Towards Mechanistic Pharmacodynamic Modeling for Cancer Precision Medicine

Marc R. Birtwistle Associate Professor Department of Chemical and Biomolecular Engineering Clemson University

Western South Carolina AIChE Meeting Greenville, SC 12 Feb 2019 Snapshot of Attrition During Drug Development

808 oral small- molecule compounds at their highest recorded phase of development

Waring et al., Nat Rev Drug Discovery, 2015

Marc R. Birtwistle 2 Simulation is Typically an Integral Component of Design • Example of airplane building – Build many airplanes, see which ones don’t crash? – No! – Sufficient understanding of fluid dynamics and physics allows simulation to screen design ideas • Human biology is far more complex and less understood—even in how to simulate it – Need more basic research o Physiological and pathophysiological mechanisms o Modeling and simulation methods to capture said mechanisms

Marc R. Birtwistle 3 Systems Pharmacology

Drug Model Outcome

1. Modeling

Drug ??? Outcome

2. Simulation

Drug Model ???

3. Control

??? Model Outcome

4 Targeted Therapy was found not to outperform Physician’s Choice

Genomics ≠ Drugs

5 BRAF CRAF BRAF Dabrafenib

MEK MEK Trametinib ERK ERK 6 What More Does Cancer Precision Medicine Need to Consider? One DriverOne TargetOne Drug 1. Systems • Driver may not be a good direct drug target • Drivers interact; 4-7 drivers per tumor (maybe more) 2. Polypharmacology • Multiple driversmultiple targetsmultiple drugs • Most targeted drugs are promiscuous 3. Dynamics • Tumors adapt and evolve on multiple time scales 4. Heterogeneity • Clonal cells show transient resistance • Cancers comprise multiple subclones with different drivers and microenvironments

Marc R. Birtwistle 7 Marc R. Birtwistle 8 Quantitative Systems Pharmacology: Mechanistic Kinetic Modeling of Biochemical Networks ka g g* E-I ki

kbm kdm m I E

E-S P kbp k S dp p dp = k m - k p I E-S-I dt bp dp Stochastic Expression dm = k g*-k m dt bm dm

dg* = k g - k g* dt a i dg = k g*-k g dt i a Marc R. Birtwistle 9 Outline • Mechanistic Models of Cancer Cell Signaling – Formulation, Building, and Training – Stochastic Cell Cycle Entry – Stochastic Cell Death

• Towards Training with Big Pharmacological Data

• Reconstructing Cell Signaling Networks from Perturbation Time Course Data

Marc R. Birtwistle 10 Marc R. Birtwistle 11 Defining Model Scope

Pathways: • RTK-RAS-RAF-MAPK • PI3K-AKT-mTOR • Cell Cycle • p53-DNA Damage

Adapted from Ciriello G et al., Nature Genetics 2013 Model is Composed of Pathway-Specific Models from the Literature

Submodel Origin

• Birtwistle MR et al., MSB 2007 Receptor • Bouhaddou M & Birtwistle MR, Tyrosine Mol Biosys 2014 • Many others

• Birtwistle MR et al., MSB 2007 Proliferation & • Nakakuki T et al., Cell 2010 Growth • Kriegsheim A et al., Nat Cell Bio 2009

DNA Damage • Batchelor E et al., MSB, 2011

• Gerard C & Goldbeter A, PNAS Cell Cycle 2009

• Albeck JG et al., Plos Biology Apoptosis 2008

Expression The standard model System of ordinary differential equations (ODEs) ~800 species and ~2800 reactions A Prettier Picture

EXTRACELLULAR SPACE

CYTOPLASM RECEPTOR DEATH TYROSINE KINASE RECEPTORS EGFR, Erbb2, Erbb3, Erbb4, cMet, PDGFR, FGFR, IGFR, INSR, EGF, HRG, HGF, PDGF, FGF, IGF, Insulin MITOCHONDRIA GROWTH TSC1, TSC2, mTOR, APOPTOSIS Rictor, Raptor, S6K, PROLIFERATION EIF4EBP1, EIF4E, Grb-2, SOS, Cbl, Sprouty, TRAIL ligand, TRAIL Ribosomes Ras, C-Raf, B-Raf, MEK, receptors (DR4-DR5), ERK, cJun, cFos, NF1, Caspases 8/3/6/9, tBID, DUSP6, DUSP1, RSK, IRS, BIM, BAX, Cytochrome C, PLCg, GRP, PI3KC1, PI3KR1, APAF, XIAP, PARP, Flip, PI3K2, PTEN, PDK1, AKT, Bar, Smac, Bad, Bcl2, FOXO, GSK3-β, bCatenin, PUMA, NOXA f cMyc

TRANSLATION DEATH EXPRESSION NUCLEUS and mRNAs TRANSCRIPTION CELL CYCLE f D/E/A/B, CDKs DNA DAMAGE 4/6/2/1, Chk1, p21, ATM, ATR, p53, WIP1, EPIGENETICS p27, E2F, Rb, , MDM2, MDM4, ARF, CDH1, CDC25A, BRCA2, MSH6, MGMT CDC25B, CDC25C, Skp2, Cdc20 DIVISION Model considers 141 genes Single Cells Have Stochastic Response to Drugs

Adapted from Gascoigne and Taylor, Cancer Cell 2008 Cell-to-cell variability: Simulating Stochastic STOCHASTIC g g* mRNA production m f

Transcriptional p f Activators and Repressors SIGNALING

(TARs) DETERMINISTIC Increasing Confidence in Models

INTEGRATED UNIT TESTING UNIT TESTING ANALYSIS Evaluate input-output Evaluate input- Use model to reason behavior of individual output behavior of about biological sub-models model as a whole observations

Cell context: Start with non-transformed MCF10A • Predictable phenotypic behaviors • Few alterations • Extensive literature data and widely studied

Marc R. Birtwistle 17 Unit Testing—Expression: Tailoring Model to Quantitative Expression Context Define “expression context”: 1. GENOME: Gene copy number 2. TRANSCRIPTOME: mRNA levels Post-Initialization 3. PROTEOME: Protein levels Concentration (nM)

PROTEOMICS (Mass Spectrometry) PROTEIN Serum- LEVELS Starved MCF10A Cells TRANSCRIPTOMICS (RNA-seq) mRNA SAMPLE INITIALIZATION LEVELS

GENOMICS* (Sequencing) GENE COPY RUN SIMULATIONS NUMBER*

* Bessette et al., Plos One 2015 Unit Testing – Receptor Tyrosine Kinase (RTK) Ligand-Receptor EGFR ErbB2 ErbB3 ErbB4 Behavior

EGF

HRG

HGF cMET PDGFR FGFR IGFR INSR PDGF

LITERATURE DICTATES Negative cooperativity (n<1) FGF No cooperativity (n=1) Positive cooperativity (n>1)

[Receptor [Receptor Complex] (nM) IGF

INS

[Ligand Dose] Unit Testing – Proliferation & Growth

EGF and Insulin

ERK

Micro-Western Blot ERK AKT

mTOR AKT

mTOR

Experiments by Rick Koch and Anne Marie Barrette Unit Testing Submodel Required Properties for Each Submodel Receptor • Ligand-receptor cooperativity matches experimental observations. Tyrosine Kinase • Receptor trafficking kinetics reflects experimental observations. Proliferation & • Receptor pathway preferences match experimental observations. • Basal activity fluxes through ERK and AKT pathways exist, tailored to the serum-starved state. Growth • Dynamic dose responses of ERK, AKT, and mTOR signaling matches experimental western blot data. Cell Cycle • Cell cycle entry is driven by induction of D mRNA. • Order and timing of cyclin/cdk complexes matches established observations. • Cell cycle duration matches that in MCF10A cells. • Upregulation of p21 arrests the cell cycle. Apoptosis • Robustness against small death signals. • Model exhibits all-or-nothing death response when apoptosis signaling surpasses threshold. • Dose and dynamics of TRAIL-induced extrinsic apoptosis matches experimental observations. • Intrinsic apoptosis signaling responds to interrupted survival signaling and DNA damage induced upregulation of pro-apoptotic proteins. DNA Damage • Convert original delayed differential equations into ordinary differential equations. • p53 dynamics corresponding to single- and double-stranded DNA breaks matches experimental observations. • Rate of DNA damage repair is dependent on levels of repair . • p53 activation dynamics exhibit “digital” and not “analog” behavior, whereby the number of p53 pulses, but not pulse height or width, scales to magnitude of DNA damage. • Etoposide-induced DNA damage is dependent on the cell cycle stage (S-phase). Expression • Model is tailored to genomic, transcriptomic, and proteomic context of MCF10A cells. • Stochastic gene expression is simulated with a computationally efficient algorithm. • Cell-to-cell variability in mRNA and protein levels matches experimental observations. • EIF4E levels possess extrinsic control over the translation rate. • Ribosomes double during the course of one cell cycle. Integrated Unit Testing – Cell Cycle How are synergistic EGF and Insulin signals integrated by the cell?

mitogens kinase inhibitors

PROLIFERATION APOPTOSIS

DEATH

CELL DNA CYCLE DAMAGE

DIVISION chemotherapy Spatiotemporal Dynamics of Signaling?

PC-12 Cells

Sustained ppERK Transient

Adapted from Marshall, Cell, 1995 HEK293 cells

Short times (under 15 min)

Marc R. Birtwistle 24 Integrated Unit Testing – Cell Cycle How are synergistic EGF and Insulin signals integrated by mitogens kinase inhibitors the cell?

Cell Fate Biochemistry PROLIFERATION APOPTOSIS SIMULATIONS EXPERIMENT EGF (μ-western blot) DEATH @6hrs

CELL DNA INS

CYCLE DAMAGE (AU) D Cyclin

EGF+INS DIVISION chemotherapy SIMULATION [CYC A/Cdk2] [CYC @6hrs % Proliferating % Cells EGF+INS EXPERIMENT +MEKi (BrdU incorporation/ Flow cytometry) Cyclin D (nM)D Cyclin @ 24hrs EGF+INS +AKTi

Time (hours) @ 24hrs % Proliferating % Analysis: Prolonged AKT Activation Explains EGF and Insulin S-Phase Synergy

EXPERIMENT (μ-western blot)

E 10nM E 1nM EGF Alone E 0.1nM E 0.01nM

I 1721nM I 17nM Insulin Alone I 1.7nM

ppERK (AU)ppERK I 0.17nM ppAKT (AU) ppAKT

High/High (E/I) High/Low Low/High Combos Low/Low ERK AKT Dynamics Dynamics

26 Inhibitor Time Course Experiments

post GF post GF post GF (~24h post post GF starvation)

0 h ~ 18 h ~42 h add ~66 h Seed cells starve treat cells Inhibitors (24 h post GF harvest cells with GF treatment) cells

ERK Pathway Inhibitor Akt Inhibitor Fold Proliferation Fold Analysis – Cell Cycle: Phospho-ERK levels dictate stochastic cell cycle entry

SIMULATION: In response to EGF + Insulin Initial Levels

Cycling (C) *** Not cycling (NC) ppERK ppERK ppERK (nM)

C NC Time (hours)

* ppAKT ppAKT ppAKT (nM)

C NC Time (hours) Analysis – Cell Cycle: Can Stochastic Cell Cycle Response Be Predicted? In MCF10A cells: 1. Lasso regression Predictors: Total initial protein levels SOS Responses: Cycling or non-cycling  BRaf and CRaf were top hits ERK 2. Train SVM classifier with top hits MEK 3. Test performance of classifier BRaf

Based on total initial protein levels CRaf

NF1

RAS

BRaf & CRaf GRB2 True Positive Rate BRaf only CRaf only ERK & AKT EGFR

False Positive Rate Kim and Bar-Sagi, Nat Rev Mol Cell Bio 2004 1.E+03 1.E+04 1.E+05 1.E+06 Protein (mpc) Emerging logic of integrative S-phase entry control

Marc R. Birtwistle 30 Analysis – Apoptosis: Mechanistic Insight into Drug Synergy

EXPERIMENT SIMULATION Flow Cytometry Data @ 48hrs @ 48hrs Drug Synergy Treatment: E + I

% Death % MCF10A cells in suspension: % Death % % Death %

pBAD BAD Bcl2 Schmelzle et al., PNAS, 2006

Total Phos- Active ppERK ppERK ppAKT BIM ppAKT BIM BIM FOXOnuc Levels MEKi OFF ON Normal Low Low BIM pBIM pFOXO FOXO AKTi ON OFF High High Low Bcl2 MEKi + OFF OFF High Low High Bax APOPTOSIS AKTi

Marc R. Birtwistle 31 Balance between BIM and Bcl2 levels over time predict the induction of intrinsic apoptosis

Initial protein levels vs. time-to-death Treatment with EGF + INS + MEKi + AKTi Treatment with EGF + INS + MEKi + AKTi

Time-to-death 80hrs Frequency 0hrs Cumulative Cumulative BIM sum

Pearson’s r Cumulative sum Bcl2 BIM and Bcl2 as predictors Treatment with TRAIL (1ng/mL and 0.1ng/mL)

Initial levels

True Positive Rate Average for 8 hours Average for 40 hours Cumulative BIM sum

False Positive Rate Cumulative sum Bcl2 Is the Model Predictive in Different Contexts?

Tailoring: Model initialized with mRNAseq data (us) and mutations (literature) from U87 cells.

MCF10A Cells Flow Cytometry Data % Death % Outline • Mechanistic Models of Cancer Cell Signaling – Formulation, Building, and Training – Stochastic Cell Cycle Entry – Stochastic Cell Death

• Towards Training with Big Pharmacological Data

• Reconstructing Cell Signaling Networks from Perturbation Time Course Data

Marc R. Birtwistle 34 Vision for Such Models

• Given a patient, what drug(s) to use? – Precision medicine – Dose and scheduling optimization

• Given a drug, what patient(s) will respond? – Inclusion in or exclusion from clinical trials – What drugs to combine

Marc R. Birtwistle 35 Tailoring the Model to 14 Glioblastoma (GBM) Patients from The Cancer Genome Atlas (TCGA)

Three Promiscuous Kinase Inhibitors or Their Combinations for a Heterogeneous Tumor

Marc R. Birtwistle 36 Modeling Three Promiscuous, Brain-Penetrant Kinase Inhibitors Drug Gene Targets Model Targets k_on (1/s/nM) k_off (1/s) Bosutinib MAP2K1/MAP2K2 MEK 1 288 RPS6KA1/RPS6KA3 RSK 1 1115 PRKCA/PRKCG PKC 1 1567 CHEK1 Chk1 1 1168 FGFR1 Fr 1 2206 IGF1R Ir 1 2285 INSR Isr 1 669 PDGFRA Pr 1 3081 Ibrutinib BRAF Braf 1 1128 EGFR E1 1 18 ERBB3 E3 1 1 FGFR1/FGFR2 Fr 1 707 GSK3B GSK3b 1 2571 IGF1R Ir 1 4882 INSR Isr 1 1326 MTOR mTOR 1 8091 PDPK1 PDK1 1 2448 PIK3CA/PIK3CB/PIK3CD/PIK3CG PI3KC1 1 2039 RAF1 Craf 1 2333 RPS6KA1/RPS6KA3/RPS6KA2 RSK 1 6447 Cabozantinib BRAF Braf 1 2961 EGFR E1 1 864 FGFR1/FGFR2 Fr 1 2153 IGF1R Ir 1 8236 INSR Isr 1 1880 MAP2K1 MEK 1 214 MET MET 1 1 PDGFRA Pr 1 1 PIK3CA PI3KC1 1 1084 PIK3R1 PI3KR1 1 1084 RAF1 Craf 1 1078 37 Results Across Drugs and Patients Apoptosis 1 2 More More

3 Death 4 5 6 7 8

Patients 9 10 11 12 13 14 Less Death BOS IBR CAB BOS+IBR BOS+CAB IBR+CAB

Cell Cycle 1

2 More Cycling 3 4 5 6 7 8

Patients 9 10 11 12 13

14 Less Cycling BOS IBR CAB BOS+IBR BOS+CAB IBR+CAB Marc R. Birtwistle 38 The Cancer Cell Line Encyclopedia (CCLE) and the Cancer Genome Project (CGP) Contain Pharmacogenomic Profiles of Cancer Cell Lines Cancer Cell Lines mRNA Sequencing Microarray, RNAseq CGP CCLE Gene Mutation Analysis e.g. BRAF V600E

Copy Number Variation e.g. EGFR amplification

Drugs Drug Perturbation Studies

CCLE CGP Marc R. Birtwistle 40 Comparing CCLE and CGP— Manual Look at U87 Responses

41 Slope and Area Under Curve Within Shared Dose Range Demonstrate Reasonable Quantitative Agreement

Many cell lines are insensitive to most drugs—IC50 is undefined and not expected to be consistent Bouhaddou et al., Nature, 2016

Marc R. Birtwistle 42 Manual Curation of Binary Sensitivity Suggests Consistency 8 independent people manually determined binary sensitivity for all 2520 shared cell line/drug pairs

Marc R. Birtwistle 43 Outline • Mechanistic Models of Cancer Cell Signaling – Formulation, Building, and Training – Stochastic Cell Cycle Entry – Stochastic Cell Death

• Towards Training with Big Pharmacological Data

• Reconstructing Cell Signaling Networks from Perturbation Time Course Data

Marc R. Birtwistle 44 Marc R. Birtwistle 45 Identifying Uncertain or Context- Specific Structural Aspects of Signaling Networks

F11 F12

x1 x2

F21 F22

Chicken and egg problemcausality when loops are present?

What experimental designs are sufficient to uniquely identify all such edges, their directionality, and some information about their magnitude?

Marc R. Birtwistle 46 Perturbation Time Courses Can Help

Context-Specific Edges

Direct vs. Indirect Effects

What perturbation time courses are sufficient to uniquely identify all such edges, their directionality, and (perhaps) some information about their magnitude?

Can we infer loops, including self-regulation? Marc R. Birtwistle 47 Dynamic Modular Response Analysis

• Requires two perturbations per node (e.g. production and consumption) • Requires estimates of 1st and 2nd time derivatives

Marc R. Birtwistle 48 A Sensible Perturbation Time Course Design Could Be Sufficient F11 F12

x1 x2

F F F21 F22 11 12

dx   1 = f (x (k 1),x (k 1) )  f (x (k),x (k) ) f (x (k),x (k) ) x (k 1) - x (k)  f (x (k),x (k) ) x (k 1) - x (k)  t=tk1 1 1 2 1 1 2 1 1 2 1 1 1 1 2 2 2 dt x1 x2 dx   2 = f (x (k 1),x (k 1)  f (x (k),x (k) ) f (x (k),x (k) ) x (k 1) - x (k)  f (x (k),x (k) ) x (k 1) - x (k)  t=tk1 2 1 2 2 1 2 2 1 2 1 1 2 1 2 2 2 dt x1 x2

F21 F22

Time Series Measurements Stimulus T1 … Tn  y (k)  x (k 1) - x (k) x (k 1) - x (k) F11(k) Initial 1 = 1 1 2 2  ( 2 )   ( 2 ) ( 2 )  F (k) Steady State y1 (k)  x1 (k) - x1(k) x2 (k) - x2 (k)   12 

 y (k)  x (k 1) - x (k) x (k 1) - x (k) F21(k) 2 = 1 1 2 2    (1)   (1 ) (1 )  F (k) y2 (k)  x1 (k) - x1(k) x2 (k) - x2 (k)   22  Perturb: Vehicle Node 1 Node 2 Calculated from Data To Learn Marc R. Birtwistle 49 Practical Implementation

Vehicle Perturb x1 Perturb x2 Single Activator Model x2

F11 = -1 F12 = 0 Stimulus x1 No No Noise

x1 x2

Stimulus Activity F21 = 3 F22 = -1 With Noise With

Time

Analytic Solution d Analytic Solution e Least Squares Solution No Noise 10:1 Signal:Noise 10:1 Signal:Noise Predicted Predicted Predicted

Actual Actual Actual Random Two Node Systems Stimulus Example F F 11 12 Simulated Time x1 x2 Courses

Stimulus F21 F22 Sample Across Values

Marc R. Birtwistle 51 Random Three Node Systems

F11 Stimulus

x1 F21 F31

Stimulus F12 F13 Stimulus

F32 x2 x3

F22 F33 F23

Marc R. Birtwistle 52 Sixteen Different Feedforward Loop Models

10:1 Noise 5:1 Noise 2:1 Noise True Positive Rate

False Positive Rate Fractioncorrect

Feed Forward Loop Structures

Marc R. Birtwistle 53 Remaining Questions

• How does performance scale to larger networks?

• How can we effectively incorporate prior knowledge?

• What about “dirty” perturbations?

Marc R. Birtwistle 54 SINGLE-CELL CANCER SYSTEMS BIOLOGY AND PHARMACOLOGY

Funding Anne Marie Mehdi Barrette –NIH/NIGMS Bouhaddou –R01GM104184 –NIH/NHGRI –LINCS Center (U54HG008098) –NIH/NCI Greg –R21CA196418 Smith

–Glaxo Smith Kline –Roche

www.birtwistlelab.com

Marc R. Birtwistle 55 Predicting Protein Levels from mRNA Levels Estimate Single mi kbpi Assume Ratio per Gene, pi = mi kbp p = kdpi i Single Ratio But Same Across kdp for All Genes Tissues

Data from GTEx and Human Proteome Map for 14 Tissue Types

Alief Moulana, Mehdi Bouhaddou and DeAnalisa Jones, Under Revision 56