The Optimal Metric of Space-Time Yield

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Space-time yield is a metric to analyze upstream process yields throughout a production campaign. This metric enables distinct methods for protein production, such as batch, fed-batch, or continuous fermentation, to be directly compared to one another. This approach for direct comparison provides researchers and process developers with the capability to consider process yields, input costs, production time, and facility constraints within their evaluation of potential unit operations for the design of a goal-oriented manufacturing strategy. This article demonstrates how to calculate space-time yield using Pichia pastoris (P. pastoris) and Chinese hamster ovary (CHO) cells as model organisms and highlights the unique differences between fed-batch and continuous fermentation processes that result in divergent space-time yields. As higher space-time yields ultimately result in more protein for less space and time, considering space-time yield when choosing a manufacturing plan can be a useful tool for lowering future commercial production costs.

Metrics for comparing cultivation modes

Product concentration, or titer, is often used to describe the productivity of fed-batch fermentations, where the goal is to achieve a large quantity of a heterologous protein for further downstream processing. Protein titer is the amount of protein present in the bioreactor at any given time reported as a concentration (e.g., g/L). The protein titer reached at the end of a fed-batch fermentation is essentially the total quantity of protein made throughout the process, which can be used to compare the productivity of processes performed in a similar format (time, volume, media, host organism, cultivation type, etc.).

In continuous processes, however, nutrients are constantly fed to the bioreactor while secreted protein and waste products are continuously removed from the bioreactor. This constant removal of waste and replenishment of nutrients results in an extremely dense biomass that can maintain protein expression at high levels throughout an extended fermentation campaign. For example, in perfusion fermentation secreted protein is continuously harvested from the healthy biomass throughout the fermentation campaign, which typically runs for time periods twice as long as similar fed-batch fermentations. In this situation, the protein titer inside the bioreactor at a given point in time is not an appropriate representation of the overall protein yield from continuous processes, because protein is continuously being removed from the bioreactor.

Space-time yield

Space-time yield is a normalized metric for productivity that can be used for any cultivation mode or protein-expressing host organism. Space-time yield is defined as the total mass of protein produced per bioreactor working volume per cultivation day irrespective of the method of cultivation, whether batch-based or continuous. This versatile metric normalizes the quantity of protein per cultivation scale and cultivation length, allowing for convenient comparison across scales or process lengths, which often differ between cultivation methods. For example, continuous fermentation campaigns are typically lengthy and can often be extended with minimal additional effort.

Fed-batch campaigns, however, are usually shorter than continuous ones and cannot be significantly lengthened due to fundamental limitations in nutrient availability and accrual of waste products as the campaign extends in time. This accrual of waste and lack of nutrients leads to increasingly unhealthy biomass over time, which ultimately causes a culture to stop producing heterologous protein in fed-batch processes. Given these differences in cultivation operations, space-time yield provides researchers and process developers with a tool to select the optimal process for their production needs based on a normalized comparison.

Space-time yield data enables the evaluation of process design improvements, including process intensification and facility layout optimization. Herein, we describe how to calculate the space-time yield for different processes and demonstrate the utility in using this metric for comparison across fermentation modes, cultivation lengths, and scales.

Comparing cultivation modes

Fed-batch and continuous fermentation of P. pastoris

The method used is based on the mathematical framework presented in Bausch et al., to determine the space-time yield of several cultivations using different manufacturing strategies and hosts (1). The key characteristics for the model cultivations are shown in Table I.

Table I. Key model parameters and assumptions used to compare cultivation processes. CHO is Chinese hamster ovary cells. (Courtesy of the authors)

The comparison of a traditional fed-batch fermentation (Process 1) to a perfusion fermentation process (Process 2) was performed using assumptions for key process parameters relevant for the fermentation of P. pastoris. For both P. pastoris fermentation modes, a two-stage process was assumed, including a biomass accumulation phase at the maximum growth rate, followed by a production phase after the maximum viable cell density is met. Fermentation lengths of six days for fed-batch and 12 days for perfusion were assumed based on literature reports and operational experience. The specific productivity, defined as micrograms of product produced per gram of cells per hour during the production phase of fermentation, is assumed to be the same in both types of operations. The maximum viable wet cell weight was assumed to be higher for the perfusion process based on the healthier cell environment provided by continuous fermentation and routine maintenance of >600 g/L wet cell weights during perfusion campaigns executed with a single-use perfusion fermentation reactor. The perfusion rate and cell bleed rate were reported in vessel volumes per day (vvd). For the continuous process, protein removed through the cell bleed line is not considered in the product yield, because it is directed to waste and not typically recovered.

Fed-batch cultivation for CHO

Parameters for the CHO fed-batch cultivation were taken from Bausch et al. (1). Production and growth were assumed to happen simultaneously. For the CHO fed-batch process, the maximum viable cell density (20 x 106 cells/mL) and specific productivity (25 pg/cell/day) were converted assuming an average mass of 2 ng per cell (1,2).

Results and discussion

In this study, the productivity of cultivation processes with different host organisms and manufacturing approaches are compared. The wet cell weight, instantaneous protein titer, cumulative protein titer, and space-time yield were calculated for each process.

Comparison of fed-batch and continuous fermentation of P. pastoris

A fed-batch and a continuous fermentation process were compared using the same host—P. pastoris (Figure 1). Two key differences in these fermentation processes are the biomass achieved during production and the overall fermentation length. Continuous fermentation provides a healthier cell environment in the bioreactor because nutrients are continuously replenished, and waste products are continuously removed. This healthier cell environment results in higher achievable biomass that can be sustained for significantly longer as compared to fed-batch processes (Figure 1A).

Figure 1. Process and productivity comparison between two P. pastoris fermentation modes. (Figure courtesy of the authors).

Figure 1B shows the comparison of protein titers between the two fermentation modes. In the fed-batch process, the titer increases over time until the fermentation is stopped due to declining cell health after day 6. The final titer reached in the bioreactor is 3.7 g/L. In the continuous process, a steady state titer of 0.73 g/L is reached after about five days. This titer is maintained for the next seven days until the end of the campaign (12 days total fermentation length) as the biological process is held in a steady state through continuous feeding and continuous removal of cell waste.

In Process 1 (fed-batch), the protein titer in the bioreactor at harvest is representative of the cumulative amount of protein made during the cultivation (Figure 2). In contrast, the titer observed upon sampling Process 2 (continuous) is not representative of the cumulative protein expressed because protein is continuously harvested during the production process.

As shown in Figure 1C, the cumulative protein in the continuous process is immediately higher than that of the fed-batch process due to the higher achievable cell mass at the time of induction. After six days, the continuous process has produced 5.6 grams of product. This is over 40% more protein expressed than during the entire fed-batch process (3.7 grams). Furthermore, the continuous process extends for twice as long as the fed-batch process, ultimately resulting in over 13 grams of harvested protein, more than three-fold more protein than the fed-batch process (Figure 2).

Figure 2. Representation of two fermentation modes and differences in cumulative protein harvest. (Figures courtesy of the authors)

As the cumulative protein harvested will vary across cultivation scales and lengths, a normalized metric is needed for a direct comparison between fermentation operations. Space-time yield, which is the total protein harvested per bioreactor volume per cultivation day, is a normalized metric for productivity that can be used for any cultivation mode.

As shown in Figure 1D, the space-time yield for a continuous process is typically also higher than that for a fed-batch process of the same length. Notably, the space-time yield of a continuous fermentation improves over longer cultivation times, because the initial cell growth period is amortized across the total cultivation length.

Comparison to CHO fed-batch cultivation

Figure 3 shows the comparison of a fed-batch cultivation using CHO cells to produce heterologous proteins to both fed-batch and continuous fermentation processes using P. pastoris as described above.

Figure 3. Process and productivity comparisons between model organisms and fermentation. CHO is Chinese hamster ovary cells. (Figures courtesy of the authors)

In this comparison, we assumed that the CHO cells had a five-fold higher specific productivity (using parameters from Bausch et al. [1]). The growth rate and maximum cell viability, however, are significantly lower for CHO cells. This results in slower biomass accumulation and significantly less biomass overall during cultivation (Figure 3A). Accumulated biomass is frequently ten times higher in P. pastoris fermentation processes compared to CHO, suggesting that researchers should consider protein composition, time constraints, and equipment usage when selecting an expression organism (3).

As shown in Figure 3B, the titer achieved in a fed-batch campaign executed with CHO cells is higher compared to either of the P. pastoris fermentation processes, but it takes substantially longer campaigns to achieve those titers, which has significant implications for facility utilization and process scheduling within a commercial operation. Using the normalized metric of space-time yield (Figure 3D), it is clear that the space-time yield achievable for Pichia-derived processes in fed-batch or continuous operations are significantly higher than that achievable for a comparable CHO-based process, even using the assumption that CHO cells are typically five-fold more productive on a per cell mass basis. Overall, the continuous fermentation process results in a nearly three-fold higher space-time yield, as compared to the campaign executed with CHO in fed-batch. It should be noted here that the calculations made in this work model space-time yields, which are ultimately derived from cell-specific productivities. This fundamental metric should be calculated for each protein and strain based on growth rate and volumetric productivity (2–4).

Conclusion

Space-time yield is a normalized metric that can be used to directly compare productivity across cultivation modes and different host organisms. Of the three processes modeled here, the continuous fermentation process using P. pastoris showed the highest achievable space-time yield, even with the assumption of a five-fold lower specific productivity than CHO. High space-time yields ultimately result in more protein for less space and time, and therefore lower process and facility investments and production operating costs. Space-time yield should be considered as a critical metric when assessing process designs to achieve translational, clinical, and commercial manufacturing goals for a given protein product.

References

1. Bausch, M.; Schultheiss, C.; Sieck, J.B. Recommendations for Comparison of Productivity Between Fed-Batch and Perfusion Processes. Biotechnol. J. 2019, 14, 1700721.
2. Kunert, R.; Reinhart, D. Advances in Recombinant Antibody Manufacturing. Appl. Microbiol. Biotechnol. 2016, 100, 3451–3461 (2016).
3. Kunert, R.; Gach, J.; Katinger, H. Expression of a Fab Fragment in CHO and Pichia pastoris. A Comparative Case Study. BioProcess Int. June Supplement 2008, 34–40.
4. Maccani, A. et al. Pichia pastoris Secretes Recombinant Proteins Less Efficiently than Chinese Hamster Ovary Cells but Allows Higher Space-Time Yields for Less Complex Proteins. Biotechnol. J. 2014, 4, 526–537.

About the authors

Laura Crowell*, laura@sunflowertx.com, is director, R&D; Stacy Martin is strategic consultant; and Kerry Love is co-founder and CEO; all at Sunflower Therapeutics PBC.

*To whom all correspondence should be addressed.

Article details

BioPharm International®
Vol. 37, No.9
October 2024
Pages: 15–19

Citation

When referring to this article, please cite it as Crowell, L.; Martin, S; and Love, K. The Optimal Metric of Space-Time Yield. BioPharm International 2024 37 (9) pp. 15–19.