Proportional-Integral-Derivative (PID) Control of Secreted Factors for Blood Stem Cell Culture

<div><p>Clinical use of umbilical cord blood has typically been limited by the need to expand hematopoietic stem and progenitor cells (HSPC) ex vivo. This expansion is challenging due to the accumulation of secreted signaling factors in the culture that have a negative regulatory effect on HSPC output. Strategies for global regulation of these factors through dilution have been developed, but do not accommodate the dynamic nature or inherent variability of hematopoietic cell culture. We have developed a mathematical model to simulate the impact of feedback control on in vitro hematopoiesis, and used it to design a proportional-integral-derivative (PID) control algorithm. This algorithm was implemented with a fed-batch bioreactor to regulate the concentrations of secreted factors. Controlling the concentration of a key target factor, TGF-β1, through dilution limited the negative effect it had on HSPCs, and allowed global control of other similarly-produced inhibitory endogenous factors. The PID control algorithm effectively maintained the target soluble factor at the target concentration. We show that feedback controlled dilution is predicted to be a more cost effective dilution strategy compared to other open-loop strategies, and can enhance HSPC expansion in short term culture. This study demonstrates the utility of secreted factor process control strategies to optimize stem cell culture systems, and motivates the development of multi-analyte protein sensors to automate the manufacturing of cell therapies.</p></div

PID control is an effective alternative to supplementation with UM729.

<p><b>[A]</b> Our PID feedback controller has a similar effect on the concentration of LAP as UM729 addition with the PID controller conditions have a significantly higher concentration only at day 4 (n = 3). <b>[B]</b> Time course CD34⁺ expansion shows that PID control performs at least as well as D = 1+UM729 at day 12. <b>[C]</b> UM729 inhibits differentiation, resulting in a higher proportion of CD34⁺ cells beyond day 4. Both conditions have a significant loss of this phenotype between days 12 and 16 (D = 1+UM729 p = 0.007, PID p = 0.047) (n = 3). <b>[D]</b> At day 12, PID control moderately outperforms D = 1⁺UM729 with regards to total cell expansion. CD34⁺ cell expansion is equivalent (p = 0.444) (n = 3). <b>[E]</b> When culture time is extended to day 16, PID control and D = 1+UM729 remain equivalent (total cells p = 0.871, CD34⁺ cells p = 0.178) (n = 3). <b>[F]</b> Higher expansion of the HSC-enriched population, CD34⁺CD45RA^-CD90⁺, is observed in D = 1+UM729 conditions at both day 12 and day 16, though the difference is not significant. # <i>p</i><0.1 NS <i>p</i>>0.1.</p

Model structure and performance.

<p><b>[A]</b> Cumulative growth curves are defined for each phenotype group to calculate expansion as a function of TGF-β1 concentration. Cell numbers are adjusted by TGF-β1 gene expression values, which increase or decrease each phenotype’s relative contribution to factor accumulation as illustrated, to predict TGF-β1 secretion rates and accumulation in the media. The TGF-β1 concentration calculated using the culture volume, where the concentration is controlled by media addition, specified as a flow rate. This flow rate can be specified as a function of time or can be calculated through an external feedback control loop. <b>[B]</b> The model (n = 10) recapitulates average in vitro (n = 3) total cell and CD34⁺ cell expansion at day 12 of culture, as well as population level variability. Error bars represent standard deviation. <b>[C]</b> The model (n = 100) accurately predicts HSPC expansion observed during the RTC experiment (n = 3). Cells were seeded at low (L), medium (M), and high (H) densities, and cultures were diluted using a linear scheme (D = 1) or the simple feedback algorithm (RTC). Adapted from Csaszar et al. 2014 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0137392#pone.0137392.ref020" target="_blank">20</a>]. * <i>p</i><0.05.</p

Model predicts optimal PID controller improves expansion by maintaining low factor concentration.

<p><b>[A]</b> Model predicts significant improvement in both total cell and CD34⁺ cell expansion over both linear dilution at one unit per day (D = 1) and volume matched linear dilution (D = 3). <b>[B]</b> Volumetric efficiency (fold expansion/fold volume increase) is recovered to D = 1 levels by using the PID controller. <b>[C]</b> Predicted <b>(i)</b> volume and <b>(ii)</b> concentration trajectories for a representative sample. # <i>p</i><0.1, *** <i>p</i><0.001, NS <i>p</i>>0.1.</p

PID controller facilitates rapid cell expansion.

<p><b>[A]</b> Average LAP concentration time course demonstrates that the PID controller maintains a lower factor concentration (n = 3) than linear medium dilution strategies during the controller action phase. <b>[B]</b> Volume trajectories for D = 1, D = 3 and 3 PID controlled samples shows controller action between days 5 and 10. <b>[C]</b> Total cell expansion compared between dilution strategies. PID control outperforms both linear dilution schemes at day 12 (n = 3). <b>[D]</b> CD34⁺ cell expansion compared between dilution strategies. PID controller outperforms both linear dilution schemes at day 12, with the effect lost by day 16 (n = 3). <b>[E]</b> Surface marker analysis of CD34⁺ frequency during culture shows rapid differentiation between day 12 and 16 with PID control (n = 3). <b>[F]</b> Despite net loss of both total and CD34⁺ cells, day 16 expansion of HSC-enriched population CD34⁺CD45RA^-CD90⁺ is not adversely affected (n = 3). * <i>p</i><0.05.</p

Model predicts a PID controller is the optimal media delivery method.

<p><b>[A]</b> Different feeding strategies were investigated in silico. When normalized to day 16 total media requirements, a simple algorithm (RTC) significantly outperforms other media delivery strategies for CD34⁺ expansion (n = 100). <b>[B]</b> The PID controller performs optimally at a set point of 85 pg/mL for any fold volume increase (n = 100). <b>[C]</b> CD34⁺ expansion is improved using 12 hour sampling over 6 hour or 24 hour sampling (n = 100). <b>[D]</b> A 50-fold volume increase using the PID controller is the minimum fold volume increase to meet both concentration constraints (<400 pg/mL TGF-β1 on day 16 and <15% of time above 150 pg/mL) (n = 100). * <i>p</i><0.05, ** <i>p</i><0.01, *** <i>p</i><0.001.</p

Empirical correlations were used to develop the model.

<p><b>[A] (i)</b> Cell numbers for each phenotype group are converted to <b>(ii)</b> growth rates, as % change per day. <b>(iii)</b> Average TGF-β1 concentrations are calculated from the time course data. <b>(iv)</b> These midpoints (day 2, 6, 10) are combined for all three media dilution rates and correlated to give growth rates (%/day) as a function of TGF-β1 concentration (pg/mL). <b>[B] (i)</b> Total cell numbers are categorized into phenotype groups and <b>(ii)</b> adjusted by TGF-β1 gene expression values to reflect each phenotype’s relative contribution to TGF-β1 accumulation. <b>(iii)</b> The new adjusted cell numbers are summed to give a total ‘adjusted’ cell number. Separately, <b>(iv)</b> TGF-β1 concentrations (pg/mL) are converted to <b>(v)</b> TGF-β1 amounts (pg) using the culture volume (mL). <b>(vi)</b> This is converted to secretion rates, in pg/day. <b>(vii)</b> These midpoints (day 2, 6, 10) are combined for all three dilution rates and correlated to give TGF-β1 secretion (pg/day) as a function of total ‘adjusted’ cell number.</p

Soluble factors regulate HSPC expansion.

<p><b>[A]</b> Mature cell phenotypes secrete factors that positively (green) and negatively (red) regulate stem and progenitor expansion <b>[B]</b> Cytokines and chemokines accumulate in fed-batch culture negatively regulating HSPC expansion. Data represents mean concentration of n = 2 (Luminex) or n = 4 (ELISA) biological replicates in fed batch culture using a linear dilution scheme (D = 1). <b>[C]</b> Schematic of the fed-batch bioreactor system with a feedback controlled flow controller. The TGF-β1 concentration is determined by measuring the concentration of the representative factor, LAP, using the microbead detection assay. The TGF-β1 concentration is input to the controller which adjusts the media flow rate to control the concentration of TGF-β1, allowing for real-time control of soluble factor accumulation.</p

PERT recovers compositions of uncultured human cord blood mono-nucleated and lineage-depleted (Lin-) cells.

<p>(A) Schematic compositions of mono-nucleated cell samples and Lin- cell samples. (B) Model predicted proportions of 11 homogeneous blood cell lineages, namely granulocytes (GRAN), erythrocytes (ERY), monocytes (MONO), precursor B cells (PREB), megakaryocyte-erythrocyte progenitors (MEP), megakaryocytes (MEGA), primitive progenitor cells (PPC), eosinophils (EOS), granulocyte-monocyte progenitors (GMP), common myeloid progenitors (CMP), and basophils (BASO) in uncultured human mono-nucleated cord blood cell samples. (C) Flow cytometry measured proportions of the 11 blood cell lineages in the uncultured human mono-nucleated cord blood cell samples shown in (B). (D) Model predicted proportions in uncultured human Lin- cord blood cell samples. (E) Flow cytometry measured proportions in the uncultured human Lin- cord blood cell samples shown in (D). (F) R² calculated from the Pearson's correlation coefficients between the model predicted cell proportions and the ones assigned by flow cytometry. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002838#pcbi-1002838-t002" target="_blank">Table 2</a> for the associated t-statistics and P-values. (G) Averaged absolute differences of model predicted cell proportions. Error bars show standard deviations of the absolute differences between model predicted and flow cytometry assigned proportions of the 11 blood cell lineages. (H) The Bayesian information criterion (BIC) calculated from the parameters in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002838#pcbi-1002838-t001" target="_blank">Table 1</a>.</p

NNML recovers known compositions of immune cell line mixtures.

<p>Microarray data of IM-9 (○), Jurkat (▵), Raji (□), THP-1 (+), and the mixtures of these four cell lines in known proportions were obtained from Abbas et al. (2009). Proportions of each cell line were predicted using (A) NNLS with cell line signature probes (reproduced from Abbas et al. (2009)), (B) NNLS without cell line signature probe, (C) NNML with cell line signature probes, and (D) NNLS without cell line signature probes. Model predictions were compared with the input proportions used to create the mixtures. Cell line signature probes were obtained from Abbas et al. (2009).</p