Accuracy was also limited by the low amount of data N available relative to the large dimensionality p, which is inherently the case in complex biological experiments where each batch of q experiments takes > 1 week to evaluate. Finally, the hyperparameters θ ∗ used in the multi-IS squared exponential kernel were deliberately regularized with prior distributions to smooth the posterior of the prediction µ. Regularization may have diminished the quality of the inter-IS correlations; the model hyperparameters ignored features where IS differed in favor of a simpler correlative structure to explain the data. This is seen in Figure 4.8b and 4.8c, where the kernel evaluations show nearly equal inter-IS correlative strength for most IS used. This may have “squished” / ignored features that could have provided additional information, but at the cost of sampling the design space too widely, again a deliberate choice of model skepticism towards outliers. Even with these limitations, the BO method clearly performs well on media optimization systems relevant to cellular agriculture, that is, those with multiple and potentially conflicting information sources with varying levels of difficulty in measuring. The media resulting from the BO algorithm supported significantly more C2C12 cell growth with only a small increase in cost. This algorithm performs better than traditional DOE in this case,plastic gutter especially in incorporating critical data from growth after the multiple passages in an affordable manner.
With these results, it should be possible to implement this type of experimental optimization algorithm in other systems of importance to cellular agriculture and cell culture production processes with difficult-to-measure output spaces, including for optimization of serum-free media for cell growth and for differentiation. In this work we applied the approach in the previous chapter to design a serum-free media, which is a necessary precondition to the development of cellular agriculture, for C2C12 cells. They developed their medium for human induced pluripotent stem cell proliferation and stability based on the combination of the DMEM/F12 basal medium and supplementation with insulin, transferrin, FGF2, TGFβ1, ascorbic acid, and sodium selenite took this approach and, by screening multiple growth factors and hormones using a one-factor-at-a-time approach, developed an albumin-enriched B8 formula for the proliferation of bovine satellite cells. Recent work by shows that merely seeding cells in serum-free media without additional preparation will be unsuccessful in optimizing serum-free media. A more robust approach is to slowly adapt a cell line to serum-free conditions over multiple passages. Sometimes this requires attachment factors or extra-cellular matrix material to allow adherent cells to affix themselves to the surface of the culture dish. For a fully animal component-free medium, ECM substitutes like Matrigel may be replaced by dilution cloning or other genetic techniques. The serum-free medium itself must contain the standard vitamins, trace elements, carbohydrates, amino acids, and salts discussed in the previous two chapters, but with additional proteins, enzymes, and growth factors that replace serum.
These components are particularly expensive and militate for a multi-objective approach to optimizing cell culture media. The field of multi-objective optimization is an extensive and valuable area of research that attempts to solve optimization problems with multiple, and often conflicting, objectives. The region of the design space where one cannot improve one objective without degrading another is the Pareto curve. Usually, there is no single point that dominates the entire design space and lies beyond the Pareto curve, so the MOO problem becomes a matter of finding sets of points X that fall on the curve, or designs that sufficiently represent the preferences of the designer. Cell culture media design, particularly for cellular agriculture, is inherently a MOO problem because improved growth is often found with expensive components used central composite designs to evaluate the effect of several components on a desirability function parameterization of lipid content, carbohydrate consumption and biomass accumulation. In work done to optimize cytokine dosing trained a regularized polynomial model and used a derivative-free optimizer to find the conditions that maximized a desirability function of cell populations. In work by, genetic algorithms VEGA and SPEA were used to maximize chemical conversion while maintaining biomass of the cyanobacteria organism. In a conference paper used a genetic algorithm MOGA to maximize plant culture biomass and minimize system cost.To get the C2C12 cells to proliferate in serum-free conditions, they were first adapted to survive in the commercial Essential 8 medium by passaging the cells, starting in DMEM and 10% FBS , in increasing amounts of E8. Once E8 comprised > 90% v/v of the medium, cell growth slowed and Matrigel was needed to provide ECM. With the Matrigel, the new C2C12 line survived fully in E8. Next we used a dilution cloning technique to select a subset cell line from these cells that could survive without Matrigel.
The surviving cells were frozen in Synth-a-Freeze at their fourth passage in -196◦C liquid N2 and are the cells used in the remainder of this chapter. Bovine satellite cells were used for verification experiments after the optimization campaign was finished to determine the generalizability of the designed media. BSCs more closely resemble the phenotypes of cells desired in the cellular agriculture industry. The media design space was based on the E8 / B8 formulation comprised of basal medium, FGF2, TGFβ1, insulin, transferrin, ascorbic acid, and sodium selenite. We chose to supplement this with nine growth factors which have either been found to improve cell proliferation in or by expert opinion. Because the basal component is comprised of >30 individual components it was broken down into groups based on function in cell culture. These component groups were varied during the optimization campaign by the algorithm which we discuss in later sections. Components believed to have significant effects on growth were individually varied. NaCl was separated from the general salts group because it had a large effect osmolarity. We utilized a multi-information source Bayesian model to combine “cheap” measures of cell biomass with more “expensive” but higher quality measurements to predict long-term medium performance. We refer to the simpler and cheap assays as “low-fidelity” IS,blueberry container and more complex and expensive assays as “high-fidelity” IS. To start an experiment for all IS, vials were thawed to 25◦C and the freezing medium was removed by centrifugation at 1500 × g for 4 min. The centrifuged cell pellet was resuspended in 17 mL of store-bought E8 and placed on 15 cm sterile plastic tissue culture dishes . Cells were incubated at 37◦C and 5% CO2 for 48 hrs. Cells were harvested using tripLE solution , diluted in PBS, and counted using a Countess II with trypan blue exclusion and disposable slides . With the known concentration of cells, 96 well plates were seeded at 2,000 cells / well and 6 well plates were seeded at 60,000 cells / well . The final density of both formats should be roughly 20,000 cells / mL of PBS and medium. After 72 hrs, all wells were measured using the IS methods shown in Table 4.2 and described in Section 4.2.2. Very briefly, the low-fidelity IS AlamarBlue and LIVE assay required staining wells with a stock chemical and reading with absorbance and fluorescence on a plate reader . Both signals correlate with cell number. The other low-fidelity IS was the Passage 1 cell count using a Countess II automatic cell counter. The high-fidelity IS, which correlates much better with long-term cell proliferation, the Passage 2 metric, was also measured using the Countess II . This additional 72 hr period is why it is considered a long-term cell growth metrics, but also why it is more tedious to use to optimize a complex media. The MOBO algorithm was tested on the computational test problems introduced in the previous chapter with an additional linear cost function that turned the single-objective optimization problem into a MOO problem.
The results are in Appendix C.2 and C.3. The new hypervolume acquisition function α performed similarly to the desirability function discussed in the previous chapter. Therefore, because the hypervolume function makes fewer assumptions about the MOO problem, it was chosen to help design experiments for this novel system. Furthermore, empirical studies of the hypervolume and noisy-hypervolume acquisition function indicate that it is superior to a wide variety of MOO and MOBO solvers on synthetic and data-based optimization problems. The most prominent result from the application of the MOBO algorithm to the serum-free experimental system was the steady improvement in both hypervolume and the Passage 2 high-fidelity IS growth metric in Figure 5.3b. Some of the interesting media designs are highlighted in Table 5.2. Only one medium dominated the control medium in both growth and cost, resulting in 23% more growth at 62.5% of the cost of the control. OM0 had notably lower concentrations of major growth factors like insulin, transferrin, FGF2, and TGFβ1 and higher concentrations of progesterone, estradiol, IL6, and LIF. OM1 was another interesting medium that had 78% more growth at only and additional 25% cost. This was due to higher concentrations of the growth factors that OM0 lacked. Finally, OM2 and OM3 had a 112% and 184% improvement in growth at an increase in cost of 62% and 71% respectively. OM2 and OM3 had even higher concentrations of both the insulin, transferrin, FGF2, and TGFβ1 growth factors, while also elevating the concentration of all factors from progesterone to PEDF. We then used the GP model to understand the correlations found in the experimental campaign. This was done by optimizing over the final model multiple times using L-BFGS-B at random starting locations for a single q = 1 experiment. This will show what the model believes to be the best distribution of experiments. In Figure 5.5 we show the result of samples for two conditions: optimizing α with ymin = 1 constraint and only maximizing growth using NEI. Simply put, α considers reducing cost while maintaining growth above ymin while NEI only maximizes growth. The max growth condition had generally higher concentrations of most growth factors but not necessarily basal components. This confirms the previous section where higher growth was achieved through higher growth factor concentrations, particularly transferrin, FGF2, TGFβ1, EGF, TGFβ3, and PDGF. Figure 5.5 only tells us what the model thinks are the best conditions and not the relative magnitude of each factor on growth. As a further means of quantifying this, we computed the integrated variogram using the VARS technique for each factor and show it in figure 5.6. VARS values suggest that FGF2, IL6, TGFβ1, and several basal components had significant effects on growth. This mostly confirms the previous section that FGF2, TGFβ1, and several other growth factors had a large effect on growth, but it is impossible to say anything more suggestive than that.The MOBO algorithm was successful because a robust, long-term data set was built over time, improving the model as more data were collected. Additionally, the acquisition function was tailored to generate high-value experiments near the Pareto trade-off curve between cell growth and media cost. A separate constraint function translated our need to primarily search for high-growth designs into a mathematical function, as we expected most of the design space to not support cell growth. Some shortcomings of this work are that we didn’t compare our MOBO method to an equivalent DOE method, though we have previously shown similar methods are significantly more efficient than traditional DOEs. Additionally, Figure 5.4 indicates media performance tended to decrease over time. This could be due to morphological changes wrought by the media, physical damage due to passaging, or accumulation of toxins in solution. Clearly, our Passage 2 metric was not enough to fully predict the rapidly changing dynamics of cell growth over multiple passages, though it did so reasonably well given the significant savings in experimental time and resources. Finally, our media did not generalize well to other cell types which limits the applicability of the designed media OM0-OM3 to C2C12 cells. However, such a result does indicate the need to re-optimize media and environmental conditions when studying new cell types or cells with significant genetic or metabolic changes, as such our methods could prove even more useful. In general, the MOBO algorithm was able to design media according to the objective function we picked for this system.