker's yeast dough (DBB), which was made without the addition of sourdough, was considered as a control.

The pH values obtained using the selected LAB strains and spontaneous sourdough are reported in Table 2. As expected, the sourdoughs made with the selected LAB strains caused a significantly (p<0.05) more pronounced decrease of pH (4.13-4.68) in comparison to DSS (4.97) and DBB (5.77). [START_REF] Diana | Free amino acids, acrylamide and biogenic amines in gammaaminobutyric acid enriched sourdough and commercial breads[END_REF] reported that the addition of sourdough to the dough formulation resulted in a linear increase in the acidity of the product. These results are consistent with those obtained by [START_REF] Suhr | Effect of weak acid preservatives on growth of bakery product spoilage fungi at different water activities and pH values[END_REF] who attested that the pH value reached 5 using yeast and 4.4 -4.8 using sourdough in the dough formulation.

After 1h 30 min of fermentation, it was noticed that the amount of reducing sugars in the control dough (DBB) was significantly (p<0.05) higher than that of other doughs except for the DLp.

Indeed, the amount of fructose was significantly (p<0.05) higher in DBB (532 ± 11 mg/100g d.w.) compared to the other dough samples (from 230 ± 7 mg/100g d.w. to 326 ± 10 mg/100g d.w.). These results can be explained by the fact that fructose is used as an electron acceptor by LAB and thus is reduced to mannitol (Wisselink et al., 2002).

Sucrose was not detected in any of the analyzed samples. This observation can be explained by several studies that already revealed the presence of a very active invertase enzyme in yeast, which promotes rapid breakdown of sucrose to glucose and fructose [START_REF] Koschwanez | Sucrose utilization in budding yeast as a model for the origin of undifferentiated multicellularity[END_REF].

The concentration of asparagine in dough samples is shown in Table 2. The effects of LAB strains on the amount of asparagine depended on the particular strains. The amount of asparagine is ranged from 9.9 ± 0.4 mg/100g d.w. in DPp to 16 ± 0.9 mg/100g d.w. in DBB, and these values were similar to those reported previously (Wang et al., 2017). A significant decrease (p<0.05) of asparagine content was shown in DSS, DPp, and DPa (14.2 ± 0.2 mg/100g d.w., 9.9 ± 0.4 mg/100g d.w., and 10.5 ± 0.1 mg/100g d.w., respectively), compared to DBB (16 ± 0.9 mg/100g d.w.), which is fermented with yeast only. The results showed that fermentation of wheat dough with LAB reduced the concentration of asparagine. These results are in agreement with those of Wang et al., (2017).

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In addition, [START_REF] Fredriksson | Fermentation Reduces Free Asparagine in Dough and Acrylamide Content in Bread[END_REF] reported that during bread dough fermentation amino acids are assimilated by yeast or LAB and metabolized as a source of nitrogen.

Analysis of acrylamide

All bread samples were evaluated for their acrylamide levels and the results are presented in Figure 1. To better understand the mechanism of acrylamide formation and its relationship to dough fermentation, the physicochemical characteristics and composition of sourdough were assessed.

The concentration of acrylamide in bread samples varied from 5.64 µg/kg to 35.6 µg/kg. The highest acrylamide content was detected in the control bread sample (BBB). According to European Commission, for this type of bread (Wheat based soft bread), the indicative value of acrylamide was estimated to 80 µg/kg (EC, 2013).

However, bread is classified as the main food contributing to the daily ingestion of acrylamide which can cause a public health problem (EFSA, 2011) and Tunisians are big consumers of bread; on average 70 Kg/person/year (Benaours, 2017).

All LAB strains were able to significantly (p<0.05) reduce the acrylamide content of bread. Especially, the P.acidilactici strain S16 allowed to decrease the acrylamide levels by 84.2% (to 5.64 µg/kg) compared to the control bread (35.6 µg/kg). The other LAB strains (L.brevis S12, L.plantarum S28, and P.pentoseus S14) provided significantly (p<0.05) decreased acrylamide levels (reduction by 55.6%, 49.2%, and 39.2%, respectively) compared to the control sample. Thus, the effect of LAB fermentation on acrylamide reduction depended on the particular LAB strain used in sourdough and its adaptability or competition with yeast in the absorption of nutrients [START_REF] Dastmalchi | The Impact of Lactobacillus plantarum, Paracasei, Casei-Casei, and Sanfranciscensis on Reducing Acrylamide in Wheat Bread[END_REF]. [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF] showed that the fermentation with a commercial L.casei strain could reduce the acrylamide content in bread samples by 29.4% on average. In the same way, [START_REF] Baardseth | Lactic Acid Fermentation Reduces Acrylamide Formation and Other Maillard Reactions in French Fries[END_REF] found that LAB could reduce the acrylamide level in French fries by 71% after 120 min of fermentation.

Besides, a significant decrease (p<0.05) of acrylamide content was noticed in bread leavened with spontaneous sourdough. This result was consistent with the findings by [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF] and [START_REF] Forstova | Acrylamide formation in traditional Czech leavened wheat-rye breads and wheat rolls[END_REF].

The concentration of glucose and sucrose in sourdoughs was significantly (p<0.05) slightly correlated to the formation of acrylamide (r = 0.565 and r = -0.617, respectively). These results were in agreement with those of [START_REF] Surdyk | Effects of Asparagine, Fructose, and Baking Conditions on Acrylamide Content in Yeast-Leavened Wheat Bread[END_REF]. Sugars seems to be the most important ingredient that influences the acrylamide formation during baking [START_REF] Baardseth | Lactic Acid Fermentation Reduces Acrylamide Formation and Other Maillard Reactions in French Fries[END_REF][START_REF] Dastmalchi | The Impact of Lactobacillus plantarum, Paracasei, Casei-Casei, and Sanfranciscensis on Reducing Acrylamide in Wheat Bread[END_REF]. Unlike sugars, the asparagine content of sourdoughs did not show a clear correlation with acrylamide concentration.

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12 Numerous studies suggested that lowering pH values by microorganisms is one of the solutions to preventing the Maillard reaction, the main path of acrylamide formation [START_REF] Benarous | Antimicrobial activity of lactic acid bacteria against pathogenic and spoilage microorganism isolated from food and their control in wheat bread[END_REF][START_REF] Keramat | Acrylamide in Foods: Chemistry and Analysis[END_REF][START_REF] Dastmalchi | The Impact of Lactobacillus plantarum, Paracasei, Casei-Casei, and Sanfranciscensis on Reducing Acrylamide in Wheat Bread[END_REF]. The first step in Maillard reaction is the generation of a Schiff base that can form 3aminopropionamide, a precursor of acrylamide [START_REF] Granvogl | Quantitation of 3-Aminopropionamide in PotatoesA Minor but Potent Precursor in Acrylamide Formation[END_REF].

Characteristics of the experimental breads

The color parameters (L*, a*, b*) of crust and crumb obtained from the bread samples are listed in Table 3. As it can be seen, the crust lightness (L*) of inoculated sourdough breads (BLb, BLp, and BPa) was significantly lower (p<0.05) than that of control bread (BBB). Moreover, all sourdoughs inoculated with LAB caused significant changes in the "a*" values of crusts, with BPp showing the lowest value. Statistical analysis indicated that the "L*" and "b*" parameters of crusts correlated positively (r = 0.486 and r = 0.510, respectively, p<0.05) with the acrylamide levels in breads. These results were in agreement with those of [START_REF] Surdyk | Effects of Asparagine, Fructose, and Baking Conditions on Acrylamide Content in Yeast-Leavened Wheat Bread[END_REF]. The crumbs of BLp, BLb, and BPp bread samples had significantly (p<0.05) high values of luminosity (L*) (74.21, 73.85, and 74.49) compared to the BSS sample (70.11). A few differences were registered for the b* and a* parameters of the crumb.

The highest hardness (5149 ± 119 g) was observed for the bread made with yeast only (BBB) (Table 3). The softest breads were those obtained from sourdoughs fermented with P.pentoseus S14 (1815 ± 216 g) and P.acidilactici S16 (2704 ± 42 g). As reported by [START_REF] Dastmalchi | The Impact of Lactobacillus plantarum, Paracasei, Casei-Casei, and Sanfranciscensis on Reducing Acrylamide in Wheat Bread[END_REF], the addition of sourdoughs reduced the firmness of bread, which depended mainly on the acidification level of sourdough.

The crumb structure of breads was evaluated by digital image analysis (Figure 2). According to Table 3, the observed void fraction and cell density were significantly (p<0.05) different from BBB. This finding confirmed that the final characteristics of the breads were influenced by the starter strains and their interactions.

Sensory attributes of breads

The results of the sensory analysis of the experimental breads are shown in Figure 3. The crust color, crumb aeration, and detection of salty or acidic taste were not significantly (p<0.05) affected by the addition of sourdough. Moreover, the appearance of bread samples showed an increasing trend towards average scores when LAB sourdoughs were added. The BPa bread sample had the higher appearance score of 6. 27,compared to BSS and BBB (6.03 and 5.41,respectively). Likewise, the crumb color and the volume attributes increased when sourdoughs were used. Organic acids, alcohols, esters, carbonyl compounds, carbon dioxide, and

Conclusion

In essence, our proposed strategy provides an effective way to reduce acrylamide formation in bread by using selected lactic acid bacteria strains for fermentation of dough. The most pronounced reduction of acrylamide formation (by 84.7%) was obtained in bread made with P.acidilactici strain S16. At the same time, the influence of lactic acid fermentation on the sensory properties of the final bread samples was studied. The obtained results indicate that the incorporation of selected lactic acid bacteria in the bread preparation can improve the texture and flavor of bread. Selected P.acidilactici strains could be potentially developed for further applications in fermented products. Finally, a continued effort is recommended to investigate the effects of other lactic bacteria strains on acrylamide synthesis during the baking of bread. S., Yu, J., Xin, Q., Wang, S., & Copeland, L. (2017). Effects of starch damage and yeast fermentation on acrylamide formation in bread. Food Control, 73(Part B), 230-236. Wisselink, H. ., Weusthuis, R., Eggink, G., Hugenholtz, J., & Grobben, G. (2002). Mannitol production by lactic acid bacteria: A review. International Dairy Journal, 12, 151-161. Yaylayan, V. A., & Stadler, R. H. (2005)

Highlights

• Four lactic acid bacteria were inoculated separately in bread sourdough.

• Incorporation of lactic acid bacteria in bread reduced acrylamide content.

• Acrylamide amount is correlated to sugar concentration in sourdough.

• Incorporation of lactic acid bacteria in bread can improve its texture and flavor.

  was analyzed using the TexCal software. Color parameters (L*, a*, b*) of the crust and crumb parts of bread samples were determined in triplicate by using a CR-300 colorimeter (Minolta, Japan).

  LAB during sourdough fermentation are the probable factors resulting in the improved volume, texture, flavor, and aroma of baked bread samples(Saeed et al., 2014).

Fig. 3 .

 3 Fig. 3. A spider web chart of the sensory analysis data for experimental breads. BSS: bread

  Figure 2.

Table 1 .

 1 . Acrylamide Formation in Food: A Mechanistic Perspective. The physico-chemical parameters and composition of sourdoughs after fermentation for 16 h.

	Journal of

Table 2 .

 2 The pH values and concentrations of glucose, fructose, total reducing sugars and asparagine in different dough samples after 90 min of fermentation.The data are presented as the mean values ± standard errors (n = 3). The mean values followed by the same letter within the column are not significantly different (p<0.05). DSS: dough made with spontaneous sourdough; DLb: dough inoculated with L. brevis S12 sourdough; DLp: dough inoculated with L. plantarum S28 sourdough; DPp: dough inoculated with P. pentoseus S14 sourdough; DPa: dough with P. acidilactici S16 sourdough; DBB: Baker's yeast dough made without the addition of sourdough.

			Glucose	Fructose	Total reducing sugars	Asparagine (mg/100g
	Samples	pH	(mg/100g	(mg/100g	(mg/100 g d.w.)	d.w.)
			d.w.)	d.w.)
	DSS	4.97 ± 0.01 d	826 ± 23 bc	230 ± 7 b	1057± 30 c	14.2 ± 0.2 b
	DLb	4.49 ± 0.02 b	833 ± 20 bc	262 ± 6 c	1096 ± 21 c	15.7 ± 0.2 c
	DLp	4.13 ± 0.04 a	1494 ± 26 d	258 ± 8 c	1752 ± 29 e	14.8 ± 0.4 bc
	DPp	4.52 ± 0.03 c	500 ± 14 a	232 ± 6 b	732 ± 19 a	9.9 ± 0.4 a
	DPa	4.68 ± 0.04 c	471 ± 19 a	326 ± 10 d	797 ± 14 b	10.5 ± 0.1 b
	DBB	5.77 ± 0.09 e	748 ± 31 b	532 ± 11 e	1281 ± 39 d	16 ± 0.9 c

Table 3 .

 3 The characteristics of bread loaves.Data are presented as the mean value ± standard error (n = 3); the mean values followed by the same letter within column are not significantly different (p<0.05); BSS: bread made with spontaneous sourdough but without LAB strains; BLb: bread made with L. brevis S12 sourdough; BLp: bread made with L. plantarum S28 sourdough; BPp: bread made with P. pentoseus S14 sourdough; BPa: bread made with P. acidilactici S16 sourdough; BBB: Baker's yeast bread. Acrylamide content in different bread samples. BSS: bread made by using spontaneous sourdough without LAB strains; BLb: bread made with L. brevis S12 sourdough; BLp: bread made with L. plantarum S28 sourdough; BPp: bread made with P. pentoseus S14 sourdough; BPa: bread made with P. acidilactici S16 sourdough; BBB: Baker's yeast bread. Representative images of the crumb samples from experimental breads (unprocessed digital images (left) and binary images thresholded using the Otsu ImageJ algorithms (right). BSS: bread made by using spontaneous sourdough without LAB strains; BLb: bread made with L. brevis S12 sourdough; BLp: bread made with L. plantarum S28 sourdough; BPp: bread made with P. pentoseus S14 sourdough; BPa: bread made with P. acidilactici S16

	Samples	Crust color L*	a*	b*	Crumb color L*	a*	b*	Hardness (g)	Void fraction (%)	Cell density (cells/mm 2 )
	BLb	60.33 ± 0.47 b 11.25 ± 0.64 c 34.64 ± 0.33 b	73.85 ± 0.41 b	-1.27 ± 0.05 bc 14.13 ± 0.24 a	4338 ± 212 b	35.11 ± 1.5 b	2888.82 ± 254.99 a
	BLp	60.91 ± 0.39 b 10.62 ± 0.33 c 35.23 ± 0.33 b	74.21 ± 0.19 b	-1.01 ± 0.02 cd 15.95 ± 0.49 b	4188 ± 444 b	47.04 ± 0.6 d 4764.22 ± 112.03 cd
	BPp	68.71 ± 0.21 e	5.94 ± 0.05 a	34.42 ± 0.19 b	74.49 ± 0.23 b	-1.64 ± 0.09 a 14.97 ± 0.64 b	1815 ± 216 a	43.99 ± 2.32 d 3949.54 ± 104.56 bc
	Bpa	58.49 ± 0.15 a 10.33 ± 0.37 bc 32.73 ± 0.32 a	71.09 ± 0.43 a	-0.84 ± 0.06 a 14.38 ± 0.2 a	2704 ± 42 a	34.89 ± 1.23 b 3217.14 ± 386.02 ab
	BSS	63.77 ± 0.44 d 9.56 ± 0.05 b	34.91 ± 0.66 b	70.11 ± 0.67 a	-1.14 ± 0.2 cd 13.85 ± 0.07 a	4060 ± 57 b	31.15 ± 0.90 a	5256.74 ± 27.67 d
	BBB	63.09 ± 0.07 d 9.58 ± 0.38 b	35.36 ± 0.11 b	74.89 ± 0.30 b	-1.53 ± 0.1 ab 14.63 ± 0.18 a	5149 ± 119 b	39.57 ± 0.87 c	3831.8 ± 659.82 b

sourdough; BBB: Baker's yeast bread.

Acknowledgements

This work was supported by the Tunisian Ministry of Higher Education and Scientific Research (LR10CBBC02).


W Tomaszewski

P Pieranski
email: pieransk@man.poznan.pl

J.-C Geminard

The motion of the freely falling chain tip

The dynamics of the tip of the falling chain is analyzed. Results of laboratory experiments are presented and compared with results of numerical simulations. Time dependences of the velocity and the acceleration of the chain tip for a number of different initial conformations of the chain are determined. A simple analytical model of the system is also considered.

I. INTRODUCTION

The problem of bodies falling in a gravitational field is so old that it is hard to imagine anything new being added to it. However, the development of numerical simulation methods has a means for the analysis of a few interesting cases, that are difficult to analyze analytically. The dynamics of a falling chain is among them.

A detailed and critical review of the history of the "falling chain" problems, in particular of some erroneous approaches to them, has been given recently by Wong and Yasui [START_REF] Wa | Falling chains[END_REF] . In one case consideration is given to a chain initially gathered in a compact heap located on a table and close to its edge. The motion starts when one of the chain ends is brought over the edge. If one assumes that the chain leaves the heap without friction the model becomes tractable analytically. The surprise is that the acceleration of the chain tip is not, as one would expect, g, but as Sousa and Rodrigues have found g/2 [START_REF] De Sousa | Mass redistribution in variable mass systems[END_REF] . Wong and Yasui confirm the result and rebuke the history of the long lasting erroneous conviction that the acceleration should be equal g/3. They locate the source of the error and propose a fool-proof Lagrangian approach to the falling chain problems concluding that "'Lagrange's method gives definitive answers with unmatched ease, clarity and elegance"'. They indicate at the same time that the method of Sousa and Rodrigues is not reliable since it provides an erroneous solution for the falling folded chain.

In the variation of the falling chain problem considered here, the chain is initially attached at both ends to a horizontal support. Then, as one of the ends is released, the chain begins to fall. The case in which the horizontal separation ∆x between the ends of the chain equals 0, i.e. the chain is tightly folded, has an analytical solution. According to Wong and Yasui, the solution was for the first time presented by Hamel [START_REF] Hamel | Theoretische Mechanik[END_REF] and then repeated by Calkin and March [START_REF] Calkin | The dynamics of a falling chain: I[END_REF] . The analytical result was confirmed both in experimental measurements [START_REF] Calkin | The dynamics of a falling chain: I[END_REF] and numerical simulations [START_REF] Schagerl | On the paradox of the free falling folded chain[END_REF][START_REF] Tomaszewski | Dynamics of ropes and chains. I. The fall of the folded chain[END_REF] . We note that Calkin also considered a different variation of the falling chain problem in which the chain was hanging initially over a smooth horizontal peg and then let to slip down one side [START_REF] Calkin | The dynamics of a falling chain: II[END_REF] . This case in not considered in the present work.

Here, we describe results of experiments analogous to those performed by Calkin and March [START_REF] Calkin | The dynamics of a falling chain: I[END_REF] . In the initial conformation the ends of the chain of length L are located at the same level but their horizontal separation ∆x varies in steps. In the experiments performed by Calkin and March the time was recorded for the tension acting on the support of the fixed end of the chain to reach its maximum value (i.e. the time at which, as they were implicitly assuming, the tip of the chain reaches its lowest position). Moreover, in their study, the largest value of ∆x was around 0.3L. In contrast, for the experiments we performed the largest value of ∆x was 0.999L, and the experimental set-up that we used allowed us to record the entire shape of the consecutive conformations of the falling chain. Analyzing the recorded conformations, we are able to quantitatively extract data concerning the time dependencies of the velocity and acceleration of the chain tip. Calkin and March compared their experimental results with the analytical solution of the ∆x = 0 model. It is clear that the model is not valid for large ∆x. To overcome this difficulty we formulated the complete equations of motion for the chain and we integrated them numerically, arriving at a quantitative comparison between the experimental and numerical results. As we shall demonstrate, the not-studied-before case in which the initial distance between the ends of the chain is very close to L (i.e. when the chain is initially stretched to its maximum length) proves to be very interesting since the vertical motion of the chain tip becomes identical with the motion of a freely falling body. In what follows we shall refer to the latter as the "'free fall"'.

II. THE FALL OF THE TIGHTLY FOLDED CHAIN -ANALYTICAL SOLUTION

To get intuitive insight into what we can expect in the experiments with the falling chain, let us consider first the case ∆x = 0. The complete analysis of this case can be found in the paper by Calkin and March 4 , thus we provide below only its essential assumptions and results. The basic assumption is that the conformations explored by the falling chain can be always considered as consisting of two sections: a) the falling section of length L a , which decreases with time; b) the almost motionless section of length L b , which increases with time. Such a division of the chain is possible when the initial horizontal separation of the chain ends equals zero and the chain consists of infinitely many, short and thin segments.

In this limit the chain can be seen as a tightly folded, perfectly flowing and infinitely thin continuous filament.

Initially both ends of the chain are attached to a point of support O, the vertical position of which y = 0. Then, at time t = 0, one of the ends of the chain is released and the chain begins to fall. Figure 1 presents schematically the geometry of the system. We assume that the chain has a total length of L and that its mass, M , is distributed uniformly along L. To simplify the final analysis of the results, we introduce a new variable h describing the distance of the freely falling tip from its initial position. The h-axis is thus oriented downwards, in the direction of the gravitational field. In what follows, we shall refer to h as the fall distance. By assuming that energy is conserved it can be shown that, the velocity, v c , acceleration, a c , and time, t c , of the chain tip versus the fall distance, h, are given by the following formula:

v c (h) = 1 + L L -h gh, (1)
a c (h) = 1 2 1 + L L -h 2 g, (2)
t c (h) = h 0 L -s gs (2L -s) ds. (3)
Thus, it can be concluded from analyzing the above equations, that both the velocity and the acceleration of the chain tip diverge at time t c (L), when the tip reaches its lowest position, h = L. On the other hand, at small h the velocity and acceleration are approximated with the well known formula describing the dynamics of the free fall:

v b (h) = 2gh, (4)
a b (h) = g, (5)
t b (h) = 2h/g. (6)
As calculated by Calkin and March, time t c (L), at which the tip of the falling folded chain reaches its lowest position, equals

t c (L) = .847213 t b (L) (7)
where t b (L) is the time of the free fall. As clearly shown in Figure 5 of their report, the experimentally established time of the chain fall decays with ∆x agreeing with the theoretically found value only at ∆x ≈ 0.05L. In section VI we shall discuss this result in more detail.

The focus of our experimental study is the dynamics of the falling chain with particular interest in comparing it to the dynamics of a freely falling weight. In order to accentuate the comparison of differences in trajectories for the two cases, we designed an experimental setup that makes it possible to record the simultaneous motions of the two objects.

The ball chain used consists of stainless-steel identical segments which are made from The chain is tightly attached at one end to a firm support O by means of a thin thread, see Figure 2. At the other edge located at point P = (x 0 , y 0 ), the chain ends with a rod (we open and remove the last sphere) to which we attach a thin nylon cord (fishing line, diameter 10 -4 m). The free-falling weight, a sinker (a lead weight used for sinking fishing lines) of mass M = 10 -2 kg, is then attached to the other end of the nylon cord (length about 5 cm). We then extend the nylon cord between two nails and a thin metallic wire (nickel, diameter 10 -4 m) as sketched in Figure 2. The whole system is adjusted so as to insure that the sinker and both ends of the chain are at the same level, y = 0. The setup can be displaced horizontally in order to choose the initial horizontal separation between the two ends of the chain. As the mass of the sinker M is about half the total mass of the chain M , the system is almost always equilibrated (in addition, mechanical equilibrium is further insured by the solid friction in the contact regions of the nylon wire with the nails and the metallic wire). Thus, the initial conformation formed by the chain after damping of all the disturbances, is close to a catenary curve 16 .

Injecting a large electric current (about 1 A) through the nickel wire results in cutting suddenly the nylon wire at the point where they make contact; the sinker and the end of the chain then simultaneously start to fall freely under the action of gravity. We point out that they both fall with a small piece of nylon cord attached to them. However, as the force that pushes the cord against the nails vanishes, the friction force vanishes as soon as the cord is cut. In addition, during the free fall, the sections of cord have no effect on the dynamics as the mass of nylon is negligible in comparison to the mass of the sinker or chain.

The falling chain and weight are imaged with a standard CCD video camera (Panasonic WV-BP550/G) and the images are recorded on a video cassette recorder. The chosen shutter speed (1/4000 s) is adequate for obtaining clear images of both the chain and sinker (Figure 3). The filmed sequences of events are digitized afterward by means of a Macintosh computer equipped with a frame grabber board (Data Translation DT2255). Further analysis with image-processing software (NIH-Image) makes possible to recover 50 images per second from the movies which are initially made from 25 interlaced images per second. The interlacing allows us to double the time resolution but results in a loss in the spatial resolution, which is typically of about 4 mm per pixel.

The positions of both the falling chain tip and the sinker at consecutive times t i , i = 0, 1, 2, ..., are determined from the digitized images. To simplify our discussion of the results, the experimentally determined positions of the falling objects will be given as the vertical distance h, and horizontal distance w which are defined by deviations of their x(t) and y(t)

coordinates from their initial values (x 0 , y 0 ):

w(t) = x 0 -x(t), h(t) = y 0 -y(t), (8)
In what follows we shall refer to the variables as the vertical, h, and horizontal, w, fall distances. According to their definitions, in the initial stages of the falling process both of the falling distances are positive. In all experiments y 0 = 0, while x 0 was varied in four steps from about 1 m to 0.25 m. Note that since the motionless end of the chain is attached to point (0, 0), the initial horizontal separation of the chain ends is ∆x = x 0 . In view of this equality, we denote the initial separation by x 0 . Experimental results are compared to numerical predictions in Section VI.

IV. MODEL OF THE FALLING CHAIN AND ITS EQUATIONS OF MOTION

One can define a few discrete models of the chain; below we present one of them. Its equations of motion will be formulated for the case, in which one of the chain ends is attached to the fixed support while the other one is free. Let us note that similar models have been considered before [START_REF] Schagerl | On the paradox of the free falling folded chain[END_REF][START_REF] Kommers | Notes on the Physics of Fly Casting Simulation[END_REF][START_REF] Galán | The parametrically excited upside-down rod: an elastic jointed pendulum model[END_REF] .

The free end of the chain moves under the action a gravitational field. To simplify the model, we first assume that the chain is constrained to move only in the vertical plane denoted by (x, y). The chain has mass M , length L and consists of n thin cylindrical rods (in the following we shall refer to them as segments) with masses m i = m = M/n, i = 1..n, and lengths l i = l = L/n, i = 1..n. All the segments are considered to be rigid and cannot be deformed. Consecutive segments are connected by joints with friction. Figure 4 shows the geometric representation of our model.

In order to formulate the equations of motion, generalized coordinates, which rigorously determine the state of the system, must be specified. Following our predecessors 8 , we describe the system using angular coordinates indicating the inclination of the consecutive segments with respect to the horizontal x-axis.

The position of the first element is determined by the angle ϕ 1 . Similarly, the position of the second element is described by the angle ϕ 2 , etc... The global conformation of the chain in the plane is uniquely expressed by all angles ϕ i , i = 1..n. The angles are referred to as generalized coordinates of the system.

The Cartesian coordinates of the i-th mass center (x i , y i ) can be written as follows:

x i = i-1 j=1 l cos ϕ j + 1 2 l cos ϕ i , y i = i-1 j=1 l sin ϕ j + 1 2 l sin ϕ i . (9)
Using the generalized coordinates we derive the Lagrange equations of motion and begin by considering the energy of the system. The motion of the chain is considered as a combination of translational and rotational motions of its segments. Each segment has a moment of inertia

I i = 1/12ml 2 , i = 1.
.n, calculated around the axis perpendicular to the (x, y) plane and passing through the center of mass of the segment. Taking into consideration the relations given in Equation ( 9), the kinetic energy of the chain is given by:

T = 1 2 n i=1 m ẋ2 i + ẏ2 i + I i φ2 i , (10)
where, the dot represents the derivative with respect to the time t. The potential energy of the i-th segment is given by mgy i , where g is the gravitational acceleration. Thus, the potential energy of the chain may be expressed as:

U = n i=1 mgy i . (11)
To make our model more general, we introduce damping through Rayleigh dissipation

function 10 : R = 1 2 r n i=1 ( φi -φi-1 ) 2 , (12)
where, r is the dissipation coefficient. We assume that the joint which connects the first element of the chain to the support is free of dissipation. This is equivalent to the assumption that φ0 = φ1 . A similar definition of dissipation was used preciously [START_REF] Schagerl | On the paradox of the free falling folded chain[END_REF][START_REF] Galán | The parametrically excited upside-down rod: an elastic jointed pendulum model[END_REF] .

The motion of the falling chain is governed by the system of Lagrange equations of the second kind:

d dt ∂L ∂ φi - ∂L ∂ϕ i + ∂R ∂ φi = 0, i = 1..n, (13)
where, L = T -U is the Lagrangian of the system. Applying ( 10), ( 11), ( 12) and ( 13) we find the set of n equations describing the motion of a chain:

n j=1 m i,j c i,j φj = - n j=1 m i,j s i,j φ2 j + r ml 2 ( φi-1 -2 φi + φi+1 ) - g l a i c i , i = 1..n, (14)
where, c i = cos(ϕ i ), c i,j = cos(ϕ i -ϕ j ), s i,j = sin(ϕ i -ϕ j ), a i = n -i + 1 2 and

m i,j =    n -i + 1 3 , i = j n -max(i, j) + 1 2 , i = j .
Section V is dedicated to the results of the numerical solutions of Equation (14).

V. NUMERICAL EXPERIMENTS

The equations of motion derived in the previous section can be integrated numerically thus allowing us to simulate the motion of the falling chain. In presence of dissipation, the resulting system of equations becomes stiff and requires specific numerical methods.

We selected the RADAU5 algorithm by Hairer & Wanner (http://www.unige.ch/ ∼ hairer/ software.html) designed for stiff problems. It is based on the implicit Runge-Kutta scheme of order five with the error estimator of order four [START_REF] Hairer | Solving Ordinary Differential Equations II: Stiff and Differentialalgebraic Problems[END_REF] .

Numerical simulations were performed to reproduce results of the experiments described in Section III. Thus, as the initial configuration of the chain, we used the discrete catenary curve shown in Figure 2 with four different separations between the ends of the chain: a)

x The only remaining free parameter was the dissipation parameter r. As such r was used to find the best agreement of the numerical results with the laboratory experiments. To compare the numerical results to the experimental data, we monitored the distance between the positions of the chain tip found in the consecutive frames of the video recordings and the positions found in the numerical simulations at the same times. The deviation between laboratory and numerical data obtained in a single experiment is defined as follows:

δ = 1 N N i=1 (w i -ŵi ) 2 + (h i -ĥi ) 2 , ( 15
)
where the N denotes the number of analyzed frames. Points (w i , h i ) and ( ŵi , ĥi ) for i = 1..N are here the horizontal and vertical deviation from the initial position of the chain tip found in consecutive frames of the laboratory and numerical experiments, respectively. In order to find the optimal value of r providing the best fit for all four experiments a), b), c) and d)

we determined the total distance

∆ = δ (a) + δ (b) + δ (c) + δ (d) . (16)
∆ depends on the chosen value of r; we have investigated its values in the range from r 1 = 0 to r 2 = 10 -4 Nms. The optimal value of dissipation parameter, found with the use of a least-square algorithm based on the SVDFIT procedure [START_REF] Press | Numerical recipes in C: The art of scientific computing[END_REF] , was equal r = 2.163 • 10 -5 Nms.

∆(r) reaches here its minimum value equal 0.02479 m. At the specified above ends of the analyzed range or r the deviation parameter ∆(r) was equal ∆(r 1 ) = 0.029845 m and ∆(r 2 ) = 0.03357 m. Table I provides a summary of how well the data for each of the four experimental cases is fit by the optimal value of r.

Figure 5 provides a further comparison between the numerical simulations and experimental results. Here the time evolution of the vertical, h, and horizontal, w, positions of the tip of the falling chain are reported. One clearly sees an excellent agreement between the simulated and experimental data.

The consecutive conformations of the falling chain found in the numerical simulations are presented in Figure 6. These conformations correspond to the same times at which we recorded the laboratory experiments. In addition, positions of the freely falling body are also shown in the figure. As one can see by comparing Figures 3 and6, the shapes of the experimental and numerical conformations are nearly identical.

VI. QUANTITATIVE ANALYSIS

Quantitative analysis of the digital images recorded in the laboratory experiments provided us with sets of discrete data representing the vertical, h, and horizontal, w, fall distances of the chain tip versus time. Using the data we have found the value of the dissipation parameter at which numerical simulations best fit the experimental data (Table I). As seen in Figure 5 the agreement is very good. Thus, to closely analyze the details of the falling chain dynamics we use the data obtained at small time steps from the numerical simulations.

We begin by analyzing the interesting question concerning the relation between the time dependencies of the vertical fall distances of the chain tip and the falling sinker (Figure 5).

It is worth noticing that in case a), where the initial conformation of the chain is straight and horizontal, the vertical fall of the chain tip and the falling sinker are identical up to the moment in time at which, having reached its maximum vertical fall distance, the tip starts moving upwards. This observation becomes clear when one notices that during the fall the chain end remains horizontal -its vertical motion must thus be identical with the falling sinker. The chain end remains horizontal because the chain displays no elasticity and no energy is stored in bent regions. This phenomenon, found both in the laboratory experiments and confirmed by the numerical simulations, suggests the existence of an approximate analytical treatment of the problem. However, we have thus far not been able to formulate an analytical solution.

In cases b), c) and d) the vertical fall distance of the chain tip, up to the moment of time t hmax at which the vertical fall distance of the chain tip reaches its maximum value h max , is seen to be always ahead of the vertical fall distance of the sinker. This observation is sometimes summarized by the general statement, that the chain falls faster than a body.

To further understand this we analyze the time dependencies of the velocity v c and the acceleration a c of the chain tip. In order to do so we have performed a series of numerical experiments with x 0 in the range of [0.1, . . . , 1.02) m. All other parameters of the numerical simulation were the same as defined in the previous section. The smallest value of the initial separation x 0 was equal to 0.1 m due to the fact that smaller initial separations produced very complex chain-fall dynamics. This fact was seen in both numerical simulations and laboratory experiments. We also note that, by velocity and acceleration we mean here the moduli of the velocity and acceleration vectors.

Figure 7 presents plots of both the velocity and the acceleration versus time for four initial spacings x 0 . Two characteristic features in these plots are the peak heights and the times at which these maxima occur. In Figure 8a, the dependence of v max on x 0 and v hmax (i.e. the velocity of the chain tip at its lowest position h max ) on x 0 is displayed. At small x 0 there exists a short interval within which v max slightly increases reaching its global maximum at

x 0 ≈ 0.1314 m. Then, over a broad interval, v max decreases reaching its global minimum value at x 0 ≈ 0.9040 m. Up to this value of x 0 , the velocity v hmax is smaller than the maximum velocity v max . For x 0 > 0.9040 m, when the maximum extension of the chain is approached, the two velocities become practically equal.

As Figure 9a reveals, the time t vmax , at which the velocity of the chain tip reaches its maximum value, precedes in general the moment of time t hmax at which the chain tip reaches its lowest position h max . The lowest position of the chain tip is reached fastest for x 0 ≈ 0.5500 m (i.e. when the initial horizontal distance between the chain ends is approximately half of its total length), while t hmax is longest when the chain is initially straight. Figure 9a provides also a comparison between the time t vmax of the maximum velocity and the time t c (L) of the velocity divergence found in the analytically solvable model presented in Section II. As seen in the figure, the two times are close to each other at the values of x 0 at which v max reaches its global maximum and minimum. In the whole range of x 0 located between the two values, t vmax is less than t c (L).

Figure 9b provides the relation between the maximum fall distance of the chain tip, h max , and the fall distance, h vmax , at which the tip reaches its maximum velocity as a function of the initial separation of the chain ends. As before one can clearly see that in general the maximum velocity is reached before the chain tip reaches its maximum fall distance. Let us note that in the whole studied range of x 0 the maximum fall distance never reaches the theoretically possible value L, although as the plot of h max vs. x 0 suggests, it tends to it at

x 0 → 0.

The last question we have addressed concerning the velocity data is the correlation between the value of the peak velocity, v max , and the time, t vmax , at which it is reached. As we have demonstrated before, the peak of the velocity is highest at a small initial separation of the chain ends, but one should not draw the conclusion that it is thus reached in the shortest time. As seen in Figure 9a the initial separation of the chain ends at which the velocity peak is reached fastest amounts to about x 0 ≈ 0.7000 m.

Figure 7b presents plots of the acceleration of the chain tip versus time for a few values of the initial separation x 0 . As in the case of the velocity plots, we also observe here distinct peaks. Figure 8b demonstrates clearly, that the highest peak in acceleration is observed at the smallest initial separation of the chain end. Its value, at the experimentally studied case of x 0 = 0.255 m, amounts to 7352 m/s 2 , thus it is about 40 times larger than the value observed at x 0 = 0.765 m, where it equals to 186.3 m/s 2 . That such large values of the acceleration are realistic was demonstrated by Krehl et. al. [START_REF] Krehl | The puzzle of whip cracking-uncovered by a corre-14 T. McMillen and A. Goriely. Shape of a Cracking Whip[END_REF] who studied the dynamics of the cracking whip. One may ask about the relation between the dynamics of the falling chain and that of the whip 14,15 . At the first sight the two systems seem to be completely different since in the cracking whip problem the gravitational forces are in general neglected. Let us notice, however, that the end of the folded whip attached to the whip handle is subject to a strong acceleration. Changing the laboratory reference frame to the non-inertial frame moving with the end of the handle, we introduce into the system strong inertial forces equivalent to the gravitational ones. Thus, all conclusions to which we arrived considering the falling chain are applicable also in the case of the accelerated whip. In particular, it becomes clear that there exists a special conformation, to which the whip should be brought before its handle starts accelerating, for which the whip tip will eventually reach the maximum, exceeding the speed of sound velocity, thus allowing one to produce the crack sound.

The last question we considered analyzing results of the laboratory and numerical experiment was if the acceleration a hmax which the chain tip reaches at its lowest position h max is the maximum acceleration a max . Figure 8b demonstrates that this is not generally the case.

VII. SUMMARY AND DISCUSSION

The experimental and numerical work here reveals new and interesting facts concerning the dynamics of the falling chain. Let us summarize them.

1. The dependencies of both the velocity and acceleration on time display distinct peaks the height of which depends on the initial separation of the chain ends. The highest peaks are observed for small initial separations. There exists an approximate, analytical description of tightly folded chain dynamics explaining the origin of the rapid increase of the velocity and acceleration. The theory is however unable to predict the finite height of the peaks. (In the analytical model both the velocity and the acceleration diverge.)

2. For our case, the velocity peak is highest at x 0 = 0.1288 L, whereas its amplitude is smallest for x 0 = 0.8863 L.

3. Quite fascinating, we find that in the case for which the initial separation of the chain ends is largest, the dynamics of the vertical fall of the chain tip proves to be identical with the dynamics of the free fall. This corresponds with the fact that the end section of the chain remains horizontal during the fall. This observation suggests the existence of an approximate analytical treatment.

4. As a rule, the time at which the chain tip reaches its maximum velocity generally comes before the time at which it reaches its lowest vertical position. Only at the initial separation of the chain ends larger than 0.8863 L we find otherwise.

5.

The ratio of the amplitudes of the highest and smallest acceleration peaks is about 166.5, which is unexpectedly large. This may have some practical implications, since at the time when the acceleration reaches its highest value, the force acting on the chain tip also becomes very large and may lead to damage of the chain.

Dynamics of the falling chain hides certainly a few more interesting details. The same, even to a larger extent, concerns the dynamics of the falling rope, since in this case the dissipation plays a much more important role and elasticity becomes a crucial factor.

formed in the experiments with chains built from a finite number of segments is not a catenary curve. That this is the case one can see immediately considering the conformation of a chain built from an odd number of segments whose ends are fixed to points located at the same level and separated in the horizontal direction by the length of a single segment. In such a case the initial conformation consists of two exactly vertical pieces. This was the conformation used by

  rods and spheres attached to each other, see Figure 2. The total length of a segment l = (4.46 ± 0.01)10 -3 m and the diameter of the spheres are φ = (3.26 ± 0.01)10 -3 m. In addition, the minimum radius of curvature for which the chain can exist without loading any elastic energy is R min = (4.8 ± 0.2) 10 -3 m. We use a chain of length L = 1.022 m, which corresponds to n = 229 segments for a total mass of M = (2.08 ± 0.01)10 -2 kg.

  0 = 1.019 m, b) x 0 = 0.765 m, c) x 0 = 0.510 m and d) x 0 = 0.255 m identical to the separations used in the laboratory experiments. These simulations were carried out for a chain with n = 229, L = 1.02 m, M = 0.0208 kg, g = 9.81 m/s 2 and time t ∈ [0, 0.5] s.

FIG. 1 :FIG. 3 :FIG. 5 :FIG. 6 :

 1356 FIG. 1: Geometry of the conformation of the tightly folded chain at time t > 0. The position of the falling chain is described in terms of h. Section a) of the chain is falling down while section b) is motionless; c a and c b are their centers of mass.

FIG. 7 :FIG. 8 :FIG. 9 :

 789 FIG. 7: Time evolution of the numerically determined moduli of the velocity and the acceleration of the falling chain tip. Initial separation of the chain ends: a) x 0 = 1.0195 m, b) x 0 = 0.765 m, c) x 0 = 0.51 m, d) x 0 = 0.255 m. r = 2.163 • 10 -5 Nms.

TABLE I :

 I Deviation between experimental and numerical results, δ r for three different values of the dissipation parameter r = 0, 2.163 • 10 -5 and 10 -4 [m].

	Tables
	Experiment: δ 0 [m] δ 2.163•10 -5 [m] δ 10 -4 [m]
	a)	0.008406	0.007672	0.01038
	b)	0.006851	0.006654	0.00659
	c)	0.006191	0.005912	0.00669
	Schagerl in his laboratory experiments 5 d) 0.008397	0.004552	0.00991

Acknowledgment

The authors would like to thank S. Breiter for helpful discussions and V. Bergeron for his critical reading of the manuscript.


Daria V Berdnikova
email: berdnikova@chemie-bio.uni-siegen.de

Yuri V Fedorov

A Fedorova

Gediminas Jonusauskas

Оlga A Fedorova

Supramolecular tuning of energy transfer efficiency and direction in a bis(styryl) dye-crown ether conjugate

Keywords:

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Photoinduced resonance energy transfer (FRET) is one of the basic processes in Nature that ensures photosynthetic conversion of the solar energy into chemical bonds in living organisms [START_REF] Hader | General photobiology[END_REF]. In artificial sys tems, photoinduced energy transfer is widely used in solar energy harvesting elements, ratiometric sensors, and organic photovoltaics [2 6]. Most of these applications require a stringent control of the FRET rate, efficiency and, especially, the direction. Along these lines, it is highly desirable that the direction of the energy transfer can be swit ched on demand. For example, such switching has been realized by changing the complexed metal cations in homo and heterodimers of metalloporphyrins [7], metallocyclodextrin assemblies [8] and [START_REF] Kundu | [END_REF] ca tenates incorporating the [Ru(tpy) 2 ] 2+ fragment [9]. The control of the FRET direction can be also accomplished by protonation/deprotonation of the donor or acceptor unit as has been shown for oligophenylene vinylene (OPV) phenanthroline [10] and OPV fullerene [11] dyads and for multichromophoric BODIPY systems [12,13]. In addition, sev eral intriguing examples of switchable FRET directions have been re ported that use site specific solvent effects [14], temperature changes [15] or the electronic difference between cation binding sites [16,17]. Nevertheless, molecules or molecule assemblies that enable the fine regulation of the energy transfer processes based on supramolecular interactions are still rare and their discovery and development remains a topical challenge.

Herein, we present a dye crown ether conjugate whose energy transfer efficiency and direction is controlled by supramolecular com plexation and protonation. The system is based on a novel bischromo phoric styryl derivative 1 that is functionalized with benzo 15 crown 5 and azadithia 15 crown 5 ether units (Chart 1). Owing to the different affinity of the crown ether fragments towards metal ions or protons, the optical properties of each chromophore can be varied independently by introduction of appropriate metal cations or protonation, thus enabling the control of the energy transfer properties.

Results and discussion

Synthesis of bis(styryl) dye 1

The bis(styryl) dye 1 was obtained in 42% yield by condensation of the corresponding formylbenzocrown derivatives with γ picoline and subsequent quaternization of the intermediate styryl(pyridine) species with 1,4 bis(bromomethyl)benzene (for details see ESI, Section 1). The parent monochromophoric dyes 2 and 3 were synthesized according to published protocols [18,19].

Steady state optical spectroscopy

The absorption spectrum of bis(styryl) dye 1 exhibits two long wavelength absorption bands centered at 420 and 486 nm (Fig. 1, Table 1). Comparison with the absorption spectra of the related monochromophoric dyes 2 (λ abs = 395 nm) [18] and 3 (λ abs = 474 nm) [19] in acetonitrile, respectively (Figs. S3 and S4, ESI), allowed to as sign the band at 420 nm to the benzocrown substituted styryl chro mophore of dye 1 and the band at 486 nm to the azadithiacrown sub stituted one. For the sake of clarity, the benzocrown functionalized chromophore will be referred to as the O chromophore and the aza dithiacrown functionalized one as the N chromophore, to indicate that the respective electron donating heteroatom of the crown ether, that is directly conjugated with the styryl(pyridinium) fragment, determines the photophysical properties of the chromophore.

Complexation of the crown ether functionalities of dye 1 with metal cations leads to a blue shift of the corresponding absorption bands. It is known that oxacrown ethers have a high affinity to alkali and alkali earth metal ions [20], whereas the introduction of N or/and S atoms leads to higher affinity towards transition metal ions [21]. Based on this difference, the attachment of different crown ethers with diverse het eroatom substitution to the two chromophoric parts of 1 enables the independent regulation of the optical properties of each chromophore by complexation with appropriate cations. For the present study, we have selected Mg 2+ and Hg 2+ cations as they have the most effective interaction with the corresponding crown ethers [22,23]. The metal cations were used as perchlorate salts. To avoid introduction of dif ferent anions that may potentially influence complexation, we used perchloric acid for protonation of the azadithiacrown ether residue.

Addition of Mg(ClO 4 ) 2 to a solution of 1 results in a blue shift (Δλ = 52 nm) of the O chromophore absorption whereas the N chro mophore absorption remains unaffected (Fig. 1A, Table 1). Conversely, the introduction of Hg(ClO 4 ) 2 and HClO 4 causes a blue shift of the N chromophore absorption (Hg(ClO 4 ) 2 : Δλ = 124 nm; HClO 4 : Δλ = 148 nm) without significant changes of the O chromophore ab sorption (Fig. 1B andC, Table 1). The stability constants of the com plexes of 1 were obtained from the spectrophotometric titration data (Figs. S1 andS2, ESI) and are collected in Table 1.

According to the classical description of the Förster resonance en ergy transfer (FRET), an efficient energy transfer requires a spectral overlap between the emission of the donor and the absorption of the acceptor chromophores [START_REF] Van Der Meer | Resonance energy transfer: theory and data[END_REF][START_REF] Lakowicz | Principles of fluorescent spectroscopy[END_REF]. To estimate the potential for an intramolecular energy transfer in dye 1 and its complexes, the optical characteristics of each chromophore were assessed separately with parent monochromophoric dyes 2 and 3 and their complexes with Mg 2+ , Hg 2+ and H + . The fluorescence of 2 overlaps significantly with the absorption of 3 (Fig. 2A). Therefore, within the bischromophoric dye 1, the O chromophore may act as an energy donor (ED), whereas the N chromophore is an energy acceptor (EA). The blue shift of the fluorescence of 2 upon complexation with Mg 2+ provides more pro nounced spectral overlap between the fluorescence of the O chromo phore (ED) and the absorption of the N chromophore (EA) (Fig. 2B), thus favoring energy transfer in complex 1 Mg 2+ . At the same time, the absorption and fluorescence spectra of dye 2 and complex 3 Hg 2+ do not overlap so that an energy transfer is not feasible in the complex of dye 1 with Hg 2+ (Fig. S5,ESI). Protonation of dye 3 results in a suf ficient spectral overlap of the fluorescence of 3 H + and the absorption of 2 which leads to a reversal of the donor and acceptor functions of the chromophores in the energy transfer process (Fig. 2C). Thus, in the bischromophoric system 1 H + the protonated N chromophore acts as energy donor and the O chromophore as energy acceptor.

Theoretical calculation of the energy transfer efficiency

To estimate the efficiency of the energy transfer in 1 and its com plexes 1 Mg 2+ and 1 H + , we performed calculations according to Förster resonance theory (for details seeESI, Section 5) [START_REF] Lakowicz | Principles of fluorescent spectroscopy[END_REF]. Taking into account the crucial influence of the interchromophoric distance on FRET efficiency, on one side, and high conformational lability of 1, on the other side, we considered two extreme conformations of dye 1 with maximally close and maximally remote mutual positions of the chro mophores (Fig. S11,ESI). After geometry optimization (MOPAC 2016, PM7), the corresponding interchromophoric distances were determined as r max = 15 Å and r min = 9 Å. Based on these values, we obtained the following theoretical intervals of the FRET efficiencies Φ FRET (th): 97.4 99.9% for 1, 93.7 99.7% for 1 Mg 2+ and 42.8 94.1% for 1 H + . Therefore, the expected FRET efficiencies in the studied species in most cases are very high. At the same time, the pronounced difference in the theoretical values Φ FRET (th) for two extreme conformations of complex 1 H + arises from the relatively small value of the Förster radius R 0 = 14 Å, i.e. the distance at which the energy transfer efficiency is 50% [START_REF] Lakowicz | Principles of fluorescent spectroscopy[END_REF], for this complex in comparison to 1 and complex 1 Mg 2+ (Table S1, ESI). For 1 H + , r max = 15 Å that is larger than R 0 which leads to the drastic decrease of the estimated FRET efficiency for the corre sponding conformation.

Time resolved fluorescence spectroscopy

The emission properties of 1 and its complexes 1 Mg 2+ and 1 H + were studied by steady state and time resolved fluorescence spectro scopy. Upon excitation of dye 1 in the O chromophore absorption band, emission of both chromophores was detected in the steady state and time resolved fluorescence spectra (Fig. 3A; Fig. S6,ESI). This result indicates that for a part of the excited molecules, energy transfer from the O chromophore to the N chromophore does not occur.

Since two different excited states are formed upon photoexcitation of dye 1, its relaxation should follow two main pathways. Thus, for a part of the molecules the excited state relaxation occurs through emission of the N chromophore that is either excited directly or in directly by energy transfer from the excited O chromophore. For the remaining molecules with the excited O chromophore, energy transfer does not occur and the system relaxes according to the deactivating pathways of the O chromophore. The resulting fluorescence lifetimes support this assumption (Fig. 4A). The fast component of the decay kinetics belongs to the relaxation of the N chromophore through the formation of TICT states due to the rotation around the single bond in the CH PhN fragment [26], as supported by close τ 1 values for dye 1 and parent monochromophoric dye 3 (Table 2). The slow component of the kinetics represents an averaged value of both decay times of the O chromophore as compared with the τ values of the parent mono chromophoric dye 2 (Table 2).

Due to the significant blue shift of the Mg 2+ bound O chromophore absorption (ED), the donor can be excited selectively at 350 nm because the N chromophore (EA) has almost no absorption at this wavelength (Fig. S4,ESI). As can be seen from the steady state and time resolved fluorescence spectra (Fig. 3B; Fig. S7,ESI), the excitation of the com plex 1 Mg 2+ at 350 nm leads only to one fluorescence band centered at 620 nm that corresponds to the emission of the N chromophore (EA), which indicates the occurrence of an efficient energy transfer from the Mg 2+ complexed O chromophore (ED) to the N chromophore (EA). Accordingly, the fast component of the decay kinetics of 1 Mg 2+ is assigned to the emission of the N chromophore (EA) through TICT states as in the parent dye 3 (Fig. 4B, Table 2). The residual long lived second component belongs to the trace amount of non complexed O chromophore due to relatively low stability constant of complex 1 Mg 2+ .

In the case of protonated dye 1 Н + the donor and acceptor functions of the chromophores are reversed in the energy transfer process, namely, the protonated N chromophore acts as ED and the O chromo phore becomes EA. Accordingly, excitation of complex 1 H + at 350 nm results in only one fluorescence band in the region of 560 nm that be longs to the emission of O chromophore (EA) (Fig. 3C; Fig. S8,ESI). The fluorescence decay curve of 1-H + is biexponential (Fig. 4C) which is typical for the relaxation of the O chromophore (cf. τ values for com pound 2, Table 2). The fast component is assigned to the relaxation through TICT states, whereas the slow component corresponds to the E Z isomerization [START_REF] Marmois | Étude photophysique de nouveaux systemes moleculaires fonctionnels bases sur les styrylpyridines L'Universite Bordeaux[END_REF].

To obtain the experimental values of the FRET efficiencies, the rate of the energy transfer process in 1 and its complexes 1 Mg 2+ and 1 H + was determined with ultrafast transient absorption spectroscopy (TRABS). Representative results from TRABS experiments in the case of energy transfer towards the N chromophore (free 1, complex 1 Mg 2+ ) are displayed in Fig. 5A taking 1 Mg 2+ as example. There are three main processes occurring after the pump pulse: i) absorption of the dimethylaniline cation radical at about 450 nm [START_REF] Shida | [END_REF], ii) ground state bleaching of the N chromophore at the region of 500 nm, and iii) sti mulated emission of the N chromophore at about 620 nm (Fig. 5A; Fig. S9,ESI). The time dependent red shift of the stimulated emission maximum arises from the dynamic solvent relaxation that reflects the rearrangement of the solvent molecules around the excited chromo phore, whose polarity changes in comparison to the ground state due to the photoinduced intramolecular charge transfer (ICT). In the case of energy transfer towards the O chromophore (protonated dye 1 H + ), two processes are observed on a TRABS map, namely: i) absorption of the isomeric dimethoxybenzene cation radicals at 450 nm [29] and ii) stimulated emission of the O chromophore at the region of 550 nm (Fig. 5B).

Analysis of the TRABS data allowed to determine the energy transfer time constants τ FRET (Table 2; Fig. S10,ESI). For free dye 1 and its complex 1 Mg 2+ , τ FRET data were obtained from the ground state bleaching kinetics of the energy acceptor (N chromophore) at 500 nm and 505 nm, respectively (Figs. S10A andS10B, ESI). For the proto nated form 1 H + , τ FRET was determined from the kinetics of develop ment of the stimulated emission band of the energy acceptor (O chro mophore) at 525 nm (Fig. S10C,ESI). Experimental energy transfer efficiencies Φ FRET (exp) were calculated from the τ FRET values according to Equation (1).

= - ⋅ Φ τ τ (1 / ) 100% FRET FRET 0 (1)
In equation ( 1), τ FRET is energy transfer time constant obtained from the TRABS experiment, τ 0 is excited state lifetime of the energy donor in the absence of the energy acceptor.

In free dye 1, the energy donor is the O chromophore, whose excited state lifetime of τ 0 = 650 ps was determined from the fluorescence decay kinetics of dye 2 that contains the isolated O chromophore [START_REF] Marmois | Étude photophysique de nouveaux systemes moleculaires fonctionnels bases sur les styrylpyridines L'Universite Bordeaux[END_REF].

In the case of complex 1 Mg 2+ , we considered the reported lifetime of τ 0 = 70 ps of the magnesium complex of dye 2 [START_REF] Marmois | Étude photophysique de nouveaux systemes moleculaires fonctionnels bases sur les styrylpyridines L'Universite Bordeaux[END_REF]. For the protonated form 1 H + , in which the energy donor is the protonated N chromo phore, the lifetime of τ 0 ∼ 5 ps was estimated tentatively from the fluorescence decay kinetics of the protonated dye 3 H + that contains the isolated N chromophore [19]. As can be seen from Table 2, the experimental FRET efficiencies Φ FRET (exp) in the studied systems are very high and in the case of free dye 1 and the complex 1 Mg 2+ exceed 99%.

Based on the previous discussion, the reasons for the incomplete energy transfer in dye 1 still need to be explained. As was shown, the evaluation of both theoretical and experimental data revealed a > 99% FRET efficiency for 1. At the same time, clear presence of the fluores cence of energy donor (O chromophore) at the region of 560 nm (Fig. 3A; Fig. S6,ESI) indicates that some of the excited molecules of 1 are not involved in the FRET process. Since the relative orientation of the dipole transition moments of the ED and the EA significantly in fluences the efficiency of the FRET [START_REF] Van Der Meer | Resonance energy transfer: theory and data[END_REF], we assume that energy transfer in 1 cannot be realized partially for geometrical reasons. In theoretical calculations, we considered the random orientation of the chromo phores in 1 due to the high conformational flexibility of the xylylene spacer (for details see ESI, Section 6). This flexibility, however, is true only for the isolated molecules of 1 in solution. At the same time, it is known that charged styryl dyes readily undergo dipole dipole ag gregation due to the highly polar character of the chromophores [30]. Considering the significantly restricted freedom of movement of the aggregated molecules, it is tempting to assume that the aggregation locks some dye molecules in a geometry that is unfavorable for energy transfer.

To provide evidence for the aggregation, we analyzed the absorp tion spectra of dye 1 and an equimolar mixture of the parent dyes 2 and 3 (Fig. 6). Hence, deconvolution of the spectrum of the monomeric dyes mixture with Gaussian shaped absorption bands gave two components at about 21000 and 25000 cm -1 corresponding to the absorption spectra of the individual chromophores (Fig. 6A). Deconvolution of the spectrum of bischromophoric dye 1 showed the presence of the same bands as in the case of the monomeric dyes mixture and additionally revealed the third component at about 19500 cm -1 (Fig. 6B). This new band is shifted to the lower energy region that is indicative of the formation of J type aggregates [31]. The detailed investigation of the aggregation pattern, however, falls beyond the scope of the present manuscript.

As a result, the spectral analysis supports the aggregation of 1 that is proposed to be a likely reason for incomplete energy transfer due to geometrical reasons. At the same time, for non aggregated molecules of 1 the efficiency of FRET is close to 100% as indicated by experimentally obtained energy transfer efficiencies Φ FRET (exp) and additionally supported by the theoretical calculations (Table 2). Unlike dye 1, the complexes 1 Mg 2+ and 1 H + show no fluorescence of the ED (Fig. 3B andC) which is in agreement with both theoretical and experimental Φ FRET values (Table 2). We explain this observation by dissociation of the aggregates upon complexation due to the decrease of the dipole moments of complexed chromophores and the increase of the overall positive charge of the molecules resulting in the electrostatic repulsion between aggregated molecules.

Conclusions

To sum up, we have designed and synthesized the novel bis(styryl) dye 1 bearing benzo 15 crown 5 and azadithia 15 crown 5 functional ities. In the free state, dye 1 undergoes efficient intramolecular energy transfer whereas upon aggregation of 1 the FRET process is partially blocked. Complexation of Mg 2+ , Hg 2+ cations and protonation allow independent manipulation of the optical properties of each chromo phore within a single dye molecule, thus enabling the regulation of the FRET parameters in 1 by supramolecular complexation. Interestingly, binding of 1 with Hg 2+ cations results in drastic decrease of the FRET efficiency, whereas interaction with Mg 2+ and H + has just slight in fluence on this parameter. Notably, complexation with Mg 2+ does not change the energy transfer direction in comparison to free dye 1, whereas protonation results in the reversion of the direction of FRET relative to the molecular structure.

Experimental section

All reagents and solvents were obtained from commercial sources and used as received. 1 H NMR spectra were recorded at 300 or 600 MHz, 13 C NMR spectra were recorded at 150 MHz at ambient temperature using 5 mm tubes. Chemical shifts were determined with accuracy of 0.01 ppm and 0.1 ppm for 1 H and 13 C spectra, respectively, and are given relative to the residual signal of the solvent that was used as internal reference. Spin spin coupling constants for the proton spectra were determined with accuracy of 0.2 Hz. The proton NMR signal assignments were performed using COSY and NOESY 2D NMR techniques. The carbon NMR signal assignments were performed by means of HSQC and HMBC 2D NMR techniques. Electrospray ionization (ESI) mass spectra were detected in the mode of full mass scanning of positive ions on a tandem dynamic mass spectrometer equipped with a mass analyzer with an octapole ionic trap. High resolution mass spectra were recorded on a time of flight instrument in a positive ion mode using electrospray ionization method. Elemental analysis was per formed at the Laboratory of Microanalysis of A. N. Nesmeyanov Institute of Organoelement Compounds of RAS, Moscow, Russia. Electronic absorption spectra were measured on Varian Cary 100 spectrophotometer. Fluorescence spectra were recorded on a Fluorolog 3 spectrofluorometer. All measurements were carried out in conven tional quartz cells of 10 mm pathlength at 20 °C. Preparation and handling of the solutions were carried out under red light.

Time resolved optical experiments were based on a femtosecond 1 kHz Ti:Sapphire system producing 30 fs, 0.8 mJ laser pulses centered at 800 nm (Femtopower Compact Pro) coupled with an optical para metric generator (Light Conversion Topas C) and frequency mixers to excite samples at the maximum of the steady state absorption band. In the case of the time resolved fluorescence measurements, the fluores cence emitted by a sample in the forward direction was collected by reflective optics and focused with a spherical mirror onto the input slit of a spectrograph (Chromex 250) coupled to a streak camera (Hamamatsu 5680) equipped with a fast single sweep unit M5676, temporal resolution 2 ps. The convolution of a rectangular streak camera slit in the sweep range of 250 ps with an electronic jitter of the streak camera trigger pulse provided a Gaussian (over 4 decades) temporal apparatus function with a FWHM of 20 ps (for more details see ESI, Section 4.1). For the TRABS experiments, white light con tinuum (360 nm 1000 nm) pulses generated in a 2 mm D 2 O cell were used as the probe. The variable delay time between excitation and probe pulses was obtained using a delay line with 0.66 fs resolution. The solutions were placed in a 2 mm circulating cell. White light signal and reference spectra were recorded using a two channel fibre spec trometer (Avantes Avaspec 2048 2). A home written acquisition and experiment control program in LabVIEW made it possible to record transient spectra with an average error less than 10 -3 of optical density for all wavelengths. The temporal resolution of the set up was better than 50 fs (for more details see ESI, Section 4.2).

Note

Authors declare no competing financial interests.

Chart 1 .

 1 Chemical structures of styryl dyes 1-3.

Fig. 1 .

 1 Fig. 1. Absorption spectra of 1 (black), (A) complex 1-Mg 2+ (red) with the Mg 2+ cation bound to the benzocrown ether residue; (B) complex 1-Hg 2+ (blue) with the Hg 2+ cation bound to the azadithia-crown ether residue; (C) protonated form 1-H + (cyan) with a proton bound to the crown ether nitrogen. In all cases c = 20 μM, in acetonitrile, T = 20 °C. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 2 .Fig. 3 .

 23 Fig. 2. Spectral overlap (grey area) between (A) the normalized fluorescence spectrum of 2 (red, ED) and normalized absorption spectrum of 3 (blue, EA); (B) the normalized fluorescence spectrum of 2-Mg 2+ (red, ED) and normalized absorption spectrum of 3 (blue, EA); (C) the normalized fluorescence spectrum of 3-H + (red, ED) and normalized absorption spectrum of 2 (blue, EA) in acetonitrile. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4 .

 4 Fig. 4. Fluorescence decay curves in acetonitrile: (A) 1, λ ex = 400 nm, λ obs = 580 nm; (B) 1-Mg 2+ , λ ex = 350 nm, λ obs = 620 nm; and (C) 1-H + , λ ex = 350 nm, λ obs = 550 nm; experimental data: empty circles, fitting curve: red line. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5 .

 5 Fig. 5. Time-resolved TRABS maps for (A) 1-Mg 2+ and (B) 1-H + , λ ex = 345 nm, acetonitrile.

Fig. 6 .

 6 Fig. 6. (A) Absorption spectrum of the equimolar mixture of monomeric dyes 2 and 3 (black, for each dye c = 20 μM) and its deconvolution: blue line corresponds to the O-chromophore, red line corresponds to the N-chromophore. (B) Absorption spectrum of bischromophoric dye 1 (black, c = 20 μM) and its deconvolution: blue line corresponds to the O-chromophore, red line corresponds to the N-chromophore, and cyan line represents the absorption of the aggregates. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1

 1 Optical properties and stability constants of 1 and its complexes in acetonitrile.

	Compound	λ abs , nm	ε × 10 4 ,	log K
			L mol 1 cm 1
	1	420, 486	3.27, 3.63	-
	1-Mg 2+	368, 486	3.12, 3.71	3.27 ± 0.03
	1-Hg 2+	373, 393	3.37, 3.43	> 7 a
	1-Н +	404, 338	3.96, 3.07	3.38 ± 0.01

a The value is too high to be determined from spectrophotometric titration.

Table 2

 2 Fluorescence lifetimes τ, energy transfer time constants τ FRET , theoretical Φ FRET (th) and experimental Φ FRET (exp) energy transfer efficiencies for dye 1, its complexes 1-Mg 2+ and 1-H + in acetonitrile. Fluorescence lifetimes τ for dyes 2 and 3 in acetonitrile.

	Compound	τ, ps	τ FRET , ps	Φ FRET (th), %	Φ FRET (exp), %
	1	120, 480	0.150	97.4-99.9	100.0
	1-Mg 2+	130, 520	0.150	93.7-99.7	99.8
	1-H +	220, 520	0.220	42.8-94.1	95.6
	2	310, 650 a	-	-	-
	3	100, 230 b	-	-	-

a Data from Ref.

[START_REF] Marmois | Étude photophysique de nouveaux systemes moleculaires fonctionnels bases sur les styrylpyridines L'Universite Bordeaux[END_REF]

. b Data from Ref.

[19]

.

Acknowledgements

This work was supported by RFBR (project 15 03 04705) and the Russian Science Foundation (project 16 13 10226). The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.0008). We thank Prof. Dr. Heiko Ihmels (Universität Siegen, Germany) for his kind assistance with the preparation of the manuscript.