# Optimization of Lactoperoxidase and Lactoferrin Separation on an Ion-Exchange Chromatography Step

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Response Surface Modeling and Design of Experiments

^{2}+ 2k + c

_{p}points, where k is the number of factors, and c

_{p}is the number of replicate runs performed at the center point. In this design, the distance α from the center point depends on the number of the factors and can be calculated by α = 2

^{(k−p)/4}. All factors have to be adjusted at five levels (−α, −1, 0, +1, +α) [20]. The quadratic polynomial model for the measured values of the results from experiments variable, Y with k factors is given by:

_{i}and x

_{j}are the design factors in coded values, β

_{0}is the constant parameter, β

_{i}, β

_{ij}, and β

_{ii}are the coefficient of the linear, interaction, and quadratic terms of the model, respectively. The coefficients of Equation (1) are estimated using statistical software packages (e.g., Minitab, Design Expert, SPSS).

#### 2.2. Mechanistic Modeling of Chromatography

_{int}indicates the interstitial velocity, ε

_{c}the column voidage, r

_{p}the particle radius, D

_{ax}the axial dispersion representing combined effect of dispersion and diffusive processes, and k

_{eff,i}epitomize combined effect of both the internal and external mass transfer resistances in one lumped film diffusion coefficient. Analogously, on a particle level, concentration change for the ith component is expressed by:

_{i}denotes the concentration of component i within the particle and ε

_{p}the particle voidage. The first term on right-hand side describes adsorption and desorption processes on particle level, i.e., the interaction between mobile and particle-bound phase.

_{i}is the characteristic charge of protein, which represents the average number of ligands, or binding sites, interacting during adsorption. ${\overline{q}}_{\mathrm{salt}}$ is the concentration of adsorbed salt counter-ions that are available for exchange, c

_{salt}is the salt concentration of the bulk.

_{i}is the steric factor, which represents the average number of counter-ions shielded per adsorbed protein molecule.

_{ads,i}and k

_{des,i}respectively denote the adsorption and desorption rates.

#### 2.3. Optimization for the ICE Separation of LP and LF

_{captured,i}is the concentration of the target component i leaving the column during the elution.

_{captured,i}is the amount of substance captured of component i.

## 3. Materials and Methods

#### 3.1. Materials, Column and Software

^{®}17 (State College, PA, USA) was used as a statistical tool for handling response surface methodology. The software MATLAB R2014a (Natik, MA, USA) was used to execute the mechanistic model.

#### 3.2. Experimental Methods

- Final concentration of salt in elution step (M)
- Length of linear elution gradient (CV)
- Superficial velocity (cm/min)

#### Protein Quantification

_{1%}= 14.9 [24]) and 412 nm. Lactoperoxidase absorbs radiation at 280 nm as well as 412 nm; it has maximum absorbance at 412 nm [25] and its purity is estimated as a ratio of A

_{412}/A

_{280}. The BCA (bicinchoninic acid) protein assay kit from Sigma (Oakville, ON, Canada) with BSA protein standard was used for further analysis of protein fractions from ÄKTA.

#### 3.3. Mathematical Method

#### 3.3.1. Screening Experiments to Determine Importance of Design Factors

#### 3.3.2. SMA Model Calibration and Validation

_{ads}, k

_{des}, σ}, can be generated by minimizing the error function F(p), defined as follows:

_{f}can be estimated from the correlation [31]:

_{eff}·d

_{p}/D

_{m}is the Sherwood number, Re = u

_{0}ρd

_{p}/η is the Reynolds number and Sc = η/ρD

_{m}is the Schmidt number.

#### 3.3.3. Optimization Method

_{max}= max (Y)

## 4. Results and Discussion

#### 4.1. Results of Response Surface Modeling

^{2}of 0.89 is probably due to the variations in the experiments at the six center points.

^{2}of about 0.66, indicates a narrow predictability. In other words, quadratic RSM can only describe 66% of the variety in the experimental data.

#### 4.2. Results of the Mechanistic Model

#### 4.2.1. Model Calibration and Validation

#### 4.2.2. Optimization Predictions Based on the Mechanistic Model

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Abbreviation

c_{p,i} | concentration of protein i in the pores of the adsorbent (M) |

c_{salt} | salt concentration in the pores of the adsorbent (M) |

c_{i} | protein concentration i in the mobile phase (M) |

D_{ax} | axial dispersion coefficient (mm^{2}/s) |

D_{m} | molecular diffusivity in mobile phase (mm^{2}/s) |

k_{eff,i} | effective mass transfer coefficient of protein i (mm/s) |

k_{ads,i} | adsorption coefficient of protein i in the SMA isotherm |

k_{des,i} | desorption coefficient of protein i in the SMA isotherm |

k_{eq,i} | equilibrium coefficient of protein i |

L | length of the column (mm) |

q_{i} | protein concentration i on the adsorbent phase (M) |

r_{p} | particle radius (mm) |

u_{int} | interstitial velocity of the fluid (mm/s) |

Y | recovery yield |

ε_{c} | column voidage |

ε_{p} | particle voidage |

ε_{t} | total voidage |

1−ε_{t}/ε_{t} | phase ratio |

Λ | total ionic capacity (M) |

ν_{i} | characteristic charge of protein i in SMA isotherm |

η | mobile phase viscosity (Pa.s) |

σ_{i} | steric factor of protein i in the SMA isotherm |

## References

- Ekstrand, B. Antimicrobial factors in milk—A review. Food Biotechnol.
**1989**, 3, 105–126. [Google Scholar] [CrossRef] - Dairy Processing Handbook. Available online: http://www.dairyprocessinghandbook.com/chapter/whey-processing (accessed on 10 January 2017).
- Barth, C.A.; Schlimme, E. Milk Proteins: Nutritional, Clinical, Functional and Technological Aspects; Springer International: Darmstadt, Germany, 1988. [Google Scholar]
- Pedersen, L.; Mollerup, J.; Hansen, E.; Jungbauer, A. Whey proteins as a model system for chromatographic separation of proteins. J. Chromatogr. B
**2003**, 790, 161–173. [Google Scholar] [CrossRef] - Gerberding, S.; Byers, C. Preparative ion-exchange chromatography of proteins from dairy whey. J. Chromatogr. A
**1998**, 808, 141–151. [Google Scholar] [CrossRef] - Hahn, R.; Schulz, P.; Schaupp, C.; Jungbauer, A. Bovine whey fractionation based on cation-exchange chromatography. J. Chromatogr. A
**1998**, 795, 277–287. [Google Scholar] [CrossRef] - El-Sayed, M.M.H.; Chase, H.A. Purification of the two major proteins from whey concentrate using a cation-exchange selective adsorption process. Biotechnol. Prog.
**2009**, 192–199. [Google Scholar] [CrossRef] [PubMed] - Fee, C.J.; Chand, A. Capture of lactoferrin and lactoperoxidase from raw whole milk by cation exchange chromatography. Sep. Purif. Technol.
**2006**, 48, 143–149. [Google Scholar] [CrossRef] - Strohmaier, W. Chromatographic fractionation of whey proteins. IDF Bull.
**2004**, 389, 29–35. [Google Scholar] - Tolkach, A.; Kulozik, U. Fractionation of whey proteins and peptides by means of membrane techniques in connection with chemical and physical pretreatments. IDF Bull.
**2004**, 389, 20–23. [Google Scholar] - Rombauts, W.A.; Schroeder, W.A.; Morrison, M. Bovine lactoperoxidase. partial characterization of the further purified protein. Biochemistry
**1967**, 6, 2965–2977. [Google Scholar] [CrossRef] [PubMed] - Flemmig, J.; Gau, J.; Schlorke, D.; Arnhold, J. Lactoperoxidase as a potential drud tarket. Expert Opin. Ther. Targets
**2016**, 20, 447–461. [Google Scholar] [CrossRef] [PubMed] - Yao, X.; Bunt, C.; Cornish, J.; Quek, S.-Y.; Wen, J. Oral delivery of lactoferrin: A review. Int. J. Pept. Res. Ther.
**2013**, 19, 125–134. [Google Scholar] [CrossRef] - Noppe, W.; Pliva, F.M.; Galaev, I.Y.; Vanhoorelbeka, K.; Mattiasson, B.; Deckmyn, H. Immobilised peptide displaying phages as affinity ligands purification of lactoferrin from defatted milk. J. Chromatogr. A
**2006**, 1101, 79–85. [Google Scholar] [CrossRef] [PubMed] - Andersson, J.; Mattiasson, B. Simulated moving bed technology with a simplified approach for protein purification Separation of lactoperoxidase and lactoferrin from whey protein concentrate. J. Chromatogr. A
**2006**, 1107, 88–95. [Google Scholar] [CrossRef] [PubMed] - Korhonen, H.; Pihlanto, A. Technological options for the production of health-promoting proteins and peptides derived from milk and colostrum. Curr. Pharm. Des.
**2007**, 13, 829–843. [Google Scholar] [CrossRef] [PubMed] - Fweja, L.W.T.; Lewis, M.J.; Grandison, A.S. Isolation of lactoperoxidase using different cation exchange resins by batch and column prodecures. J. Dairy Res.
**2010**, 77, 357–367. [Google Scholar] [CrossRef] [PubMed] - Ahamed, T.; Nfor, B.K.; Verheart, P.D.E.M.; van Dedem, G.W.K.; van der Wielen, L.A.M.; Eppink, M.H.M.; van der Sandt, E.J.A.X.; Ottens, M. pH-gradient ion-exchange chromatography: An analytical tool for design and optimization of protein separations. J. Chromatogr. A
**2007**, 1164, 181–188. [Google Scholar] [CrossRef] [PubMed] - Mandenius, C.-F.; Brundin, A. Bioprocess optimization using design-of-experiments methodology. Biotechnol. Prog.
**2008**, 24, 1191–1203. [Google Scholar] [CrossRef] [PubMed] - Bezerra, M.A.; Santelli, R.E.; Oliveira, E.P.; Villar, L.S.; Escaleira, L.A. Response surface methodology (RSM) as a tool for optimization in analytical chemistry. Talanta
**2008**, 76, 965–977. [Google Scholar] [CrossRef] [PubMed] - Iyer, H.; Tapper, S.; Lester, P.; Wolk, B.; van Reis, R. Use of the steric mass action model in ion-exchange chromatographic process development. J. Chromatogr. A
**1999**, 832, 1–9. [Google Scholar] [CrossRef] - Shukla, A.A.; Bae, S.S.; Moore, J.A.; Barnthouse, K.A.; Cramer, S.M. Synthesis and Characterization of High-Affinity, Low Molecular Weight Displacers for Cation-Exchange Chromatography. Ind. Eng. Chem. Res.
**1998**, 37, 4090–4098. [Google Scholar] [CrossRef] - Brooks, C.A.; Cramer, S.M. Steric mass-action ion exchange: Displacement profiles and induced salt gradients. AIChE J.
**1992**, 38, 1969–1978. [Google Scholar] [CrossRef] - Carlström, A. The heterogeneity of lactoperoxidase. Acta Chem. Scand.
**1965**, 19, 2387–2394. [Google Scholar] [CrossRef] [PubMed] - Bardsley, W.G. Steady-state kinetics of lactoperoxidase-catalyzed reactions. Immunol. Ser.
**1985**, 27, 55–87. [Google Scholar] - Guiochon, G.; Felinger, A.; Shirazi, D.G.; Katti, A.M. Fundamentals of Preparative and Nonlinear Chromatography; Academic Press: San Diego, CA, USA, 2006. [Google Scholar]
- Davis, M.E. Numerical Methods and Modeling for Chemical Engineers; John Wiley & Sons: New York, NY, USA, 1984. [Google Scholar]
- Danckwerts, P.V. Continuous flow systems. Chem. Eng. Sci.
**1953**, 2, 1–13. [Google Scholar] [CrossRef] - Shampine, L.F.; Reichelt, M.W. The MATLAB ODE Suite. SIAM J. Sci. Comput.
**1997**, 18, 1–22. [Google Scholar] [CrossRef] - Sherwood, T.K.; Pigford, R.L.; Wilke, C.R. Mass Transfer; McGraw-Hill: New York, NY, USA, 1975. [Google Scholar]
- Gunn, D.J. Axial and radial dispersion in fixed beds. Chem. Eng. Sci.
**1987**, 42, 363–373. [Google Scholar] [CrossRef] - Faraji, N.; Zhang, Y.; Ray, A.K. Determination of adsorption isotherm parameters for minor whey proteins by gradient elution preparative liquid chromatography. J. Chromatogr. A
**2015**, 1412, 67–74. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**The coefficient plot resulting from the response surface regression of the screening experiments. The values on y-axis represents corresponding values of variables depicted on x-axis.

**Figure 6.**The cumulative distribution for the calibration and validation experiments plotted against the relative residual error.

**Table 1.**Coded and un-coded values of the process factors in screening experiments of central composite.

Run | Salt | Coded Length of Gradient | Flow Velocity | Salt (M) | Un-Coded Length of Gradient (CV) | Flow Velocity (cm/min) |
---|---|---|---|---|---|---|

1 | −1 | −1 | −1 | 0.35 | 15 | 2.1 |

2 | 1 | −1 | −1 | 1.1 | 15 | 2.1 |

3 | −1 | 1 | −1 | 0.35 | 30 | 2.1 |

4 | 1 | 1 | −1 | 1.1 | 30 | 2.1 |

5 | −1 | −1 | 1 | 0.35 | 15 | 4.998 |

6 | 1 | −1 | 1 | 1.1 | 15 | 4.998 |

7 | −1 | 1 | 1 | 0.35 | 30 | 4.998 |

8 | 1 | 1 | 1 | 1.1 | 30 | 4.998 |

9 | −1.681 | 0 | 0 | 0.094 | 22.5 | 3.549 |

10 | 1.681 | 0 | 0 | 1.355 | 22.5 | 3.549 |

11 | 0 | −1.681 | 0 | 0.725 | 9.88 | 3.549 |

12 | 0 | 1.681 | 0 | 0.725 | 35.1 | 3.549 |

13 | 0 | 0 | −1.681 | 0.725 | 22.5 | 1.112 |

14 | 0 | 0 | 1.681 | 0.725 | 22.5 | 5.985 |

15 | 0 | 0 | 0 | 0.725 | 22.5 | 3.549 |

16 | 0 | 0 | 0 | 0.725 | 22.5 | 3.549 |

17 | 0 | 0 | 0 | 0.725 | 22.5 | 3.549 |

18 | 0 | 0 | 0 | 0.725 | 22.5 | 3.549 |

19 | 0 | 0 | 0 | 0.725 | 22.5 | 3.549 |

20 | 0 | 0 | 0 | 0.725 | 22.5 | 3.549 |

**Table 2.**Optimum factor set for maximum yield of lactoperoxidase based on the design of experiments–response surface methodology (DoE–RSM) approach.

Concentration of Salt (M) | 1.10 |

Flow velocity (cm/min) | 3.77 |

Gradient length (CV) | 15 |

Predicted yield (%) | 96.41 |

Experimental yield (%) | 78.04 |

Protein | ${\mathit{k}}_{\mathbf{eq}}$ | $\mathsf{\nu}$ | ${\mathit{k}}_{\mathbf{des}}$ | σ |
---|---|---|---|---|

lactoperoxidase | 0.22 ± 0.005 | 3.07 ± 0.014 | 19.89 ± 0.071 | 1283 |

lactoferrin | 11.65 ± 0.003 | 2.73 ± 0.006 | 0.98 ± 0.22 | 0.98 |

Concentration of Salt (M) | 0.82 |

Flow velocity (cm/min) | 4.32 |

Gradient length (CV) | 16.28 |

Predicted yield (%) | 89.92 |

Experimental yield (%) | 86.73 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Faraji, N.; Zhang, Y.; Ray, A.K.
Optimization of Lactoperoxidase and Lactoferrin Separation on an Ion-Exchange Chromatography Step. *Separations* **2017**, *4*, 10.
https://doi.org/10.3390/separations4020010

**AMA Style**

Faraji N, Zhang Y, Ray AK.
Optimization of Lactoperoxidase and Lactoferrin Separation on an Ion-Exchange Chromatography Step. *Separations*. 2017; 4(2):10.
https://doi.org/10.3390/separations4020010

**Chicago/Turabian Style**

Faraji, Naeimeh, Yan Zhang, and Ajay K. Ray.
2017. "Optimization of Lactoperoxidase and Lactoferrin Separation on an Ion-Exchange Chromatography Step" *Separations* 4, no. 2: 10.
https://doi.org/10.3390/separations4020010