Modelling of Excipient Concentration during the Final

Diafiltration step of Therapeutic MAbs

Suhas Shalome RajeevaSouhardya Roy

Objective• Parameter Determination and Calculation.• Developing a numerical model to calculate the electric potential around an

Electric Double Layer (EDL) developed on a protein surface. • Prediction of Charged Excipient concentration inside the EDL. • Prediction of Charged and Uncharged Excipients in the overall Retentate

fraction. • Generate Conductivity and pH vs Protein Concentration Data for Diafiltration

Runs. • Prediction of pH in the Overall Retentate Fraction. • Flow Pattern Modelling of a self-designed TFF stirrer.

Parameter Determination: Known • Constants:

• Ɛ : Electric Charge = 1.602x10-23 C• D : Dielectric Constant of Protein in Buffer ≈ 80.4 (taken as that of water)• K : Boltzmann’s Constant = 1.38064852 × 10-23 m2 kg s-2 K-1

• T : Temperature of the system = 298 K

• Parameters (known or solved for): • Co : Overall Histidine Concentration in Diafiltration Buffer• Ψ : Electric Potential inside the EDL• r : Distance from the Protein Surface• Cp : Protein Concentration

Parameter Determination: Protein Mass • Mp: Protein Mass.

• Mass and composition of Protein Molecule can be determined from the sequence of the protein.

• Formula used:• Molecular weight = sum of individual residues weights - water molecular weight x ( number of

residues - 1 )• Mass Determined:

• (49326.47 + 23317.65 + 49198.3 + 23317.65) D = 145.16 KD

Composition

Parameter Determination: Protein Charge• From sequence analysis we have:

• Total number of Amino acids = 1325• Theoretical pI = 8.1737• Extinction Coefficient = 1.35

• Protein Charge: • Total number of Positively charged residues = 137• Total number of Positively charged residues = 124• Net Charge = + 23 (pH : 6.04 as of Histidine Buffer)

• Formula Used: • q = 1/(1 + 10(pH-pK)) : Protonisation of uncharged group• q = -1/(1 + 10(pH-pK)) : Dissociation of uncharged group• Q(pH) = q1 + ... + qn : Net Charge Calculated

Parameter Determination : Unknown • Vp : Protein Partial Volume = 0.97 ml/mg

• Calculated from the Density Meter Experiment.• Key parameter, from which remaining parameters can be estimated.

• Ɵ : Protein Volume Fraction : Function of the Protein Concentration.• Ɵ = (Cp/Mp)(Na)(4/3πa3)

• Na = 6.023x1023 : Avogadro's Number• a = Effective radius of the protein

• Vδ : Partial Volume of EDL: Depends on the Initial Histidine concentration.

Parameter Determination : Calculated • a : Effective Radius of Protein = 3.84 nm

• R: Distance from centre point to midpoint of two closest protein molecules : Function of the protein concentration.

• δ : EDL thickness : Function of the initial histidine concentration in buffer.

Calculation of Electric Potential in EDL• Model based on Poisson Boltzmann Equation, which predicts for the excipient-colloid charge

interaction. • Assumptions:

• Proteins as impermeable sphere• Uniform distribution of charge

• Distribution of charged excipients:• Uneven within the EDL• Homogeneous outside the EDL

• Graph: • Electric Potential vs Distance from Protein Surface for concentrations:

• 50mg/ml• 100 mg/ml • 150mg/ml

• Potential varied as a function of Protein Concentration and not Histidine concentration.

• Equation Solved: ODE

• Boundary Conditions:

• Reduced Form (Non dimensional):

• Boundary Condition:

Substitution:

Methodology and AnalysisCode: • Electric Field can be obtained by solving the given ordinary differential equation and the

accompanying boundary conditions. • MatLab ODE solver function: ‘ode45’ has been used to solve the Non-dimensional form of above

equation.

Analysis: • The electric field decreases with distance from the protein surface, the nature of decrease being

convex. • For higher concentration of protein in buffer, relatively higher electric fields are obtained. • EDL strength as well as charge separation increases with increasing protein concentration.

Prediction of Charged Excipients inside the EDL• Positively charged Histidine concentration inside the EDL: (Boltzmann’s Law)• Average charged Histidine concentration inside the EDL:

• Overall charged Histidine Concentration:

• Overall uncharged Histidine Concentration:

• Total Histidine Concentration in Retentate:

Methodology and AnalysisCode: • Histidine concentration obtained as a function of Protein Concentration in Buffer. • Corresponding plots obtained, for three different values of the protein effective radius, ‘a’: 3,3.5

and 4 nm.

Analysis: • Histidine concentration decreases linearly with increasing protein concentration.• Since both Histidine and Protein (Mab) are positively charged, owing to electrostatic repulsion,

histidine concentration is supposed to decrease, there by justifying the model. • The extent of decrease however goes on decreasing as the protein effective radius increases,

thereby suggesting a weakening in the corresponding electric field of the EDL.

Histidine Concentration Prediction• Using Curve Fitting in Matlab, the following equation predicts the Histidine concentration in

Product as a function of the Histidine concentration in Buffer. • Equation (Linear): C_His_Pdt = 0.9272 x C_His_Buf – 3.625• Using the above equation, following Histidine concentrations are predicted for higher Histidine

concentrations:

0 20 40 60 80 100 120 140 1600

20

40

60

80

100

120

140

160

Predicted Histidine Concentration

Buffer Histidine Concentration

Rete

ntat

e Hi

stidi

ne C

once

ntra

tion

Analysis• The equation predicting the Histidine concentration in Product as a function of the corresponding Buffer

concentration suggests: • Slope close to 1 (0.9272)• Intercept: negative (-3.625)

• Result: • At lower Histidine Buffer concentrations, intercept will be more dominant than the slope.

Consequently, there will be a significant difference in the two histidine concentrations. • At higher Histidine Buffer concentrations, slope will be much more dominant than the negative

intercept. Also, since it is closed to 1, it suggests that the Product Histidine Concentration will very closely approach the Buffer Histidine Concentration.

• Conclusion: Thus, we can conclude that at higher Excipient concentrations, the effect of Protein

concentration or charge on the subsequent excipient concentration in the retentate will not be that significant.

Experiment DesignDesign:• 25 mL of Retentate samples collected during the diafiltration run of a positively charged MAb in Histidine Buffer at specific

expected concentration intervals:

Analysis: • Subsequent Analysis for:

• Density ~ Densitometer.• Viscosity ~ Viscometer.• Concentration ~ UV Spectrometer. • pH ~ pH Probe. • Conductivity ~ Conductivity Probe.

Formulation Buffer

• Expected Concentration:• 9 • 10• 20• 30• 40

Buffer Exchange

• At concentration: • 40 mg/mL• 8

Diavolumes of Buffer required

Conductivity Trend

5 10 15 20 25 30 35 402.1

2.12

2.14

2.16

2.18

2.2

2.22

2.24

2.26

2.28

Formulation Buffer

Protein Concentration (mg/mL)

Cond

uctiv

ity (m

S)

30 40 50 60 70 80 900

100

200

300

400

500

600

700

Histidine Buffer

Protein Concentration (mg/mL)

Cond

uctiv

ity (u

S)

0 10 20 30 40 50 60 70 80 900

500

1000

1500

2000

2500

Conductivity Trend

Protein Concentration (mg/mL)

Cond

uctiv

ity (u

S)

pH Trend

5 10 15 20 25 30 35 407.5

7.5057.51

7.5157.52

7.5257.53

7.5357.54

7.5457.55

7.555

Formulation Buffer

Protein Concentration (mg/ml)

pH

30 40 50 60 70 80 906.25

6.3

6.35

6.4

6.45

6.5

6.55

6.6

Histidine Buffer

Protein Concentration (mg/mL)

pH

0 10 20 30 40 50 60 70 80 905.5

6

6.5

7

7.5

8

pH Trend

Protein Concentration (mg/mL)

pH

Analysis: Conductivity and pH

• Conductivity• Conductivity decreases with Protein concentration for Formulation Buffer, but in an insignificant fashion. • For Histidine Buffer, conductivity increases in a linear fashion, with a significant variation. • There is a significant difference in the conductivity of the two buffers. It is much lower in the histidine buffer,

compared to Formulation Buffer. • The linearly increasing value of Conductivity can be accounted for due to increasing protein concentration (positively

charged) and a slight decrease in the histidine concentration (positively charged). • The dip in conductivity is due to the lower dissolution of protein ions in Histidine buffer, compared to the

formulation buffer.

• pH• pH change is insignificant in the formulation buffer. • For histidine buffer, there is a slight increase in pH. It is because with increasing protein concentration, its basic

nature neutralizes Histidine acidic nature, and hence pH starts approaching 7. • However, there is a dip in pH below 7 from formulation buffer to histidine buffer, clearly due to the acidic nature of

Histidine buffer, whose pH should be 6.0.

Density Trend

5 10 15 20 25 30 35 400.998

1

1.002

1.004

1.006

1.008

1.01

1.012

Formulation Buffer

Protein Concentration (mg/mL)

Dens

ity (g

/L)

30 40 50 60 70 80 901

1.005

1.01

1.015

1.02

1.025

Histidine Buffer

Protein Concentration (mg/mL)

Dens

ity (g

/L)

0 10 20 30 40 50 60 70 80 900.99

0.995

1

1.005

1.01

1.015

1.02

1.025

Density Trend

Protein Concentration (mg/mL)

Dens

ity (g

/L)

Viscosity Trend

5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

Formulation Buffer

Protein Concentration (mg/mL)

Visc

osity

30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Histidine Buffer

Protein Concentration (mg/mL)

Visc

osity

0 10 20 30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Viscosity Trend

Protein Concentration (mg/mL)

Visc

osity

Analysis: Density and Viscosity

• Density• Density increases with a linear trend for both the Formulation Buffer and the Histidine Buffer.• The linear density trend rather proves the goodness of the Concentration TFF run. • However, there is a slight dip in the density owing to the buffer exchange.

• Viscosity• Viscosity increases overall as we go on increasing the concentration. • However, there seems to be no established trend, which might be due to experimental errors. • However, on an approximation, viscosity should be follow a trend parallel to he density, and hence

should be monotonously increasing with concentration.

pH Prediction in overall Retentate fraction

0 10 20 30 40 50 600

1

2

3

4

5

6

pH

Histidine Concentration (mg/mL)

pH

pH of the retentate goes on increasing, thereby approaching 7 as the Histidine Concentration is increased in the Buffer.

The nature of increase follows the Logarithmic trend, thereby justifying the following Logarithmic relation used to calculate the pH of the Retentate:

i.e. the Henderson Hasselbalch equation.

Velocity Profile: TFF Stirrer Flow Pattern

TFF Stirrer Flow Pattern• Simulation and Modelling:

• Velocity profile has been obtained for a custom TFF stirrer, using COMSOL Multiphysics 4.4.• Simulation results are presented as static velocity profiles, which give some rough idea about the mixing pattern inside

the stirrer.

• An analysis of the simulation results shows:• Mixing is more near close to the inlet, outlet and near the stirrer blades. • The distance of the stirrer bottom from the tank bottom serves as an important parameter in homogenising the

mixture. • Adding Baffles designs to the tank wall will also increase the mixing capacity. • However, every attempt to increase mixing increases randomness, and hence there is a higher chance to reach

turbulence even at slightly lower velocities than the turbulent limit.

• Future Goals:• For a clearer view of the same, CFD analysis is required, with higher complexity in simulation. This can be considered

as a target to achieve in near future.

Thank You.