A subset selection strategy was unable to consistently improve on the regular NNGA-DYCORS performance by focusing the coordinate search on the most sensitive sets of parameters. This may be because the RBF does not adequately model a given test function, so it does not correctly identify the most important parameters in the database, or the coordinate search method does not properly exploit the narrowed parameter space. Generically, it may be useful to reduce the dimensionality of the parameter space, but the strategy of doing so using model adherence ‘drop-out’ experiments was not uniformly successful. This article demonstrates that the NNGA-DYCORS hybrid learning algorithm outperforms its constituent algorithms in the important criteria of robustness and generalizability to different kinds of problems. Thus, this algorithm can be applied to a wide variety of physical and biological design optimization problems with a degree of assurance that parameter estimates will be optimal while minimizing necessary resources. In addition, as this hybrid is both robust and highly generalizable to many types of design problems, it should be useful for practitioners who are not experts in surrogate optimization methods, and work on a variety of problems of diverse complexity. Optimizing media for biological processes, such as those used in tissue engineering and cultivated meat production, is difficult due to the extensive experimentation required, number of media components,grow raspberries in pots nonlinear and interactive responses, and the number of conflicting design objectives.
Here we demonstrate the capacity of a nonlinear design- of-experiments method to predict optimal media conditions in fewer experiments than a traditional DOE. The approach is based on a hybridization of a coordinate search for local optimization with dynamically adjusted search spaces and a global search method utilizing a truncated genetic algorithm using radial basis functions to store and model prior knowledge. Using this method, we were able to reduce the cost of muscle cell proliferation media while maintaining cell growth 48 h after seeding using 30 common components of typical commercial growth medium in fewer experiments than a traditional DOE . While we clearly demonstrated that the experimental optimization algorithm significantly outperforms conventional DOE, due to the choice of a 48 h growth assay weighted by medium cost as an objective function, these findings were limited to performance at a single passage, and did not generalize to growth over multiple passages. This underscores the importance of choosing objective functions that align well with process goals. Cell culture media is a critical component of bio-processes such as pharmaceutical manufacturing and the emerging field of cultivated meat products. Optimizing culture media is a difficult task due to the extensive experiments required, number of media components, nonlinear and interactive responses from each component, and conflicting design objectives. Additionally, for cultured meat products, media needs to be less expensive than those currently deployed for other cell culture processes , food-grade, consider safety, component stability, and effects on sensory characteristics of final products. Without much in the way of first principles models for these objectives, especially for adherent mammalian muscle cells used for cultivated meat production , media optimization must be done experimentally with constraints on inputs, outputs, and number of experiments.
Optimizing one factor at a time or with random experiments is still the most common way of exploring design space. This strategy is very inefficient for large systems and is unable to consider interactions among media components. Design-of-Experiments methods are better able to manage large numbers of components in fewer experiments using Factorial, Fractional Factorial, Plackett-Burman, and Central Composite Designs where linear and polynomial models can correlate first order and interactive effects of media components. In general, DOE methods are able to optimize < 10 variables and with the help of screening designs can solve problems > 25 variables , though at the expense of ignoring interactions, screened variables, and easily costing > 100 experiments . Experimental optimization of media has also been done using stochastic methods such as genetic algorithms and this approach is generally suited to optimizing systems of dimensionality > 15 where DOE methods can become experimentally cumbersome, but also take ∼ 200 experiments. Because the size of the design space increases exponentially with the number of design variables, a natural advance was to use response surface models to capture information about interactions and nonlinearity. These techniques can then be used to sequentially identify optimal culture conditions while simultaneously improving modeling accuracy. Oftentimes experimenters will employ polynomial models to find optimal culture conditions but only after extensive DOE to reduce the dimensionality of the problem space to < 5. More advanced modeling techniques are neural networks, decision trees and Gaussian processes which are often better at generalizing noisy, nonlinear, and multi-modal data. When combined with global optimization methods.
Zhang and Block demonstrated that these response surface methods can optimize problems with > 20 variables in less than half the number of experiments as traditional DOE. In the previous chapter, this author further improved the robustness of this algorithm by using a hybrid optimization scheme validated on simulated design problems . Here we employ this novel nonlinear experimental design algorithm to optimize the proliferation of C2C12 cells while simultaneously reducing media cost by modeling the response surface of culture conditions using an RBF with a hybridized global/local optimization scheme. We then compare this approach to a more traditional DOE method. The organization of this article is as follows: Section 3.2 includes an outline of the experimental and computational methods use in media optimization, Section 3.3 goes over the results and Section 3.4 details a discussion of the results and current challenges.Using the trained RBF model, the two arms of our algorithm, TGA and DYCORS, each suggest five experimental conditions for a total of 10 experiments per batch within the design space [×1/2, ×2] of the GM that optimize α. Because the model is based on a small amount of noisy data, the genetic algorithm is stopped before it can converge to implicitly consider model and experimental uncertainty. The DYCORS arm of the algorithm searches in the region around the best design and picks the best predicted set of designs in that region,plant pot with drainage which expands and contracts based on the quality of previous experiments. The new experiments are conducted and the resulting data is used to correct and retrain the RBF model. To allow the RBF model to generalize better during early periods of optimization, 30 randomly selected experimental conditions were taken initially. The optimization loop was stopped when the α quality of the media showed a lack of improvement. The general framework for the HND is shown in Figure 3.1. As a control method, a traditional DOE was used to optimize the same media design problem in three steps.
A ’Leave-One-Out’ experiment was conducted where a media composed of all components at their GM concentrations, excluding each individual component,were tested for their proliferation capacity using the %AB metric , similar to what was done in previous work. The lowest performing components had their concentrations fixed at their respective GM concentrations. Next a Folded/Un-Folded Plackett-Burman design was implemented with the remaining components at the upper and lower bounds of the design problem. This was done to determine the first order linear effects of each component on the objective function α. A linear model to predict α was used in conjunction with a LASSO algorithm to rank the most important first order effects, and all but the highest impact components were kept at their GM concentrations. Finally, the remaining components were used to design a Central Composite Design where experiments are spread out across the design space to more thoroughly explore potential optimal designs.The best α design from this DOE method was considered the optimal DOE design. The DOE-LOO step identified Ferric Nitrate, MgSO4, Glycine, L-Isoleucine, Choline Chloride, Riboflavin, and Thiamine HCl as components that, when left out of GM, had no statistical effect on %AB after 48 hr post-seeding . These components were set to their respective GM concentration for all subsequent DOE experiments. Next, the DOE-PB with LASSO identified the six most α-important components of the remaining 23 components . To reduce the number of experiments for the DOE-CCD design, LCystine and L-Serine were kept constant at × 1/2 normalized units above and below their GM midpoint concentrations respectively based on the sign of their coefficients . The remaining four components in the CCD had their upper/lower bounds changed to × 1/2 normalized units above and below their GM midpoints. The remaining components were varied in a CCD design, with the best medium being 200 mg/L KCl, 388 mg/L L-Glutamine, 9000 mg/L Glucose, 5% FBS shown in detail in Table 3.1. An 80% increase in α at 48 hr post-seeding over GM was measured using 50% less FBS than GM. For the HND optimization loop, α was used as the objective function and calculated using %AB measured at 48 hr post-seeding at 96 well plate scale . The RBF was initially trained with 30 randomly selected experiments. Figure 3.2 shows that the average HND designs improved in both α and %AB metric over time quickly overcoming standard GM and achieving similar results to the best DOE design with 70 experiments. We have included the proliferation metric in Figure 3.2 for completeness even though it was not used as the objective function α in this work. The HND was stopped at 70 experiments because both %AB and α stopped improving. The best medium found had an α measured to be 56% better than GM during the optimization loop using 32.5% less FBS than GM. Figure 3.3 shows the differences between the optimal media. For the most part the HND identified optimal concentrations that were slightly elevated compared to DOE, except for KCl, FBS, and Glucose. It is also notable that both HND and DOE determined that Glucose and FBS should be elevated and reduced in relative to GM. Figure 3.4 shows the media efficiency metric α plotted against the component concentrations for all experiments, demonstrating the nonlinear, interactive, and ultimately non-trivial nature of this experimental design optimization problem. These α-optimal HND and DOE designs were then tested against GM using %AB at 24, 48, and 72 h post-seeding , where the designed media have high %AB relative to GM but that advantage is reduced over time. As a further check, α was calculated using raw cell number normalized by the volume of FBS in each experiment where it was found HND and DOE again outperformed GM in terms of the objective function α due to their lower cost. However, both HND and DOE produced 8% and 9% fewer cells respectively, using 70 and 103 total experiments respectively. It is notable that, despite 30 components used, the HND was able to design a similar media to DOE with a similar degree of proliferation %AB and α in fewer experiments. Additionally, this DOE was more efficient than any single DOE, suggesting that the HND is much more efficient and simpler to use than the typical approach to high dimensional optimization. This is valuable in optimizing media due to the difficulty in collecting large amounts of data with many components. The reasons for the success of this method are likely the balance between global and local optimization, and the ability of the HBD to accumulate information using the RBF, which can regress on nonlinear, noisy, and interaction-heavy problems, reducing the need for cumbersome dimensionality-reduction experiments used in the traditional DOE. For the most part HND suggested higher concentrations of most media components than GM or DOE, except for KCl, FBS, and Glucose. This is likely because the DOE method utilized dimensionality reduction. That is, factors that demonstrated insignificant effects were fixed at their GM level and no longer included in the optimization. On the other hand, HND could vary components throughout the optimization process, including increasing component concentrations when they had even a small positive effect. Inclusion of a per component cost might dampen this effect. While the RBF can model nonlinear and interactive processes, the effect of each component on α is unclear without further experiments or model validation, a disadvantage of the HND approach. Nonetheless, sensitivity analysis using VARS was conducted and indicates FBS, Glucose, and MgSO4 likely have a significant effect on α, while other effects are more difficult to determine with the limited data available.