Optimal loading flow rate trajectory in monoclonal antibody capture chromatography

In this paper, we determined the optimal flow rate trajectory during the loading phase of a mAb capture column. For this purpose, a multi-objective function was used, consisting of productivity and resin utilization.

Journal of Chromatography A 1635 (2021) 461760 Contents lists available at ScienceDirect Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma Optimal loading flow rate trajectory in monoclonal antibody capture chromatography Joaquín Gomis-Fons a,b,1,∗, Mikael Yamanee-Nolin a,1, Niklas Andersson a, Bernt Nilsson a,b a b Department of Chemical Engineering, Lund University, Lund, Sweden Competence Centre for Advanced BioProduction by Continuous Processing, Royal Institute of Technology, Stockholm, Sweden a r t i c l e i n f o Article history: Received August 2020 Revised 23 October 2020 Accepted 23 November 2020 Available online 26 November 2020 Keywords: Flow programming Flow trajectory Protein A chromatography Monoclonal antibody Multi-objective optimization Chromatography scale-up a b s t r a c t In this paper, we determined the optimal flow rate trajectory during the loading phase of a mAb capture column For this purpose, a multi-objective function was used, consisting of productivity and resin utilization Several general types of trajectories were considered, and the optimal Pareto points were obtained for all of them In particular, the presented trajectories include a constant-flow loading process as a nominal approach, a stepwise trajectory, and a linear trajectory Selected trajectories were then applied in experiments with the state-of-the-art protein A resin mAb Select PrismATM , running in batch mode on a standard single-column chromatography setup, and using both a purified mAb solution as well as a clarified supernatant The results show that this simple approach, programming the volumetric flow rate according to either of the explored strategies, can improve the process economics by increasing productivity by up to 12% and resin utilization by up to 9% compared to a constant-flow process, while obtaining a yield higher than 99% The productivity values were similar to the ones obtained in a multicolumn continuous process, and ranged from 0.23 to 0.35 mg/min/mL resin Additionally, it is shown that a model calibration carried out at constant flow can be applied in the simulation and optimization of flow trajectories The selected processes were scaled up to pilot scale and simulated to prove that even higher productivity and resin utilization can be achieved at larger scales, and therefore confirm that the trajectories are generalizable across process scales for this resin © 2021 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Introduction Monoclonal antibodies (mAbs) are used to treat a wide range of different diseases, such as rheumatoid arthritis, Crohn’s disease and chronic lymphocytic leukemia [1] However, mAb treatments can become very expensive due to high manufacturing costs [2] and low research and development productivity [3] Further considering the fact that downstream processing may account for over 60% of the total manufacturing cost of a mAb product, and that the capture step is crucial to overall process efficiency, improvements of this step will have great impact on process economics [2] ∗ Corresponding author at: Dept of Chemical Engineering, Lund University, P.O Box 124, SE-21100, Lund, Sweden E-mail addresses: joaquin.gomis_fons@chemeng.lth.se (J GomisFons), mikael.yamanee-nolin@chemeng.lth.se (M Yamanee-Nolin), niklas.andersson@chemeng.lth.se (N Andersson), bernt.nilsson@chemeng.lth.se (B Nilsson) Joaquín Gomis-Fons and Mikael Yamanee-Nolin are co-first authors with equal contribution Most processes for the purification of mAbs are currently operated in batch mode, and these processes are simple, robust, and well-known [4,5]; however, they are also inefficient [6-8] To increase efficiency, an alternative is to adopt an integrated and continuous bioprocess (ICB), which could lead to higher productivity, lower cost of goods, and higher resin utilization, as shown in previous implementations and studies [7,9,10] Most downstream steps in previous ICB studies are based on multi-column chromatography processes, which for example include sequential multi-column chromatography (SMCC) [11], capture simulated moving bed (CaptureSMB) [12], multi-column counter-current solvent gradient purification (MCSGP) [13,14], and periodic countercurrent chromatography (PCC) [6,15] In general, these strategies make use of multiple columns, valves and pumps with a sequential operation; thus, this adds an extra layer of complexity to the process design and operation In addition, there are technology gaps that need to be address before the implementation of these processes at commercial scale [16], which is why integrated and continuous biomanufacturing is still not prevalent at commercial scale [7] https://doi.org/10.1016/j.chroma.2020.461760 0021-9673/© 2021 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) J Gomis-Fons, M Yamanee-Nolin, N Andersson et al Journal of Chromatography A 1635 (2021) 461760 Building upon the findings of Sellberg et al [21,22], the purpose of the current work is to optimize different flow trajectories in a protein A step for the capture of mAb with the novel resin mAb Select PrismATM , and demonstrate their potential in an experimental validation In comparison to the work by Ghose et al [20], we present a more comprehensive study where different flow programming strategies are explored, and we apply the optimal results to a state-of-the-art protein A resin The loading phase in the protein A capture step is often the rate-limiting step in a mAb downstream process [20] Therefore, flow programming was only considered in the loading step To obtain the optimal flow trajectories, a model-based multi-objective optimization approach was first applied, utilizing a General Rate model [23], in order to find and compare optimal trajectories for three approaches: Fig Illustrative comparison of the breakthrough curves (BTC) with constant flow rate (u1 ) and variable flow rate (u2 ) I A nominal approach, applying a constant flow rate II A stepwise trajectory approach, applying Nu > decision horizons with stepwise flow rate changes III A linear trajectory approach, applying a flow rate changing linearly with time Another approach towards increasing efficiency is to apply a programmed variable flow rate in the loading of the chromatography steps, and the underlying idea is illustrated in Fig The theoretical background is that higher loading flow rates lead to higher productivity, but they also result in a flatter breakthrough curve [6,17] As a result of a flatter breakthrough curve, the loading time must be shortened in order to keep the yield high, thus leading to a decreased resin utilization Similarly, when a lower flow rate is applied, the breakthrough curve is sharper, and the resin utilization for a specific yield requirement is increased In order to find the optimal balance between high productivity and high resin utilization, flow programming can be used to find an optimal flow trajectory Using this technique, a higher flow rate is applied at the beginning when all binding sites are available, and a lower flow rate is used to give the protein more time to diffuse into the pores As shown in Fig 1, the breakthrough curve of the variableflow process appears earlier as a result of a higher flow rate at the beginning, but as the flow rate diminishes, mass transfer in the column improves leading to less product loss in the breakthrough Flow programming has been previously used [18], showing a productivity increase with a variable flow rate profile obtained with a design of experiments (DoE) approach Lacki [19] has also demonstrated the potential of flow programming, but their results also showed that if the flow rate trajectory is not chosen properly, the productivity could be even lower than in the corresponding constant-flow operation In order to avoid sub-optimal flow rate trajectories and their resulting performance in terms of process economics, model-based optimization can be a useful tool to optimize key process performance indicators such as productivity, resin utilization, and yield This approach has been explored by Ghose et al [20], who applied a dual-flow rate loading strategy with a variable switching time and showed that it outperformed single-loading strategies without requiring any extra equipment or columns This strategy was expanded later to include any number of constant flow rates evenly distributed over the loading phase [21] This in-silico study, which was not based on mAbs but on a model protein instead, further highlighted the potential to increase productivity and resin utilization by modifying the flow rate during the loading phase of a capture step, whilst retaining the simplicity of the singlecolumn setup operated in batch mode Further proof of the potential of model-based optimal trajectories in chromatography has been shown by Sellberg et al [22], who obtained optimal elution trajectories with variable modifier concentration in ion exchange chromatography The mass transfer behind this process is different from the one behind the loading of a protein A column, but it shows the experimental feasibility of applying general trajectories obtained with a computer-aided optimization A Pareto front for each of the three approaches was obtained, and they were then implemented at laboratory scale for proof-ofconcept The experimental results in combination with the modelbased results highlight the potential to improve efficiency and process economics of the mAb production process using a simple yet high-value solution, i.e., a single-column, batch-mode capture step with variable flow rate during the loading phase The primary advantage compared to an ICB process is that the batch technology and equipment currently used commercially can still be used applying the proposed flow-programming strategies Scalability of the flow-trajectory processes from laboratory scale to pilot scale is crucial to be able to maintain the same process through the development phases of the biopharmaceutical For that reason, the processes studied were scaled up and simulated to demonstrate that the trajectories can be applied even at a larger scale and are general at any scale for the resin mAb Select PrismA This is, to be the best of our knowledge, the first time that process scale-up is addressed in relation to flow programming The remainder of the paper is structured as follows: Section introduces the model-based approach, with the process model and the optimization problem This is followed by a description of the experimental setup and procedure, and of the scale-up method The results of the model-based optimization, the laboratory experiments and the process scale-up are then presented and discussed in Section The major conclusions are then presented in the final section Material and methods 2.1 Model-based optimization 2.1.1 Process model The chromatography column was modeled using the General Rate model featuring a heterogeneous binding mechanism with fast and slow sites [23], to simulate and optimize the loading of the capture step The particular model applied in the current work has been previously implemented in Matlab and calibrated successfully in our previous study [6], using the Finite Volume Method [24] The model was calibrated for several constant flow rates and mAb concentrations to ensure a good fitting for a broad range of conditions The mobile phase and particle concentrations are described by Eqs and 2, respectively, with boundary conditions specified by equations 1a, 1b, 2a, and 2b, and Eq describing the kinetics ∂c ∂ 2c v ∂c − = Dax − − ∂t ∂z c ∂z c c k c − c p|r=r p rp f (1) J Gomis-Fons, M Yamanee-Nolin, N Andersson et al ∂c v = (c − cF ) at z = ∂z D c ax ∂c = at z = L ∂z ∂ cp ∂ cp ∂ = De f f r2 ∂t ∂r r ∂r ∂ cp = at r = ∂r − Journal of Chromatography A 1635 (2021) 461760 for the stepwise constant flow rates, and the total duration of the loading phase, giving a total of Nu + decision variables; Y represents yield, and Y is the minimum required yield, set to 99%; and [DVlb,i , DVub,i ] are the lower and upper bounds for the decision variables, set to [0.2, 1.5] mL/min for the flow rates and [60, 300] for the loading time The optimization problem for Approach III is presented in Eq 5: (1a) (1b) ∂ ( q1 + q2 ) ∂t p kf ∂ cp = (c − c p ) at r = r p ∂r De f f qi ∂ qi = ki (qmax, i − qi )c p − ∂t K (2) Objective functions : F = −[P, U ] (2a) Decision variables : DV = u0 , ut f , t f (2b) Constraints : Y ≥ Y , DVi = DVlb,i , DVub,i In this problem, the objectives and constraints were the same as the ones used in Approaches I and II, but the decision variables were different The decision variables were in this case only the initial and final flow rates, u0 and ut f , respectively, and the duration of the loading phase, t f , and the resulting trajectory was linear over time The control action at time t, i.e., the volumetric flow rate, ut , was in this approach calculated according to Eq (3) Here, c is the mobile phase mAb concentration, cF is the inlet mAb concentration, c p is the particle mAb concentration, q is the adsorbed mAb concentration, Dax is the axial dispersion coefficient, v is the superficial fluid velocity, k f is the particle layer mass transfer coefficient, De f f is the effective pore diffusivity, εc is the column void, ε p is the particle porosity, r p is the particle radius, L is the column length, qmax is the maximum column capacity, K is the Langmuir equilibration constant, and ki is the adsorption rate constant, where i can be either or 2, for fast or slow kinetics, respectively The axial dispersion coefficient was obtained using a Peclet number correlation [25], the void and porosity parameters were obtained from Pabst et al [26], and the mass transfer coefficient was estimated with an empirical correlation [27] The choice of the chromatography resin has an impact on the model as the particle diameter and pore size of the resin affect the mass transfer significantly A higher particle diameter leads to a longer average distance between the particle surface and the binding sites, which results in a slower overall mass transfer inside the particle; and a small pore diameter hinders mass transfer through the pores by decreasing the effective pore diffusivity [28] Therefore, a new model calibration and optimization should be carried out for a different resin ut f − u0 ut = tf t + u0 (6) Furthermore, for the three approaches, the three key performance indicators were defined according to Eqs 7-9: 2.1.2 Optimization problem The main idea behind the optimization problem was to modify the volumetric flow rate during the loading phase as well as the duration of the loading phase (decision variables) in order to improve the process economics, by maximizing productivity and resin utilization (objective functions) for a specific yield requirement (constraint) Two different types of flow trajectories were employed: a stepwise trajectory with Nu decision horizons corresponding to constant flow rate levels distributed evenly across the full duration of the loading phase was employed in Approach I (a single decision horizon, thus corresponding to the nominal constant-flow process) and Approach II (Nu > decision horizons), whereas a linear trajectory was obtained over time and applied in Approach III The choice of these two types of trajectories resulted in two slightly different optimization problems The optimization problem for the stepwise trajectories employed in Approaches I and II is presented in Eq below: Objective functions : F = −[P, U ] (5) Pn = ma t f Vc (1 − P= Pn − Pmin Pmax − Pmin c Un = ma qeqVc (1 − U= Un − Umin Umax − Umin Y = ma ) ; (7a) (7b) c ) ; (8a) (8b) (9) where ma is the amount of adsorbed mAb, which is determined as the difference between the amount of mAb loaded (min ) and the product loss in the breakthrough, calculated by the area under the breakthrough curve; Vc is the column volume; and Pmin , Pmax , Umin , and Umax are nominal minimum and maximum values of the productivity and resin utilization, based on nominal loading processes at minimum and maximum volumetric flow rates and loading phase durations Eq 7a defines the productivity as the amount of adsorbed mAb divided by the duration of the loading phase and the resin volume Eq 8a defines the resin utilization as the amount of adsorbed mAb per volume of resin divided by the stationary phase mAb concentration at equilibrium, whose definition is also based on volume of resin Furthermore, Eqs 7b and 8b define the productivity and resin utilization normalized to the range 0-1 for all operating conditions, which are used in the objective function Eq defines yield as the amount of adsorbed mAb divided by the amount of mAb loaded It should be noted that the key performance indicators, as applied in the current work, are based on the loading phase of the capture step only, i.e not include other phases such as elution and CIP, and ignore any remaining mAb in the mobile phase at the end of the loading phase For this reason, the way that productivity is defined in Eq 7a results in higher values compared to how productivity of capture processes is usually reported [6,12], since, in this case, only the process time for the loading phase is included in the definition of productivity For comparison with other processes, the productivity values should be (4) Decision variables : DV = u0 , u1 , , uNu , t f Constraints : Y ≥ Y , DVi = DVlb,i , DVub,i Here, F is the objective function vector consisting of the normalized productivity, P , and the normalized resin utilization, U; DV is the decision variable vector containing Nu decision variables J Gomis-Fons, M Yamanee-Nolin, N Andersson et al Journal of Chromatography A 1635 (2021) 461760 adjusted to include the process time corresponding to the whole capture step The optimization problems were solved using a Matlab variant of the elitist non-dominated sorting genetic algorithm (NSGA-II), which is available as part of the built-in gamultiobj function The constraint tolerance was set to machine epsilon, with the function tolerance set to 10−6 , and the population size was set 300 Using this kind of global, multi-objective algorithm, a set of Pareto optimal solutions are offered to the user, who can then make a decision a posteriori regarding how to weigh the objectives [29] necessary in Approach I, thus resulting in constant flow rate during the whole loading phase 2.2.4 Analytics The breakthrough curve was detected online with a UV sensor at a wavelength 280 nm For the experiments with pure mAb, this signal was used to obtain the breakthrough curve in mg/mL using an extinction coefficient of 1.4 (mg/mL)−1 cm−1 [34] For the experiments with supernatant sample, the breakthrough baseline was above the linear range of the UV detector, which is 20 0 mAU, due to the high concentration of impurities that went through the column For that reason, the outlet stream was collected in fractions of mL and analyzed offline For the analysis of the fractions, an ÄKTA Explorer 100 equipped with an autosampler was used The autosampler was set up so that mL of each fraction was taken and loaded onto the column A mL prepacked HiTrapTM column with mAb Select PrismATM resin was used for the analyses The process conditions regarding buffers and flow rates were the same as in the flow trajectory experiments, described above However, the elution time was longer to be able to see the whole elution peak Knowing the injected volume and the extinction coefficient, the concentration of each fraction was calculated with the area of the eluate peak 2.2 Experimental setup 2.2.1 Buffers and sample preparation Experiments were conducted using two different samples: (i) a 0.48 mg/mL purified mAb solution for a clear illustration of the results, and (ii) a 0.48 mg/mL clarified supernatant for proofof-concept The mAb concentration of the latter was adjusted to match the concentration at which the experiments with the purified mAb were performed, so that a direct comparison of the experiments with the two different samples could be done According to the equilibrium data obtained in our previous study [6], the adsorbed concentration at equilibrium for mobile phase concentrations above 0.5 mg/mL is nearly constant, and the mass transfer coefficients in the model remain almost constant for higher concentrations provided the viscosity does not increase significantly Therefore, the relationship between the feed concentration and the time it takes for the product to break through the column is nearly linear For that reason, almost the same breakthrough curves would be obtained for equal protein loads in units of mass of product loaded per volume of resin, if the residence time is the same Consequently, it can be assumed that the optimal flow trajectories are general for any feed concentration above 0.5 mg/mL as long as the protein load is maintained by adjusting the loading time The buffers, column volumes and flow rates (except the loading flow rates) were the ones recommended by the resin manufacturer for a protein A capture process [30] 2.3 Scale-up method The processes studied were scaled up to pilot scale with a factor of 10 0 and simulated to investigate whether the found trajectories were generalizable across process scales for the mAb Select PrismA resin A method to scale up the process is to keep the column length constant and increase the diameter, in a way that both the flow velocity and the residence time are kept constant This scale-up method has been proposed by Heuer et al [35] The flow rate trajectories would be converted to velocity trajectories, by dividing the flow rates by the column section (in this case 0.38 cm2 ), and the same velocity trajectories could be used for any process scale In this work, the column length was 2.5 cm, therefore it was not practical to keep the same length at larger scales For that reason, another scale-up method is to change both the column diameter and length, so that the residence time is kept constant, even if the velocity is not This method, proposed by Hansen [36], provides flexibility to choose an appropriate length to fulfill a maximum diameter-to-length ratio constraint He shows that the number of theoretical plates, which is an indication of the column efficiency, increases at a higher column length and constant residence time, based on a simplified version of the van Deemter equation: 2.2.2 Chromatography station setup In order to carry out the capture experiments using the optimal trajectories found via model-based optimization, a single ÄKTATM pure 150 unit, provided by Cytiva (Uppsala, Sweden), was used with its standard setup, and it was equipped with the following devices: two gradient pumps, inlet valves for buffer selection, column valve with built-in pressure sensor, a fractionator, an outlet valve, and a sensor package that included a UV, a conductivity and a pH sensor The sample was injected onto the column with a 100 mL SuperloopTM The column was a mL prepacked HiTrapTM column with mAb Select PrismATM resin, from Cytiva (Uppsala, Sweden), and the column length and diameter were 2.5 cm and 0.7 cm, respectively N= A L (10) + Cτ where N is the number of theoretical plates, L is the column length, τ is the residence time, and A and C are constant terms in the van Deemter equation In this work, this scale-up method was applied, and an empirical expression for the pressure drop over a packed bed [37] was used to obtain the column length: 2.2.3 Process control The ÄKTA pure system used during experiments was controlled with the Python-based software Orbit, which has been described in detail elsewhere [31-33] For the particular control problem in the current work, a function to modify the flow rate based on the elapsed time was implemented In Approach II, the total load duration (t f ) was divided by Nu to obtain equal time horizons with stepwise constant flow rates The list of flow rates found through the optimization was specified manually, and used by Orbit to update the flow rate at the start of each horizon In Approach III, the linear trajectory was approximated by stepwise constant control actions updated at a sampling rate, i.e Hz, which is much more frequent than in Approach II Additionally, no flow rate change was P = αvL = α L2 τ (11) where P is the pressure drop over the column, v is the superficial velocity, which equals the column length divided by the residence time, and α is an empirical constant, which was determined by fitting experimental data of pressure drop against velocity provided by the resin’s vendor At a higher column diameter-to-length ratio, the bed compression increases for a specific velocity and column length due the loss of wall support [37] In turn, this leads to an increase of the empirical constant α For this reason, the experimental data used to obtain α corresponded to a large-scale column J Gomis-Fons, M Yamanee-Nolin, N Andersson et al Journal of Chromatography A 1635 (2021) 461760 with a diameter-to-length ratio of 50, which was higher than the expected ratio The value of α obtained was 1.5•10−4 bar h cm−2 By solving Eq 11 for L, the maximum column length could be calculated as follows: Lmax = Pmax τ α (12) where the maximum pressure drop over the column ( Pmax ) was the one provided by the resin’s vendor minus a safety margin of 20%, resulting in a value of 1.6 bar Once the column length was determined, the column diameter was obtained to achieve the desired column volume while maintaining the residence time Results and Discussion 3.1 Optimization results The results from the model-based optimization are compiled as Pareto fronts and presented in Fig 2, in which the nominal approach – Approach I (black) – is compared with Approach II (gold) and Approach III (red) in the upper and lower panel, respectively It should be noted that the productivity and resin utilization results are presented as actual (not normalized) values, for an easier comparison with results from other authors As can be seen when comparing the optimal solutions in the three approaches, there is potential for improvements by adopting a variable flow rate instead of a constant flow rate, with strikingly similar improvements resulting from the two trajectory strategies explored in this work The two strategies presented in Approach II and Approach III always outperform Approach I, except for the Pareto area at maximum productivity, where the Pareto fronts collapse into each other due to the flow rate being set to the upper bound at all times Following from the Pareto fronts, it is possible to improve the loading phase in terms of productivity and resin utilization to different degrees, depending on the point of current operation Pareto fronts were obtained for Approach II for several numbers of horizons (Nu ): 2, and 10 For a number of horizons higher than 5, the performance indicators (productivity and resin utilization) did not improve enough to warrant the increased complexity of the optimization problem, and thus the increased computation time and resources to solve the problem At the same time, the results were slightly better for the 5-horizons approach than the dual-flow rate approach, thus showing an improvement with respect to the strategy presented by Ghose et al [20] For these reasons, the only Pareto front of Approach II considered for comparison with the other approaches corresponds to a number of horizons equal to Regarding Approach III, the linear trajectory was compared with a quadratic trajectory, with no significant difference found Due to a higher simplicity, it was decided to consider only the linear trajectory in the comparison of the three approaches For comparative reasons, the results for and 10 horizons as well as the results for the quadratic trajectory are attached in the Supplementary materials section, presented in Figures S1 and S2, respectively Fig The Pareto fronts generated in the model-based multi-objective optimization The Pareto front for the stepwise trajectory with five horizons is presented in panel A; and the front for the linear trajectory is presented in panel B The Pareto front for one horizon (constant flow rate) is plotted in both panels for comparison The points selected for experimental trials are marked by circles, in total five cases: the constant-flow nominal case (Case I), and two cases for each trajectory approach, one with improved resin utilization but nearly the same productivity as in Case I (Cases IIa and IIIa), and one with improved productivity but nearly the same resin utilization (Cases IIb and IIIb) from the Pareto fronts Experiments using a purified mAb solution were run for all five points to be able to see the breakthrough curve online without the need of offline analyses For proof-ofconcept, one of the points (Case IIb, i.e the high-productivity point for the stepwise trajectory approach) was tested with clarified supernatant The optimal flow trajectories are presented in Fig 3, while the maximized productivity and resin utilization values are shown in Fig The constant-flow Case I has a loading duration of 75 minutes and a flow rate of 0.77 mL/min, resulting in a productivity of 0.55 mg/min/mL resin and a resin utilization of 31.4%, with a yield of 99.1% The two stepwise trajectories differ from the nominal case in the loading duration, and in the flow rate levels In Case IIa, with an improved resin utilization but constant productivity, the loading duration is roughly minutes longer than Case I (in total 80 minutes), and the average flow rate is 0.77 mL/min, giving a productivity of 0.55 mg/min/mL resin and a resin utiliza- 3.2 Experimental validation The five points highlighted by circles in Fig were selected for applying the optimal flow rate trajectories in the laboratory A point from the Pareto front of Approach I, denoted by Case I, was selected as the nominal case Two points with approximately the same productivity as that of the Case I and higher resin utilization, were selected from the Pareto fronts of Approaches II and III, and they were denoted by Cases IIa and IIIa, respectively Similarly, two more points with approximately the same resin utilization and higher productivity, denoted by Cases IIb and IIIb, were selected J Gomis-Fons, M Yamanee-Nolin, N Andersson et al Journal of Chromatography A 1635 (2021) 461760 Fig Optimal productivity and resin utilization values for Case I (black), Cases IIa and IIb (gold), and Cases IIIa and IIIb (red) The laboratory-scale values obtained from the simulation are compared with the ones obtained experimentally with pure monoclonal antibody and with raw supernatant (the latter only for Case IIb) The five cases were also simulated at pilot scale with a scale factor of 10 0 wise trajectory does not approximate a linear trajectory In addition, as mentioned, a quadratic trajectory or stepwise trajectories with higher number of horizons did not lead to any significant difference respect to the linear trajectory This may lead to the conclusion that complex trajectory shapes may not be necessary to achieve a more efficient process, but rather simple yet optimized trajectories are enough to accomplish this goal The differences between the simulated results and the experimental ones were ultimately insignificant, as shown in Fig In the case with highest deviations (Case IIb), the simulated yield, productivity and resin utilization were 99.4%, 0.61 mg/min/mL and 31.5%, respectively, while the experimental data were 99.7%, 0.62 mg/min/mL and 31.4% This shows that a model calibrated using constant flow rate can be successfully used to optimize a trajectory with variable flow rate Fig Optimal loading flow rate trajectories The stepwise trajectories plotted in panel A correspond to Cases IIa and IIb, and the linear trajectories plotted in panel B correspond to Cases IIIa and IIIb The constant-flow process (Case I) is shown in both panels for comparison tion of 34.2%, which means a relative increase in resin utilization of 8.9%, while the yield is 99.4% Even with an increase in loading duration, the productivity is nearly the same, and this is primarily due to the increase of adsorbed antibodies onto the resin as an effect of the decrease of the flow rate towards the end of the loading phase Similarly, but conversely, the loading duration is shorter by roughly minutes in Case IIb compared to Case I, i.e., in total 67 minutes, with an average flow rate of 0.86 mL/min, resulting in a productivity of 0.62 mg/min/mL resin and a resin utilization of 31.5%, which means a relative productivity increase of 11.8%, and a yield of 99.7% The linear trajectories of Case IIIa and Case IIIb are similar to their corresponding cases of Approach II, with loading durations and average flow rates of 81 and 0.77 mL/min, and 67 and 0.86 mL/min, respectively; the resulting productivity and resin utilization for the two cases are 0.55 mg/min/mL resin and 34.0%, and 0.61 mg/min/mL resin and 31.2%, respectively The yield is in both cases above 99% Given that the performance of the selected points for Approaches II and III were highly similar, it can be expected that the trajectories are similar as well However, it seems that the step- 3.3 Pilot-scale flow rate trajectories The selected cases were scaled up to pilot scale as described in Section 3.4 As shown in Table 1, both the column volume and the flow rate were increased 10 0 times compared to laboratory scale The column length was approximately times higher than at laboratory scale for Case I, while it was 4.5-5 times higher for the other cases The reason for this difference is that the maximum flow rate was lower in Case I than in the other cases, which means that the residence time was higher, and consequently, by Eq 12, the resulting column length was also higher The column diameter was around 10 cm for all cases, leading to a diameter-to-length ratio between 0.6 and 0.9, which is much lower than the value of 50 that was considered as a worst-case scenario for the prediction of the pressure drop over the column This means that the predicted pressure drop is overestimated, thus giving an extra safety margin Regarding the superficial velocities, they were higher than at laboratory scale, as expected, since the column length was increased and the residence time was maintained J Gomis-Fons, M Yamanee-Nolin, N Andersson et al Journal of Chromatography A 1635 (2021) 461760 Table Column design results for five selected process cases at pilot scale Process casesa) Column volume (L) Column length (cm) Column diameter (cm) Max flow rate (L/min) Max velocity (cm/h) Case Case Case Case Case 1 1 15.2 11.6 11.4 12.6 11.6 9.2 10.5 10.6 10.0 10.5 0.77 1.32 1.36 1.12 1.31 703 919 934 845 917 I IIa IIb IIIa IIIb a) Case I: Constant-flow loading; Case II: Stepwise flow rate trajectories; Case III: Linear flow rate trajectories; Cases IIa and IIIa are processes with similar productivity as the one of Case I; Cases IIb and IIIb are processes with similar resin utilization as the one of Case I The pilot-scale cases were simulated with the column dimensions and flow rates obtained, and the productivity, resin utilization and yield were calculated The productivity and resin utilization values for the simulated pilot-scale process are shown in Fig for all process cases In agreement with Hansen’s statement [36], the column efficiency is higher if the column length is increased and the residence time remains constant This leads to a sharper breakthrough curve, which in turn results in a higher yield (data not shown) A lower amount of product loss in the breakthrough leads to a slightly higher productivity and resin utilization, as shown in Fig Another aspect revealed is that having a variable loading flow rate does not make a significant difference in terms of process scale-up regardless the type of flow trajectory applied, as the differences in productivity and resin utilization between the pilot-scale and the laboratory-scale processes are similar for all the cases studied, as can be seen in Fig Another aspect about the scale-up is the wall effects To avoid wall effects the recommended minimum number of resin particles per column section is 200 [38], and with the mL HiTrapTM column used, this number is at highest 117 (obtained by dividing the column diameter, 0.7 cm, by the particle diameter, 60 μm) This indicates that wall effects were present at laboratory scale, but they should not be present at a larger scale with a broader column, which means that the separation would be at least the same and probably better at a larger scale However, further experimental research at pilot scale is required to validate this statement, as well as to find out the aforementioned effect of the loss of wall support at a larger scale explained in our previous study [6] However, in order to implement a PCC process, a more complex setup is needed, with a minimum of two pumps and numerous valves to determine the pathways This could be limiting in cases where there is shortage of resources like chromatography systems and pumps In addition, the benefit of a higher resin utilization in a multi-column process could not pay off the cost of adapting an already-existing batch process to the multi-column setup in some cases Therefore, the potential improvements in productivity and resin utilization with a flow-programming strategy compared to a conventional capture process, combined with the lower complexity and cost of adapting the process setup, may warrant consideration as an alternative to multi-column continuous chromatography processes Conclusions Optimal flow trajectories for the loading phase of the capture of monoclonal antibodies were obtained for the novel protein A resin mAb Select PrismA The two flow-programming approaches presented in this paper are better in terms of productivity and resin utilization than the constant-flow approach, as shown in the optimal Pareto fronts obtained The productivity can be increased by up to 12%, and up to a 9% increase in resin utilization can be achieved, while keeping yield above 99% In this work, several types of flow trajectories were studied and compared with each other with a model-based multi-objective optimization method, leading to the conclusion that simple but optimized trajectories are sufficient to achieve a more efficient process compared to a constant-flow approach Experimental validation was carried out for selected trajectories, both with purified mAb and with clarified supernatant, and results indicate that the predicted increase in the two performance indicators can also be achieved experimentally, which shows that a model calibrated with constant-flow experiments can successfully be used in variable-flow applications In addition, the optimal processes selected were scaled up and simulated to show that the productivity, resin utilization and yield are slightly increased at a larger scale, thus showing that the optimal flow trajectories obtained are generalizable and applicable across scales for this specific protein A resin The productivity obtained in the variable-flow processes implemented in this work are in the same range as the one obtained in a multi-column continuous PCC process [6] Although the resin utilization is significantly lower than in the PCC process, flowprogramming approaches can be an alternative to complex multicolumn continuous capture processes due to their simplicity and ease of implementation The combination of the practical simplicity of the flow-programming approaches, which requires only a single column operated in batch mode with a variable volumetric flow rate, and the potential improvements in process performance indicators, makes this an effective approach towards reducing the cost of the purification of monoclonal antibodies In turn, such improvements can potentially help reducing treatments costs, and by 3.4 Comparison with multi-column continuous capture A variable-flow process can be an alternative to multi-column continuous processes for the increase of the efficiency in the capture of mAbs In a comparison between the variable-flow processes presented here and a PCC process presented in our previous study [6], where the protein A resin and the protein concentration were the same as in this work, it can be said that productivity values are similar In order to compare both processes, it is fairer to use the total capture time in the definition of productivity instead of only the loading time, because in the results from the PCC process, the total capture time is considered The total capture time is the 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we apply the optimal results to a state-of-the-art protein A resin The loading phase in the protein A capture step is often the rate- limiting step in a mAb... a flow rate changing linearly with time Another approach towards increasing efficiency is to apply a programmed variable flow rate in the loading of the chromatography steps, and the underlying idea... the loading phase of a capture step, whilst retaining the simplicity of the singlecolumn setup operated in batch mode Further proof of the potential of model-based optimal trajectories in chromatography