Selekman

Improving Efficiency of Human Pluripotent StemCell Differentiation Platforms Using an IntegratedExperimental and Computational Approach

Joshua A. Selekman, Amritava Das, Nicholas J. Grundl, Sean P. Palecek

Department of Chemical and Biological Engineering, University of Wisconsin,

3637 Engineering Hall, 1415 Engineering Drive, Madison, Wisconsin, 53706;

telephone: 608-262-8931; fax: 608-262-5434; e-mail: [email protected]

ABSTRACT: Human pluripotent stem cells (hPSCs) have anunparalleled potential for tissue engineering applicationsincluding regenerative therapies and in vitro cell-basedmodels for studying normal and diseased tissue morphogen-esis, or drug and toxicological screens.While numerous hPSCdifferentiation methods have been developed to generatevarious somatic cell types, the potential of hPSC-basedtechnologies is hinged on the ability to translate theseestablished lab-scale differentiation systems to large-scaleprocesses to meet the industrial and clinical demands forthese somatic cell types. Here, we demonstrate a strategy forinvestigating the efciency and scalability of hPSC differenti-ation platforms. Using two previously reported epithelialdifferentiation systems as models, we t an ODE-basedkinetic model to data representing dynamics of various cellsubpopulations present in our culture. This t was performedby estimating rate constants of each cell subpopulations cellfate decisions (self-renewal, differentiation, death). Sensitivi-ty analyses on predicted rate constants indicated which cellfate decisions had the greatest impact on overall epithelial cellyield in each differentiation process. In addition, we foundthat the nal cell yield was limited by the self-renewal rate ofeither the progenitor state or the nal differentiated state,depending on the differentiation protocol. Also, the relativeimpact of these cell fate decision rates was highly dependenton the maximum capacity of the cell culture system. Overall,we outline a novel approach for quantitative analysis ofestablished laboratory-scale hPSC differentiation systemsand this approach may ease development to produce largequantities of cells for tissue engineering applications.

Biotechnol. Bioeng. 2013;110: 30243037.

2013 Wiley Periodicals, Inc.

KEYWORDS: pluripotent stem cell; differentiation; model;parameter estimation; cell fate self-renewal; expansion;scale-up

Introduction

Both human embryonic stem cells (hESCs) and humaninduced pluripotent stem cells (hiPSCs) have propertiesof indenite self-renewal and the capability to generate allsomatic cell types (Takahashi et al., 2007; Thomsonet al., 1998; Yu et al., 2007). It is because of thesecharacteristics that all human pluripotent stem cells (hPSCs)possess a tremendous potential for tissue engineeringapplications including regenerative medicine, in vitro modelsystems to study development and disease, and pharmaceu-tical and toxicological screening. Researchers have designedinnovative culture and reprogramming systems for generat-ing different somatic cell populations from hPSCs. However,translating these laboratory-scale hPSC differentiation pro-tocols to large-scale bioreactor production processes forproducing high purity and high yield populations of somaticcells is one of the current bottlenecks in satisfying demandfor therapeutically relevant cell types and ultimately realizingthe potential of hPSC-based technology (Azarin andPalecek, 2010; Serra et al., 2012). The scale-up of currenthPSC differentiation systems will necessitate a thoroughunderstanding of what mechanisms govern dynamics of adifferentiating cell population. In addition, design of newlarge-scale bioprocesses will require quantitative approachesthat can ideally be applied to any established laboratory-scalehPSC differentiation system to model and predict strategiesto optimize the expansion and differentiation of various cellsubpopulations present in culture.

Current laboratory-scale hPSC differentiation systems aredesigned to guide populations of undifferentiated hPSCstoward a particular cell lineage using microenvironmentalcues. Such cues, in the form of soluble factors, extracellularmatrix, mechanical forces, cellcell contact, or various

Additional supporting information may be found in the online version of this article at

the publishers web-site.

No competing financial interests exist.

Correspondence to: S.P. Palecek

Contract grant sponsor: National Science Foundation

Contract grant number: CBET-1066311

Contract grant sponsor: University of Wisconsin Stem Cell and Regenerative Medicine

Predoctoral Fellowship

Contract grant sponsor: National Institutes of Health Training

Contract grant number: NIDCD T32 DC009401

Received 6 April 2013; Revision received 23 May 2013; Accepted 28 May 2013

Accepted manuscript online 5 June 2013;

Article first published online 9 July 2013 in Wiley Online Library

(http://onlinelibrary.wiley.com/doi/10.1002/bit.24968/abstract).

DOI 10.1002/bit.24968

ARTICLE

3024 Biotechnology and Bioengineering, Vol. 110, No. 11, November, 2013 2013 Wiley Periodicals, Inc.

combinations of these, must be introduced in a spatiotem-poral-specic manner (Dellatore et al., 2008; Discher et al.,2009; Hazeltine et al., 2013; Metallo et al., 2008a; Serraet al., 2012). Several groups have developed sub-cellular,cellular, or population models to predict cell fate decisions asfunctions of these cues in various cellular systems, includinghPSCs, hematopoietic stem cells (HSCs), or mouse pluripo-tent stem cells (mPSC; Glauche et al., 2007; Prudhommeet al., 2004; Task et al., 2012; Ungrin et al., 2012; Viswanathanet al., 2005; Zandstra et al., 2000). For example, Viswanathanet al. (2005) established a computational model to predictmPSC population behavior in response to exogenous stimuliwhile taking into account endogenous cellular signals at asub-cellular level. Glauche et al. (2007) developed a modelof HSC lineage specication by integrating intracellulardynamics, in terms of estimating propensity for lineagespecication, as well as cell population dynamics, which areinuenced by microenvironmental signals that may directdifferentiation. In both of these cases as well as other studiesfocused on modeling stem cell behavior, it was important torecognize that the total cell population is a dynamicheterogeneous composition of various cell subpopulations,including undifferentiated and differentiated cells, each ofwhich exhibit distinct rates of self-renewal, differentiation,and death that are dictated by the cellular microenvironment(Cabrita et al., 2003; Kirouac and Zandstra, 2006; Prud-homme et al., 2004).A study by Prudhomme et al. (2004) investigated

individual contributions of different microenvironmentalcues on mouse embryonic stem cell (mESC) differentiation.By acquiring data on the kinetics of the transition betweenundifferentiated and differentiated cells, represented byOct4 and Oct4 cells respectively, a cell populationdynamics model was t to these data to decouple kineticrates of self-renewal and differentiation responses ofeach subpopulation (Prudhomme et al., 2004). Using thisapproach, it was possible to estimate cell fate parametersof the specic cell subpopulations present in culturewithout requiring understanding of underlying intracellularmechanisms.Here, we outline an approach to quantitatively investigate

the efciency and scalability of distinct hPSC differentiationprotocols. By using two robust hPSC epithelial differentiationmethods as examples (Lian et al., 2013; Metallo et al., 2010),we rst collected cell subpopulation dynamics data andsubsequently t a mathematical model to these data usingparameter estimation to calculate various rate constantsrepresenting cell fate decisions (self-renewal, differentiation,and apoptosis) for each individual cell type. In performingthese analyses, we were able to answer three key questions: (1)Which cell-fate decisions are most limiting in terms ofefciency of the differentiation process? (2) What is themost advantageous stable cell state (i.e., hPSC, progenitor,differentiated cell) at which to target expansion to improveyield or purity of the desired cell type? (3) Given multipledifferentiation methods to achieve the same cell type, whichmethod is more favorable for scalable production?

Materials and Methods

Methods are included in Online Supplementary Information.

Results

Compartmentalization of hPSC Differentiation Systems

To investigate efciency and scalability of hPSC differentia-tion, we selected epithelial commitment as a model system.Epithelial differentiation, like differentiation of many celltypes, involves stable cell states, including a progenitor stateand a nal differentiated state, that are identiable byexpression of specic marker proteins. Numerous hPSCdifferentiation protocols exist to generate epithelial cells thatexpress cytokeratin 18 (K18) by using retinoic acid (RA),bone morphogenetic protein 4 (BMP4), or ascorbic acid toinduce differentiation (Aberdam et al., 2008; Hewittet al., 2009; Metallo et al., 2008b). Such cells can furtherdifferentiate to yield specic epithelial cell types, includingkeratinocyte progenitor cells, which express cytokeratin 14(K14), coupled with a loss of K18, when cultured underspecic conditions (Aberdam et al., 2008; Itoh et al., 2011;Metallo et al., 2008b, 2010).In this study, we investigated two robust epithelial

differentiation protocols that yield K18 simple epithelialcells and, subsequently, K14 keratinocyte progenitors (Lianet al., 2013; Metallo et al., 2010). A population is comprisedof several proliferating subpopulations (Prudhomme et al.,2004). Therefore, it is essential to quantitatively analyze thenumbers of cells in each subpopulation and transitionsbetween these subpopulations. We have dened distinct celltypes present throughout both epithelial differentiationsystems and illustrated the self-renewal and differentiationprocesses associated with these various cell subpopulations(Fig. 1A). Both differentiation protocols involved an initialcommitment of hPSCs, identied by expression of Nanog, toan epithelial progenitor cell, identied as a cell that expressesK18 but not Nanog. The K18/Nanog simple epithelialcells further differentiated to epidermal keratinocyte pro-genitors, which expressed K14 but lost expression of K18 andNanog. We have also universally dened an undesirable cellpopulation as one that consists of cells that do not expressK14, K18, or Nanog. Given these identiable stable cell states,we monitored the dynamics of each of these cell subpopu-lations throughout differentiation.Each cell subpopulation has distinct self-renewal, differ-

entiation, and apoptosis rates that are dependent upon themicroenvironment. Both differentiation processes, Protocols1 and 2, involve multiple changes in culture conditions, andtherefore a dynamic cellular microenvironment, throughoutdifferentiation. For this reason, we have compartmentalizedthese differentiation processes into multiple phases, eachphase dened by a specic set of culture conditions (Fig. 1B,Table I). Such compartmentalization has been incorporatedinto other cell differentiation models (Glauche et al., 2007).We have dened Phase 0 as themaintenance and expansion of

Selekman et al.: Efficiency of hPSC Differentiation Platforms 3025

Biotechnology and Bioengineering

Figure 1. Establishment of cell states and compartmentalization of differentiation processes. A: Schematic representing the four cell states present during epithelialdifferentiation and the protein markers used to distinguish each cell state. Arrows indicate self-renewal or differentiation events among the various subpopulations. Rate constants

representing either self-renewal or differentiation rates are also indicated. B: Schematic illustrating the compartmentalization of the differentiation process. Each phase is defined

by a specific microenvironment and the primary differentiation or expansion event for each phase is indicated.

Table I. Description of each differentiation phase for two epithelial differentiation protocols.

Differentiationphase

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0 72 mTeSR1/Matrigel 72 mTeSR1/MatrigelI 168 UMRA/Matrigel 72 UM SU/MatrigelII 240 K-DSFM/Gelatin 144 K-DSFM 5% FBS/MatrigelIIIa N/A N/A 96 UMRABMP4/MatrigelIII 240 K/DSFM/Gelatin 240 K-DSFM/Matrigel

Duration (in hours) and culture conditions (culture medium/substrate) for each differentiation phase are reported.

3026 Biotechnology and Bioengineering, Vol. 110, No. 11, November, 2013

undifferentiated hPSCs. Phase I is the initial commitment ofhPSCs to an epithelial cell fate resulting in K18/Nanogsimple epithelial cells. The expansion of these simpleepithelial cells occurs in Phase II. In Protocol 2, there is anadditional phase of differentiation, Phase IIIa, involving adifferent set of culture conditions in which the K18/Nanog cells expand. Finally, Phase III involves thematuration of a K18/Nanog simple epithelial cell to anal cell type, K14/K18/Nanog keratinocyte progenitorcells.For each phase, we obtained cell subpopulation dynamics

data by multiplying the absolute number of cells in culture bythe percentage of cells in each subpopulation, obtained viaow cytometry. Subsequently, we t a set of ordinarydifferential equations (ODEs) to these data representingaccumulation of the different cell types present in culture. Auniversal form of an ODE representing a cell subpopulationaccumulation consists of rst-order terms representing self-renewal, differentiation, or apoptosis and a maximumcapacity limit representing the physical boundaries of theculture system, and thus providing a second-order relation:

dCidt kaiCa kii kijCi C1

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where Ci is the concentration, or density, of cell type i inculture, C1 is the maximum density of cells that can bepresent in culture,SC is the total number of cells in culture, kiiis the net self-renewal rate (proliferation minus cell death)constant for cell type i, Ca is the concentration or density ofcell type a in culture, kai is the differentiation rate constantrepresenting conversion of cell type a into cell type i, and kij isthe differentiation rate constant representing conversionof cell type i to cell type j or the apoptosis rate of cell type i.Using parameter estimation, we calculated the rate constantsthat represent the various cell fate decisions for each cellsubpopulation. We have assumed that all parameters aredependent upon the specic microenvironmental conditionsand are independent of time (Prudhomme et al., 2004). Adescription of each cell subpopulations parameter set and thedifferentiation phase in which it is estimated is tabulated inTable II. We t these ODEs to kinetic data collected in eachphase of both differentiation systems to eventually identifywhich cell fate decisions may be limiting overall cell yield.

Phase 0: hPSC Expansion (Nanog)We rst investigated the expansion of H9 hESCs in apluripotent state prior to differentiation. In Phase 0, wemonitored kinetics of cell growth by counting the number ofcells at various time points (Fig. 2A) and quantifying thepercentage of cells that wereNanog (Fig. 2B). No signicantapoptosis was detected in Nanog cells by co-staining forthe active form of caspase 3 (Fig. 2C). We then plotted thedynamics of Nanog cell expansion as a function of time andt an ODE model representing Nanog cell growth,

Equation (S1), to estimate the self-renewal rate of Nanogcells in Phase 0 (Fig. 2D). The growth rate of Nanog cells inthis phase was determined to be 0.0358 h1, or in otherwords, this population was estimated to have a doublingtime of about 19.6 h, similar to reported doubling times ofhESCs under similar conditions (Harb et al., 2008; Nagaokaet al., 2010). These results were applied to analysis of bothProtocols 1 and 2 since hPSC expansion conditions wereidentical for each differentiation method prior to Phase I.

Phase I: Initial Commitment to Progenitor State(K18/Nanog)We next investigated the commitment of hPSCs toward anepithelial cell fate where an enriched Nanog populationgenerates a population enriched in K18/Nanog cells. Thekinetic data showing absolute cell counts as a function of timeare clearly different in Protocol 1 (Fig. 3A-left panel) andProtocol 2 (Fig. 3A-right panel) since differentiation in thetwo protocols is initiated at different hPSC densities.However, in both systems, the kinetics of loss of Nanogexpression and acquisition of K18 expression were similar(Figs. 3B, S1A and B). One striking difference we foundbetween the two protocols was the substantially greaterpercentage of apoptotic cells in Protocol 2.Whereas apoptosislevels were minimal (

Protocol 2. We t a set of ODE equations, Equations (S2)(S4), to these data to estimate cell fate rate constants in PhaseI for Protocol 1 (Fig. 3D-left panel) and Protocol 2 (Fig. 3D-right panel).

Rate constants estimated for Protocol 1 indicated that therewas very little self-renewal of the Nanog cell population(k11). However, the self-renewal rate of the K18/Nanogpopulation (k22) was estimated at 0.0459 h

1, which was theby far the greatest value, and therefore themost dominant cellfate decision, estimated in this system (Fig. 3). In contrast, themodel t indicated that in Protocol 2, there was no signicantself-renewal of any cell type and the system was primarilydominated by differentiation of Nanog cells to K18/

Nanog cells (k12), with a value of 0.0685 h1, and apoptosisof K18/Nanog cells (k24), with a value of 0.030 h1.In addition, qualitatively, it is apparent that these twodifferentiation protocols resulted in vastly different cellsubpopulation dynamics during the initial differentiationphase.

Phase II: Expansion of Progenitor Cells (K18/Nanog)At the conclusion of Phase I in both epithelial differentiationplatforms, cell populations were subcultured and plated indifferent culture conditions and therefore are exposed to anew microenvironment dictating the need for new cell fate

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Figure 2. Analysis of hPSC expansion (Phase 0). A: Total cell number as a function of time in Phase 0. B: Flow cytometry data representing population breakdown as a functionof time in terms of percentage cells expressing Nanog. C: Total apoptosis levels in culture as a function of time as measured by percentage of cells expressing the active form of

caspase3. D: Model fit to data where data points represent the total number of Nanog H9 hESCs in culture as a function of time in the Phase 0 culture conditions. Line representsmodel fit to data by estimating the self-renewal rate of Nanog cell growth (k00). k00 value (in h1) and quality of fit, indicated by the residual sum of squares (RSS) value, are denoted.Error bars represent standard deviation (N 3).


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Figure 3. Analysis of Phase I of epithelial differentiation. A: Total cell number as a function of time in Phase I for Protocol 1 (left) and Protocol 2 (right). B: Flow cytometry datarepresenting population breakdown as a function of time in terms of the percentage of cells that express exclusively Nanog (grey), express K18, but not Nanog (black), or express

neither marker (white) for Protocol 1 (left) and Protocol 2 (right). C: Apoptosis levels in culture as a function of time as measured by the percentage of the total number of cells

expressing caspase3 in Protocol 1 (left) or the percentage of K18/Nanog cells expressing caspase3 in Protocol 2 (right). D: Model fits to data where data points represent cellsubpopulation dynamics in Phase I. The total number of either Nanog, K18/Nanog, or K18/Nanog cells in culture are plotted as a function of time during Phase I of Protocol 1(left) or Protocol 2 (right). Lines represent model fits to data by estimating the various self-renewal and differentiation rates pertinent to this differentiation phase for each protocol.

For Protocol 2, a death rate of the K18/Nanog cell population (k24) was incorporated into the model and estimated with the other cell fate decision rate constants. Values for eachestimated rate constant (in h1) in each system, as well as the RSS value, are denoted. Error bars indicate standard deviation (N 3).



parameters. This next phase, Phase II, involves the expansionof the cell population which is enriched in K18/Nanogepithelial progenitor cells. The total cell number (Fig. 4A-leftand middle panels) and the purity of the K18/Nanogprogenitor cell populations (Figs. 4B-left and middle panels

and S2) were used to calculate the number of K18/Nanogcells as a function of time for Protocol 1 (Fig. 4C-left panel)and Protocol 2 (Fig. 4C-middle panel). We performed thisanalysis analogously to how we evaluated Phases 0 and I.Equation (S5) was used to t the kinetic data and estimate the

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Figure 4. Analysis of Phase II of epithelial differentiation. A: Total cell number as a function of time in Phase II for Protocol 1 (left), Protocol 2 (middle), and in Phase IIIa forProtocol 2 (right). B: Flow cytometry data representing population breakdown as a function of time in terms of the percentage of cells that express K18, but not Nanog or K14 for

Phase II in Protocol 1 (left), Protocol 2 (middle), and Phase IIIa in Protocol 2 (right). C: Model fits to datawhere data points represent the total number of K18/Nanog cells in cultureas a function of time during Phase II of either Protocol 1 (left) or Protocol 2 (middle). In addition, the number of K18/Nanog cells in Phase IIIa, an additional phase specific toProtocol 2, was analyzed (right). Lines represent model fits to data by estimating the self-renewal rates of the K18/Nanog cells in Phase II (k55a) or Phase IIIa (k55b). Values for theestimated rate constants (in h1), as well as the RSS value, are denoted. Error bars indicate standard deviation (N 3).


self-renewal rate of the K18/Nanog cells in protocol 1(Fig. 4C-left panel) and in protocol 2 (Fig. 4C-middle panel).The self-renewal rate (k55a) of the K18/Nanog epithelialprogenitors was over threefold greater in Phase II of Protocol2 (0.0197 h1) than Protocol 1 (0.0058 h1). Phase II analysisof Protocol 2 was carried out for 2 weeks to estimate theself-renewal rate of the K18/Nanog cells (Fig. 4C-middlepanel), however the actual differentiation process truncatesPhase II after 6 days of K18/Nanog cell expansion prior toentering the next phase of differentiation.Following Phase II, Protocol 2 incorporated an additional

phase, Phase IIIa, involving expansion of the K18/Nanogsimple epithelial cells under different culture conditions(Table I). There is no equivalent phase in the differentiationsystem dened in Protocol 1. The self-renewal rate of theseepithelial progenitor cells was estimated based on the t ofEquation (S5) to kinetic data (Fig. 4C-right panel) obtainedby total cell counts (Fig. 4A-right panel) and ow cytometryfor the percentage of K18/Nanog cells (Figs. 4B-rightpanel and S2). The value of this epithelial progenitors self-renewal rate (k55b) was found to be 0.0229 h

1, slightlygreater than the self-renewal rate estimated in Phase II. Fourdays in Phase IIIa precedes the nal phase of differentiation,Phase III.

Phase III: Differentiation to Final Cell State (K14/K18)The nal phase of differentiation, Phase III, directs thetransition from a K18/Nanog epithelial progenitor cell toa K14/K18 keratinocyte progenitor cell. Data showedsteady increases in total cell population during both Protocol1 (Fig. 5A-left panel) and Protocol 2 (Fig. 5A-right panel).Both systems also exhibited a monotonic increase in thefraction of K14/K18 cells as a function of time duringPhase III (Figs. 5B and S3). Caspase3 staining indicated lowlevels of apoptosis in both systems (

k55 k56 k57 k66 k67 k77 RSS Protocol 1 0.00138 0.00813 0.00002 0.00488 0.00049 0.00027 1.77 Protocol 2 0.000002 0.00513 0.000002 0.0177 0.0016 0.000021 2.86

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Figure 5. Analysis of Phase III of epithelial differentiation. A: Total cell number as a function of time in Phase I for Protocol 1 (left) and Protocol 2 (right). B: Flow cytometry datarepresenting population breakdown as a function of time in terms of the percentage of cells that express exclusively K18, but not Nanog or K14 (black), cells that express K14, but not

K18 (dark gray), or cells that express none of these markers (white) for Protocol 1 (left) and Protocol 2 (right). C: Apoptosis levels in culture as a function of time as measured by the

percentage of the total number of cells expressing caspase3 in Protocol 1 (left) or in Protocol 2 (right).D: Model fit to data where data points represent cell subpopulation dynamics in

Phase III. The total number of either K18/Nanog, K14/K18, or K14/K18 cells in culture are plotted as a function of time during Phase III of either Protocol 1 (left) or Protocol2 (right). Lines represent model fits to data by estimating the various self-renewal and differentiation rates pertinent to this differentiation phase for each protocol. Values for each

estimated rate constant (in h1) in each system, as well as the RSS value, are denoted in the table. Error bars indicate standard deviation (N 3).


we observed a striking difference inwhich parameters had thegreatest impact on keratinocyte progenitor yield. In a systemwith no maximum capacity limits, changes in the self-renewal rate of the K18/Nanog progenitor cells in Phase I(k22) had the greatest impact on overall cell yield. Thissuggests that in an unconstrained system, one should aim toimprove K14/K18 cell yield by changing the microenvi-ronment in Phase I to facilitate a higher K18/Nanog self-renewal rate. In addition, the K18/Nanog progenitor cellsin Phase I would be the most advantageous cell state forexpansion to scale-up epithelial cell production. Protocol 2does not have a single dominant parameter that, if changed, ispredicted to drastically affect overall K14/K18 cell yield.Rather, ve parameters (k00, k24, k55a, k55b, k66) are predictedto have a comparable impact on keratinocyte progenitoryield. Unlike the conditions with a maximum capacity limit,it appears that there is no clear cell state that is mostadvantageous for scale-up and expansion for Protocol 2 butthere instead exist multiple states that regulate K14/K18cell yield.

Model Validation With Microenvironmental Change

The sensitivity analyses predicted which cell fate decisionswere potentially limiting K14/K18 epidermal keratino-cyte progenitor yield in the two differentiation processes. Wenext sought to validate these model predictions by changingthe microenvironment in such a way to inuence specic cellfate decisions and identify the resulting changes in overallkeratinocyte progenitor yield. Specically, we targeted theself-renewal rate of the K18/Nanog cells in Phase II ofProtocol 1 (k55a) since this rate was predicted to limit the yieldof K14/K18 cells (Fig. 6A). To alter the microenviron-ment, we cultured these cells on Synthemax plates rather thangelatin-coated plates since we have previously found thissubstrate to facilitate greater proliferation of these simpleepithelial cells (Selekman et al., 2013). We collected kineticdata on the total number of cells in culture (Fig. 7A-left panel)

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7k7

7

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ivi

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Protocol 1Protocol 2

A

B

Figure 6. Sensitivity analysis of epithelial differentiation protocols. Sensitivityvalues were calculated to determine the impact of a 10% change in an individual

parameter to the resulting K14/K18 cell yield as predicted by the model. Acomparison between the sensitivity values for each of the two protocols is shown in

either (A) the lab-scale system analyzed with a maximum capacity or (B) a hypothetical

unconstrained system lacking a maximum capacity assumption.

Table III. Summary of critical cell fate decisions in each phase of differentiation for both protocols.


Phase 0 Self-renewal of Nanog cells Self-renewal of Nanog cellsPhase I Self-renewal of K18/Nanog cells Cell death of K18/Nanog cellsPhase II Self-renewal of K18/Nanog cells Self-renewal of K18/Nanog cellsPhase III Self-renewal of K14/K18 cells Self-renewal of K14/K18 cells

The most critical cell fate decision for the entire differentiation process is indicated in bold for each protocol.

Table IV. Summary of critical cell fate decisions in each phase of differentiation for both protocols in a hypothetical system without a maximumcapacity limit.


Phase 0 Self-renewal of Nanog cells Self-renewal of Nanog cellsPhase I Self-renewal of K18/Nanog cells Cell death of K18/Nanog cellsPhase II Self-renewal of K18/Nanog cells Self-renewal of K18/Nanog cellsPhase III Self-renewal of K18/Nanog cells Self-renewal of K14/K18 cells

The most critical cell fate decision for the entire differentiation process is indicated in bold for each protocol.



k55a k55 k56 k57 k66 k67 k77 RSS 0.0072 0.00595 0.0108 0.00000091 0.008385 0.000979 0.00011 13.51

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432 480 528 576 624 672

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Figure 7. Effect of microenvironmental changes on estimated cell fate parameters and overall epithelial cell yield. A Synthemax substratewas used in lieu of a gelatin substrateand data was collected to show (A) total cell number in Phase II (left) and Phase III (right) as a function of time. B: Flow cytometry data demonstrating high purity K18/Nanog cellsduring Phase II (left) and the population breakdown as a function of time in terms of the percentage of cells that express exclusively K18, but not Nanog or K14 (black), cells that

express K14, but not K18 (dark gray), or cells that express none of these markers (white) during Phase III (right). Cell subpopulation dynamics data were collected and fit to

corresponding models in Phase II (left) and Phase III (right) of Protocol 1. Estimated rate constant values (in h1) in each phase are denoted as well as the RSS value for the model fit.Error bars indicate standard deviation (N 3).


and the composition of the population (Fig. 7B-left panel).We t the same ODE model to these data as was done in thePhase II analysis discussed previously. In tting this model tothe cell subpopulation dynamics data, we estimated the self-renewal of the K18/Nanog simple epithelial cells to be0.0072 h1 (Fig. 7C-left panel), about 25% higher than whatwas calculated for these same cells on a gelatin substrate(Fig. 4C-left panel). Given this change, the model predictedan overall K14/K18 keratinocyte progenitor yieldof about 1.3 million cells on Synthemax compared to0.90 million cells when cultured on gelatin-coated plates.However, our experimental yield was actually 1.900.31 million keratinocyte progenitor cells, indicating thatother cell fate decisions were potentially altered by changingthe substrate from gelatin to Synthemax.To identify other cell fate parameters that culture on

Synthemax changed, we investigated cell fate transitionsduring Phase III of Protocol 1 on a Synthemax substrate.Analogous to our investigation of a modied Phase IIdescribed above, we collected kinetic data on absolute cellnumber in culture (Fig. 7A-right panel) and the populationcomposition (Fig. 7B-right panel). We t these data to thesame set of ODEs used in our original Phase III analysis ofProtocol 1 and surprisingly found that Synthemax increasedthe differentiation rate of K18/Nanog cells into K14/K18 cells to 0.00813 h1 as well as the self-renewal rate ofthe K14/K18 cells to 0.00488 h1 (Fig. 7C-right panel).Both of these parameters were predicted to have a signicanteffect on overall K14/K18 cell yield, albeit a smallerimpact relative to k55a (Fig. 6A). Given these changes, ourmodel predicted a nal K14/K18 cell yield of 2.1 million,which was within the range of our experimental yield at1.90 0.31 million. In identifying specic cell fate decisionsfound to be bottlenecks of differentiation, we successfullydemonstrated to facilitate changes in these cell fate decisionsby altering the microenvironment, which, as our modelpredicted, would result in a greater keratinocyte progenitoryield.

Discussion

Here, we have outlined a novel approach for improving theefciency or investigating the scalability of an established lab-scale hPSC differentiation process. The process of compart-mentalizing a differentiation system based on distinctchanges in cellular microenvironments and dening differentcell subpopulations present in culture allows identication ofthe cell fate decisions that may limit yield of a differentiatedcell population (Fig. 8). In collecting cell subpopulationdynamics data and tting a set of ODEs representing thekinetics of the differentiation process, we were able todecouple the rate constants of the various cell fate decisions(self-renewal, differentiation, apoptosis) in two differentdifferentiation systems to generate a similar cell type. Byperforming a sensitivity analysis on these different cell fateparameters, we predicted which parameters would have thegreatest effect on overall cell yield of our desired epithelial cell

type in our lab-scale system and in a hypothetical large-scalesystem. Finally, we were able to validate our model by alteringthe microenvironment to facilitate changes in cell fatedecisions that enhanced keratinocyte progenitor yield. Theapproach outlined in this study should be applicable to anyestablished lab-scale system involving the engineering ofhPSCs to generate populations of a desired cell type in whichthere is a desire to scale-up to meet industrial or clinicaldemands for such cell types.The ability to distinguishmultiple stable ormetastable cells

states in culture is imperative for this analysis and suchinformation is required to apply this method to other stemcell differentiation systems. However, it is important tohighlight a few key assumptions made in this study. Weassumed that all parameters were independent of time. Inreality, time-dependent changes in total cell number and thevarying composition of cells could conceivably have animpact on cell fate decision rates. Temporal changes in cellcell contact and paracrine signaling in each differentiationphase can alter the microenvironment resulting in dynamicchanges in cell fate decision rates. However, without priorknowledge as to how these rates would individually change asa function of total cell number or population composition, itis difcult to incorporate this consideration into the model.The framework outlined in this study is conducive for modelrenement in the event additional complexities or nuances ofspecic differentiation systems are well understood.Another assumption we made in this study was to

characterize Nanog/K18/K14 cells as a single subpopu-lation of undesired cells with distinct self-renewal anddifferentiation rates. While it is likely that this population wascomprised of a heterogeneous mixture of cells, we did notfurther characterize this population was given its relativelylow abundance in culture. Distinguishing multiple discreteundesired cell types, however, might be necessary for otherdifferentiation processes, however.In tting ODE-based models to our population dynamics

data, we were able to decouple the rates of various cell fatedecisions for each subpopulation using parameter estimationsimilar to what has been performed in other cell-basedcontexts (Ackleh and Thibodeaux, 2008; Task et al., 2012).The parameter sensitivity analyses were limited to the cell fatedecision rates and did not include analysis of parameters suchas plating efciency during subculture or time spent in thedifferent differentiation phases. While these are also impor-tant factors in determining overall differentiation efciencyand could be investigated using a similar approach, wespecically focused on cell fate decisions for insight intowhich of these cellular processes were most integralto differentiation efciency and, potentially, scale-upapplications.For two distinct epithelial differentiation protocols, we

identied which cell fate processes may be bottlenecks to thedifferentiation process, and therefore should be targeted forimprovement in epithelial cell yield. Others have also targetedbottlenecks of stem cell differentiation processes to improvedifferentiation efciency or yield. For example, in an elegant



study, Ungrin et al. (2012) identied a parameter represent-ing cell yield loss and specically targeted this parameter toimprove efciency of denitive endoderm progenitors fromhPSCs. The use of ROCK inhibitor, Y27632, to prevent thisyield loss due to cell death resulted in a 36-fold increase incell yield. In another set of studies, embryoid bodies (EBs)derived from hESCs in porous alginate scaffolds wereshown to have twofold better viability and reported betterproliferation in a slow turning lateral vessel bioreactorcompared to EBs in static culture (Gerecht-Nir et al.,2004a,b). These studies illustrate how microenvironmentalchanges facilitated improvement in overall cell yield viachanges in cell fate decision rates or efciency.

The output generated from the approach described herecould be used for bioreactor design for large-scale differenti-ation processes. Additionally, the analysis performed in thisstudy could also be applied to small or scalable bioreactorsfor hPSC growth and differentiation (Cameron et al., 2006;Cme et al., 2008; Fernandes et al., 2009; Gerecht-Niret al., 2004a,b; Kehoe et al., 2010; Krawetz et al., 2010; Lock

and Tzanakakis, 2009; Nie et al., 2009; Niebruegge et al., 2009;Oh et al., 2009; Shafa et al., 2012). Further experimentationto determine actual technical feasibility of scaling-up (i.e.,applicability of scalable stem cell culture technology such asmicrocarriers (Jing et al., 2010; Tang et al., 2012; Wilson andMcDevitt, 2013) to facilitate differentiation and expansion)is out of the scope of this study, yet is equally crucial tolarge-scale bioreactor design.

The authors acknowledge the University of Wisconsins CarboneCancer Center Flow Cytometry Laboratory for the use of theirservices. This work was supported by National Science FoundationGrant CBET-1066311 (S.P.P.), a University of Wisconsin Stem Celland Regenerative Medicine Predoctoral Fellowship (J.A.S.), and aNational Institutes of Health training grant NIDCD T32 DC009401(J.A.S.).

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Lab-scale hPSC dierenaon system

Disnguish mulple cell subtypes using markers

Develop ODE model to represent kinecs of each cell subtype in each phase

Compartmentalize system into phases (each dened by specic microenvironment)

Fit models to data by esmang cell fate

decision rate constants

Model renement

Perform sensivity analysis on each rate constant

Idenfy liming cell fate decisions (i.e. those that have the greatest impact on overall yield)

Monitor dynamics of each cell subtype in each phase

Compare scalability of mulple dierenaon

strategies

Target appropriate cell states for expansion

and scale-up

Large-scale hPSC dierenaon system design

Alter microenvironment to improve specic cell

fate decision rates

Figure 8. Schematic representing an approach to investigating efficiency and scalability of laboratory-scale hPSC differentiation protocols. Gray boxes represent the strategyoutlined throughout this study to bridge the gap between laboratory differentiation systems and bioprocess design and improvements.


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