# Digital Twin Based Design and Experimental Validation of a Continuous Peptide Polishing Step

^{1}

^{2}

^{3}

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*Processes*in 2023)

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Feed Mixtures, Buffers and Stationary Phases

#### 2.2. Batch Chromatography

## 3. Chromatography Modeling

#### 3.1. General Rate Model

#### 3.1.1. Mass Balance of Mobile Phase

#### 3.1.2. Mass Balance of Stationary Phase

_{p,i}and surface diffusion D

_{S,i}[17,22]:

_{eff}[1,22]

#### 3.1.3. Adsorption Equilibrium

_{i}. All notations can be transferred into the other with:

#### 3.2. Model Parameter Determination

#### 3.2.1. Fluid Dynamics

#### 3.2.2. Adsorption Equilibrium

#### 3.2.3. Mass Transport

#### 3.3. Model Validation

^{2}is 0.99.

^{2}exceeds 0.95 for every run. Thus, the simulations describe the reality very well.

## 4. Results and Discussion

#### 4.1. MCSGP

#### 4.2. Continuous Twin Column Chromatography (CTCC)

- Yield: Loading (orange lines) indicates the amount of product in product fraction compared to the overall amount loaded (feed plus reloading fractions) in this cycle. This should roughly resemble the batch yield.
- Yield: Cycle (gray) indicates the amount of product in product fraction compared to the amount of feed loaded in this cycle. Option A reaches 100% after the first cycle. There is no product lost at all. Option B loses 7% in fraction 3.
- Yield: Overall (yellow) indicates the overall amount of product gained compared to the overall amount of feed loaded. This starts at the batch yield and approaches the cycle yield, which it would reach after an infinite number of cycles. The gap between the cycle yield and the overall yield is caused by the amount of product stored in the fractions. Since this amount stays roughly the same, the yield loss caused by this becomes more and more unimportant compared to the overall amount of protein produced.

#### 4.3. Experimental Validation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

${c}_{i}$ | (g/L) | Concentration of component i |

${c}_{p,i}$ | (g/L) | Concentration of component i inside the pores |

CTCC | Continuous Twin Column Chromatography | |

CV | Column Volume | |

${D}_{ax}$ | (cm^{2}/s) | Axial dispersion coefficient |

D_{eff} | (cm^{2}/s) | Effective diffusion coefficient |

${D}_{m,i}$ | (cm^{2}/s) | Molecular diffusion coefficient |

${d}_{p}$ | (cm) | Particle diameter |

D_{p,i} | (cm^{2}/s) | Pore diffusion coefficient |

D_{S,i} | (cm^{2}/s) | Surface diffusion coefficient |

${\epsilon}_{p,i}$ | (-) | Porosity |

${\epsilon}_{s}$ | (-) | Voidage |

H_{i} | (-) | Henry coefficient of component i |

K_{i} | (L/g) | Langmuir coefficient of component i |

${k}_{eff}$ | (cm/s) | Effective mass transport coefficient |

k_{f} | (cm/s) | Mass transport coefficient |

l | (cm) | Length |

MCSGP | Multicolumn Countercurrent Solvent Gradient Purification | |

PAT | Process Analytical Technology | |

$P{e}_{i}$ | (-) | Peclet-Number |

q_{i} | (g/L) | Loading of component i |

q_{max,i} | (g/L) | Maximum loading capacity of component i |

r | (cm) | Radius |

Re | (-) | Reynolds-Number |

${R}_{p}$ | (cm) | Particle Radius |

$S{h}_{i}$ | (-) | Sherwood-Number |

t | (s); (min) | Time |

$\stackrel{-}{{t}_{i}}$ | (s); (min) | Mean residence time |

${u}_{int}$ | (cm/s) | Interstitial velocity |

v | (cm/s) | Velocity |

$\dot{V}$ | (mL/min) | Volumetric flow |

${V}_{column}$ | (mL) | Volume of column |

$\eta $ | (mg/cm·s) | Dynamic viscosity |

$\rho $ | (g/L) | Density |

${\sigma}^{2}$ | (s^{2}) | Variance |

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**Figure 1.**Batch chromatogram of the peptide polishing step. The solid blue line is the chromatogram at 280 nm measured with a diode array detector (DAD), assigned to the right axis. The left concentration axis is zoomed in to show the side components (SC), which are represented with dots.

**Figure 2.**Comparison between measurements (dotted lines) and simulations (solid lines) for two different volumetric flows (0.33 CV/min, yellow; 0.66 CV/min, green). Time scale and volumetric flow are normalized to CV and CV/min, respectively.

**Figure 3.**Comparison between measurements (dotted lines) and simulations (solid lines) for a batch chromatography run. The target component is given in orange. Side components in blue. The gradient is shown with a green line.

**Figure 5.**MCSGP scheduling for column 1 (upper) and 2 (lower). Gray lines indicate fraction cut points. The color shifting arrows (red to gray) indicate the transfer of fraction 1 or 3 from one column to the other. Pure red arrows indicate pure product elution. Orange (above) and blue (below) lines indicate feed loading.

**Figure 7.**Purity (blue line) and yield for (

**A**) reloading of fraction 1 and 3 and (

**B**) reloading fraction 1 only.

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**MDPI and ACS Style**

Zobel-Roos, S.; Vetter, F.; Scheps, D.; Pfeiffer, M.; Gunne, M.; Boscheinen, O.; Strube, J.
Digital Twin Based Design and Experimental Validation of a Continuous Peptide Polishing Step. *Processes* **2023**, *11*, 1401.
https://doi.org/10.3390/pr11051401

**AMA Style**

Zobel-Roos S, Vetter F, Scheps D, Pfeiffer M, Gunne M, Boscheinen O, Strube J.
Digital Twin Based Design and Experimental Validation of a Continuous Peptide Polishing Step. *Processes*. 2023; 11(5):1401.
https://doi.org/10.3390/pr11051401

**Chicago/Turabian Style**

Zobel-Roos, Steffen, Florian Vetter, Daniel Scheps, Marcus Pfeiffer, Matthias Gunne, Oliver Boscheinen, and Jochen Strube.
2023. "Digital Twin Based Design and Experimental Validation of a Continuous Peptide Polishing Step" *Processes* 11, no. 5: 1401.
https://doi.org/10.3390/pr11051401