Analysis of Single-Cell Data : ODE Constrained Mixture Modeling and Approximate Bayesian Computation

108 Pages·2016·4.456 MB·English

by  Carolin Loos (auth.)

Carolin Loos
Analysis of
Single-Cell Data
ODE Constrained Mixture
Modeling and Approximate
Bayesian Computation
BestMasters
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Carolin Loos
Analysis of
Single-Cell Data
ODE Constrained Mixture
Modeling and Approximate
Bayesian Computation
Carolin Loos
München, Germany
BestMasters
ISBN 978-3-658-13233-0 ISBN 978-3-658-13234-7 (eBook)
DOI 10.1007/978-3-658-13234-7
Library of Congress Control Number: 2016935216
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Acknowledgements
IwouldliketobeginbyofferingmysincerestgratitudetomysupervisorDr. JanHase-
nauer for his immense support, advice and encouragement, and for truly inspiring my
interest in this field of research. I also gratefully acknowledge Dr. Carsten Marr for
always taking the time to answer my questions and help me with my problems. Fur-
thermore, I would like to thank the members of the groups Data-driven Computational
Modeling and Quantitative Single Cell Dynamics for their feedback, explanations and
interesting discussions. I am highly indebted to Prof. Dr. Dr. Fabian Theis for giving
me the opportunity to work on this interesting project at the ICB. It was a pleasure
to explore this fascinating field of research and to write my thesis in such an inspiring
working environment. Last, but not least, I would like to thank my family and friends
fortheircompanyandconstantsupportthroughouttheyears.
CarolinLoos
Abstract
Investigatingcellularheterogeneityisofgreatimportanceforaholisticunderstandingof
biologicalprocessesandisthereforeafocusofsystemsbiology. Thistaskrequiressophis-
ticated models of single-cell data, which in turn need parameter estimation approaches
thatareabletofitthesemodelstogivenmeasurementdata.
The first part of this thesis focuses on using ODE constrained mixture models (ODE-
MMs)fortheanalysisofsingle-cellsnapshotdata. Withthesemodelssubpopulationscan
beidentifiedandeventhesourceofdifferencesbetweensubpopulationscanbedetected.
Weinvestigatethemethod’sapplicabilitytothestudyofthealterationofsubpopulation
response by the cellular environment with novel data of NGF-induced Erk signaling, a
processrelevantinpainsensitization. Weenhancethemethodbyprovidingamechanistic
descriptionofthevariabilityofthesubpopulationsusingmomentequations. Inaddition,
weproposeODE-MMsfortheanalysisofmultivariatemeasurements,whichaccountsfor
correlations among the measurands. Applying our method to artificial data of a con-
version process and to real multivariate data for NGF-induced phosphorylation of Erk
enablesanimprovedinsightintotheunderlyingsystem.
In the second part of this thesis, we study stochastic dynamics of individuals cells that
aremodeledwithcontinuoustimeMarkovchains(CTMCs). Weintroducealikelihood-
free approximate Bayesian computation (ABC) approach for single-cell time-lapse data.
Thismethodusesmultivariatestatisticsonthedistributionofsingle-celltrajectories. We
evaluateourmethodforsamplesofabivariatenormaldistributionandforartificialequi-
libriumandnon-equilibriumsingle-celltime-seriesofaone-stagemodelofgeneexpression.
Inaddition,weassessourmethodbyapplyingittodatageneratedwithparametervari-
ability and to tree-structured time-series data. A comparison with an existing method
usingstatisticsrevealsanimprovedparameteridentifiabilityusingmultivariatestatistics.
In summary, this thesis introduces two novel approaches for the analysis of multivari-
atedatathatcanbeusedtostudycellularheterogeneitybasedonsingle-celldata.
Kurzfassung
Ein tiefgehendes Verst¨andnis fu¨r die Mechanismen von biologischen Prozessen erfordert
die Erforschung der Heterogeneit¨at von Zellpopulationen. Aus diesem Grund bildet die
Untersuchung heterogener Zellpopulationen aktuell einen Forschungsschwerpunkt in der
Systembiologie. Hierfu¨r werden komplexe mathematische Modelle ben¨otigt, welche wie-
derumParametersch¨atzungsmethodenerfordern,dieinderLage,sinddieseModellemit
gegebenenMessdatenzusammenzufu¨hren.
DerersteTeildieserArbeitbefasstsichmitderAnalysevonEinzelzelldaten,fu¨rwelcheje-
weilsdieVerteilungendergemessenenKonzentrationenindenZellenzueinembestimmten
Zeitpunkt gegeben sind. Fu¨r diese Analyse nutzen wir ODE constrained mixture models
(ODE-MMs),sogenannteMischmodelle,welchedurchgew¨ohnlicheDifferentialgleichungen
beschr¨ankt sind. Mit diesen Modellen k¨onnen Subpopulationen innerhalb einer Zellpo-
pulation ermittelt, und sogar die Ursache fu¨r den Unterschied zwischen den Subpopu-
lationen identifiziert werden. Wir verwenden diese Methode erstmals zur Untersuchung
vonVer¨anderungvonSubpopulationsreaktionenaufgrundderZellumgebung.DieseAna-
lyseerfolgtaufneuenDatenfu¨rdiedurchNGFinduziertePhosphorylierungvonErk,ein
fu¨rdieSchmerzsensitivierungrelevanterProzess.WirverbesserndieMethode,indemwir
Momentengleichungenfu¨rdiemechanistischeBeschreibungderSubpopulationenverwen-
den.Daru¨berhinausentwickelnwirODE-MMszurAnalysevonmultivariatenMessungen,
wodurchKorrelationenzwischenMessungenberu¨cksichtigtwerden.WirtestenunsereMe-
thodeanhandvonartifiziellenDateneinesKonversionsprozessesundanhandmultivariater
Messungenfu¨rNGFinduzierteErk-Phosphorylierung.Eszeigtsich,dassunsereMethode
einengenauerenEinblickindaszugrundeliegendebiologischeSystemerm¨oglicht.
ImzweitenTeildieserArbeitanalysierenwirstochastischeDynamikenvonindividuellen
Zellen,welchedurchMarkovketteninstetigerZeitmodelliertwerden.Hierfu¨rstellenwir
eineaufApproximateBayesianComputation(ABC)basierende,Likelihood-freieMethode
zur Parametersch¨atzung von Einzellzellzeitreihen vor. Diese Methode nutzt multivariate
StatistikenaufderVerteilungvonEinzellzelltrajektorien.WirevaluierenunsereMethode
X Kurzfassung
sowohl fu¨r Daten, die durch eine bivariate Normalverteilung generiert wurden als auch
fu¨rartifizielleEinzellzellzeitreiheneineseinstufigenGenexpressionmodells,welchesichin
und außerhalb ihres station¨aren Gleichgewichts befinden. Der Vergleich mit einer exis-
tierenden Method, die Statistiken verwendet, verdeutlicht, dass durch eine multivariate
BetrachtungdieModellparameterbesseridentifiziertwerdenk¨onnen.
Zusammenfassend werden in dieser Arbeit zwei neuartige Methoden zur Analyse von
multivariatenDatenentwickelt.Diesesindgeeignet,umheterogeneZellpopulationenba-
sierendaufEinzelzelldatenzuuntersuchen.
Contents
List of Figures XIII
List of Tables XV
List of Abbreviations XVII
List of Symbols XIX
1 Introduction 1
1.1 ModelingandParameterEstimationforSingle-CellData . . . . . . . . . . 1
1.2 ContributionofthisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Background 5
2.1 ExperimentalData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 ModelingChemicalKinetics . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 ParameterInference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 ODE Constrained Mixture Modeling for Multivariate Data 15
3.1 IntroductionandProblemStatement . . . . . . . . . . . . . . . . . . . . . 15
3.2 AssessmentofODE-MMsUsingNovelDataforNGF-InducedErkSignaling 17
3.3 ModelingVariabilitywithinaSubpopulation . . . . . . . . . . . . . . . . . 25
3.4 SimultaneousAnalysisofMultivariateMeasurements . . . . . . . . . . . . 40
3.5 ApplicationExample: NGF-InducedErkSignaling. . . . . . . . . . . . . . 50
3.6 DiscussionandOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Approximate Bayesian Computation Using Multivariate Statistics 57
4.1 IntroductionandProblemStatement . . . . . . . . . . . . . . . . . . . . . 57
4.2 ExtendedIntroductiontoApproximateBayesianComputation . . . . . . . 59
4.3 ApproximateBayesianComputationwithMultivariateTestStatistics . . . 65
4.4 SimulationExample: Single-CellTime-SeriesofaOne-StageModelofGene
Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74