Multi-information source Bayesian optimization of culture media for cellular agriculture

Abstract

Culture media used in industrial bioprocessing and the emerging field of cellular agriculture is difficult to optimize due to the lack of rigorous mathematical models of cell growth and culture conditions, as well as the complexity of the design space. Rapid growth assays are inaccurate yet convenient, while robust measures of cell number can be time-consuming to the point of limiting experimentation. In this study, we optimized a cell culture media with 14 components using a multi-information source Bayesian optimization algorithm that locates optimal media conditions based on an iterative refinement of an uncertainty-weighted desirability function. As a model system, we utilized murine C2C12 cells, using AlamarBlue, LIVE stain, and trypan blue exclusion cell counting assays to determine cell number. Using this experimental optimization algorithm, we were able to design media with 181% more cells than a common commercial variant with a similar economic cost, while doing so in 38% fewer experiments than an efficient design-of-experiments method. The optimal medium generalized well to long-term growth up to four passages of C2C12 cells, indicating the multi-information source assay improved measurement robustness relative to rapid growth assays alone.

Keywords: Bayesian optimization; Gaussian process; cellular agriculture; expected improvement; media optimization; multi-information source.

Figure 1

BO algorithm. This loop describes the Bayesian Optimization algorithm to maximize some acquisition function $\alpha \left(x\right)$ for a process $Y=f\left(X\right)$ given $q_0$ high‐fidelity IS and $q-q_0$ low‐fidelity IS samples per batch of experiments. After each batch, the process is repeated until process is optimized or resources are exhausted. BO, Bayesian optimization

Figure 2

Simulation results. (a) Number of cumulative high‐fidelity simulations used plotted against average (with standard deviation for five runs of the entire optimization loop) optimal output from $f$ across five sequential iterations of the optimization framework. The multi‐IS GP (solid) had access to $q=15$ total simulations with $q_0=2$ high‐fidelity and $q-q_0=13$ low fidelity simulations per iteration (multi‐IS GP has stopped one iteration early to reduce computational burden). The regular GP (dotted) only had access to the $q_0=2$ high‐fidelity simulations per iteration. Each test function $\{f_1,f_2,f_3,f_4\}$ had two biased low‐fidelity versions whose correlations are described by plots (b). Squares and triangles represent a given $f_{\mathit{bias}1}$ and $f_{\mathit{bias}2}$ respectively. The solid line represents the underlying high fidelity IS $f$. Hyperparameter and acquisition function optimization was done using multistart L‐BFGS‐B implemented in botorch/scipy.

Figure 3

Learning curve and trade‐off curve of BO method. (a) Learning curve of $D\left(x\right)$ shows BO and DOE method designing experiments over the course of the optimization study. The line and dots represent the high‐fidelity IS optima and designs, the dashed and dotted lines represent the DMEM control and DOE optima values for $D\left(x\right)$ respectively. Each IS experiment is shown in (b) the trade‐off curve indicating a clear tradeoff between cost $c\left(x\right)$ and cell number $y\left(x\right)$, where the dots, triangles, squares, and “x's” represent Passage 2, Passage 1, AlamarBlue, and Live Stain respectively. (c) Simulated trade‐off curve also shown for high‐fidelity IS also showing a predicted parabolic relationship between competing objectives $y\left(x\right)$ and $c\left(x\right)$. BO, Bayesian optimization; DMEM, Dulbecco's modified Eagle's medium; DOE, design‐of‐experiments

Figure 4

Learned optimal concentration. The conditions of each experiment (concentration ranges in Table 1) are shown plotted as a function of the cumulative number of experiments in the BO (circle) and DOE (box) study. The moving average (solid and dashed line for BO and DOE respectively) shows how each method searches for optimal concentrations. The horizontal line represents the final BO optimal concentration. BO, Bayesian optimization; DOE, design‐of‐experiments

Figure 5

Long‐term validation of optima media. The optimal BO‐designed (dots), DOE (triangles), and DMEM control (squares) media performance up to Passage 4 Each passage was 72 h of growth at 37°C and 5% CO₂. Trypsinization took place after each 72 h period to count cells and replate them to allow for further growth (standard deviations indicated). The BO method designed an optimal media with substantially improved long‐term growth capacity than the DOE or DMEM control. BO, Bayesian optimization; DMEM, Dulbecco's modified Eagle's medium; DOE, design‐of‐experiments

Figure 6

Predicted first and second‐order effects. First‐order predicted effects of each component of the high‐fidelity IS are shown on diagonal plots (y‐axis is not to scale) with solid and dashed lines representing predicted cell number $y\left(x\right)$ and desirability $D\left(x\right)$ respectively. The “above” diagonal plots are second‐order plots for cell number $y\left(x\right)$ and “below” are those for desirability $D\left(x\right)$. The range of all components as described in Table 1. Labels are left off for clarity; to find the axis labels read the x‐axis labels horizontal from the diagonal label and read the y‐axis labels vertical from the label.

Figure 7

Variogram sensitivity analysis. The local (horizontal hatching), global (diagonal hatching), and mid‐range sensitivity of each component on $D\left(x\right)$ is indicated by the height of the bars. Albumin, FBS, dexamethasone, and glutamine have the largest effect on $D\left(x\right)$, with FBS being by far the most critical component with respect to global sensitivity. Predicted variogram ${\gamma }_i$ for each component was formed from $R=300$ random samples from domain $\left[\mathrm{0,1}\right]$. FBS, fetal bovine serum.

Figure 8

Kernel plots and IS distributions. (a) and (b) Show the output of the kernel $\Sigma (x_m,x_{m^{\prime }}^{\prime })$ for all data collected $\{X_N,Y_N\}$ and a simulated data set where only $x_{\mathit{FBS}}$ is varied from $\left[\mathrm{0,1}\right]$, respectively. Darker regions indicate large values of $\mathrm{\Sigma }$, and thus a correlation. Also (c) the various IS cell number/correlate distributions (diagonal histograms) are shown. Above the diagonal (squares) are the actual inter‐IS correlations for each IS with their respective R ² values, and below the diagonal (circles) are the predicted inter‐IS correlations for a random data set.