Ngoc-Ly Hoang

Antonin Landolfi

Anastasiya Kravchuk

Etienne Girard

Jonathan Peate

Javier Matias Hernandez

Marianne Gaborieau

Olena Kravchuk

Robert G Gilbert

Yohann Guillaneuf

Javier M Hernandez

Patrice Castignolles
email: p.castignolles@uq.edu.au

Toward a full characterization of native starch: Separation and detection by size-exclusion chromatography

Keywords: size-exclusion chromatography (SEC), separation, repeatability, labeling, UV detection, starch

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

the polysaccharides. This may cause degradation of the sample. Another polar organic solvent that has been used for SEC of starch is dimethylsulfoxide (DMSO) [27], used not infrequently in the literature (e.g. [25,32]). DMSO can completely solubilize starch granules [18], and when dry, complete dissolution is expected after 20 to 30 min at 80 °C according to an NMR study of the kinetics of dissolution of some rice starches by some of the authors [33] although this needs to be adapted for each sample and 29 h hours have been allowed to dissolve potato starches [25]. Starch is usually dissolved in a mixture of DMSO and water (e.g. [22,24,34,35]). Note that the presence of water in DMSO slows down the kinetics of dissolution of starch [33], even though is accelerates the loss of crystallinity [36,37] of the starch granules. Unfortunately, the high viscosity of DMSO makes its use as an eluent tedious, as it will build up pressure inside the column. Even more importantly, the high viscosity generates shear scission forces that are likely to degrade high molar mass materials, such as amylopectin. Degradation from shear scission has been recorded for higher molar masses of polystyrene in tetrahydrofuran [38,39], in toluene, with w M above 510 6 (flow rate = 0.5 mL•min -1 , concentration = 0.25 g•L -1 ) and for polyethylene [40]. Varying experimental conditions can modify the extent of degradation, and while it can be minimized, it may be impossible to avoid it entirely [41,42].

Full characterization of amylopectin, and possibly amylose, should thus be performed in an eluent containing DMSO to ensure minimal degradation and quantitative dissolution and another co-solvent decreasing the viscosity of the eluent. Although water is less viscous than DMSO, introducing low levels of water in DMSO leads to an increase of viscosity because the mixture is not ideal [43].

The present paper gives various evolutionary advances on these techniques, with an aim to improve starch structural characterization. Building on advances by Striegel, we employ an eluent combining DMSO and DMAc towards overcoming some of the problems (poor repeatability or reproducibility, biased injection, low recovery, shear degradation etc.) that have plagued this endeavor in the past.. LiBr is added to prevent adsorption of starch onto the SEC columns [44]. To determine whether our system allows us to perform meaningful comparative studies [45], we study the separation and detection repeatability (experiments with the same method on identical test material in the same laboratory by the same operator using the same equipment within short intervals of time [46]) and reproducibility (experiments with the same method on identical test material in different laboratories with different operators using different equipment [46]).

The similarity of the refractive indices of organic polar solvents and starch [17] results in a low RID sensitivity, which in turn makes quantification of the signal difficult because of a low signalto-noise ratio. This difficulty is further increased by the fact that amylopectin has a very high molar mass, and accordingly must be injected at low concentration. Thus the detection must be improved in the least degradative conditions possible. Labeling starch with UV-active or fluorescent groups is a good method to increase the sensitivity of the detection. Due to the selectivity (specific wavelength for the adsorption) and high extinction coefficient available with appropriate chromophores, UV or fluorescent spectroscopy is specific and highly sensitive towards the active groups. To help overcome the problem of detector sensitivity, we propose what appears to be the first means of randomly labeling starch on the backbone of the polysaccharide, i. e. by reaction on any anhydroglucose unit, to have access to the mass distribution with high sensitivity. 2 Experimental section 2.1 Materials. N,N-dimethylacetamide (DMAc, 99.8 %, HPLC grade) and dimethylsulfoxide (DMSO, HPLC grade) were purchased from Sigma-Aldrich, acetonitrile and isopropanol (both AR grade) from Lab-scan analytical science, DMSO-d6 (99.9 % D) and acetonitrile-d3 (99.8 % D) from Cambridge Isotope Laboratories Inc. When used for starch dissolution, DMSO and DMSO-d6 were dried using 3 Å molecular sieves (Sigma-Aldrich) before use. Lithium bromide (LiBr, Sigma-Aldrich) was dried in a vacuum oven at 160 o C under vacuum for 10 h and then stored in a dessicator. A 0.2 m membrane filter (hydrophilic Teflon, Millipore) was used to remove any particulates prior to use. The starch used was rice starch (Sigma-Aldrich, S-7260. 11.6 wt% moisture content); its amylose content was found to be 36 % by the iodine binding method (see supporting information).

Triethylamine (Et3N) and N,N-disuccinimidyl carbonate (DSC) were purchased from Merck and Fluka respectively. Toluene (HPLC Grade), 2-naphthylamine (98 %) and 2-(2-naphthyl)-ethylamine (97 %) were supplied by Sigma-Aldrich. The poly(vinyl alcohol) was purchased from BDH chemicals (specified by the supplier to have a molar mass of 14 000 g.mol -1 ). Note that when DMSO is used, any contact with rubber should be carefully avoided (see [33] and supporting information). Moreover, DMSO is sometimes considered as toxic [20] although its safety data sheet (MSDS) does not state this. DMAc is toxic and requires special care.

Synthesis of -(1,4) glucans ("linear starch")

The synthesis has been adapted from [47], described previously [26] and is summarized as follows. Glucose-1-phosphate and maltoheptaose were dissolved in 3-(Nmorpholino)propanesulfonic acid (MOPS) buffer (50 mM, pH 7.2) containing adenosine monophosphate (1 mM) and dithiothreitol (2 mM). The reaction was initiated by addition of rabbitmuscle phosphorylase a at 30 C and typical reaction times were 8-16 h. Termination was by heating in boiling water for 5 min. The concentration of glucose-1-phosphate, maltoheptaose and phosphorylase a were respectively 50.00 mM, 0.100 mM and 0.001 mM. An aliquot was injected into aqueous SEC immediately after termination to minimize retrogradation. The rest of the reaction medium was freeze-dried and then solubilized in NaOH (1 M, 200 L) at 70 or 80 C with gentle shaking for 10 min and injected into the aqueous SEC. Precautions were taken to avoid contamination by amylases (e.g. from saliva) [5].

Aqueous size-exclusion chromatography.

Aqueous SEC was performed on a Shimadzu system (LC-10ATVP pump, DGU-14AVP degasser, SIL-10ADVP autoinjector, CT10ACVP column oven) connected online with a Wyatt OPTILAB EOS refractive index detector (at 30 ˚C). Waters columns were used: Ultrahydrogel 250, Ultrahydrogel 120 and Ultrahydrogel Guard column connected in series in a column oven at 60 C. The aqueous eluent used was 0.05 M ammonium acetate (pH 5.2) at a flow rate of 0.5 mLmin -1 . SEC traces obtained were flow-rate corrected using ethanol as a marker. The Mark-Houwink-Sakurada parameters for linear - (1,4) glucans in this particular eluent and at 60 C have been determined to be K = 0.0544 mLg -1 and  = 0.486, while those of pullulan have been determined to be K = 0.0126 mLg -1 and  = 0.733 [48]. The calibration curve for linear -(1,4) glucan using pullulan standards (Shodex) range was between 504 and 710,000 gmol -1 (529 and 2,490,000 gmol - 1 linear -(1,4) glucan equivalent), which fully covers the range of molar mass or size of the injected samples. Data were acquired using Astra ® software. Data treatment (normalization, baseline subtraction, flow-rate correction, calculation of the molar mass distributions) was performed using Excel and Origin software. More details are available in [26].

Organic size-exclusion chromatography

The eluent was prepared by mixing the solvents DMSO and DMAc in the proportion 10:90 w/w, before adding 0.05 % LiBr and mixed using magnetic stirring for 1h prior to filtration on 0.45 m hydrophilic Teflon® filters. Starch samples were dissolved in anhydrous DMSO at 1 wt % for at least 2 h in a thermomixer (Bio-Rad) at 80 °C, 300 rpm. The sample was then diluted with a solution of 0.055 wt% LiBr in DMAc to achieve a final starch concentration of 1 g•L -1 (corresponding to 0.1 wt%). The starch samples were not filtered (it is generally recommended to filter SEC samples; amylose samples can be filtered [6] but amylopectin is highly likely to undergo degradation by shear [21]). The solutions were then either injected immediately at 80 °C or allowed to cool down for 80 min prior to injection at the controlled room temperature of 23 °C .

The SEC set-up was based on an Agilent 1100 Series equipment (isocratic pump, autosampler without temperature control, UV variable wavelength detector) with additional online degasser and refractive index detector (RID, Shimadzu Industries). The injection volume was 10 µL. The flow rate was 0.3 mL•min -1 . Separation was by a GRAM 10,000 analytical column (Polymer Standards Services, PSS, Mainz, Germany) thermostated at 80 °C. Detectors were both thermostated at 60 °C. The UV wavelength was set up at 280 nm. The data stream was recorded using WinGPC software (PSS), and further data treatment was performed using Origin software (Origin Labs). Flow-rate correction was performed using the water (negative) peak on the RID. Calibration of the columns was performed using polystyrene and poly(methyl methacrylate) standards (PSS) using the molar mass indicated by the supplier (see Supporting Information). Higher molar mass polystyrene standards exhibit an anomalous calibration curve (no separation in a region still within the exclusion limit), while poly(methyl methacrylate) standards can be used on the whole range of molar mass. The polystyrene standard used to test repeatability was from PSS (peak molar mass Mp = 312,000, number-average molar mass n M = 305,000, dispersity 1.05). Apparent molecular weights [49] for starch are not presented since starch is a complex branched macromolecule [50] and such a means of presenting the data is easily open to misinterpretation, since the axis is not a true molecular weight of the sample.

The apparent recovery using the RID was measured to be 71 (17) % (see supporting information).

Starch does not absorb in the UV above the cut-off of our eluent (ca 260 nm); however, it exhibits a signal on the UV detector (signal-to-noise ratio around 10). This weak signal might be due either to light scattering by the large starch molecules or to stronger UV absorption by dimethylacetamide due to a bathochromic effect of the interactions of starch with dimethylacetamide. This weak signal qualitatively matches the RID signal for the amylopectin peak but the amylose peak seems to be polluted by other peaks at the highest elution volumes (these peaks might correspond to degradation products of the dimethylacetamide which would be present in very small quantities, not detected by the RID, but UV-absorbing). 2.5 Model labeling of isopropanol ( 1 H solution-state NMR study) 1 H NMR was performed on a Bruker Avance TM spectrometer equipped with a TXI5z probe, at a 1 H Larmor frequency of 500.13 MHz, in 5 mm tubes spinning at 20 Hz (1200 rpm). All spectra were acquired and processed with Topspin  software (Bruker Biospin). The temperature was calibrated with an ethylene glycol standard [51]. The chemical shift scale was calibrated using the residual solvent signal: 2.58 ppm at 25 °C, 2.57 ppm at 40 °C, 2.55 pm at 60 °C and 2.53 ppm at 80 °C respectively in DMSO-d6 [52], and at 1.94 ppm in acetonitrile-d3 [53]. Toluene was used as an internal standard for integrals normalization.

In situ time-resolved 1 H NMR experiments were carried out as follows to monitor the kinetics of reaction of DSC with isopropanol (first step of isopropanol labeling). Isopropanol (2.5 mg, 1 equivalent), Et3N (9.5 mg, 3 equivalents), and toluene (9 L) were dissolved in 1 mL of solvent (anhydrous DMSO-d6 or acetonitrile-d3); in one case 3.7 mg LiBr was also added. This solution was used to lock, shim and tune the spectrometer, and a spectrum of it was recorded. Subsequently, DSC (16 mg, 1.5 equivalents) was added. Consecutive 1 H spectra of the reaction mixture were then recorded overnight with 72 scans and a 4 s relaxation delay (4.8 min per experiment); the origin on the reaction time scale is the time at which the DSC was mixed in.

A similar protocol was followed to monitor the reaction kinetics for the second step at 25 °C. The original sample was prepared as previously and mixed for 24 h. A first 1 H NMR spectrum showed a 13 % yield for the first step of the reaction. Then 2-(2-naphthyl)-ethylamine (8.56 mg) or 2-naphthylamine (7.2 mg) was added and the kinetics of the second reaction step was followed by recording consecutive 1 H spectra overnight with 72 scans and a 4 s relaxation delay (4.8 min per experiment).

Single 1 H spectra of reaction mixtures containing isopropanol, Et3N, DSC and toluene in anhydrous DMSO-d6 (same quantities as above) after 10 h reaction at respectively 40, 60 and 80 °C, were recorded at 25 °C with 72 scans and a 4 s relaxation delay. Single 1 H spectra of DSC (25 mg) in 1 mL of anhydrous DMSO-d6 or acetonitrile-d3 were recorded at 25 °C, with a 4 s relaxation delay, and 32 or 72 scans respectively. 2.6 Model labeling using poly(vinyl alcohol) 0.1 g of poly(vinyl alcohol) (0.454 mmol of OH groups -targeting labeling every 5 OH group) was dissolved in 10 mL of anhydrous DMSO by stirring slowly with a magnetic stirrer at 80 ºC. Then Et3N (190 µL, 1.36 mmol) and DSC (524 mg, 2.05 mmol) were added, and the mixture stirred at room temperature for 24 h. The 2-(2-naphthyl)-ethylamine (93 mg, 0.545 mmol) was then added and the mixture stirred at room temperature for 24 h. Note that a large excess of DSC (1.5) was used to compensate for the hydrolysis caused by the water coming from the polymer sample. 2.7 Labeling of the starch sample. 0.1 g of starch (1.85 mmol of OH group in total -targeting the labeling of every 20th OH group , i.e. 0.0925 mmol of OH groups) was dissolved in 10 mL of anhydrous DMSO by stirring slowly at 80 ºC for more than 2 h (the kinetics of dissolution in these conditions has been previously studied to take less than 2 h [33]). Then the magnetic stirrer was removed, the solution cooled at room temperature was left overnight on molecular sieves (4Å) and nitrogen bubbling. Then Et3N (38.7 µL, 0.277 mmol) and DSC (35.56 mg, 0.138 mmol) were added, and the mixture was left on molecular sieves with nitrogen bubbling and the labeling was allowed to proceed for 24 h. The 2-(2naphthyl)-ethylamine (2.4 mg, 0.0139 mmol) was then added and the mixture was left on molecular sieves under nitrogen bubbling for 24 h.

Results and Discussion

Starch separation using aqueous (ammonium acetate) eluent

An aqueous eluent comprising 0.05 M ammonium acetate, pH 5.2, employed by Batey et al. [20] was used. This eluent, however, like most aqueous-based solvents, is a non-solvent for starch, and any unprocessed starch that is forced to dissolve in such an eluent is only metastable. The principle of the mechanism of separation by SEC is purely by hydrodynamic volume, and so it is important that the mobile phase is a good solvent for the polymer being analyzed. An incomplete amylopectin apparent recovery has been reported using ammonium acetate as eluent [28]. Further attempts to quantify apparent recovery of debranched starches lead to non-repeatable apparent recovery values, likely due to the non-stability of the debranched starch "solutions", also reported in the literature [20].

Starch powder does not dissolve in ammonium acetate buffer, even at high temperature (80 C) under stirring for a week (most of the starch stays in its solid form). Basic conditions have to be used to obtain clear aqueous solutions from the powder. Note that a true solution of starch in a solvent has to be clear (transparent) but this criterion is not sufficient [33] Solubilization of starch in NaOH can cause degradation [54]. This was seen during the resolubilization of short-chain linear -(1,4) glucans ("linear starch") in the present study. The -(1,4) glucans were injected directly after their synthesis and also after freeze-drying and redissolution. The number distribution of linear -(1,4) glucans after resolubilization in NaOH was compared to the original distribution that was obtained immediately after termination of the synthesis by phosphorylase a (Figure 1). The comparison shows that after resolubilization the peak maximum is shifted towards significantly lower degree of polymerization, suggesting the NaOH is depolymerizing the starch. There is a controversy in the literature about the degradation being due to oxygen [27] or not [5] and degradation was observed to take place even in the absence of oxygen by at least two different pathways [54]. Aqueous SEC (alkaline conditions) has been used to compare different batches of commercial starch samples [6]. The aqueous system would however not be useful for any study requiring meaningful comparison because of the significant degradation during sample preparation.

Insert Figure 1 3.2 Starch separation using DMSO/DMAc/LiBr SEC

The starch chromatogram obtained with this eluent exhibits two features: the main bimodal peak and the "end of column" peaks (Figure 2). The "end of column" peaks are due to the slight difference of composition between the eluent and the sample solvent which were prepared separately. The first part of the bimodal sample peak (at 7.5 mL in elution volume) corresponds to amylopectin, which has a higher molar mass, whereas the second part (maximum at 9.4 mL in elution volume) corresponds to amylose. Note that the relative amylose to amylopectin content can not be determined from this chromatogram since the two components are not separated (and have never been separated by any form of SEC). Deconvolution of the peaks is not possible since no mathematical function is known to fit either amylose or amylopectin peak (both these peaks correspond in fact to a mixture of a very large number of molecules differing in molecular weight and structure).

Insert figure 2 3.2.1 Repeatability

Meaningful characterization of starch can be obtained only if the separation is adequately repeatable. Repeatability was estimated by injecting a single sample several times in succession. The resulting chromatograms were then compared numerically and the repeatability was quantified. SEC chromatograms can be compared by using the distinguished points method, [START_REF]Size Exclusion Chromatography[END_REF] implemented by Fuzes [45]. Fuzes' analysis was modified to allow quantification of the repeatability with a small number of replicates. The distinguished points (DPts) were chosen as the elution volumes corresponding to 10 %, 30 %, 50 %, 70 %, and 90 % of the total area under the peak for a specific chromatogram. The repeatability of chromatograms was evaluated separately at each of the five DPts. At each DPt and for each curve, the RID signal intensity and the corresponding elution volume were identified. Then for each DPt, the average (µ) and standard deviation (σ) of the RID signal intensities and of the elution volumes were calculated for the replicates of the chromatograms. The absolute error at each DPt was quantified as the standard deviation from the replicates. The relative error at each DPt was quantified as the coefficient of variation CV = σ/ µ. The lower CV, the better the repeatability.

Before analyzing the repeatability of starch injections, it is necessary to determine the highest repeatability that can be obtained using our chromatographic system. Injections of polystyrene are highly repeatable both for room-temperature tetrahydrofuran SEC and high-temperature trichlorobenzene SEC [START_REF] Samay | [END_REF]. To provide a comparison basis, the modified method of distinguished points was first applied to chromatograms obtained by injecting a polystyrene standard five times in the same conditions as the one used for starch (eluent DMSO and DMAc in the proportion 10:90 w/w with 0.05 % LiBr). The very high repeatability of polystyrene injections can be seen graphically (Figure 3) and numerically: the curves overlap perfectly and the coefficients of variation are lower than 5 % at each DPt, the largest being 4.11 % for the RID signal intensity and 0.24 % for the elution volume Vel (Table 1). The measurements thus exhibit a remarkably high repeatability, which is comparable to the most optimized SEC systems, such as tetrahydrofuran SEC [46]. Note that using distinguished points is necessary to be able to quantify the repeatability of polystyrene and starch injections. Residual plots would enable comparison of the full chromatograms for two injections of the same sample but would not allow quantification of the repeatability or reproducibility. Insert Table 1, Figure 3 The temperature at which the samples are stored and injected has been shown in the literature to play a very important role for aqueous solution: molar masses measured by low-angle laser light scattering aqueous SEC decrease by 30 % when samples are stored at 45 °C, while there is no apparent differences (no statistical treatment is presented) when samples are stored at 100 °C [5]. The repeatability of starch injections in this work using organic polar solvents was tested for two different conditions: with injections at 80 °C or at 23 °C (room temperature). The auto-sampler was not thermostated, and hence the samples injected at 80 °C stayed in the thermomixer (80 °C, 300 rpm) between injections. The data displayed in Figure 4 and Table 1 (second part) were obtained with five injections at 80 °C and five injections at 23 °C.

Figure 4

The coefficients of variation for injections at both 80 °C and 23 °C are below 5 %. Starch injections at 80 °C exhibit remarkably low CVs and standard deviations, as low as those of polystyrene injections: the largest CV is 4.7 % for RID signal intensity and 0.7 % for the elution volume. The injections at 23 °C exhibit a slightly larger variation: the largest CV is 5.1 % for the RID signal and 0.9 % for the elution volume. The high repeatability of the injections at 80 °C suggests that interactions between starch chains and the columns are minimized. Lower repeatability at room temperature might be due to limited precipitation or retrogradation of starch. After the dissolution at 80 °C, it is thus advisable to store and inject the starch samples at 80 °C as well.

In current starch literature, the repeatability of aqueous SEC has never been quantified; indeed, in the case of ammonium acetate eluent, it is our experience that starch samples show some precipitation too rapidly to allow 5 successive injections with the same sample.

Reproducibility

Performing complete reproducibility tests is tedious as every parameter should be varied, and in particular, different SEC set-ups should be used, which is beyond the scope of the present publication. In this work, the effects of the sample preparation and of the operator were investigated. To investigate the effect of the sample preparation, one operator performed the following experiments over a short time period, such that all injections were carried out under similar conditions: same eluent bottle, same solution of DMAc/LiBr. Five samples were prepared: two were injected at 80 °C (Figure 5a, dashed line) and three injected at room temperature (Figure 5b, dashed line).

The normalized chromatograms were compared to the chromatograms from the repeatability experiment at the corresponding temperature, which is considered as the reference (Figure 5). The comparison at each DPt and the significance of the discrepancies observed was quantified with the two-sample t-test (Minitab Inc., Relase [57]). Differences are deemed to be significant at the 5 % level. Insert Figure 5 As can be seen on Figure 5, the reproducibility is satisfactory at 80 °C. The intensity of the RID signal at the peaks varies from 4 % (at 7.4 mL) to 9 % (at 9.4 mL). The RID signal intensity is robust to the difference in conditions; there was no significant difference between the reference and reproduced curves at any DPt. The elution volume was less reproducible. At 80 °C, the elution volume of the reproduced samples was significantly lower than the elution volume of the reference at the 10 %, 30 % and 50 % DPts. The largest magnitude of that elution volume discrepancy was 0.02 mL at DPt 50 %. This is probably due to slight changes in the pump flow rate and show the importance of the flow-rate correction (which was performed in this work) and also its limitations.

At room temperature, the reproducibility of the elution volume was satisfactory. However, the RID signal intensity was not reproducible: the curves do not overlap and the intensity of the RID signal at the peaks varies from 0 % to 24 % (Figure 5b). The RID intensity discrepancies were significant at all DPts. This is not due to the chromatographic set-up but more likely to a change in the injected solution with time, even within a few hours, when stored at room temperature. This confirms the importance of preparation and also storage and injections of the samples at 80 C.

Another experiment was performed to evaluate the importance of the operator effect in our method. In this experiment, two different operators prepared a starch sample each following the same procedure. Both samples were injected twice under the same conditions. This experiment was performed twice at room temperature. The resulting chromatograms were normalized, the reference being repeatability injections at room temperature and compared to each other. Insert Figure 6 Both operators followed the same protocol using the organic SEC system, but it is impossible to obtain identical concentrations of starch in each sample. This is because of the many uncontrollable factors contributing to differences in RID signal curves (Figure 6): the evaporation effect, the time samples were stored before injection, the actual weights of DMSO and starch. For both operators, the internal repeatability of the two injections of each sample was good and comparable to that in the repeatability study: CVs at all DPts were smaller than 5% for both Vel and RID signal intensity.

The significance of disagreement between the samples was evaluated with one-way ANOVA with sub-samples (GLM, Minitab Release 15). There was no significant difference in terms of the elution volume among the four samples. The shape of the peaks is still the same from one sample to another, regardless of the operator (Figure 6). On the other hand, the differences in the RID signal intensity were significant at all DPts; the intensity of the RID's signal varied from 7 % to 20 % for one operator and from 9 % to 27 % for the second operator.

Unfortunately, the differences in concentrations of samples and the operator effect were confounded in our trial. However, we were able to use the two samples in Figure 6, whose concentrations were similar, in order to estimate a pure operator effect in terms of sample preparation, in particular how well the samples were homogenized. The analysis showed that the operator effect on the elution volume was insignificant. The operator effect on the RID signal intensity was significant at all DPts. We thus conclude that the method can detect differences in concentrations, although the reproducibility is low when injections are performed at room temperature.

The high repeatability and the acceptable reproducibility of starch injections shown in this paragraph indicate that adsorption is unlikely to play a role in the separation. The competition between SEC mechanism of separation and absorption mechanisms would have reduced the repeatability of experiments. Comparison of samples can be performed and the quantification of the reproducibility together with the software above allows determining whether differences between starch samples are meaningful or not. This is very important to determine whether differences observed between starch samples originate from differences in their size distribution or not, which is the first step toward meaningful structure-property relations. Note that however, the system does not offer full recovery and that thus some retrogradation of starch molecules or adsorption likely takes place in the system.

Improvement of the sensitivity

The new eluent system allows separation of starch with very high repeatability and acceptable reproducibility. This enables the use of multiple-detection SEC to characterize many types of branched or debranched starch; RID yields a weight molar mass distribution and is critical when using multiple detection to obtain accurate molar mass distribution [11].. However the ability to increase the detection limits is crucial to further develop research into starch structural characterization. Detection after a SEC column is currently done by RID; however using ultraviolet (UV) or fluorescent detection could considerably increase the sensitivity of the technique.

Labeling the starch chains with a UV-active or fluorescent label will increase the limits of detection. the labeling of the starch chains has to be randomly performed among the anhydroglucose units to access to weight molar mass distributions, the distributions obtained by the RID. The most common derivatization procedure for carbohydrates with a UV-active or fluorescent label [23,[58][59][60] labels only the reducing end of the carbohydrate chains,. There is only one reducing end-group per starch molecule. While this method is thus excellent for determining number distributions, it cannot give the best detection sensitivity for mass distributions. Only the hydroxy groups of the anhydroglucose unit can be used to add labels to the chain. Labeling of anhydroglucose units in relatively extreme conditions has already been performed on cellulose, since the grafting of functional group onto the backbone to tune the material properties is a major concern in this field. [61] Recently, some reactions using an activated ester based on carbonyldiimidazole [62] or using click chemistry [63,64] have been tested to introduce new functional groups under relatively mild conditions. However even those "relatively mild" conditions (e.g. heating the polymer at 100 °C for 24 h [63]) are undesirable as they might lead to the degradation of starch molecules. It is therefore desirable to develop a methodology to label the starch using only mild pH and temperature.

As numerous potential chromophores bear an amine group, we investigated the possibility of coupling between the hydroxy group of the anhydroglucose unit and the amino group borne by the label (Scheme 1). N,N'-Disuccinimidyl carbonate (DSC) is well known as a versatile reagent for active ester synthesis. [65] The reactions of DSC with alcohols to form mixed active carbonates and their subsequent utility in the synthesis of functionalized carbamates has been investigated by Ghosh [66] and this method has proved to be an efficient and mild method for alkoxycarbonylation of amines. This method has been used to mimize potential starch degradation during its labeling. A typical procedure comprises two steps. Alcohols are first treated with DSC in the presence of triethylamine to give mixed carbonates. The carbonate-containing mixtures, isolated or not, are then mixed with Et3N and the desired amine to yield carbamate products. Ikegami et al. [67] showed that the use of a succinimidyl group as an activating group was the most effective for the synthesis of the mixed -carbonates of 2,3,4,6-tetra-O-benzoyl or 2,3,4,6-tetra-O-pivaloyl-D-glucopyranose. The proposed synthetic pathway using DSC as a coupling agent for starch labeling is shown in Scheme 1.

Insert Scheme 1 3.3.1 Model labeling using isopropanol

As a preliminary to labeling starch, the experimental conditions for the labeling were explored using a simpler organic model. A secondary alcohol, isopropanol, was chosen to model the alcohol groups present on the starch backbone. Ethanol could have been used, but a primary alcohol would react faster than a secondary one, and isopropanol has a higher boiling point than ethanol and is easier to manipulate. In their work, carried out in acetonitrile, Ghosh et al. [66] followed the disappearance of alcohol or amine by thin layer chromatography (TLC). Due to starch solubility problems, the reactions have to be conducted here in DMSO, which has a very low volatility. TLC could therefore not be used, and 1 H NMR was chosen to monitor the reactions. The initial step, the activation of isopropanol by DSC, which yielded a mixed carbonate, was examined first. In the 1 H NMR spectra, the methyl groups of the isopropanol and of the activated isopropanol exhibit distinct chemical shifts, respectively at 1.11 and 1.40 ppm in DMSO-d6 at room temperature (both signals being doublets, Figure 7a), and their evolution with time can be followed independently. Toluene was used as an internal standard, and its methyl signal (singlet) at 2.38 ppm was used for normalization.

Insert Figure 7 The formation of activated isopropanol versus time was followed overnight (Figure 7a andb). All reactants excluding DSC were mixed and an initial spectrum was obtained. Then DSC was added and a spectrum recorded every few minutes overnight. The reaction proceeded for 20 h and stopped at a conversion of 12 %. However, in the literature this reaction has been reported to be quicker and more efficient (80 % in 4 h) [66]. In addition to a lower concentration, a solvent effect could explain the slow rate observed in the present work. Ghosh et al. [66] indeed showed that the first step takes 4 h in acetonitrile compared to 12 h in dichloromethane. To test this hypothesis, two experiments were conducted: the same reaction was performed both replacing DMSO-d6 with acetonitrile-d3 (to check whether the reaction time is in agreement with the literature one), and adding LiBr (to prevent the formation of H-bonds between DMSO and isopropanol). The results presented in Figure 7b show that the kinetics in acetonitrile is quite similar to that in DMSO with a slightly higher conversion after 24 h (15 % instead of 12 %), but no significant solvent effect was observed. On the other hand, the addition of LiBr does not improve the reaction and in fact decreases the rate of reaction and conversion. The difference in acetonitrile between the literature data and our results likely arises from the concentration (5 times lower) for both DSC and alcohol, leading to a 25 times decrease in the rate of this bimolecular reaction.

The second parameter examined was the effect of the temperature on the kinetics and on the yield. The reaction was carried out at 25 °C, 40 °C, 60 °C and 80 °C for 10 h, and the 1 H NMR spectra of the final reaction mixture revealed respectively a 13, 7.5, 6.1 and 5.9 % yield. Thus the higher the temperature, the lower the conversion of isopropanol, implying that the yield would be increased at a lower temperature. Unfortunately, it is not possible to decrease the temperature below 20 °C as DMSO would start to freeze. The full reaction kinetics was followed at 60 °C (Figure 7b). As predicted, the conversion reached at 60 °C is lower than at 25 °C. However, the conversion is faster during the first few hours when the temperature is high. As the yield of the first step was poor to moderate in all cases, we examined the possible cause(s) of this phenomenon. When the consumption of DSC was followed as a function of time, it was found that at least three equivalents of DSC reacted with one equivalent of isopropanol; this fitted the appearance of Nhydroxysuccinimide. It is hypothesized that a competitive relationship exists between the activation of isopropanol and the hydrolysis of DSC. Mass balance showed that hydrolysis and labeling were the only two reactions occurring. The challenge was then to remove all the water, to prevent the hydrolysis of DSC. It was found that the DMSO-d6 quickly became contaminated with some H2O, and 1 H NMR spectra of DSC in DMSO-d6 always showed a mixture of DSC and Nhydroxysuccinimide, whereas in acetonitrile-d3 only DSC was present. Traces of water were also found in all other reactants (isopropanol, toluene, triethylamine). An experiment was performed using molecular sieves in the NMR tube to see if the yield could be increased. In that condition, the yield increased to 25 % in 10 h (Figure 7b).

The second step was also followed by in situ time-resolved 1 H NMR. The labeling was performed with two different labels: 2-naphthylamine and 2-(2-naphthyl)-ethylamine (Scheme 1), to investigate the effect of an alkyl spacer group between the amino group and the aromatic rings. The delocalization of the amine doublet to the rings could have a detrimental influence on the reactivity of the amine group [60]. The reaction was monitored through the increase of the signal of the NH groups of the final product, respectively at 4.4 and 9.1 ppm for the amine with and without spacer. It correlated with a decrease of the signal of the activated alcohol at 1.40 ppm. Figure 7c shows that 2-(2-naphthyl)-ethylamine is substantially more efficient than 2-naphthylamine with a conversion of 77 % after 4 h. When the amine group is directly linked to the aromatic rings, the conjugation of the doublet seems to make it less reactive. 3.3.2 Model labeling using poly(vinyl alcohol) Having set up the experimental conditions using isopropanol to model the reactivity of the hydroxy group, we tested the same procedure on a polymer. A linear polymer, poly(vinyl alcohol), was chosen to investigate whether the labeling is randomly done along the backbone, avoiding the complexity of mechanism of SEC separation for branched polymers. Figure 8 shows the RID and UV signals of the poly(vinyl alcohol) before and after labeling (injected on the organic SEC at the same concentration), superimposed and normalized at the same peak height. Insert Figure 8 The RID signal of the unlabeled polymer shows that the poly(vinyl alcohol) elutes at 14 mL, with a signal-to-noise ratio of 18. The unlabeled poly(vinyl alcohol) has no UV signal. Once labeled, the intensity of the whole RID signal of the labeled polymer is higher because the label modifies the refractive index of the polymer, increasing the dn/dc (n is the refractive index of the polymer solution and c is the polymer concentration), but with a similar signal-to-noise ratio. A peak is observed with the UV detector at an elution volume of 14 mL for the labeled polymer with a signalto-noise ratio of 310. This shows that labeling has occurred and has dramatically improved the detection sensitivity (by a factor of 17). The RID signals of the unmodified and of the labeled poly(vinyl alcohol) have the same shape, showing that the labeling does not significantly modify the structure or the SEC separation mechanism of the polymer. Furthermore, the UV (chromophoresensitive) and RID (mass-sensitive) signals of the labeled poly(vinyl alcohol) overlay perfectly, which proves that labeling is random.

Starch labeling

The first starch labeling experiments were designed to have one label per 1000 units. However the injections were unsuccessful, with the UV signal being indistinguishable for the labeled and unlabeled samples. To ensure that the labeling reaction was effective, the concentration of the reactants was increased to aim at one label per 20 alcohol groups. Injections of labeled starch were then carried out in the same conditions (same eluent, same concentration on the organic SEC) as injections of non-labeled starch (Figure 9).

Insert Figure 9 The RID signals (Figure 9a top) show that the labeled sample elutes at the same elution volume as the non-labeled starch without encountering separation issues. The intensity of the RID signal is higher after labeling as in the case of poly(vinyl alcohol), the label modifying the refractive index of starch (increasing the dn/dc). The UV signal is twenty times more intense after labeling (Figure 9b), increasing the signal-to-noise ratio from 56 in RID to 180 in UV. This proves that chromophoric groups were covalently bound on starch.

Removal of the water in the mixture is paramount for the yield of the reaction to prevent hydrolysis of the DSC. This explains the absence of labeling when low concentrations of reactants were used. All the sources of contamination must be identified and the water must be removed from the solution, which is difficult as DMSO is hygroscopic. Starch granules are known to contain 10 % (± 2 %) of water, [68] which is released during dissolution in DMSO. Working with 1 g of starch in 100 mL of DMSO would release around 10 mg of water (5.5 mM), which is in the same range as the reactant concentrations. To remove this water, molecular sieves were added upon dissolution of the starch. Then the reaction was performed as previously and the sample injected into the SEC (Figure 9a andb). The RID and UV signal of starch remains at the same elution volume and the peaks have the same shape. The UV absorbance was more than doubled when the labeling reaction was performed in the presence of the molecular sieves and was more than forty times higher than that of non-labeled starch. This result highlights the impact that the water has on the efficiency of the labeling and hence on the detection sensitivity. Water needs to be removed so that the residual UV signal observed with non-labeled starch can be neglected.

The molecular structures of amylose, having a few long-chain branches, and amylopectin, a highly-branched polymer, are very different and might lead to different efficiency in labeling. The literature contains few studies about the chemical modification of fully dissolved starch molecules and a possible bias has never been examined. Labeling of the glucose unit in the center of the amylopectin molecules may have been less efficient because of the high density of this molecule compared to amylose. The comparison of the RID signals before and after labeling (residual plots on Figure 9a bottom) shows no bias of the labeling toward amylose (more efficient labeling of the amylose would have resulted in monotonically increasing residual plots). The same comparison on UV chromatograms would be meaningless at this stage due to the huge end of column peak (which conceals a part of the starch chromatogram) observed only for the labeled starch and likely corresponding to non-reacted UV-active label.

This work gives the proof-of-concept that labeling on the glucose monomer unit has the potential to significantly improve detection of starch after SEC separation. Further conclusions will require optimization of the labeling reaction as the large amount of free label remaining in solution has an influence on the elution profile of the starch. Elution in SEC is known to be sensitive to "pollution" by small molecules (i.e. polystyrene standards elute at different positions in anhydrous and wet tetrahydrofuran [69]). To account for this effect an experiment should be performed using the same labeling, but with the amount of amine added in the second step minimized (i.e. taking into account a low yield for the first step) to avoid the broad end-of-column peak. The repeatability of the labeling process and the repeatability of the injections of labeled starch should then be investigated.

Conclusions

A new eluent composed of dimethylsulfoxide, dimethylacetamide and lithium bromide has been successfully tested for size-exclusion chromatography (SEC) starch. Full dissolution in dimethylsulfoxide is followed by separation in a lower viscosity medium containing dimethylacetamide. This eluent allows meaningful comparative studies, since repeatability of the separation is very high and reproducibility acceptable. Dissolution as well as sample storage and injections need to be performed at a relatively high temperature (80 ºC) to obtain these repeatability and reproducibility. Successful random labeling along starch backbone has been performed in mild conditions, successfully tested on model compounds. The glucose units on the two different components of starch, amylose and amylopectin, are shown to be labeled with similar efficiency, despite the strong differences in amylose and amylopectin structures. This reaction, with further optimization, will permit the use of sensitive UV detection to determine mass distributions. After quantification of the labeling (e.g. by NMR) and determination of the molar extinction coefficient, this separation will be further studied using multiple detection SEC (viscometry and light scattering) [10] to investigate effect of branching on the mechanism of separation [11,12].

Apparent recovery

Apparent recovery was measured using the refractive index detector (RID) calibrated with poly(methyl methacrylate) (PMMA) standards relating ARID, the total area of the signal of the polymer peak, to C, the concentration of the standard (injection volume is not considered here since it was the same for the injections of standards and starch):

ARID = K dn/dc C
K is an instrumental constant. The specific refractive increments values, dn/dc, were determined as 0.073 mL•g -1 for PMMA and 0.101 mL•g -1 for starch, found by interpolating from literature and measurements (not given here, manuscript in preparation). The calibration constants for the RID are given in Table 1. These values (12.52 with a standard deviation of 10%) were not taken into account due to a lower accuracy to the dn/dc (taken as the same as starch) . The recovery is high but the precision of the measurement is not high. The accuracy is calculated as follows. The apparent recovery is given by the formula: The error in eluent mass is negligible (at least 100 mg was weighted with a precision balance, accuracy ca 1 mg) as well as the water content in starch (given as 11.6 % by Sigma-Aldrich) while the error on weight of starch and PMMA can be estimated to 1 % since at least 10 mg were weighed on a high-precision balance (accuracy ca 0.1 mg). This choice of 10 mg was driven by an important inaccuracy on the error by preparing initially only 1 mg of starch; the error was thus increased to 10 %. The error on the dn/dc is estimated to 10 % but could be reduced with further measurement. The error on the measurement of the area of the polymer peak on the chromatogram can be estimated to be around 15 %. This error could be reduced only by increasing the sensitivity, using further the labeling reaction developed in this work.

Recovery = R =
The error on the apparent recovery measurement can be estimated to 30 %.

The apparent recovery is thus estimated as the average of all measured values at 71 %. The standard deviation is 17 confirming the quantitative recovery but the low precision of this measurement. While PMMA and PS exhibit similar calibration curves at intermediate and high elution volumes, they are significantly different at low elution volume, i.e high molecular weight. PMMA are separated up to a molecular weight of a few millions as expected from this large pore GRAM 10,000 column. Polystyrene on the other hand exhibits an exclusion-limit like behaviour. This is probably not due to the exclusion limit but rather an artifact due to either lack of solubility of high molecular weight polystyrene in the eluent (DMSO is a poor solvent of polystyrene) or to degradation by shearing [14].

Density values for the solvent

Protocol for the determination of the amylose content of Sigma starch

In a 100 mL vol flask, 100 mg of starch were weighed, 1 mL ethanol was poured to disperse the starch, followed by 9 mL of NaOH (1M). It was refluxed until a clear and transparent dispersion was obtained. Then the ethanol was evaporated and 91 mL of water were added. A iodine solution was prepared by dissolving 0.2 g of iodine and 2 g of KI in 250 mL of water. In a different flask, 1 mL of the previous starch dispersion was poured, followed by 2 mL of a 7.005 gL -1 aqueous solution of citric acid, 1 mL of the iodine solution and finally 16 mL of water. After exactly 20 min, the absorbance of the sample was measured at 620 nm on a UV-Vis spectrometer (a blank was prepared following the previous protocol, except no starch was added). The amylose content of the starch sample was calculated from the measured absorbance (average of 6 single measurements) using a calibration curve established with standard samples of known amylose content.

Figure 1 .

 1 Figure 1. Number molar mass distribution obtained by aqueous (ammonium acetate) SEC directly after the synthesis of a model (1,4)-glucan (dashed line) and after freeze-drying and re-dissolution of the same sample (full line).

Figure 2 .

 2 Figure 2. Typical chromatogram of Sigma rice starch obtained as described in the text with the polar organic SEC.

Figure 3 .

 3 Figure3. Repeatability for injections of standards. Overlay of 5 chromatograms obtained from 5 injections of the same polystyrene standard using polar organic SEC.

Figure 4 .

 4 Figure 4. Repeatability of starch injections at 80 °C and room temperature on the polar organic SEC. Overlay of 5 injections at 80 °C of a sample A (full black line) and 5 injections at room temperature (23 C, dotted black line) of a sample B. The vertical gray full lines represent roughly the regions where the DPts (10 %, 30 %, 50 %, 70 % and 90 % of the total of the peak's area) should be.

Figure 5 .

 5 Figure 5. Reproducibility of starch injections at a) 80 °C, b) room temperature (23 °C) on the polar organic SEC. The reference chromatogram (full line) is compared to the injection of new prepared sample from the same batch (dashed line).

Figure 6 .

 6 Figure6. RID signal intensity and elution volume reproducibility of injections of starch at room temperature on the polar organic SEC: different operator, different sample preparation (from the same batch). Three sample preparations and injections by operator 1 (black lines): five injections displayed already for repeatability on figure4(full line) and compared to two other sample preparation: twice two injections (dashed lines and dotted lines). Two samples preparation by operator 2 (gray lines) each injected twice (dashed lines and dotted lines). The vertical gray full lines represent roughly the regions where the DPts (10 %, 30 %, 50 %, 70 % and 90 % of the total of the peak's area) should be.

Figure 7 . 20 Figure 8 .

 7208 Figure 7. a) Sequential 1 H NMR spectra recorded during the reaction of isopropanol and DSC in anhydrous DMSO-d6 at 25 °C after the spectra have been normalized with respect to the toluene signal at 2.38 ppm. The spectra shown were recorded after respectively 0, 0.5, 1, 2 and 5 h of reaction. b) Time evolution of signal integrals during the reaction of isopropanol and DSC, obtained by time-resolved 1 H NMR in different conditions: in DMSO-d6 at 25 °C (solid line), in acetonitrile-d3 at 25 °C (dotted line), in DMSO-d6 and LiBr at 25 °C (dashed line), in DMSO-d6 at 60 °C (gray solid line), in DMSO-d6 at 25 °C with molecular sieves (gray dashed line),. c) Time evolution of signal integrals during the reaction of activated isopropanol and amines, obtained by time-resolved 1 H NMR: 2-(2-naphthyl)-ethylamine (full squares), 2-naphthylamine (empty circles).

Figure 9 .

 9 Figure 9. a) Comparison of the RID chromatogram (left axis, top of the graph) obtained with the organic polar SEC for the unlabeled starch (solid line), the starch labeled with (dashed line) and without (dotted line) molecular sieves in the reaction medium; the residual plots are also presented (right axis, bottom graph) for the chromatogram of the starch labeled with (dashed line) and without (dotted line) molecular sieves in the reaction medium after subtraction of the chromatogram of the unlabeled starch normalized with respect to the whole chromatogram area. b) Same comparison for UV chromatograms. Residual plots are not given because of the presence of a large peak corresponding to the non-reacted UV-labeler on the chromatograms of the labeled starch.

  m X is the mass of X and d X is the density of X. The error in the densities is considered to be negligible compared those of the other parameters. The error in the measurement of the apparent recovery can thus be estimated as:

For

  the most precise measurement of concentration of the injected solutions, the quantity were measured by weighing and the weight of solvent was converted into volume using density values. The density values were obtained at 80 C by interpolation of literature values given in Table 3 and the following fit for the density, d, in g•mL -1 , as a function of temperature T: o for dimethylacetamide (DMAc) (correlation coefficient 0.965): ln d = -0.0010 T -0.0400 and d DMAc (80 C) = 0.886 o for dimethylsulfoxide (DMSO) (correlation coefficient 0.965): ln d = -0.0009 T+ 0.1093 and d DMSO (80 C) = 1.038 o for the eluent, d eluent , the density was calculated as 0.9 d DMAc (80 C) + 0,1 d DMSO (80 C) = 0.901 (assuming the 0.05 wt% lithium bromide does not significantly change the density).

  The two figures below show injections of polystyrene standards after dissolution in glass tube fitted with rubber Teflon tape. No unexpected peaks are obtained on the UV detector on the left. The polymer peaks on the DRI detector (8-12 mL) in the right have a conventional shape.

											0,10
				PS Mw = 34 000
				PS Mw = 319 000
											PS	Mw	=	34	000
	UVD response			PS Mw = 3 000 000	RID response	0,08 0,04 0,06	PS PS	Mw Mw	= =	319 3 000 000 000
											0,02
											0,00
											0	2	4	6	8	10	12	14	16	18
				Elution Volume (mL)	Elution	Volume	(mL)
		0,20		PS	Mw	=	34	000
											0,100
				PS	Mw	=	319	000
				PS	Mw	=	3	000	000
	UVD response	0,05 0,10 0,15									RID response	0,025 0,050 0,075	PS PS PS	Mw Mw Mw	= = =	34 319 000 000 3 000 000
		0,00
											0,000
		0	2	4	6			8		10	12	14	16	18
											0	2	4	6	8	10	12	14	16	18
											Elution	Volume	(mL)
				Elution	Volume	(mL)

Table 1 :

 1 calibration constants K for the RID from PMMA standardsThe average value was taken as the final calibration constant: 8.38 (standard deviation 13 %).The constant was also determined on pullulan standards and given in table 3:

	Sample (Mp value
	from the		PMMA
	manufacturer, g•mol -		Weight	Eluent
	1 )	Area	(mg)	(mg)	C (g•mL -1 ) K
	110,000	0.000967	14.34	6.8914	1.9837	6.68*
	217,000	0.00151	14.22	6.7909	1.9962	10.36
	520,000	0.00116	11.30	5.3990	1.9952	7.96
	981,000	0.000913	15.24	14.5643	0.9975	12.54*
	4,070,000	0.000489	13.23	12.6253	0.9990	6.71
	110,000	0.00121	18.13	8.6507	1.9979	8.30
	217,000	0.00129	10.74	5.1144	2.0019	8.83
	520,000	0.00113	11.84	5.6492	1.9980	7.75*
	981,000	0.000591	13.18	12.5906	0.9979	8.11
	4,070,000	0.000883	13.16	12.5440	1.0001	12.09*
	* extreme values, discarded

Table 2 :

 2 calibration constants K for the RID on period 2 from pullulan standards

	Sample (Mp value
	from the		Pullulan
	manufacturer, g•mol -		Weight	Eluent
	1 )	Area	(mg)	(mg)	C (g•mL -1 ) K
	106,000	0.000828	11.28	5.4422	1.9759	4,15*
	200,000	0.00225	10.2	4.8622	1.9998	11,14
	404,000	0.00282	10.31	4.9143	2.0000	13,96*
	710,000	0.00267	10.75	5.1628	1.9850	13,32
	1,540,000	1.30E-03	10.63	10.3244	0.9815	13,11
	* extreme values, discarded

Table 3 :

 3 apparent recovery values for the different injections of the starch sample. + once the dry starch has been dissolved in DMSO, a fraction of the solution (weight given in the column) is pipetted and then mixed with DMAc (weight given in the next column)

	Weighed	Est. dry	DMSO	Solution +	DMAc	c in (g/L)	expected	actual area	apparent
	Starch	starch	(g)	(g)	(g)		area	(average)	recovery
	(mg)	(mg)							(%)
	36.33	32.12	3.6350 0.1155	1.0573 0.000784 0.00066351 0.000579	87.3
	32.57	28.79	3.2554 0.1048	0.9429 0.000797 0.00067481 0.000572	84.7
	31.12	27.51	3.1149 0.1161	1.061 0.000785 0.00066428 0.000568	85.5
	29.54	26.11	2.9571 0.1310	1.1766 0.000797 0.00067483 0.000550	81.5
	31.31	27.68	3.1808 0.1082	0.9716 0.000786 0.00066510 0.0000533	80.2
	32.09	28.37	3.2016 0.1052	0.9682 0.000782 0.00066214 0.000413	62.3
	31.15	27.54	3.1153 0.1390	1.2539 0.000795 0.00067279 0.000444	66.1
	36.42	32.20	3.6894 0.1072	0.9798 0.000775 0.00065628 0.000439	66.9
	34.16	30.20	3.4026 0.1211	1.0943 0.000797 0.00067444 0.0004078	60.5
	32.60	28.82	3.2840 0.1128	0.9981 0.000803 0.00067983 0.00029048	42.7
	37.84	33.45	3.7805 0.1158	1.0468 0.000794 0.00067219 0.00041775	62.1

Table 1 :

 1 density values for dimethyl acetamide and dimethyl sulfoxide

		DMAc			DMSO
	T (C)	d (g•mL -1 )	Ref.	T (C)	d (g•mL -1 )	Ref.
		0.935	[1]	25	1.09602
		0.93169 0.93164	[3]	30 35	1.09038 1.08524	[2]
		0.9367		40	1.08064
		0.9363 0.9321	[4]	45 20	1.07683 1.0894
		0.9275		20	1.0896
		0.9276	[6]	20	1.091
		0.9376 0.9372	[7]	20 20	1.0906 1.090269
		0.9468		25	1.0853
		0.9421	[8]	25	1.0847
		0.9375		25	1.087
		0.950064		25	1.0856
		0.950272		30	1.0803	[5]
		0.950058		30	1.0797
		0.95013		30	1.0806
		0.949977		30	1.08046
		0.940846		35	1.0753
		0.941054		35	1.0748
		0.94084		40	1.0703
		0.940914		40	1.0698
		0.94076		40	1.06062
		0.936233		45	1.0655
		0.93644		25	1.0957
		0.936227 0.936304	[9]	25 30	1.0954 1.0907	[4]
		0.936149		35	1.0858
		0.931618		25	1.0955
		0.931826		25	1.096
		0.931612		25	1.0955
		0.931689		30	1.0904
		0.931534 0.922369		40 40	1.0803 1.0804	[10]
		0.922579		50	1.0702
		0.922363		75	1.0454
		0.922441		100	1.02
		0.922287		125	0.9946
		0.913094		20	1.100401	[11]

Acknowledgements

PC would like to thank Chun-Wai Wayne Yuen and David Page for their help to set up the separation with organic solvent. We are grateful to the Australian Research Council (ARC) for funding through Discovery Project DP 665360.

Supporting information for

Toward a full characterization of native starch: separation and detection by size exclusion chromatography Ngoc-Ly Hoang, Antonin Landolfi, Anastasiya Kravchuk, Etienne Girard, Jonathan Peate, Javier M. Hernandez, Marianne Gaborieau, Olena Kravchuk, Robert G. Gilbert, Yohann Guillaneuf,

Patrice Castignolles

Importance of not using rubber septum during sample preparation

The two figures below show injections of polystyrene standards after dissolution in a glass tube fitted with rubber septa (no direct contact between the eluent and the septum). Unexpected peaks are obtained on the UV detector on the left (polystyrene has a limited UV absorbance at the used wavelength of 280 nm). The polymers peaks on the DRI detector on the right have anomalous shape.

Calibration curves for the organic eluent Size Exclusion Chromatography (SEC)


Obaida Alrazouk
email: obaida.alrazouk@univ-evry.fr

Amine Chellali

Lamri Nehaoua

Hichem Arioui

Efficient Real-Time Road Curvature Estimation : Visual-Inertial Approach

Road curvature is an essential parameter of road geometry, and it is crucial to set vehicle design and operating speeds. It can be utilized to identify the maximum stable velocity of a Powered Two Wheeled Vehicle (P2WV) and predict other safety-related events, including Lane departure and lane crossing. This paper proposes a new vision-based approach to estimate the road's curvature accurately and efficiently under real-time constraints for P2WV. The proposed method is based on the vanishing point approach to estimate the relative heading and its dynamics. Combined with the available vehicle speed and the yaw rate given by the inertial measurement unit (IMU), the instantaneous curvature of the road is reconstructed. The proposed algorithm is then tested using various simulated scenarios of different speeds and curvatures to validate the approach. Then it was compared to other estimation methods based on Inverse Perspective Mapping (IPM) to investigate the validity and efficiency in all scenarios regarding accuracy and time complexity. The proposed method shows very promising results in terms of error and real-time execution.

INTRODUCTION

Road safety has improved significantly during the past decades, thanks to higher quality training programs that have produced more qualified drivers on roads and increased adoption of driver's assistance and warning systems. In particular, Powered Four-Wheeled Vehicles (P4WV) have been gradually equipped with Advanced Driver Assistance Systems (ADAS), many of which have become required by law (e.g., Electronic Stability Control, Anti-lock Braking System, airbag systems). Despite these improvements, little has been done for P2WV. Riders are still among the most vulnerable road users. A study published in 2019 ONISR (2019) shows that P2WV crashes are 22 times more fatal than P4WV, accounting for 23% of all traffic fatalities. Most P2WV crashes are due to problems when maneuvering curves.

For a novice driver, negotiating a bend in P2WV can be very complicated. The rider must adapt his speed to the geometry of the road, anticipate his trajectory, and carry out the vehicle's movement. The slightest error may lead to a fall. Even for expert riders, bends are high-risk areas due to inappropriate speeds or poor road conditions. [START_REF] Schneider | Effects of horizontal curvature on singlevehicle motorcycle crashes along rural two-lane highways[END_REF] and [START_REF] Clarke | In-depth study of motorcycle accidents[END_REF] conducted studies concerning the influence of road geometry on P2WV accidents. They clearly showed that curvature impacts the frequency and severity of P2WV accidents. They point out that 15% of all fatal P2WV accidents take place in bends for riders who are, in general, inexperienced. Among the factors involved, the authors identify the radius of the road curvature. It seems evident that adequate driver assistance systems could significantly contribute to reducing the number of P2WV accidents when cornering.

When cornering, the rider is supposed to anticipate the trajectory to perceive and decipher all the relevant safety cues. In addition to safety requirements, such as maintaining the traffic lane, it is necessary to consider the possibility of adapting the trajectory by narrowing it or widening it to avoid possible obstacles on the roadway. Therefore, the road's curvature determines the maximum safe speed to execute a maneuver.

Vision-based techniques to estimate road curvature have existed for a while. They all rely on the detection of lane markers. In the early 1980s, [START_REF] Dickmanns | A CURVATURE-BASED SCHEME FOR IMPROVING ROAD VEHI-CLE GUIDANCE BY COMPUTER VISION[END_REF] proposed the first idea of using the extra information from the road lane markers to reconstruct the road curvature, vehicle's lateral offset, and relative heading using vision. After that, several algorithms have been developed using monocular cameras [START_REF] Pomerleau | RALPH: rapidly adapting lateral position handler[END_REF] or stereo vision systems [START_REF] Bertozzi | GOLD: a parallel real-time stereo vision system for obstacle and lane detection[END_REF], region-based [START_REF] Alvarez | Novel Index for Objective Evaluation of Road Detection Algorithms[END_REF], feature-based [START_REF] Liu | Vision-Based Real-Time Lane Marking Detection and Tracking[END_REF], and spline fitting [START_REF] Wang | Lane detection using spline model[END_REF] and [START_REF] Kim | Realtime lane tracking of curved local road[END_REF]. However, since all these methods were developed with a P4WV in mind, they relied on IPM to achieve a bird's eye view (BEV) of the road and then recover the lanes under the assumption of negligible roll dynamics.

However, these methods suffer from some problems. The limitation on the vehicle speed and the need for a road model, which are mostly assumed circular ignoring the change in curvature. Which sometimes could be significant. In addition, most of these approaches also rely on the assumption of a negligible roll angle. This assumption does not hold for P2WV as the rolling dynamics are significant, and thus making the IPM requires extra information about the roll angle based on inertial measurements. Estimating angles using an IMU sensor is vulnerable to drift errors.

Regarding curvature estimation, only a few studies have been done using a motorcycle. However, in a recent work, [START_REF] Damon | Image-based lateral position, steering behavior estimation, and road curvature prediction for motorcycles[END_REF] built on Dickmanns findings and extended to motorcycles to estimate the lateral offset, relative heading, and road curvature, taking into account the roll motion of the vehicle. However, the results for the curvature had large errors, despite assuming that the IMU provides a perfect angular position.

To solve this problem, a model-free, real-time, vision-based technique is proposed using a monocular camera aided with angular rates reading from the IMU to accurately estimate the curvature without needing a road model. First, the lane markers are detected, each fitted to a line, then the vanishing point of these lines is calculated, then the relative heading is estimated. After that, the relative heading rate is combined with the vehicle yaw rate to estimate the road's curvature more precisely.

DEFINITION AND OVERVIEW

Consider the case of a P2WV with a monocular camera traveling on a curved planar road under the assumption of visible lane markers. Let R w the world inertial frame. R o is the ground reference frame, where the x, y axes are in the plane of the road and its z-axis is upwards. This frame follows the road lane marker as its x-axis is always tangent to the lane marker. R v is the vehicle body frame, defined at the front wheel contact point when there is no steering. R cs is the camera frame which results from rotating R v around it y-axis with a known fixed angle µ. Let R cp be another camera frame that follows the pinhole camera frame definition, where its origin is the optical point, its z-axis is the optical axis. Its x and y axes are the same orientation of the image's plane x and y directions, and finally, let R ocp be a local reference frame where its z-axis is always a tangent to the road lane marker, its x-axis it perpendicular to the lane marker to the inside of the road, and its y-axis is pointing downwards. It can be seen easily that the rotation matrix from R ocp to R o and from R cp to R cs are given by:

o R ocp = cs R cp = 0 0 1 -1 0 0 0 -1 0 (1)
The last two reference frames are defined in this way to facilitate the estimation of the yaw angle. ψ k is the relative heading angle between the vehicle heading and the x-axis of R o . v is the vehicle velocity at C. ψ tan is the angle between x o and x w , and ψ v is the vehicle's yaw angle. v is the velocity value, and v x is the longitudinal velocity. Figures 1 and2 illustrate the frames. Based on that definition, it can be shown that:

ψ k = ψ tan -ψ v (2)
Taking the derivative of equation ( 2) and dividing by v x : ψk

v x = ψtan v x - ψv v x (3)
Under the assumption of near steady turning, one can estimate the curvature of the road as:

ρ = ψtan v x (4)
Substituting equation ( 4) in ( 3) and isolating ρ gives:

ρ = ψk + ψv v x (5)
By approximating the value of v x by v:

ρ = ψk + ψv v (6)
Assuming the knowledge of v and ψv , which is outputted by the IMU, ψk is the only one left to recover the curvature. The latter actually can be estimated using vision.

ESTIMATING RELATIVE HEADING AND ITS DERIVATIVE

Estimating pan angle from a vanishing point

Vanishing point detection is widely used in the literature to calibrate or recover the camera's pose. A vanishing point is where the perspective projections of parallel lines intersect, defining a point at infinity at real-world coordinates.

For a pinhole camera, the equation of perspective projection in the homogeneous coordinates is as follows:

s • u v 1 = K × [ cp R ocp |t] ×    X Y Z 1    (7)
Where u, v are the pixel coordinates, and X, Y, Z are the coordinates in camera frame in meters, K is the 3x3 calibration matrix, cp R ocp is the 3x3 rotation matrix, t is the translation vector between R cp and R ocp .

The interest is to find the vanishing point where the two road lanes intersect, which is in the z direction in the road frame R ocp . This vanishing point is expressed in the homogeneous coordinate system as

V z = [0 0 1 0] T (8)
The zero at the last component indicates that the point lies at infinity. Assuming that v pix is the coordinates in pixel of the vanishing point in the image plane:

v pix = K × [ cp R ocp |t] × [0 0 1 0] T (9) which leads to v pix = K × r 3 .
(10) Where r 3 is the 3 rd column of the rotation matrix cp R ocp , knowing that r 3 should have a unit length:

r 3 = K -1 × v pix K -1 × v pix (11)
However, r 3 can be expressed using pan and tilt angles only (α, β respectively) as:

sin α • cos β -sin β cos α • cos β = K -1 × v pix K -1 × v pix (12)
Because of the way the camera is defined, it is only possible to get the last row of the rotation matrix cp R ocp from the vanishing point. In order to estimate pan and tilt, a representation that enables to calculate the two angles just from the last column has to be chosen. Thus the use of the Y XZ Euler representation, where the rotation matrix takes the following form:

cp R ocp = c α c γ + s α s β s γ c γ s α s β -c α s γ s α c β c β s γ c β c γ -s β -c γ s α + c α s β s γ c α c γ s β + s α s γ c α c β (13)
Where s θ is sin θ, and c θ is cos θ. It can be seen that the last column is just composed of the pan and tilt angles. From this, the connection between the vanishing point and the pan and tilt angles can be concluded:

r 3 = sin α • cos β -sin β cos α • cos β (14)
Which gives the equations of both α and β as follows:

α = atan2(r 3 (1), r 3 (3)), β = -asin(r 3 (2)) (15) where r 3 (1), r 3 (2), r 3 (3) are the components of r 3 . However, these pan and tilt angles are represented in Y ZX Euler representation as seen in the next section, not the standard ZY X representation of interest.

From Y ZX to XY Z Euler representation

It can be shown that α is exactly the yaw angle of R cs from R o , and β is the pitch angle of the frame R cs from R o following an XY Z Euler angles representation. In order to prove that α and β are the yaw and pitch angles in XY Z representation, o R cs need to be written in terms of α and β and compare it with the rotation matrix in the XY Z convention. Starting from cp R ocp as illustrated in equation ( 13), it can be found that: 14) and ( 17) in ( 16) results in:

o R cs = o R ocp × ocp R cp × cp R cs (16) Where o R ocp is available from equation (14). Moreover, it is known that: ocp R cp = cp R T ocp (17) Substituting (
o R cs = cp R T cs × cp R T ocp × cp R cs (18)
Furthermore, from (13) by substituting by values:

cp R ocp = c α c β -s α c β s β c γ s α -c α s β s γ c α c γ + s α s β s γ c β s γ -c α s β c γ -s α s γ s α s β c γ -c α s γ c β c γ (19)
On the other hand, the rotation matrix constructed from the XYZ Euler convention can be given by:

o R cs = R x (-ϕ) × R y (θ) × R z (ψ)
(20) By doing the matrices product, it can be shown that:

cp R ocp = c ψ c θ -s ψ c θ s θ c ϕ s ψ -c ψ s θ s ϕ c ψ c ϕ + s ψ s θ s ϕ c θ s ϕ -c ψ s θ c ϕ -s ψ s ϕ s ψ s θ c ϕ -c ψ s ϕ c θ c ϕ (21) Since -π 2 < α, β, γ < π
2 the rotation is unique, that means there is only one set of (α, β, γ) that constructs this rotation, thus ψ = α, θ = β, ϕ = γ. This proves that α is indeed the yaw angle and β is the pitch angle of the camera in the XY Z Euler convention.

That proves that α, β are the yaw and pitch of the camera in the XY Z representation. However, the interest is in the vehicle's relative yaw angle in ZY X representation.

From camera's yaw angle to vehicle's yaw angle

Writing the camera's rotation matrix starting from the vehicle's transformation matrix in ZY X representation:

o R cs = o R v × v R cp (22)
Which is equal to:

o R cs = R z (ψ v ) × R y (θ v ) × R x (ϕ v ) × R y (µ) (23)
On the other hand, writing the rotation matrix of the camera in XY Z representation gives the following:

o R cs = R x (ϕ c ) × R y (θ c ) × R z (ψ c ) (24)
Since the rotation matrix is the same regardless of the representation, the following can be written:

R z (ψ v )×R y (θ v )×R x (ϕ v )×R y (µ) = R x (ϕ c )×R y (θ c )×R z (ψ c ) ( 25
)
The aim is to express ψ v by only terms of ψ c , θ c , µ. However, this is not directly available from equation (25).

Luckily, by utilizing a simple approximation of θ v ≈ 0 which translates to cos θ ≈ 1, sin θ ≈ 0, the matrix on the left side of (25) can be simplified. By taking the second column of both sides, it can be shown that:

c θc c ψc -c θc s ψc s θc = c µ c ψv -s µ s ϕv s ψv -c ϕv s ψv c ψv s µ + c µ s ϕv s ψv (26) Which leads to: c θc c ψc -c µ c ψv c θc s ψc s θc -c ψv s µ = -s µ s ϕv s ψv c ϕv s ψv c µ s ϕv s ψv (27)
By dividing the first row by the third in equation ( 27):

c θc c ψc -c µ c ψv s θc -c ψv s µ = -s µ c µ (28)
Which leads to the following equation:

cos ψ v = cos θ c cos ψ c + tan µ sin θ c tan µ sin µ + cos µ (29)
Using equation ( 29) it is possible to recover the value of the required angle. However, it is known that arccos does not recover the sign. To recover the sign of the angle, the second row from equation ( 27) can be used:

sign(sin ψ v cos ϕ v ) = sign(cos θ c sin ψ c ) (30) since -π 2 < ϕ v , θ c < π 2 that means that cos ϕ v , cos θ c > 0. Which translates to: sign(sin ψ v ) = sign(sin ψ c ) (31) Which gives: sign(ψ v ) = sign(ψ c ) (32)
From ( 32) and ( 29), it can be concluded that:

ψ k = ψ v = sign(ψ c ) arccos ( cos θ c cos ψ c + tan µ sin θ c tan µ sin µ + cos µ ) (33)
Before estimating the ψ k rate, one should consider filtering ψ k to remove the noise and smooth the function. A Gaussian average filter with a window size of the number of samples in a second is applied. After filtering, the derivative at sample n is estimated using the following:

ψk,n = ψ k,n -ψ k,n-1 t n -t n-1 (34)
Where ψ k,n is the estimated filtered relative heading at sample n, and t n is the time at sample n.

Detecting the vanishing point

For detecting the pixel coordinates of the vanishing point, many methods exist in the literature [START_REF] Dixon | An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics[END_REF] and [START_REF] Huang | Fuzzy chaos control for vehicle lateral dynamics based on active suspension system[END_REF] but basically, they all rely on the same principle, detecting the lane edges (and other parallel lines) remove the outliers and find the intersecting point of these lines. The same basic idea is used assuming that the two edge lane markers are always visible to the camera, empty road, clear sky, and no strange objects nearby. First, the image is converted to a binary image through thresholding, then detecting connected components and filtering them out according to their size, then picking the left and right lanes, extracting one edge of each lane for the first few meters in front of the camera, fit each edge points with a line, then intersecting these two lines to detect the tangent point. Figure 3 illustrates these steps. The growth of computational power allowed to build, calculate, and simulate complex vehicle models. Advanced simulator software that help simulate different scenarios are available cheaply, more conveniently, and accurately enough without experimenting on actual vehicles and with the ability to measure different variables by installing cameras and IMUs on a specific point. One of the most popular software to simulate P2WV is BikeSim, which is used here to create different driving scenarios. Several roads were constructed with known curvatures at each point and tested several scenarios with sections of low curvature, changing curvature, fixed curvature, and straight road. It is important to mention that the roads are planar, empty with a well-lit environment, and no strange objects in the scene. The camera was installed at the height of h = 1.1m and tilted µ = 15 • in the virtual environment. The camera's resolution was (1080x720) at 60 FPS with a horizontal field of view of 80 • . All these tests were carried out on a Matlab R2020b environment, installed on Windows 10, on a mid-range laptop with an AMD Ryzen 3750H chip.

Clothoid track

The clothoid track has varying curvature, so it is considered hard to estimate, especially at high speeds. Which is defined by C(l) = C 0 + C 1 .l where C 0 is the initial curvature, C 1 is the curvature rate, and l is the curve length.

This part has been simulated at 80km/h. The estimation of curvature for the clothoid is very good and accurate, as in figure 4.a, with an RMS value of 1.1 * 10 -4 [m -1 ]. One important thing to note is that the estimation preserved the linearity of curvature change despite being very small.

Circular track

In this scenario, the circular track is a road with fixed curvature. Usually, it is not hard to estimate, but this becomes more difficult to estimate the lower the curvature and the higher the speed. Thus, estimating such a slight curvature of 10 -3 [m -1 ] at high speed 120km/h is very interesting because it asses the algorithm's performance. The estimation of the slight curvature is also very good and accurate, as in figure 4.b, with an RMS value of 2.3 * 10 -5 [m -1 ].

Straight road

The straight line is technically the easiest for the algorithm and has a curvature of zero (infinite radius). The estimation of curvature for the clothoid is also very good, as in figure 4.c, with an RMS value of 3.2 * 10 -5 .

Complex track with multiple sections

This track represents a challenging scenario where the track is changing shape. It is constructed from several connected sections. Each section is a straight line, a circle, or a clothoid. The curvatures are high; this is why this scenario is done at a low speed of 50km/h, which took approximately 144 sec to achieve. In figure 4.d, the approximation is very accurate, with more significant errors on the points of discontinuity. The most popular methods for curvature estimation are the ones that utilize the IPM technique. After doing the IPM, the lanes are fitted to a 3 rd degree polynomial or a circle. A comparison between the proposed method, the 3 rd degree polynomial fitting using IPM presented by [START_REF] Damon | Image-based lateral position, steering behavior estimation, and road curvature prediction for motorcycles[END_REF], and circle fitting presented by [START_REF] Pratt | Direct least-squares fitting of algebraic surfaces[END_REF], which also uses the least squared method to optimize for the curvature is presented in figure 5.a, and a comparison of errors of estimation, is provided in figure 6.d for the long multi-section track. The same dataset was fed to the three different algorithms to compare their accuracy. Table 1 demonstrates the RMSE of each method for all types of roads mentioned earlier. It is seen that the proposed method has orders of magnitude less error on clothoid and straight roads compared to the other methods. Figure 6.d illustrate the estimation error in each case.

In figure 5.a, the 3 rd degree polynomial fitting is the least accurate. It suffers significantly on section change, clothoid section, and even on a circular section with fixed curvature. The circle fitting method performs better in general but also fails on the clothoid section and overshoots for circular sections. It can be clearly seen that the proposed method In addition, there is also a difference in performance. The proposed method can do a stable 120fps on the resolution of (1080x720), while the other two methods can only do a stable 60fps on the exact image resolution. This is because the IPM step is computationally expensive. Table 2 shows the maximum FPS that each method can perform.

DISCUSSION

As stated in the simulation section, the estimation is very close in all scenarios and performs better than the state of art that utilize IPM techniques in terms of accuracy and computation time. However, the approximation for the points of discontinuity for curvature is less accurate, as illustrated in figure 5.b, and as represented in sharp pulses of error in figure 6.d. The reason for this lies in the visual approach itself because the fitted lane markers are parts of the foreseen curvature, not the actual curvature at the motorcycle position, but the difference is very small depending on how much distance ahead is captured by the camera. More precisely, the approximation of ψ k from the vanishing point approach using vision relies on fitting the lane marker visible in the image, which is always a little ahead of the actual curve point assumed to be calculated. This effect can be dramatically reduced by using a large field of view camera.

As seen in table 1, the algorithm proves to be very accurate in all scenarios with very low RMSE values. It has orders of magnitude less error than the compared methods in clothoid and straight roads and half the error in the others.

In addition, it preserves the linear change in curvature for a clothoid road. As seen from figure 5.a and 6.d, the proposed method performs significantly better than the other compared methods, At (1080x720), and as seen in table 2, the proposed method can perform twice as fast. It can do 135fps compared to the 78fps in IPM with circle fit and 77fps in IPM with 3 rd degree polynomial. The main reason for the time complexity difference is the utilization of the computationally expensive IPM technique.

While increasing the image's resolution will significantly improve the IPM-based methods, it has little to no effect on the proposed method because it relies on the calculation of the tangent point, which is done by intersecting the fitted lines to have sub-pixel coordinates of the intersection point. Increasing the resolution after a threshold will not change the equations for the fitted lines, thus the intersection point does not change. A primary disadvantage of the IPM-based techniques is the utilization of the roll angle, which suffers from drift due to the integration of the IMU roll rate. In comparison, the proposed method utilizes the yaw rate directly measured by the IMU, leading to no drift error.

CONCLUSION

Road curvature is a very important parameter for P2WV, as it can set the maximum safe speed and help predict lane departure and crossing. This work introduces a visualinertial approach to estimate road curvature in real time. The advantage of this method is that it does not assume a road model, works on P2WV with significant rolling dynamics, and is faster than other IPM-based techniques.

Under the assumptions of a planar road, lane marks that are visible at all times, empty roads, and good lighting conditions, the proposed method can accurately estimate the instantaneous curvature of the road. For each image taken, the relative heading is estimated using the vanishing point approach by extracting the lane markers in the near vicinity and fitting them into straight lines, then intersecting these lines to have the vanishing point coordinates, which will give the relative heading. After that, the derivative of the relative heading is estimated and added to the yaw rate measured from the IMU. Combined with the velocity, the latter sum estimates the curvature.

The proposed method was tested on several simulated driving scenarios on different tracks, varying in difficulty and speed. It was able to estimate the curvature accurately. It was also compared using a long track with several sections of different curvatures to IPM-based techniques that use 3 rd degree polynomial fit and circle fit to esti-mate the lane markers curve in the image. The proposed method performed better than the others in every scenario, especially scenarios where the curvature is changing.

ACKNOWLEDGMENT

This work has been financially supported by projet ANR eMC2 number ANR-22-CE22-0012.

Fig. 1 .

 1 Fig. 1. P2WV on a curved road, frames definition-Top view

Fig. 2 .

 2 Fig. 2. P2WV on a curved road, with frames definition

Fig. 3 .

 3 Fig. 3. Estimating relative heading-algorithm steps

Fig. 5 .

 5 Fig. 4. Estimating curvature in various scenarios

Fig. 6 .

 6 Fig. 6. Curvature error estimation in different scenarios outperforms the other techniques significantly, plus it conserves the linear change of curvature for clothoid sections.

Table 1 .

 1 RMSE of curvature estimation in different scenarios for different methods

	Scenario	IPM 3 rd deg	IPM circle fit	Proposed
		poly fit [m -1 ]	[m -1 ]	method[m -1 ]
	Straight road	0.0011	7.70E-05	3.25E-05
	Circular road	0.0014	1.04E-04	5.40E-05
	Clothoid	0.0438	0.0144	3.80E-04
	road
	Combined	0.0038	0.0025	0.0012
	sections

Table 2 .

 2 FPS values for different methods

	Method	IPM 3 rd deg	IPM circle fit	Proposed
		poly fit		method
	FPS (Hz)	77.4	78.5	135.3