Systems and methods of pH modeling and control
The disclosure relates to systems and methods for controlling the pH of a sample, comprising measuring an initial pH, adding an amount of titrant and measuring a second pH, and using non-dimensional modeling to normalize titrant and determine the amount of titrant needed to reach a final pH. The systems and methods can be used to control pH during viral inactivation or titration of protein samples.
1 . A method comprising:
generating a reference titration curve from a reference sample;
generating a model based on a regression of the reference titration curve;
measuring an initial pH (pH initial ) of a sample;
adding at least a first amount of titrant (Titrant n ) to the sample and measuring at least a first additional pH value (pH n ), Titrant n being an amount of titrant added to the sample to reach pH n , wherein pH n is different from pH initial , and wherein the initial pH (pH initial ) and the first additional pH value (pH n ) are measured using a pH probe or a pH meter of a pH flow cell;
applying the model to determine a second amount of titrant (Titrant n+1 ) to reach a target pH based on pH initial , Titrant n , and pH n , wherein the target pH is a first intermediate target pH; and
based upon the result obtained by the model for determining a second amount of titrant Titrant n+i ), adding the second amount of titrant (Titrant n+1 ) to the sample.
2 . The method of claim 1 , wherein the method further comprises:
measuring a second pH (pH n+2 ); and
applying the model to determine a third amount of titrant (Titrant n+2 ) to reach a second intermediate target pH, based on pH initial , Titrant n+1 , and pH n+2 .
3 . The method of claim 2 , further comprising adding the third amount of titrant (Titrant n+2 ) to the sample and measuring a third pH (pH n+3 ).
4 . The method of claim 3 , wherein addition of the third amount (Titrant n+2 ) of titrant to the sample results in a pH that is within 0.05 to 0.10 pH units of a final target pH (pH final ).
5 . The method of claim 4 , further comprising adding a fourth amount of titrant (Titrant n+3 ) to the sample.
6 . The method of claim 5 , wherein the method comprises no more than 4 additions of titrant to change the pH of the sample from pH initial to pH final .
7 . The method of claim 1 , further comprising:
normalizing the reference titration curve to generate a regression of a normalized reference titration curve, wherein generating the model based on the regression of the reference titration curve includes generating the model based on the regression of the normalized reference titration curve.
8 . The method of claim 4 , wherein generating the reference titration curve comprises:
(i) measuring an initial pH of the reference sample (pH initial_ref );
(ii) adding an amount of titrant to the reference sample (Titrant n_ref ) and measuring an additional reference pH value (pH n_ref ), Titrant n_ref being the amount of titrant added to the sample to reach pH n_ref , wherein pH n_ref is different from pH initial_ref ;
(iii) repeating step (ii) until the reference sample reaches a final pH (pH final_ref ) by adding a total amount of titrant to the reference sample; and
(iv) plotting amount of titrant added versus pH of the reference sample.
9 . The method of claim 8 , wherein an amount of titrant added to the reference sample is normalized by:
normalized
Titrant
n
_
ref
=
Titrant
n
_
ref
-
Titrant
2
_
ref
Titrant
2
_
ref
-
Titrant
2
_
ref
,
wherein Titrant 1_ref is an amount of titrant added to the reference sample to reach pH 1_ref , and Titrant 2_ref is an amount of titrant added to the reference sample to reach pH 2_ref .
10 . The method of claim 9 , wherein the reference titration curve comprises a single titration curve, and wherein pH 1_ref =pH initial_ref , and pH 2_ref =pH final_ref .
11 . The method of claim 9 , wherein the reference titration curve comprises a plurality of reference titration curves, wherein each reference titration curve comprises a pH initial_ref and pH final_ref , and wherein:
a. pH 1_ref is a pH initial_ref from one of the plurality of reference titration curves,
b. pH 2_Ref is a pH final_ref from one of the plurality of reference titration curves, and
wherein pH 1_ref and pH 2_ref are selected to encompass a maximal difference in value while still encompassing pH values covered by all of the plurality of reference titration curves.
12 . The method of claim 9 , wherein the initial pH of the sample (pH initial ) and pH 1_ref are about the same, or wherein the initial pH of the sample (pH initial ) and pH 1_ref are not the same.
13 . The method of claim 12 , wherein pH final and pH 2_ref are about the same, or wherein pH final and pH 2_ref are not the same.
14 . The method of claim 9 , wherein pH initial , pH initial_ref and pH 1_ref are the about the same, and wherein pH final , pH final_ref and pH 2_ref are the about the same.
15 . The method of claim 4 , wherein pH final is less than the initial pH of the sample (pH initial ), and the titrant is an acid.
16 . The method of claim 11 , wherein pH 1_ref is about 4.0 to about 4.3, and pH 2_ref is about 3.4 to about 3.9.
17 . The method of claim 15 , wherein pH initial is about 4.0 to about 4.5.
18 . The method of claim 15 , wherein pH final is about 3.0 to about 3.8.
19 . The method of claim 4 , wherein pH final is greater than the initial pH (pH initial ), and the titrant is a base.
20 . The method of claim 19 , wherein pH 1_ref is about 3.0 to about 3.8, and pH 2_ref is about 5.3 to about 8.5.
21 . The method of claim 19 , wherein pH initial is about 3.0 to about 3.8.
22 . The method of claim 19 , wherein pH final is about 5.3 to about 8.5.
23 . The method of claim 1 , further comprising correcting for pH meter calibration when determining pH values of the sample or the reference sample.
24 . The method of claim 1 , wherein the sample comprises a first protein of interest, and wherein the first protein of interest comprises an antibody, a receptor Fc fusion (TRAP) protein, or a glycosylated protein.
25 . The method of claim 4 , wherein the method improves accuracy of reaching pH final compared to a method whereby pH is measured by inserting a pH probe directly into the sample or a continuous slip stream drawn from the sample.
26 . The method of claim 1 , wherein the method reduces sample waste compared to a method whereby pH is measured by a pH meter inserted into a continuous slip stream drawn from the sample.
27 . The method of claim 1 , wherein a difference between a measured sample pH and the model identifies an error in calibration of the pH probe or the pH meter used to measure sample pH.
28 . The method of claim 1 , wherein the initial pH (pH initial ) of the sample is 4.0 or greater, and the method further comprises:
adding the second amount of titrant (Titrant n+1 ) to the sample to reach pH acid_target ;
holding the sample at pH acid_target for a period of time sufficient to inactivate a virus in the sample;
adding a first amount of basic titrant (Titrant n_base ) to the sample and measuring a first base pH value (pH n_base ), Titrant n_base being an amount of titrant added to the sample to reach pH n_base , wherein pH n_base is different from pH acid_target the pH acid_final ;
applying the model to determine a second amount of basic titrant to add to the sample to change the pH of the sample to a target basic pH (pH target_base ); and
adding the second amount of basic titrant to the sample to reach pH target_base .
29 . The method of claim 28 , wherein pH acid_target is an intermediate pH, wherein the method further comprises adding additional titrant to the sample to reach pH acid_final from pH acid_target , and wherein pH acid_target is within 0.05 to 0.10 pH units of pH acid_final .
30 . The method of claim 28 , wherein pH n_base is within 0.05 to 0.10 pH units of pH final_base .
31 . The method of claim 28 , wherein pH acid_final is between about 3.0 to about 3.8.
32 . The method of claim 28 , wherein pH final_base is between about 5.3 to about 8.5.
33 . The method of claim 28 , further comprising correcting for pH meter calibration.
34 . The method of claim 28 , wherein the sample comprises a protein of interest.
35 . The method of claim 1 , wherein the sample comprises dupilumab.
36 . The method of claim 1 , wherein the reference sample comprises dupilumab.
37 . The method of claim 28 , wherein pH acid_final is about 3.3 to about 3.7, and wherein pH final_base is about 5.5 to about 8.0.
38 . The method of claim 28 , wherein pH acid_target is within 0.05 to 0.10 pH units of pH acid_final , and pH n_base is within 0.05 to 0.10 pH units of pH final_base .
39 . The method of claim 11 , wherein pH 1_ref is about 0.1 to about 0.9 pH units within pH 2_ref .