Closed-loop optimization of chromatography column sizing strategies in biopharmaceutical manufacture

Abstract

Background: This paper considers a real-world optimization problem involving the identification of cost-effective equipment sizing strategies for the sequence of chromatography steps employed to purify biopharmaceuticals. Tackling this problem requires solving a combinatorial optimization problem subject to multiple constraints, uncertain parameters, and time-consuming fitness evaluations.

Results: An industrially-relevant case study is used to illustrate that evolutionary algorithms can identify chromatography sizing strategies with significant improvements in performance criteria related to process cost, time and product waste over the base case. The results demonstrate also that evolutionary algorithms perform best when infeasible solutions are repaired intelligently, the population size is set appropriately, and elitism is combined with a low number of Monte Carlo trials (needed to account for uncertainty). Adopting this setup turns out to be more important for scenarios where less time is available for the purification process. Finally, a data-visualization tool is employed to illustrate how user preferences can be accounted for when it comes to selecting a sizing strategy to be implemented in a real industrial setting.

Conclusion: This work demonstrates that closed-loop evolutionary optimization, when tuned properly and combined with a detailed manufacturing cost model, acts as a powerful decisional tool for the identification of cost-effective purification strategies. © 2013 The Authors. Journal of Chemical Technology & Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Keywords: antibody purification technologies; biopharmaceutical manufacture; closed-loop optimization; downstream processing design; evolutionary computation; process economics.

Figure 1

Typical flowsheet for an antibody manufacturing process.

Figure 2

Schematic of closed-loop optimization. The genotype of a candidate solution is generated on the computer but its phenotype is experimentally prototyped or alternatively realized by running an expensive computation simulation. The quality or fitness of a solution may be obtained experimentally too and thus may be subject to measurement errors (noise).

Figure 3

Schematic of the closed-loop platform employed comprising an optimization algorithm (EA) linked to a detailed process economics model; the interaction between the two components is supported by a database. The process economics model (its structure is illustrated using a UML diagram) performs mass balance and cost calculations and the EA determines the best chromatography equipment sizing strategies. A chromatography equipment sizing strategy is defined by the column bed height h_i, column diameter d_i, number of cycles n_CYC,i and number of columns n_COL,i for each chromatography step  i = 1, …, k employed. Different sizing strategies may yield the same overall column volume but nevertheless vary in the objective COG/g.

Figure 4

A candidate solution (sizing strategy) with k = 3 chromatography steps. Each step i = 1, …, k is defined by the parameters h_i,  d_i,  n_CYC,i  and n_COL,i.

Algorithm 1

Pseudocode of the search algorithms with constraint handling strategies

Figure 5

Boxplots showing the distribution of the (a) length and (b) final fitness (COG/g) of 1000 adaptive walks for different USP:DSP ratios. The box represents the 25th and 75th percentile with the median indicated by the dark horizontal lines. The whiskers represent the observations with the lowest and highest value still within Q1-1.5×IQR and Q3+1.5×IQR, respectively; solutions outside this range are indicated as dots. Q1 and Q3 are the 25th and 75th percentile, and the interquartile range is IQR=Q3-Q1.

Figure 6

(a) Average best COG/g (and its standard error) obtained by different search algorithms as a function of the population size μ; the number of fitness evaluations available for optimization was fixed to #Evals = 2000, i.e. the number of generations is G = ⌊2000/μ⌋. (b) Average best COG/g, as a function of the generation counter g, obtained by GA-ES using different repairing strategies. Both experiments were conducted on a chromatography equipment sizing problem featuring a ratio of USP:DSP trains of 4:1. For each setting shown on the abscissa, a Kruskal–Wallis test (significance level of 5%) has been carried out. In (a), GA-ES performs best for μ > 40 while, in (b), RS1 performs best in the range 1 < g < 15.

Figure 7

Average best COG/g (and its standard error) obtained by (a) GA-ES and (b) SGA in a deterministic and stochastic environment (using different values for the number of Monte Carlo trials m) as a function of the generation counter g. For each setting shown on the abscissa, a Kruskal–Wallis test (significance level of 5%) has been carried out. In (a), GA-ES with m = 10 performs best for g > 15, while, in (b), SGA, deterministic, performs best in the range 1 < g < 6.

Figure 8

Column sizing strategies for the most expensive chromatography step (i = 1) found by GA-ES at the end of the search across 20 independent algorithm runs (within an uncertain optimization environment) (bubbles) for the scenarios (a) 1USP:1DSP, (b) 2USP:1USP and (c) 4USP:1DSP. The size of a bubble is proportional to the variable d₁; all solutions feature the setup n_COL,1 = 1. The COG/g values of all solutions found by the EA for a particular scenario are within 3% of each other. For each scenario, the filled bubble represents the optimal setup found by the EA. The base case setup is indicated with a filled diamond and was not part of the solution set found by the EA for the scenarios 1USP:1DSP and 4USP:1DSP.

Figure 9

Percentage change in key performance criteria of the best solution found by the stochastic EA relative to the base case for different ratios of USP:DSP trains (COG = average COG/g, sd = standard deviation of COG/g, time = DSP time, kg = average product output, waste = average amount of product wasted due to titer fluctuations). The stochastic values for the base case sizing strategies were obtained by running the same number of Monte Carlo simulations on batch titer as performed for the best solution found by GA-ES.

Figure 10

Column sizing strategies for the most expensive chromatography step (i = 1) found by GA-ES at the end of the search across 20 independent algorithm runs for the scenario 1USP:1DSP. The size of a bubble is proportional to the column diameter d₁; all solutions feature the setup of 1 column per step, n_COL,1 = 1. Black bubbles: d₁ > 1.6m. Grey bubbles: bed height h₁ > 22 or h₁ < 18 cm, white bubbles: meet both constraints.