In-silico prediction of concentration-dependent viscosity curves for monoclonal antibody solutions

Figures & data

Table 1. Concentration dependent viscosity data on 16 mAbs used in this study.^*

Name	C20	η (cP)	C50	η (cP)	C60	η (cP)	C75	η (cP)	C100	η (cP)	C125	η (cP)	C150	η (cP)	C175	η (cP)	C200	η (cP)
mAb1	19	1.1 ± 0.0	49	1.5 ± 0.0					98	2.6 ± 0.0	126	3.7 ± 0.0	153	5.4 ± 0.1	172	8.0 ± 0.1	204	13.5 ± 0.2
mAb2	18	1.2 ± 0.0	52	1.6 ± 0.0					97	2.7 ± 0.0	127	3.7 ± 0.1	149	5.4 ± 0.1	171	8.1 ± 0.2	195	13.3 ± 0.7
mAb3	23	1.2 ± 0.0	46	1.5 ± 0.0					95	2.9 ± 0.1	126	4.0 ± 0.0	148	6.2 ± 0.1	171	11.1 ± 0.6	198	19.1 ± 3.7
mAb4			51	1.9 ± 0.4					102	2.9 ± 0.0	133	4.7 ± 0.5	161	6.8 ± 0.2			198	21.3 ± 0.4
mAb5	19	1.1 ± 0.0	45	1.4 ± 0.0					99	2.7 ± 0.0	126	4.1 ± 0.1	147	6.6 ± 0.1	176	12.2 ± 0.6	196	20.4 ± 0.9
mAb6	21	1.2 ± 0.0	48	1.7 ± 0.0			74	2.3 ± 0.0	98	3.3 ± 0.0	129	5.3 ± 0.0	150	8.4 ± 0.1	175	14.1 ± 0.2	203	28.9 ± 0.8
mAb7	19	1.2 ± 0.0	46	1.7 ± 0.0					101	3.7 ± 0.0	124	6.1 ± 0.0	150	10.7 ± 0.3	176	19.2 ± 0.6	206	39.1 ± 2.4
mAb8	17	1.2 ± 0.0	43	1.5 ± 0.0			91	3.3 ± 0.0	114	5.0 ± 0.1	137	8.3 ± 0.1	160	14.5 ± 1.1			189	33.0 ± 2.7
mAb9	25	1.3 ± 0.0	49	1.7 ± 0.0					105	3.9 ± 0.0	127	6.9 ± 0.0	153	12.9 ± 0.1	183	27.6 ± 0.2
mAb10	25	1.3 ± 0.0	50	1.7 ± 0.0					107	4.2 ± 0.1	134	7.6 ± 0.1	155	15.6 ± 0.6			191	44.9 ± 1.8
mAb11	19	1.1 ± 0.0	53	1.5 ± 0.0					96	3.2 ± 0.2	125	6.4 ± 0.6	150	13.9 ± 0.5	170	27.3 ± 4.5
mAb12	18	1.2 ± 0.0	46	1.6 ± 0.0					99	4.0 ± 0.0	126	7.0 ± 0.1	148	13.7 ± 0.2	172	31 ± 0.6	212	113 ± 2.7
mAb13	20	1.3 ± 0.0	40	1.9 ± 0.0	61	3.1 ± 0.03	83	5.8 ± 0.0	102	11.0 ± 0.1	126	28.9 ± 3.2	132	33.5 ± 2.4
mAb14	20	1.6 ± 0.0	41	3.4 ± 0.0	62	7.5 ± 0.03	81	15.4 ± 0.1	106	30.2 ± 0.2	130	57.9 ± 0.5	150	103.6 ± 1.0
mAb15			51	1.9 ± 0.0					91	5.0 ± 0.0	122	13.2 ± 2.2	149	29 ± 2.9	172	70.5 ± 0.6	199	226 ± 16.0
mAb16	19	1.2 ± 0.0	52	2.5 ± 0.0					103	15.4 ± 0.2	131	43.6 ± 0.6	149	94.7 ± 0.6

* A total of 105 concentration-antibody measurements were performed. Each viscosity value is an average of 3 independent measurements.

Table 2. Experimentally observed values of parameters A and B for the 16 mAbs.^*

	Number of viscosity measurement points	ln A	A	B	R^2	Heavy chain germline	Light chain germline	Isotype	D0 (10^−7 cm^2/s)
mAb1	7	−0.37	0.69	0.0133	0.98	IGHV3–23^*03	IGKV2–30^*02	IgG1κ	4.1
mAb2	7	−0.33	0.72	0.0133	0.98	IGHV3–11^*05	IGKV1D-33^*01	IgG1κ	4.3
mAb3	7	−0.44	0.64	0.0154	0.97	IGHV1–2^*05	IGKV4–1^*01	IgG4κ	4.6
mAb4	5	−0.52	0.59	0.0159	0.92	IGHV1–2^*02	IGKV2–29^*02	IgG1κ	n.d.
mAb5	7	−0.54	0.59	0.0163	0.97	IGHV4-b^*01	IGLV3–19^*01	IgG1λ	4.2
mAb6	8	−0.47	0.62	0.0171	0.98	IGHV3–23^*04	IGKV1–39^*01	IgG1κ	4.3
mAb7	7	−0.49	0.62	0.0187	0.99	IGHV1–46^*03	IGKV1–39^*01	IgG4κ	4.5
mAb8	7	−0.52	0.59	0.0192	0.98	IGHV3–48^*01	IGKV1–39^*01	IgG4κ	4.5
mAb9	6	−0.53	0.59	0.0193	0.98	IGHV1–2^*02	IGLV1–40^*01	IgG1λ	4.5
mAb10	6	−0.62	0.54	0.0208	0.96	IGHV1-f^*01	IGKV1–16^*01	IgG2κ	4.6
mAb11	6	−0.73	0.48	0.0213	0.96	IGHV1–18^*04	IGKV4–1^*01	IgG2κ	4.5
mAb12	7	−0.74	0.48	0.0233	0.96	IGHV1–46^*03	IGKV3–20^*01	IgG1κ	4.3
mAb13	7	−0.67	0.51	0.0299	0.99	IGHV1–46^*03	IGKV1–6^*01	IgG2κ	4.2
mAb14	7	−0.17	0.84	0.032	0.99	IGHV3–43D^*01	IGLV6–57^*01	IgG1λ	2.6
mAb15	6	−1.34	0.26	0.0321	0.99	IGHV3–23^*04	IGKV3–11^*01	IgG2κ	4.3
mAb16	5	−0.79	0.46	0.0341	0.99	IGHV1–46^*03	IGLV3–1^*01	IgG1λ	4.1
Average values	6.56±0.79 (Total: 105)	−0.58±0.26	0.58±0.13	0.021±0.0069

* Values for parameters A and B for all antibodies in the database were obtained by linear regressions to experimental data shown in Table 1. Each linear regression was performed for logarithm of relative viscosity versus concentration (Eq. 3(3) $\text{ln}\frac{\eta }{{\eta }_0}=\ln \mathrm{ A} +Bc$(3) ). R² is the linear correlation coefficient obtained from each regression. The number of different concentrations at which viscosity was measured for each mAb is listed in the second column. In total, 105 different antibody and concentration combinations were used for viscosity measurements and each measurement reports average of 3 independent observations. The germlines of both the chains of the antibody molecules in this database were identified using IgBLAST¹ that is based on IMGT® classification system (http://www.imgt.org). The D₀ value for mAb4 was not determined (n.d.) due to lack of material.

Figure 1. Experimentally determined concentration-dependent viscosity behaviors for the 16 antibodies in our database (Table 1). Dots are experimentally obtained data points while lines are least square fits to the data using equation 3(3) $\text{ln}\frac{\eta }{{\eta }_0}=\ln \mathrm{ A} +Bc$(3) . c is the concentration of the antibody in the solution, η is the viscosity of the solution, and η₀ is the viscosity of the platform formulation buffer. All the antibody molecules show exponential dependence of viscosity on concentration, as is clear from the R² values in Table 2. As a guide to the eye, well-behaved antibodies are shown in green, poorly-behaved antibodies are shown in red, and rest of the antibodies are shown in blue.

Figure 2. Concentration-dependent viscosity behaviors of 4 antibodies of IgG₁λ isotype. Dots represent experimental data, c is concentration in mg/mL, and η is viscosity in cP. Lines are guide to the eye. These 4 mAbs of the same isotype show different concentration-dependent viscosity behaviors. mAb5 and mAb9 have considerably lower viscosity behaviors than mAb14 and mAb16. Therefore, viscosity behaviors of antibody molecules are encoded in their amino acid sequences at a finer level than isotypes.

Table 3. Correlation coefficient (R), square of correlation coefficient (R²) obtained from a linear regression between experimentally derived value of parameter B and each computationally estimated descriptor. The results from t-tests for the significance of the correlations are also shown and significant correlations are highlighted. ^*

Computationally estimated descriptors	R	R^2	Parameter Index	t value	p value
ZVH (Charge on VH region)	−0.49	0.24	x3	2.1032	0.0258
ZVL (Charge on VL region)	−0.48	0.23	x7	2.0473	0.0287
ZmAb (Charge on the antibody)	−0.43	0.18	x2	1.7821	0.0469
ZHinge (Charge on the hinge region)	−0.20	0.04	x5	0.7638	0.2281
ZCH1 (Charge on the CH1 region)	−0.21	0.04	x4	0.8037	0.2167
ZFc (Charge on the Fc region)	0.22	0.05	x6	0.8438	0.2056
ZCL (Charge on the CL region)	0.31	0.10	x8	1.22	0.1201
APTango (Aggregation propensity predicted by TANGO)	−0.21	0.04	x9	0.8037	0.2167
APWaltz (Aggregation propensity predicted by WALTZ)	0.56	0.32	x10	2.5291	0.0112
pISequence (Sequence-based pI)	−0.48	0.23	x11	2.0473	0.0287
pIStructure (Structure-based pI)	−0.41	0.17	x1	1.6819	0.0560
ASAhyd (Hydrophobic surface area)	0.54	0.29	x13	2.4006	0.0144
vdwA (van der Waals surface area)	0.43	0.19	x12	1.7821	0.0469
ASAhlic (Hydrophilic surface area)	0.25	0.06	x14	0.9661	0.1742
DmAb (Dipole moment of the antibody)	−0.50	0.25	x15	2.1602	0.0231
ζmAb (Zeta potential of the antibody)	−0.43	0.18	x16	1.7821	0.0469

* The straight line fits are shown in Supplemental Material.

Figure 3. Prediction using Eq. 1(1) $\text{B} = 1+ \text{x}3*\text{x}7 +\text{x}3*\text{x}13 +\text{x}5*\text{x}7 +\text{x}7*\text{x}13$(1) . The model was trained on the full data set (Left Panel). The model was trained after leaving one antibody molecule out of the data set (Right Panel). The error bars have the same size as 95% confidence intervals. B_Exp refers to the experimentally obtained values of the parameter B while B_Pred refers to the prediction made using Eq. 1.

Figure 4. Comparison of experimentally observed and predicted concentration-dependent viscosity behaviors of 3 representative antibodies. The parameter B is obtained after training Eq. 1(1) $\text{B} = 1+ \text{x}3*\text{x}7 +\text{x}3*\text{x}13 +\text{x}5*\text{x}7 +\text{x}7*\text{x}13$(1) on the complete data set. The parameter A is taken as the average of A values for all the antibodies (i.e., 0.58, as listed in Table 2). An antibody with low viscosity (mAb3), an antibody with moderate viscosity (mAb9), and an antibody with high viscosity (mAb16) are shown in this figure. Dashed lines are predictions made using one standard deviation about the predicted value of B. Similar concentration-dependent viscosity behavior curves can be constructed for any antibody in the database after the parameter B is predicted using Eq. 1(1) $\text{B} = 1+ \text{x}3*\text{x}7 +\text{x}3*\text{x}13 +\text{x}5*\text{x}7 +\text{x}7*\text{x}13$(1) . Further examples for predicted concentration-dependent viscosity behaviors are provided in Section 3 in Supporting Information.

Figure 5. Prediction of concentration-dependent viscosity behavior of an antibody currently under development at Pfizer. The experimental data are shown as black circles and the predictions are shown as curve. The parameter B was predicted using Eq. 1(1) $\text{B} = 1+ \text{x}3*\text{x}7 +\text{x}3*\text{x}13 +\text{x}5*\text{x}7 +\text{x}7*\text{x}13$(1) . This predicted value of B and average value of A (Table 2) was used for creating the concentration-dependent viscosity curves from Eq. 2(2) $\frac{\eta }{{\eta }_0}= A\mathrm{ exp }Bc$(2) . For comparison predictions using the real value of A for TestmAb (0.73) are also shown. Equation 1(1) $\text{B} = 1+ \text{x}3*\text{x}7 +\text{x}3*\text{x}13 +\text{x}5*\text{x}7 +\text{x}7*\text{x}13$(1) is correctly able to predict the concentration-dependent viscosity behavior of TestmAb. Moreover, the agreement between predicted and experimentally observed viscosity behavior improves when the real value of A for TestmAb is used. The dotted red lines are viscosity predictions using the real value of A for TestmAb (0.73) and within one standard deviation about the predicted value of B.

Figure 6. Hinge region sequence alignment of human IgG₁, IgG₂, and IgG₄ antibodies. Note that number of charged residues in the hinge regions of different isotypes is different.

Table 4. Steps followed in this scheme to develop viscosity prediction algorithm. Analogous schemes can be used to develop predict viscosity behaviors of antibodies for different formulations (different buffers, excipients and pH).

Step	Action
I	Collect concentration dependent viscosity curves for different antibodies in the same buffer under the same formulation conditions following the same experimental protocol by performing experiments
II	Build full-length homology models of those antibodies in step I
III	Computationally estimate various descriptors listed in Table 3
IV	Fit the concentration dependent viscosity behavior observed in step 1 to the Eq. 3(3) $\text{ln}\frac{\eta }{{\eta }_0}=\ln \mathrm{ A} +Bc$(3) to identify the intercept and slope parameters
V	Perform linear regression of the slope parameter (response variable) with the descriptors identified in step IV (predictor variables)

Figure 7. Concentration-dependent viscosity curves for 3 commercially developed antibody molecules using the descriptors from homology models. Equation 1(1) $\text{B} = 1+ \text{x}3*\text{x}7 +\text{x}3*\text{x}13 +\text{x}5*\text{x}7 +\text{x}7*\text{x}13$(1) was used to predict the parameter B for these antibody molecules and average values of A was taken from Table 2. All 3 antibody molecules were predicted to show viscosity less than 20 cP at concentrations greater than 150 mg/mL.

Reichert JM. Antibodies to watch in 2016. mAbs 2016; 8:197-204; PMID:26651519; http://dx.doi.org/10.1080/19420862.2015.1125583

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