# Production of Chondroitin Sulphate from Head, Skeleton and Fins of Scyliorhinus canicula By-Products by Combination of Enzymatic, Chemical Precipitation and Ultrafiltration Methodologies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Enzymatic Hydrolysis of Head Cartilages. Effect of pH and Temperature (T)

**Figure 1.**Kinetics of cartilage hydrolysis from Scyliorhinus canicula heads using alcalase in each one of the experimental conditions defined in Table 1. The experimental data (symbols) were fitted to the Weibull Equation (4) (continuous line).

**Table 1.**Parametric estimations corresponding to the Weibull Equation (4) applied to the enzymatic hydrolysis kinetics at the experimental conditions studied. Independent variables are expressed in natural values in brackets. Numerical values of the parameters are shown with their confidence intervals. Determination coefficients (R

^{2}) and p-values from F-Fisher test are also summarized. H

_{m}is the maximum degree of hydrolysis; β is a parameter related with the maximum slope of cartilage hydrolysis; τ is the time required to achieve the semi-maximum degree of hydrolysis and v

_{m}is the maximum hydrolysis rate at the τ-time.

Experimental Conditions | H_{m} (%) | v_{m} (%·min^{−1}) | τ (min) | β | R^{2} | p-value |
---|---|---|---|---|---|---|

T:−1 (37.3 °C)/pH:−1 (6.9) | 5.05 ± 0.31 | 0.030 ± 0.004 | 51.51 ± 6.00 | 0.89 ± 0.10 | 0.982 | <0.001 |

T:1 (72.7 °C)/pH:−1 (6.9) | 9.85 ± 0.04 | 0.262 ± 0.007 | 9.82 ± 0.34 | 0.75 ± 0.03 | 0.993 | <0.001 |

T:−1 (37.3 °C)/pH:1 (11.1) | 14.04 ± 0.46 | 0.067 ± 0.005 | 54.65 ± 3.73 | 0.75 ± 0.03 | 0.996 | <0.001 |

T:1 (72.7 °C)/pH:1 (11.1) | 5.93 ± 0.21 | 0.045 ± 0.002 | 139.0 ± 3.17 | 3.03 ± 0.19 | 0.991 | <0.001 |

T:−1.41 (30.0 °C)/pH:0 (9.0) | 12.80 ± 0.33 | 0.079 ± 0.005 | 44.88 ± 2.32 | 0.80 ± 0.03 | 0.994 | <0.001 |

T:1.41 (80.0 °C)/pH:0 (9.0) | 15.81 ± 2.03 | 0.082 ± 0.071 | 14.11 ± 12.42 | 0.21 ± 0.02 | 0.992 | <0.001 |

T:0 (55.0 °C)/pH:−1.41 (6.0) | - | - | - | - | - | - |

T:0 (55.0 °C)/pH:1.41 (12.0) | 4.34 ± 0.15 | 0.059 ± 0.003 | 190.23 ± 1.83 | 7.47 ± 0.44 | 0.993 | <0.001 |

T:0 (55.0 °C)/pH:0 (9.0) | 18.83 ± 0.14 | 0.225 ± 0.006 | 19.65 ± 0.45 | 0.68 ± 0.02 | 0.997 | <0.001 |

T:0 (55.0 °C)/pH:0 (9.0) | 23.44 ± 0.28 | 0.162 ± 0.006 | 30.10 ± 0.93 | 0.60 ± 0.01 | 0.999 | <0.001 |

T:0 (55.0 °C)/pH:0 (9.0) | 19.86 ± 0.16 | 0.179 ± 0.004 | 26.70 ± 0.52 | 0.69 ± 0.01 | 0.998 | <0.001 |

T:0 (55.0 °C)/pH:0 (9.0) | 22.67 ± 0.20 | 0.209 ± 0.006 | 23.80 ± 0.55 | 0.63 ± 0.01 | 0.998 | <0.001 |

T:0 (55.0 °C)/pH:0 (9.0) | 21.06 ± 0.18 | 0.206 ± 0.006 | 23.21 ± 0.53 | 0.66 ± 0.02 | 0.998 | <0.001 |

_{p}as %). The design and numerical responses of the 2-factor rotatable design are listed in Table 2. For these two responses, the average and corresponding errors (calculated as the intervals of confidence in the five replicated conditions) were: 9.01 ± 0.36 g/L of CS and 89.61% ± 0.53% for I

_{p}.

**Figure 2.**Predicted response surfaces by empirical equations summarized in Table 3 corresponding to the combined effect of pH and T on the different dependent variables evaluated for the study of head-cartilages proteolysis by alcalase.

**Table 2.**Summary of the independent variables (T, pH) in the response surface design with the corresponding experimental (Y

_{e}) and predicted (Y

_{p}) results of alcalase head-cartilage hydrolysis, CS production and CS purity regarding total protein (I

_{p}). Natural values of experimental conditions are in brackets.* Determination of CS and I

_{p}was only done at the end of the hydrolysis time (4 h).

Independent Variables | H_{m} (%) | v_{m} (% min^{−1}) | τ (min) | CS (g/L) * | I_{p} (%) * | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

X_{1}: T | X_{2}: pH | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} |

−1 (37.3) | −1 (6.9) | 5.05 | 5.21 | 0.030 | −0.018 | 51.5 | 41.7 | 7.09 | 6.86 | 85.12 | 84.64 |

1 (72.7) | −1 (6.9) | 9.85 | 11.67 | 0.282 | 0.178 | 9.8 | −21.3 | 9.21 | 8.35 | 89.43 | 86.33 |

−1 (37.3) | 1 (11.1) | 14.04 | 11.67 | 0.067 | 0.119 | 54.7 | 79.1 | 3.85 | 4.74 | 76.48 | 74.85 |

1 (72.7) | 1 (11.1) | 5.93 | 5.21 | 0.045 | 0.041 | 139.0 | 142.1 | 3.00 | 3.25 | 77.42 | 73.17 |

−1.41 (30) | 0 (9.0) | 12.80 | 14.58 | 0.079 | 0.065 | 44.9 | 24.7 | 7.45 | 7.40 | 85.25 | 86.01 |

1.41 (80) | 0 (9.0) | 15.81 | 14.58 | 0.082 | 0.148 | 14.1 | 24.7 | 7.38 | 7.40 | 82.02 | 86.01 |

0 (55) | −1.41 (6.0) | 0.00 | 2.45 | 0.00 | 0.055 | 0.00 | 24.9 | 6.00 | 6.78 | 80.12 | 81.69 |

0 (55) | 1.41 (12.0) | 4.34 | 2.45 | 0.059 | 0.055 | 190.2 | 166.5 | 2.50 | 1.69 | 62.32 | 65.51 |

0 (55) | 0 (9.0) | 18.83 | 21.17 | 0.225 | 0.196 | 19.7 | 24.7 | 9.02 | 9.01 | 89.77 | 89.60 |

0 (55) | 0 (9.0) | 23.44 | 21.17 | 0.162 | 0.196 | 30.1 | 24.7 | 9.00 | 9.01 | 89.64 | 89.60 |

0 (55) | 0 (9.0) | 19.86 | 21.17 | 0.179 | 0.196 | 26.7 | 24.7 | 9.60 | 9.01 | 90.28 | 89.60 |

0 (55) | 0 (9.0) | 22.67 | 21.17 | 0.209 | 0.196 | 23.8 | 24.7 | 8.99 | 9.01 | 89.71 | 89.60 |

0 (55) | 0 (9.0) | 21.06 | 21.17 | 0.206 | 0.196 | 23.2 | 24.7 | 8.45 | 9.01 | 88.63 | 89.60 |

**Table 3.**Second order equations describing the effect of T and pH on alcalase cartilage hydrolysis, CS production and I

_{p}-index (coded values according to criteria defined in Table 1). The coefficient of adjusted determination (${R}_{adj}^{\text{2}}$) and F-values (F

_{1}, F

_{2}, and F

_{3}) is also shown. S: Significant; NS: Non-significant.

Parameters | H_{m} | v_{m} | τ | CS | I_{p} |
---|---|---|---|---|---|

b_{0} (intercept) | 21.17 | 0.196 | 24.69 | 9.01 | 89.60 |

b_{1} (T) | - | 0.029 | - | - | - |

b_{2} (pH) | - | - | 50.21 | −1.80 | −5.74 |

b_{12} (TxpH) | −3.23 | −0.069 | 31.50 | −0.74 | −0.84 |

b_{11} (T^{2}) | −3.31 | −0.045 | - | −0.81 | −1.80 |

b_{22} (pH^{2}) | −9.42 | −0.071 | 35.73 | −2.40 | −8.05 |

${R}_{adj}^{\text{2}}$ | 0.929 | 0.752 | 0.874 | 0.927 | 0.882 |

F_{1} | 53.62 $[{F}_{9}^{3}=3.86]\Rightarrow S$ | 5.33 $[{F}_{8}^{4}=3.84]\Rightarrow S$ | 28.86 $[{F}_{9}^{3}=3.86]\Rightarrow S$ | 39.01 $[{F}_{8}^{4}=3.84]\Rightarrow S$ | 23.40 $[{F}_{8}^{4}=3.84]\Rightarrow S$ |

F_{2} | 0.39 $[{F}_{3}^{8}=8.85]\Rightarrow S$ | 0.67 $[{F}_{4}^{8}=6.04]\Rightarrow S$ | 0.41 $[{F}_{3}^{8}=8.85]\Rightarrow S$ | 0.52 $[{F}_{4}^{8}=6.04]\Rightarrow S$ | 0.54 $[{F}_{4}^{8}=6.04]\Rightarrow S$ |

F_{3} | 1.17 $[{F}_{4}^{9}=6.00]\Rightarrow S$ | 5.09 $[{F}_{4}^{8}=6.04]\Rightarrow S$ | 24.76 $[{F}_{4}^{9}=6.00]\Rightarrow NS$ | 2.71 $[{F}_{4}^{8}=6.04]\Rightarrow NS$ | 21.11 $[{F}_{4}^{8}=6.04]\Rightarrow NS$ |

_{m}and CS) was successfully described by the second order equations. In any case, the agreement among experimental and predicted data was always greater than 75% and the robustness was good in all cases; it demonstrated the predictive capacity of the empirical equations in the range of T and pH here studied. The results of the multivariate analysis showed significant quadratic negative terms for pH and T (p < 0.05). This translates graphically in a dome (convex surface) with clear maximum points for the experimental domains of pH and T (Figure 2). The inverse response obtained for τ-parameter (concave surface) is in agreement with the fact that when the enzymatic hydrolysis is greater and faster (high H

_{m}and v

_{m}), the values of τ are shorter.

_{opt}and T

_{opt}) that maximize the corresponding measured responses (Y

_{max}) can be obtained by mathematical optimization using numerical or manual derivation [19] (Table 4). The optimal ranges depending on the variable of response were 55–62.6 °C and 8.14–9 for T and pH, respectively. Because all responses are equally important, it has been established the average of the values from Table 4 as the compromise option to select the best condition of pH

_{opt}and T

_{opt}. Thus, the values for the subsequent treatment in the alkaline hydroalcoholic solution were: pH = 8.5 and T = 58.1 °C.

**Table 4.**Optima values of the two independent variables (T

_{opt}and pH

_{opt}) to obtain the maximum responses from the equations defined in Table 3 and for the different dependent variables studied.

^{a}In this case, the optima values of T and pH are those that minimize the response of τ.

H_{m} | v_{m} | τ | CS | I_{p} | |
---|---|---|---|---|---|

T_{opt} (°C) | 55.0 | 62.6 | - | 58.3 | 56.5 |

pH_{opt} | 9.0 | 8.6 | 9.0 ^{a} | 8.14 | 8.23 |

Y_{max} | 21.17 | 0.204 | - | 9.38 | 90.6 |

#### 2.2. Enzymatic Hydrolysis of Skeletons and Fins Cartilages

**Figure 3.**Enzymatic hydrolysis at two pH levels for different cartilages from S. canicula wastes (left). To the right, long hydrolysis at the best pH selected are additionally shown. Experimental data were fitted to the Weibull Equation (4). (

**A**) Fins; (

**B**) Heads and (

**C**) Skeletons.

**Table 5.**Parametric estimations corresponding to the Weibull Equation (4) applied to the enzymatic hydrolysis kinetics at the two pH indicated. Numerical values of the parameters are shown with their confidence intervals. In addition, CS concentrations and I

_{p}-index obtained by selective precipitation under standard conditions are also summarized.

^{a}In this case, the kinetics were prolonged up to 18 h.

FINS | H_{m} (%) | v_{m} (%·min^{−1}) | τ (min) | β | R^{2} | CS (g/L) | I_{p} (%) |
---|---|---|---|---|---|---|---|

pH: 7.3 | 10.73 ± 0.06 | 0.058 ± 0.001 | 31.82 ± 0.56 | 0.50 ± 0.00 | 0.991 | 5.65 | 77.5 |

pH: 8.5 | 13.59 ± 0.10 | 0.132 ± 0.003 | 22.84 ± 0.45 | 0.64 ± 0.01 | 0.999 | 6.50 | 83.7 |

^{a} pH: 8.5 | 21.13 ± 0.10 | 0.110 ± 0.002 | 30.82 ± 0.65 | 0.46 ± 0.01 | 0.992 | 6.75 | 88.3 |

HEADS | |||||||

pH: 7.4 | 7.08 ± 0.01 | 0.094 ± 0.001 | 16.53 ± 0.09 | 0.64 ± 0.00 | 0.990 | 7.79 | 79.9 |

pH: 8.5 | 15.64 ± 0.02 | 0.111 ± 0.001 | 29.26 ± 0.10 | 0.60 ± 0.00 | 0.999 | 9.44 | 86.9 |

^{a} pH: 8.5 | 17.72 ± 0.07 | 0.080 ± 0.001 | 42.60 ± 0.84 | 0.56 ± 0.01 | 0.992 | 9.68 | 89.6 |

SKELETONS | |||||||

pH: 6.8 | 6.85 ± 0.02 | 0.037 ± 0.001 | 42.54 ± 0.26 | 0.67 ± 0.00 | 0.997 | 4.79 | 76.7 |

pH: 8.5 | 11.93 ± 0.29 | 0.222 ± 0.021 | 9.25 ± 0.01 | 0.50 ± 0.04 | 0.969 | 6.07 | 80.4 |

^{a} pH: 8.5 | 13.49 ± 0.04 | 0.074 ± 0.001 | 31.69 ± 0.84 | 0.50 ± 0.01 | 0.995 | 6.91 | 87.1 |

#### 2.3. Optimisation of Alkaline Hydroalcoholic Treatment of Enzymatic Hydrolysates

_{p}responses (experimental and predicted) from such treatments of S. canicula hydrolysates are summarized in Table 6.

**Table 6.**Summary of the independent variables (NaOH: N, EtOH: E) in the response surface design with the corresponding experimental (Y

_{e}) and predicted (Y

_{p}) results of selective precipitation of CS from S. canicula wastes. Natural values of experimental conditions are in brackets.

HEADS | FINS | SKELETONS | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Independent Variables | CS (g/L) | I_{p} (%) | CS (g/L) | I_{p} (%) | CS (g/L) | I_{p} (%) | |||||||

X_{1}: N | X_{2}: E | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} | Y_{e} | Y_{p} |

−1 (0.20) | −1 (0.46) | 0.25 | 0.45 | 4.13 | 6.63 | 0.10 | 0.01 | 20.56 | 18.27 | 0.10 | −0.45 | 22.20 | 15.48 |

1 (0.70) | −1 (0.46) | 0.50 | 1.33 | 5.88 | 15.01 | 0.80 | 1.89 | 17.14 | 34.64 | 0.10 | 1.36 | 22.20 | 37.50 |

−1 (0.20) | 1 (1.24) | 0.70 | 1.75 | 8.24 | 19.74 | 5.74 | 4.75 | 86.05 | 72.17 | 5.26 | 4.00 | 83.63 | 68.67 |

1 (0.70) | 1 (1.24) | 7.32 | 9.00 | 87.04 | 105.17 | 5.72 | 5.90 | 86.34 | 92.25 | 5.39 | 5.81 | 85.13 | 90.69 |

−1.41 (0.10) | 0 (0.85) | 1.03 | 0.53 | 11.54 | 5.87 | 1.61 | 2.40 | 32.09 | 44.31 | 0.10 | 1.38 | 22.20 | 37.49 |

1.41 (0.80) | 0 (0.85) | 7.67 | 6.27 | 87.08 | 72.00 | 5.41 | 4.53 | 85.86 | 70.00 | 5.14 | 3.93 | 83.42 | 68.54 |

0 (0.45) | −1.41 (0.30) | 0.10 | −0.24 | 2.54 | −1.46 | 0.44 | −0.25 | 22.61 | 12.57 | 0.10 | −0.40 | 22.20 | 16.02 |

0 (0.45) | 1.41 (1.40) | 7.62 | 6.08 | 88.09 | 71.34 | 5.32 | 5.92 | 84.78 | 91.18 | 5.30 | 5.88 | 84.43 | 91.02 |

0 (0.45) | 0 (0.85) | 7.68 | 7.71 | 87.44 | 86.77 | 5.76 | 5.67 | 85.71 | 85.33 | 5.26 | 5.47 | 84.00 | 84.19 |

0 (0.45) | 0 (0.85) | 7.54 | 7.71 | 86.79 | 86.77 | 5.46 | 5.67 | 85.22 | 85.33 | 5.70 | 5.47 | 84.71 | 84.19 |

0 (0.45) | 0 (0.85) | 7.70 | 7.71 | 86.43 | 86.77 | 5.74 | 5.67 | 85.91 | 85.33 | 5.45 | 5.47 | 83.59 | 84.19 |

0 (0.45) | 0 (0.85) | 7.72 | 7.71 | 86.19 | 86.77 | 5.72 | 5.67 | 85.19 | 85.33 | 5.47 | 5.47 | 84.73 | 84.19 |

0 (0.45) | 0 (0.85) | 7.89 | 7.71 | 86.77 | 86.77 | 5.66 | 5.67 | 84.57 | 85.33 | 5.49 | 5.47 | 83.93 | 84.19 |

**Table 7.**Second order equations describing the effect of N and E on selective precipitation of CS (coded values according to criteria defined in Table 6). The coefficient of adjusted determination (${R}_{adj}^{\text{2}}$) and F-values (F

_{1}and F

_{2}) is also shown. S: Significant.

HEADS | FINS | SKELETONS | ||||
---|---|---|---|---|---|---|

Parameters | CS | I_{p} | CS | I_{p} | CS | I_{p} |

b_{0} (intercept) | 7.71 | 86.77 | 5.67 | 85.33 | 5.47 | 84.19 |

b_{1} (N) | 2.04 | 23.45 | 0.76 | 9.11 | 0.91 | 11.01 |

b_{2} (E) | 2.24 | 25.81 | 2.19 | 27.88 | 2.23 | 26.59 |

b_{12} (N × E) | 1.59 | 19.26 | −0.18 | 0.93 | NS | NS |

b_{11} (N^{2}) | −2.17 | −24.06 | −1.11 | −14.17 | −1.42 | −15.68 |

b_{22} (E^{2}) | −2.41 | −26.07 | −1.43 | −16.83 | −1.38 | −15.43 |

${R}_{adj}^{\text{2}}$ | 0.897 | 0.905 | 0.885 | 0.830 | 0.857 | 0.849 |

F_{1} | 21.97 $\left[{F}_{7}^{5}=3.97\right]S$ | 23.88 $\left[{F}_{7}^{5}=3.97\right]S$ | 19.54 $\left[{F}_{7}^{5}=3.97\right]S$ | 12.71 $\left[{F}_{7}^{5}=3.97\right]S$ | 18.92 $\left[{F}_{8}^{4}=3.84\right]S$ | 17.85 $\left[{F}_{8}^{4}=3.84\right]S$ |

F_{2} | 0.67 $\left[{F}_{5}^{8}=4.82\right]S$ | 0.66 $\left[{F}_{5}^{8}=4.82\right]S$ | 0.67 $\left[{F}_{5}^{8}=4.82\right]S$ | 0.69 $\left[{F}_{5}^{8}=4.82\right]S$ | 0.55 $\left[{F}_{4}^{8}=6.04\right]S$ | 0.56 $\left[{F}_{4}^{8}=6.04\right]S$ |

**Figure 4.**Predicted response surfaces by empirical equations summarized in Table 7 corresponding to the combined effect of NaOH and EtOH on the selective treatment of CS from hydrolysate cartilages of S. canicula.

_{max}values showed in Table 8. The optima levels of alkali and alcohol were higher than those found for cartilages of Raja clavata [12]. Ethanol has been reported to be an excellent reagent for the selective precipitation of CS, removing the major protein presents in the extract [35]. However, increases in the quantity of ethanol used for the extraction of CS from shark cartilage, did not lead to increases in the yield of the CS obtained [34,36].

**Table 8.**Optima values of the two independent variables (NaOH

_{opt}and EtOH

_{opt}) to obtain the best responses from the equations defined in Table 7 and for the two dependent variables studied (CS concentration and purity).

HEADS | FINS | SKELETONS | ||||
---|---|---|---|---|---|---|

CS | I_{p} | CS | I_{p} | CS | I_{p} | |

NaOH_{opt} (M) | 0.63 | 0.65 | 0.52 | 0.54 | 0.53 | 0.54 |

EtOH_{opt} (V) | 1.12 | 1.16 | 1.14 | 1.18 | 1.16 | 1.24 |

Y_{max} | 9.24 | 106.4 | 6.59 | 98.6 | 6.52 | 97.6 |

#### 2.4. Purification of CS by Ultrafiltration-Diafiltration Processes

^{2}> 0.988) (Table 9). All the parameter determinations and the estimation of CS and protein rejection at three diavolumes (R

_{3D}) are also defined in Table 9.

**Figure 5.**UF-DF process for CS purification from S. canicula cartilages of three origins at 30 kDa. Top: Concentration of retained protein (○) and CS (●) in linear relation with the factor of volumetric concentration (fc) showing experimental data (points) and theoretical profiles corresponding to a completely retained solute (discontinuous line). Bottom: Progress of protein (○) and CS (●) retention with the increase of diavolume from DF process (D). Equation (6) was used to fit the experimental data. Error bars are the confidence intervals (α = 0.05; n = 2).

**Table 9.**Parametric estimates from DF purification data (with MWCO of 30 kDa) of CS and proteins fitted to the Equation (6). Determination coefficients (R

^{2}) are also shown. NS: Non-significant.

CS | Proteins | ||
---|---|---|---|

R_{0} | 2.52 ± 1.84 | 100.0 ± 22.6 | |

R_{f} | 97.4 ± 1.91 | 0.0 | |

HEADS | s | 0.829 ± 0.189 | 0.134 (NS) |

R^{2} | 0.996 | 0.988 | |

R_{3D} | 1.01 | 92.6 | |

R_{0} | 23.2 (NS) | - | |

R_{f} | 76.8 ± 41.8 | - | |

FINS | s | 0.985 ± 0.030 | - |

R^{2} | 0.999 | - | |

R_{3D} | 1.02 | - | |

R_{0} | 20 (NS) | 100.0 ± 13.5 | |

R_{f} | 80 (NS) | 0.0 | |

SKELETONS | s | 0.994 ± 0.119 | 0.561 ± 0.115 |

R^{2} | 0.998 | 0.992 | |

R_{3D} | 0.36 | 73.2 |

_{f}> 76% and R

_{3D}< 1.1%). In the case of proteins, the permeation of fin solutions was complete at the beginning of the DF and needed more than 3 or 4 relative diavolumes for the heads and skeletons samples, respectively. The complete desalination of retentates was also observed (data not shown). These results reveals the high efficiency of the 30 kDa UF-DF system as a final step to CS retention and recovery and protein discard from S. canicula wastes. The purity of CS retentates (in terms of I

_{p}-values) after drying was: 98%, 97% and 96.2% for head, skeleton and fins. If an ulterior purification might be still required, dried samples could return to the alkaline-alcoholic treatment and UF-DF separation, in similar conditions to those described previously. The final yields of CS were (as % of wet weight cartilage): 4.8, 3.3 and 1.5 for heads, fins and skeleton materials, respectively. Membrane separation techniques have been used as the last step of purification of chondroitin sulphate from different cartilage sources, because of the high separation efficiency, different cut-off membranes, ease of scale-up and cost effectiveness [37]. Lignot et al. [31] using the UF technique showed lower concentration factors for CS in skate, than those found in this study (up to nine times).

## 3. Experimental Section

#### 3.1. Cartilage Preparation and Compositional Analysis

#### 3.2. Analytical Determinations

_{p}), defined as I

_{p}(%) = CS × 100/(CS + Pr), was also calculated in all purification stages.

#### 3.3. Enzymatic Hydrolysis of Cartilages

_{b}is the normality of NaOH; M

_{p}is the mass (g) of initial protein (N × 6.25); h

_{tot}is the total number of peptide bonds available for proteolytic hydrolysis (8.6 meq/g), and α is the average degree of dissociation of the amino groups in the protein substrate, and was calculated as follows:

#### 3.4. Mathematical Modelling of the Proteolysis Kinetics

_{m}is the maximum degree of hydrolysis (%); β is a parameter related with the maximum slope of cartilage hydrolysis (dimensionless); τ is the time required to achieve the semi-maximum degree of hydrolysis (min) and v

_{m}is the maximum hydrolysis rate at the τ-time (% min

^{−1}).

#### 3.5. Experimental Designs and Statistical Analysis

Codification | Decodification |

V_{c} = (V_{n} − V_{0})/ΔV_{n} | V_{n} = V_{0} + (ΔV_{n} × ΔV_{c}) |

V_{n}: Natural value of the variable to codifyV _{0}: Natural value in the centre of the domainV _{c}: Codified value of the variableΔV _{n}: Increment of V_{n} per unit of V_{c} |

_{0}is a constant coefficient, b

_{i}is the coefficient of linear effect, b

_{ij}is the coefficient of interaction effect, b

_{ii}the coefficients of squared effect, n is the number of variables and X

_{i }and X

_{j}define the independent variables. The statistical significance of the coefficients was verified by means of the Student t-test (α = 0.05), goodness-of-fit was established as the adjusted determination coefficient (${R}_{adj}^{\text{2}}$) and the model consistency by the Fisher F test (α = 0.05) using the following mean squares ratios:

the model is acceptable when | |

F1 = Model/Total error | $F1\ge {F}_{den}^{num}$ |

F2 = (Model + Lack of fitting)/Model | $F2\le {F}_{den}^{num}$ |

F3 = Total error/Experimental error | $F3\le {F}_{den}^{num}$ |

#### 3.6. Ultrafiltration-Diafiltration Process

^{2}, Millipore Corporation, Bedford, MA, USA) of 30 kDa molecular weight cut-off (MWCO). The operation mode was the following: An initial phase of ultrafiltration (UF) at 40 °C with total recirculation of retentate was performed, immediately followed by a diafiltration (DF) step. During UF, the inlet pressure remained constant (<1 bar) to determine the drops of flow rate due to the increased concentration of the retentate and to possible adhesions to the membrane. The final retentate (after DF) was lyophilized and stored at 4 °C for further analysis. Permeate of the UF step was analysed and finally discarded. For modelling the membrane process, we fixed a DF with constant volume (filtration flow = water intake flow), where the concentration of a permeable solute in the retentate was predicted by using the first-order equation [12]:

_{0}is the permeate concentration (%), R

_{f}is the asymptotic and retentate concentration (%), D is the relative diavolume (volume of added water/constant retentate volume) and s is the specific retention of protein or CS with variation between 0 (the solute is filtered as the solvent) and 1 (the solute is totally retained). Thus, using normalized values (%): R

_{0}+ R

_{f}= 100, with R

_{0}= 0 if all protein or CS are permeable. In addition, the percentage of protein or CS eliminated by three diavolumes (R

_{3D}) was calculated by substituting in Equation (6) the value of parameter D by 3.

#### 3.7. Numerical Methods for Non-Linear Curves Modelling

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Blanco, M.; Fraguas, J.; Sotelo, C.G.; Pérez-Martín, R.I.; Vázquez, J.A.
Production of Chondroitin Sulphate from Head, Skeleton and Fins of *Scyliorhinus canicula *By-Products by Combination of Enzymatic, Chemical Precipitation and Ultrafiltration Methodologies. *Mar. Drugs* **2015**, *13*, 3287-3308.
https://doi.org/10.3390/md13063287

**AMA Style**

Blanco M, Fraguas J, Sotelo CG, Pérez-Martín RI, Vázquez JA.
Production of Chondroitin Sulphate from Head, Skeleton and Fins of *Scyliorhinus canicula *By-Products by Combination of Enzymatic, Chemical Precipitation and Ultrafiltration Methodologies. *Marine Drugs*. 2015; 13(6):3287-3308.
https://doi.org/10.3390/md13063287

**Chicago/Turabian Style**

Blanco, María, Javier Fraguas, Carmen G. Sotelo, Ricardo I. Pérez-Martín, and José Antonio Vázquez.
2015. "Production of Chondroitin Sulphate from Head, Skeleton and Fins of *Scyliorhinus canicula *By-Products by Combination of Enzymatic, Chemical Precipitation and Ultrafiltration Methodologies" *Marine Drugs* 13, no. 6: 3287-3308.
https://doi.org/10.3390/md13063287