Cell culture is widely used in biotechnology to manufacture various useful products for applications such as pharmaceuticals, food, biofuel, and industrial products. Cell culture production systems in industry and research span different kingdoms of life from free living microbes such as bacteria, archaea, and fungi, to cell lines derived from multicellular organisms including insect and mammalian species. Products include pharmaceuticals such as antibiotics and monoclonal antibodies; food products such as rennet, single-cell protein, and cultivated meat; biofuel from lipid-producing algae; industrial products such as cleaning enzymes and organic acids.

In cell culture, culture media is a crucial input that provides energy and materials required by cells to grow, proliferate and produce the products of interest. The components that make up culture media and their concentrations within the media affect important aspects of cell growth, productivity and product quality, and are instrumental to the success of the cell culture application (Yao and Asayama, 2017; Ritacco et al., 2018). In most laboratory applications, a universal standardized media is used but to achieve cost-efficient upscaling to industrial production, there is a need to identify a combination of concentrations for media components that optimize for the desired property, such as biomass or specific biomolecule yield in the cell culture system. There have been many methods using optimization algorithms developed for culture media optimization for both microbial systems and animal cell culture. Despite this, there is a lack of systematic review and comparison of these different methods from an algorithmic perspective that provides researchers with a comprehensive overview of the available algorithms and provides perspectives on the applicability of these methods in new contexts.

A few other review articles are available on culture media optimization. The review by Singh et al. (2017) focuses on fermentation media for microbial systems. While it lists some of the techniques used in literature, it does not include several types of algorithms that were typically used in media optimization, and also lacked a benchmark comparison between the methods. Similarly, the reviews by van der Valk et al. (2010) Ritacco et al. (2018) and Galbraith et al. (2018) does not go into depth on the available optimization algorithms. The unique requirements of the culture media optimization problem, such as the need for a low number of iterations due to experimental resource constraints, and noisy results are also unaddressed by reviews of optimization algorithms for black-box functions that evaluate algorithms in a general context.

The purpose and unique contribution of this review is to provide readers with a comprehensive overview of the main types of algorithms applicable to culture media optimization. We synthesized existing works and provided a generalized framework for understanding and designing culture media optimization experiments. We have examined and summarized the strategies adopted by previous works, classify and explain them using this framework and examine algorithmic features that were designed and chosen during past efforts to address specific challenges of this problem. We have also provided recommendations on the type of algorithm to use based on benchmark comparisons and identify gaps for future research.

Following the taxonomy proposed by Stork et al. (2022), metaheuristics optimization can be broadly classified as population type, hill climbing type and trajectory type. For iterative experiments in cell culture experiment settings, the use of automated liquid handlers to prepare solutions allows multiple candidates to be tested in each iteration. Population-type algorithms are most suitable to leverage this capability and provide faster optimization.

Popular population-type metaheuristics include evolution-inspired algorithms such as genetic algorithm, evolutionary strategies, and differential evolution, and swarm-inspired algorithms such as particle swarm algorithm and ant-colony algorithm. We will introduce the algorithms that have been applied for cell culture optimization. For more in-depth details on metaheuristics optimization, we refer interested readers to Du and Swamy (2016).

Surrogate-based optimization (SBO) can be viewed as comprising three separate components: the surrogate model, the acquisition function, and the acquisition method (Forrester and Keane, 2009). The surrogate model refers to the model that is used to approximate the actual function of interest by fitting experimental data. Before the first iteration, the model is fitted with the data collected from the initial DOE. The acquisition function refers to the function or criterion that is used to decide which candidates to propose and evaluate in the next round of experiments. The acquisition method refers to how the candidates are found by optimizing the acquisition function. (Note: The acquisition of new points, i.e., both the choice of acquisition function and acquisition method may also be referred to as infill strategy or infill criteria in literature (Zhou et al., 2020). It is also closely related to the concept of active learning in machine learning, which seeks to improve the model’s accuracy with less training data by systematically acquiring training sample (Ren et al., 2021).

To illustrate with an example, a common SBO workflow used in media optimization is the ANN-GA method. In this method, the surrogate model used is an artificial neural network (ANN), that predicts the response given a valid media design as input. The ANN is trained with actual response values collected from experiments performed with the initial DOE candidates. As we assume that the ANN is an accurate predictor of the response, and we would like to maximize the response, we would then computationally find the input that maximizes the predicted response of the ANN. The acquisition function in this case would be the predicted value (PV) because we acquire new candidates based on the predicted value output by the surrogate model. These candidates are found by running GA on the ANN as the objective function. GA in this case would be the acquisition method. The acquired candidates that maximize the response of ANN are then evaluated experimentally and added to training data to update the ANN model in the next iteration.

We will introduce the common types of surrogate models, acquisition functions and acquisition methods (if they have not been covered in Section 5), that have been applied for cell culture optimization. We also refer interested readers to (Forrester and Keane, 2009, Jiang et al., 2020) for more in-depth resources on surrogate optimization.

There are several key characteristics of culture media optimization problems. These should be taken into consideration when choosing the method of optimization and is what differentiates this problem from others.

Firstly, the number of iterations for optimization is limited. This results from the fact that cell culture experiments are time-consuming and therefore experimental groups cannot afford to optimize for a large number of iterations. Many works perform a one-step optimization, where only an initial design of experiment was cultured, followed by one batch of proposed candidates based on the initial DOE. The average number of iterations performed across all works was 2.73 (including one-step optimization) and 6.22 (excluding one-step optimization). In most benchmarking of black-box optimization algorithms, the number of iterations far exceeds what can be afforded for culture media optimization.

Because of this, optimization algorithms that are slow in improvement or convergence are not suitable. Based on studies that compare the two, a surrogate model-based approach may be more suitable as the rate of improvement tends to be higher than metaheuristics algorithms in early iterations.

Secondly, the number of candidates is limited and dependent on the nature of the cell culture and available experiment equipment. For example, if one were to use the standard cell culture plate size of 96 wells with at least three replicates per candidate, that would limit the experiment to a maximum of 32 candidates, not accounting for limitations like the edge effect (Mansoury et al., 2021). Of course, researchers need not be restricted to using one plate and can also use other multiwell plates like 384-well or 1536-well plates, however, these come with their own limitations such as format restrictions of the equipment available. The average batch size used in all the works surveyed was 27.01.

Given the limitations in both iterations and batch size, the number of variables that can be optimized given certain experiment budget while achieving statistical power is an important consideration in media optimization experiments. In all works surveyed that used a surrogate model, the average number of candidates tested in total was found to be 40.46, with 7.40 candidates tested per factor. The average number of factors used was 8.10 (including one-step optimization) and 14.44 (excluding one-step optimization).

For experiments that use a 2nd order polynomial RSM for optimization, a typical number of factors used is 5. Using the average number of candidates tested, this gives roughly 2 datapoints per coefficient for fitting, which is sufficient to achieve power of approximately 0.8 with a R² of 0.5 and a significance level of 0.05. However, with 6 factors, achieving the same power would need 50 candidates. It is important to consider the experimental budget and the need for sufficient statistical power when designing experiments to fit the response surface.

For non-parametric approaches or other machine learning models, validation sets can be used to estimate the accuracy of the model and determine if the number of datapoints is sufficient. Empirical rules of thumb may also be used as guides to decide on number of factors to choose given certain budget or conversely the number of experiments given certain number of factors. For example, a common guideline is to have data 10 times the number of factors. For metaheuristics algorithms, several studies (Bolufé-Röhler and Chen 2013; Chen et al., 2015) have looked at how population size affects performance at different dimensions. However, these have focused on metrics such as convergence time and closeness to optima after convergence, which is not entirely relevant to media optimization. Nevertheless, we may reference some guidelines such as having a population size larger than and preferably 10 times the dimension (Bolufé-Röhler and Chen 2013; Mallipeddi and Suganthan 2008).

Lastly, another key factor to consider is the effect of passaging. Often, bioprocesses require cells to be passaged continually for a few rounds. After each passage, the characteristics of the cells change which likely results in a change in the true function of the optimization problem. These characteristics include key gene functions, morphology, proliferation rate, and expression levels (Hughes et al., 2007). Currently, none of the black-box optimization algorithms account for this. One interesting approach used by Cosenza et al. (2022) was to include information about cell count by incorporating ‘low-fidelity’ information sources such as biochemical assays and ‘high-fidelity’ information sources like cell proliferation rate over one passage with a Bayesian optimization tool, thereby including single-passage and multiple-passage information into culture media optimization problems and accounting for the change in cell characteristics.

The use of optimization algorithms for culture media optimization was first reported in 1992 by Freyer et al. (Dirk Weuster-Botz and Wandrey 1995), where GA was used to optimize media for formate dehydrogenase production in Candida boidinii. In the late 1990s and early 2000s, many researchers followed suit and started using GA for culture media optimization problems (Viennet et al., 1996; Patil et al., 2002; Marteijn et al., 2003; Bapat and Wangikar, 2004). Notably, Cockshott & Hartman (2001) were the first to implement PSO for the purpose of fermentation media optimization, where they hypothesized that PSO would perform better than GA based on previous reports that PSO performs better for smaller population sizes and converges to the optimum faster compared to GA. SBO for culture media optimization was first described by Coleman et al. (2003) where they used an ANN ensemble surrogate model to optimize Escherichia coli fermentation, based on previous studies in enology and other fermentation processes. Since then, many researchers have used optimization algorithms for the purpose of culture media optimization.

Of all the research articles available on the topic, approximately 70% reported using an SBO approach, of which roughly 43% used ANN as the surrogate model, PV as the acquisition function, and GA as the acquisition method (SBO(ANN)-PV-GA). The reason for the popularity of this method is unclear; many papers do not cite their reasons for choosing a particular model over others. Most of the papers compare SBO(ANN)-PV-GA to either classical methods such as OFAT screening (Desai et al., 2006) or to the use of statistical RSM as a surrogate (Desai et al., 2008; Pal et al., 2009; Baskar and Renganathan, 2010; Du et al., 2012; Gurunathan, 2012). Some cited the ability of ANN to excel in pattern recognition and modeling nonlinear relationships (Haider et al., 2008; Singh et al., 2008; Pal et al., 2009; Du et al., 2012; Peng et al., 2014) and its ability to work well with a small number of candidates (Desai et al., 2008) and noisy data (Pathak et al., 2015) as reasons why ANN models should be developed for biological systems. The next most popular approaches adopted were an SBO with RSM as the surrogate model, PV as the acquisition function, and GA as the acquisition method (SBO(RSM)-PV-GA); and direct optimization with GA. The papers that have compared SBO(ANN)-PV-GA and SBO(RSM)-PV-GA have usually concluded that ANN is a better model (Liu et al., 2009; Khaouane et al., 2012; Katla et al., 2019; Selvaraj et al., 2019; Suryawanshi et al., 2019) for media optimization problems, likely due to the nonlinear nature of the objective function.

Some less commonly used methods include neuro-fuzzy networks as a surrogate model (Aquino et al., 2016), elastic net regularized general linear model as a surrogate model (Grzesik and Warth, 2021), and ensemble modeling (Liu and Gunawan, 2017). Interestingly, most researchers opted for parametric approaches as opposed to non-parametric approaches like GP or SVM, since nonparametric methods are known to outperform parametric methods for high-dimensional and nonlinear data (Liu et al., 2020). Figure 6 shows the trend in methods used over the years.

As shown in Figure 7, there is also an overrepresentation of bacteria and fungi as the cell line of choice in media optimization studies, due to the interest in optimizing the fermentation process in yeast strains. Despite rising interest in cultured meat production and the importance of antibody production, mammalian cells have not been studied extensively in media optimization research.

With the expansion of the cultured meat industry and the increasing need for therapeutic antibody discovery, media optimization in more mammalian cell contexts would be beneficial. Optimization for mammalian cell culture media poses a more complex challenge as compared to microbial culture media due to higher number of components. This means the existence of more and potentially higher-order interactions between components, leading to a much more complex objective function. Increasing the number of interactions would also complicate the screening process - the methods currently implemented may not effectively identify the most important components when the number and complexity of interactions between components in the media increase.

In most studies, researchers have used a single measure of enzyme of interest activity or a measurement that is representative of the protein expression level like fluorescence from GFP expression. However, these measurements may not always accurately indicate the actual protein yield in the cells. A related problem is the use of lower-fidelity measurements to reduce experimental burden while complementing with fewer high-fidelity but expensive or time-consuming measurements. In such cases, the need to synthesize multiple information sources related to the outcome will be useful. Cosenza et al. (2022) introduced the use of multi-information source Bayesian optimization where information from multiple assays was combined to measure cell growth. This is achieved with a modification to the kernel of the GP, by adding an additional Gaussian kernel to account for the deviation of the lower-fidelity measurement away from the true function value (assumed to be equal to high-fidelity measurement). The allocation of each batch of candidates between high and low fidelity for measurement is decided through the combination that produces the highest multi-point expected improvement.

Another possible addition to media optimization problems would be multi-objective optimizations. Often, optimization problems involve multiple objectives that sometimes conflict, such as maximizing cell growth and minimizing cost, that can be optimized simultaneously. Examples include maximizing metabolic activity (Havel et al., 2006) and maximizing cell count (Kim and Audet, 2019). Multi-objective optimization would allow for the prediction of a more universal solution set that can be chosen from depending on the unique constraints or subjective desired outcomes. For more information on multi-objective optimization, we refer interested readers to (Collette and Siarry 2004).

Lastly, there is also a lack of use of newly developed algorithms in culture media optimization research. Recently, Yoshida et al. (2022) and Tachibana et al. (2021) have used deep neural networks (DNN) with 4 hidden layers for fermentation media optimization and have found that they perform better than other machine learning models. Although deep learning has gained recent popularity in many other applications, it remains to be seen if DNNs will improve outcomes in media optimization application considering limited studies. There are other advanced optimization methods worth implementing for media optimization, including deep kernel regression as surrogate models (Wilson et al., 2015), and derivative-free reinforcement learning methods like neuroevolution of augmenting topologies (NEAT) (Qian and Yu, 2021). In this review, we will not be exhaustively expanding upon or analyzing the methods not currently found in culture media optimization literature.

As described in Section 2.3, simulation experiments were done to compare the available methods for media optimization problems. To compare the algorithms’ performance across all functions, an average performance score is defined as follows: N o r m a l i s e d   f u n c t i o n a l   v a l u e = y i n i t i a l − y f i n a l y i n i t i a l − G l o b a l   o p t i m u m where y_initial refers to the functional value at the first iteration; y_final refers to the functional value at the last iteration and the global optimum is the near-optimal solution found by running DE for 1000 iterations. The average performance score for an algorithm across all different functions can be defined as the mean of the scores on individual functions.

The following methods were compared throughout our simulation experiments:

Metaheuristics methods.

• Genetic Algorithm (GA)

Various SBOs with differing surrogate models, with PV as the acquisition function and GA as the acquisition method.

• Second-order polynomial (SBO(2OP)-GA-PV)

Kriging SBO with a different acquisition function.

• EI (SBO(KRG)-GA-EI)

Kriging SBO with different acquisition methods, with PV as the acquisition function.

• Truncated GA (maximum number of generations = 10) (SBO(KRG)-truncGA-PV)

These models were chosen as they were the most popular methods used in the field of culture media optimization. Kriging was chosen as the model for comparison against other infill strategies as according to our preliminary data, it was the best performing surrogate model. As explained in Section 2.3, the experiments were conducted at three levels of dimensions to represent the varying complexities of different types of culture media. The performance of the methods was also compared in experiments with noise to evaluate its effect on various methods.

For the low dimension experiment (dim = 5), a comparison of three different DOE methods, LHS, CCD and BBD was also done to understand how each DOE affects the performance of the methods. BBD was supplemented with LHS to ensure an equal number of candidates across the DOE. This comparison was only done for the low dimension experiment as the number of candidates would be too high and unfeasible to replicate experimentally for higher dimensions. BBD was found to be the best performing DOE (Supplementary Table S2).

Figure 8 shows the performance of the various methods in each respective context. In the ‘noiseless’ experiments, some variation exists in output values across the replicates due to the stochastic nature of the methods. The relative performance of the methods does not differ significantly across the different DOE in the low dimension experiments (data not shown). According to Figure 8A, in the low dimension experiments without additive noise Kriging with truncated DE as the acquisition method and PV as the acquisition function is the best method across all iterations.

In the experiments with added noise, the performance of all the methods deteriorates significantly. However, SBO(KRG)-truncDE-PV remains the best performing method across all iterations (Figure 8B), with PSO being a close second at higher iterations. According to Figure 8B, methods such as SBO(2OP)-GA-PV and SBO(SVR)-GA-PV perform comparatively well until iteration 4, which is congruent with the many papers that had success with RSM methods with just one iteration (Liu et al., 2009; Khaouane et al., 2012; Parkhey et al., 2017). Another popular method, SBO(MLP)-GA-PV, however, performed less well compared to the others. The SBO with the acquisition method as a local optimizer (SBO(KRG)-L-BFGS-B-PV) performed the worst consistently across all iterations and its performance seems to degrade significantly in the presence of noise (Figures 8A, B).

Figure 8C shows the results for the medium dimension (dim = 20) experiments without additive noise. Interestingly, in this case SBO(KRG)-truncGA-PV performs better than SBO(KRG)-truncDE-PV at certain iterations. These two methods perform significantly better than the other methods, while the performance of PSO, DE, SBO(KRG)-L-BFGS-B, SBO(KRG)-GA-PV and SBO(KRG)-GA-EI is comparable across iterations.

Similar to the low dimension experiments, the performance of all the methods deteriorates with the addition of noise. The performance of SBO(KRG)-truncGA-PV, SBO(KRG)-truncDE-PV and PSO are comparable from iteration 4 onwards, with significantly better performance as compared to the other methods. Notably, the performance of SBO(2OP)-GA-PV is much lower compared to its performance in the low dimension experiment.

The results of the high dimension (dim = 40) experiments without additive noise (Figure 8E) are very similar to that of Figure 8C, barring a significant deterioration in the performance of SBO(SVR)-GA-PV.

In the high dimension experiments with additive noise, SBO(KRG)-truncDE-PV is clearly the best choice over almost all iterations, with PSO as a feasible substitute.

Overall, the SBO methods with truncated acquisition methods seemed to triumph across all the contexts. This was likely due to the conserved diversity in the proposed candidates which prevented convergence to a local optimum, thus allowing the method to find a near-optimal solution faster. PSO has also fared relatively well across the experiments even with additive noise. Notably, the hypothesis that SVM would perform well with small datasets has generally held true. It is also surprising that SBO(KRG)-GA-EI did not perform better than its PV counterpart across all experiments, as EI helps to balance exploration of the input space with exploitation. This could be because the parameters set for GA allow it to strike a good balance between exploration and exploitation such that the use of EI as an acquisition function disrupted this balance, resulting in too much exploration and thus wasting resources on solutions that are less likely to be near-optimal. ANN did not seem to perform well across the experiments. The popularity of ANNs and their improved performance against RSM as reported in many media optimization studies is therefore surprising. This could be because most such studies conduct a one-step optimization which is not sufficient to determine the performance at higher number of iterations. Another reason could be the lack of hyperparameter tuning in the implementation of the MLP or other differences in implementation.

Table 1 shows a compilation of all the methods used in culture media optimization literature and their corresponding rankings according to the normalized values reached at the 10th iteration; and the number of iterations needed to achieve the 1st iteration normalized value reached by SBO(KRG)-truncDE-PV, averaged across all noisy experiments. There is a lack of papers that have used the best performing methods we have found, meaning that the use of these methods could result in better improvements than reported.

Based on the results of the simulation experiments, we recommend Kriging SBO together with a truncated metaheuristics acquisition method as a highly competitive optimization method that would likely meet the needs of most culture media optimization experiments.

While the simulation experiments conducted were quite extensive, they were not exhaustive and were focused more on the methods proven to yield promising results. For example, methods such as variable neighborhood search, simulated annealing and a variety of direct search methods like mesh adaptive direct search have not been evaluated in the culture media optimization context. Given that PSO performs well as a metaheuristic, it would also be interesting to know whether using it as an acquisition method would improve the current best method of SBO(KRG)-PV, or in general for other surrogate models. It would also be useful to verify if the truncated acquisition methods improve the performance of surrogate models other than Kriging. Furthermore, the number of generations for truncated acquisition methods could be optimized such that the diversity of the suggested candidates is maintained while also converging faster to the global optimum. Lastly, while the BBOB test suite makes for a suitable alternative to time-consuming experimental validation, the validity of these results should be proven through experimental validation.

Since its inception, cell culture is playing an increasingly important role in the production of various useful products including biopharmaceuticals, enzymes and chemicals. The market size for products manufactured with microbial fermentation is estimated to be USD 28.3 billion (Custom Market Insights, 2022) and the market size for biopharmaceuticals manufactured using animal cell systems is estimated to be USD 24.6 billion (‘Cell Culture Market Size, Share & Trends Report, 2022–2030’ 2018). In recent years, new applications are emerging in cell culture for food production known as cellular agriculture, which includes cultured meat, single-cell proteins and precision fermentation. The market for cellular agriculture is projected to grow to USD 515.2 billion by 2030 (Research 2021). In scalable cell culture production systems, culture media is often the crucial determinator of techno-economic viability through its effect on product yield and its role as the main contributor to production costs. For example, in monoclonal antibody production using animal cell cultures, culture media is estimated to account for 30%–40% of the production cost (Batista and Fernandes, 2015). Thus, optimizing the culture media for yield and cost is very important for the success of scalable commercial applications and for reducing the cost for many products.

Given the expansive literature on culture media optimization, we recognize the challenge researchers face in perusing existing works and selecting a suitable optimization methodology for their own cell culture application. In the absence of studies that summarize and compare between various available methods, it is common to default to methods that were used in similar studies when a better method may exist.

In this review article, we hoped to (i) provide a generalized framework for understanding and designing culture media optimization experiments; (ii) summarize and classify the large number of existing works; (iii) examine common challenges and algorithmic features that were designed and chosen during past efforts to such challenges; (iv) provide recommendations on the type of algorithm to use based on benchmark comparisons.

For standard applications of culture media optimization, the benchmark comparison may serve as a reference to help select the algorithm that is likely to perform well on generic unknown functions within experimental resource constraints. For applications where existing methods provide limited results, and are seeking to develop improved algorithms, we identify a few possible areas where efforts might be fruitful.

Development of better surrogate models is an area where advances in data-driven predictive models can be applied. As discussed in Section 10, advances in machine learning algorithms and deep learning may find useful application especially for higher dimension problems. From the benchmark experiments, the method of acquisition has a significant effect on optimization performance. Hence designing of better acquisition methods is also likely to yield improvements. Acquisition methods that can successfully balance exploitation and exploration through clever designs can achieve fast improvement while avoiding premature convergence. Other areas where new developments have been made are discussed in detail in Section 10.

In this review, we have focused exclusively on methods used in cell culture media that are knowledge-blind. However, it should be recognized that there are methodological limitations of relying on such optimization approaches where only media component concentrations/levels and output responses are collected and used. Biological data of cell response, such as the cell transcriptomes, or analysis of spent media can be used to enhance predictive surrogate models. Chemical information about the media components may also be incorporated into such models, opening up the possibility of building surrogate models that can generalize to other media components outside the original list of components used in the experiment. Various AI, bioinformatic and chemoinformatic approaches may find potential use in the discovery, design and optimization of cell culture media.