(361o) Modeling and Control of Antibody Purification Via Protein a Affinity Chromatography

Monoclonal and polyclonal antibodies are essential therapies to treat many life-threatening diseases from cancer to Covid 19[1]. During the production of such therapies, the most expensive process step is the Protein A chromatography step used to selectively bind and elute the antibody to a high level of purity[2]. Many companies increase the resin residence time to maximize the antibody extraction capacity[3] and, as a result, minimize the amount of resin needed. Unfortunately, the existence of host cell proteins, which include destructive enzymes[4], can affect the antibody production yield if left in contact with the antibody for far too long. Therefore, lower resin residence time can improve antibody yield but, unfortunately, leads to inefficient lower resin capacity and expensive resin usage.

Since the antibody yield is improved at high flow rate but resin capacity is improved at low flow rate, we looked into maximizing the resin capacity starting at high controllable flow rate. Therefore, the objective of this work is to apply optimal control on an accurately derived dynamic model, representing the affinity chromatography step, to maximize the efficient use of the Protein A resin.

Methods:

An improved version of the Yoon-Nelson model[5] was used in our work to predict the effluent concentration of the antibody extraction. The model was obtained by finding a direct relationship between the two model parameters and the Protein A resin residence time. The first 4 temporal moments[6] are formulated to represent the dynamic chromatographic process model in the form of ordinary differential equations (ODEs). The moments, utilized in this work to represent the effluent conditions, are the zeroth moment/concentration ratio, the first moment/inflection time, the second moment/variance, and the third moment/skewness.

Optimal control is accomplished via the application of the Pontryagin’s maximum principle (PMP)[7] through the following steps: (i) integrate the Yoon-Nelson model with the method of moments[8] (ii) determine the dynamic influent flow rate profile to achieve maximum antibody extraction, and (iii) apply optimal control to predict a robust operating policy. Therefore, the moments represent the state variables describing the affinity chromatography process. PMP requires the introduction of adjoint variables to complement the state variables[9]. The optimal control objective function is then rewritten as a Hamiltonian function[10], combining state and adjoint variables. Optimality is achieved when the Hamiltonian function deviation with flow rate is minimized at every time step.

Results:

The Yoon-Nelson predictive model includes two parameters with direct correlation to the process flow rate, the controlling element, allowing the use of such model in optimal control strategies. One of the model parameter was linearly related to the residence time while the other parameter was inversely related. When applying the Pontryagin’s maximum principle to maximize the resin loading capacity at a defined breakthrough point, the residence time, initially starting at the fast rate of 3 minutes, decreased after several hours to the final rate of 10 minutes. This control strategy allows for more feed to be introduced to the affinity resin in a minimum amount of time. The effectiveness of such control strategies was successful at maximizing the limited capacity of the protein A resin while minimizing the effect of the whole cell proteins on the process yield.

Implications:

Antibody concentration can vary with every feed but the affinity chromatography column size cannot be modified for each feed concentration. Adding optimal control on the flow rate will allow the use of any size column via control of the residence time. Our work will allow the efficient use of the most expensive step in the antibody downstream processing, the protein A affinity resin, via maximizing yield and resin capacity in downstream processes.

References:

[1] R.-M. Lu et al., “Development of therapeutic antibodies for the treatment of diseases,” J. Biomed. Sci., vol. 27, no. 1, p. 1, Dec. 2020, doi: 10.1186/s12929-019-0592-z.

[2] S. Arora, B. V. Ayyar, and R. O’Kennedy, “Affinity Chromatography for Antibody Purification,” in Protein Downstream Processing, vol. 1129, N. E. Labrou, Ed. Totowa, NJ: Humana Press, 2014, pp. 497–516. doi: 10.1007/978-1-62703-977-2_35.

[3] A. M. Ramos-de-la-Peña, J. González-Valdez, and O. Aguilar, “Protein A chromatography: Challenges and progress in the purification of monoclonal antibodies,” J. Sep. Sci., vol. 42, no. 9, pp. 1816–1827, May 2019, doi: 10.1002/jssc.201800963.

[4] R. Molden et al., “Host cell protein profiling of commercial therapeutic protein drugs as a benchmark for monoclonal antibody-based therapeutic protein development,” mAbs, vol. 13, no. 1, p. 1955811, Jan. 2021, doi: 10.1080/19420862.2021.1955811.

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[7] I. M. Ross, A primer on Pontryagin’s principle in optimal control. Carmel, Calif. : Collegiate Publishers, 2009., 2009. [Online]. Available: https://search.library.wisc.edu/catalog/9910894537702121

[8] M. N. Goltz and P. V. Roberts, “Using the method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives,” Water Resour. Res., vol. 23, no. 8, pp. 1575–1585, Aug. 1987, doi: 10.1029/WR023i008p01575.

[9] P. T. Benavides and U. Diwekar, “Studying various optimal control problems in biodiesel production in a batch reactor under uncertainty,” p. 9, 2013.

[10] K. M. Yenkie and U. Diwekar, “Stochastic Optimal Control of Seeded Batch Crystallizer Applying the Ito Process,” Ind. Eng. Chem. Res., p. 120604103933002, Jun. 2012, doi: 10.1021/ie300491v.