The Physics in Biology Modeling Tumor Growth and Angiogenesis

1. The Physics in Biology Modeling Tumor Growth and Angiogenesis Rui Travasso Centro de Física Computacional Universidade de Coimbra

2. Material Properties Superconductivity Superfluidity Turbulence Chaos Life Consciousness Social Relations G. Relativity ? Classical Mech. Number of Particles Quantum Mech. Physics Today Mass galaxy 1040 black hole 1031 1030 Sun 1024 Earth Man 100 dust 10-12 DNA 10-21 atoms 10-27 electrons 10-31

3. Physics in Biology • Physics is needed • Physical processes entangled with biology • Tumor growth • Embryonic development • Consciousness • Interdisciplinary subject • Physics • Biology • Mathematics • Chemistry • Informatics

4. Simple Systems • Liquid membranes • Canham-Helfrish energy • Minimization of energy provided surface and volume constant

5. Curvature Energy Relevant • Influence of changing c0 • Constant: pearling instability • Gradient: tube formation

6. So? • Simple models present rich behavior • Biologically relevant • Mechanical effects are important in cell behaviour • Red blood cells change mechanicalproperties if patient has malaria • Organization of endothelial cells through mechanical adhesion • But • Insight is important but not sufficient • Interdisciplinary study is essential for advance of field

7. Cancer and Physics • Physics important in developing imaging tools for detection andfollowing tumor growth but recently... • Physics may be important for understanding tumor growth • Physics meets Biology meets Chemistry • Mechanical interactions, viscoelasticdynamics, protein diffusion, chemicalreactions, gene regulatory networks, population dynamics, evolution Physics World, June 2010

8. Crescimento de Tumores - Mutações • Fase 1: Mutações genéticas • Genes que regulam processos essenciais • Ciclo celular  Reprodução descontrolada • Sistemas de reparação do DNA e de proteínas • Perda de mecanismo de morte programada

9. Crescimento de Tumores - Tecido • Fase 2: Interacção com o tecido celular • Células cancerígenas inibem células imunitárias • Ou recrutam células imunitárias(que recrutam vasos sanguíneos) • Sobrevivem em condições adversas (ambiente ácido e baixos níveis de oxigénio) Célula Tumoral Célula do sist. imunitário

10. Crescimento de Tumores - Caderinas • Fase 3: “Cadherin switch” • Células interagem com vizinhas através de proteínas da membrana • Caderinas • Mutação deste mecanismo pode levar a altas taxas de proliferação mesmo quando densidade celular alta.

11. Necroticas Quiescentes Proliferativas Zona Necrótica Alta Pressão Reprodução Descontrolada Células Saudáveis Crescimento de Tumores - Esferóides • Fase 4: Células cancerígenas ganham forma: Esferóide • Difusão macroscópica de células • Formação de zonas necróticas • Tumor com diâmetro 1-2 mm

12. M. D. Anderson Cancer Center, Univ. of Texas Crescimento de Tumores - Angiogénese • Tumor necessita nutrientes para crescer • Busca activa de nutrientes • Fase 5: “Angiogenic switch” • Segregação de proteínas que promovem formaçãode novos vasos sanguíneos • Rede vascular aberrante

13. Crescimento de Tumores - Metástase • Fase 6: Metástase • Células cancerígenas entram nacirculação sanguínea • Invasão de regiões saudáveis • Pulmão • Fígado

14. Alguns Tópicos sobre Tumores • Reprodução desregulada de células cancerínenas • Grande diversidade de material genético das células • Maior adaptabilidade • Tumor vive num ambiente que lhe é extremamente hostil • A destruição do hospitaleiro é uma vitória da adaptação. • Infelizmente isso significa a morte do tumor também • Vasos saguíneos frágeis • O tumor sangra • Angiogénesis contínua • O tumor é uma ferida que não sara

15. Understanding Tumors Through Modeling • Effect of pressure inside tumors in affecting circulation • Vessel collapse • Tumor surface instabilities as a function of limitations in transport of nutrients • May lead to phenotypic alterations • Balance between cell-cell adhesion and nutrient delivery • Tumor adaptability and tumorstem cells • Guide treatment • Use of modeling as a tool for predicting patient-specific evolution and treatment of tumors

16. Tumor Modeling • Many models • Review article:Nonlinearity, 23, R1 (2010) • 578 references • Each paper introducesdifferent model for a specific application • Classification of models • Discrete: Cellular automata, Agent based, ... • Continuous: Multiphase, Interface focused, ...

17. Discrete Models • Focus on individual cells • Mutations • Contact forces • Cell division • Movement and growth • Gene regulatory networks • Advantage • Some parameters may be obtained from single cell experiments • Limitations • Challenging to simulate millions of cells • Large number of parameters (which ones are controlling factors?) Shirinifard et al, PLoS One, 4, e7190

18. Continuous Models • Interface focused • Map tumor surface behavior to existing interface models • In general do not include biological details • Multiphase modeling • From mixture theory • Consider different components • Conservation laws (mass, momentum) • Constitutive relations specificfor each component • Thermodynamic consistency • Possibility of including biological processes • Fewer parameters than discrete methods Preziosi et al, J.Math.Biol., 58, 625

19. -1 1  = 1 Phase 1  Phase 2 = -1 f Phase-Field Models • Approach to moving boundary problems • Phases associated with value of f • Interface implies  = 0 • Diffuse interface • Original problem obtained when e→ 0 • Dynamics of f • Can be derived from a free energy F[,] • Non-conserved order parameter: Allen-Cahn equation • Conserved order parameter: Cahn-Hilliard equation

20. Canham-Helfrisch energy Phase separation of elastic phases Phase-field model in tumor growth Dendritic growth Travasso, Castro, Oliveira, Phil. Mag. (2011) Examples

21. Example of Multiphase and Phase-Field • A multiphase model Cristini et al, J.Math.Biol., 58, 723 (2009) Mass balance for each component Momentum conservation Constitutive Relations Incompressibility

22. Example of Multiphase and Phase-Field • Formation of ramified structures • More dramatic at low proliferation rate • Fingering occurs at zero chemotaxis • Instability driven by non-linear mobility Cristini et al, J.Math.Biol., 58, 723 (2009)

23. Therefore... • Phase-Field is focused at the interface • Link between phase-field and multiphase • Further reduction of parameters • Variability of existing phase-field modelslead to possibility of direct applicationin tumor growth • Able to answer questions on the evolutionof tumor size BUT... • Do not include competing populations oftumor cells or mutations • Hybrid models are a possible solution

24. Gerlee, Anderson, J Theor Biol 2007 Tumor Growth - Competition - Evolution • Deregulated proliferation • Mutations • Darwin selection • Metabolism and migration • Anaerobic matabolism • 2 ATP instead of 36 • No need of Oxygen • Produces acid • Helps migration • Prevailing phenotype • Acid resistant Acid

25. Chaplain et al, Annu Rev Biomed Eng 2006 MackLin et al, J Math Biol 2009 Tumor Growth - Angiogenesis Switch - Vascular Phase • The tumor promotes thedevelopment of nearbyvessels to have oxygen • Challenging simulations • Many parameters • Cell based • Continuous • Hybrid

26. Gerhardt et al, Cell (2003) Lee et al, Cell (2007) Angiogenesis • Sprouting of new blood vessels from existing ones • Relevant in varied situations • Morphogenesis • Inflammation • Wound healing • Neoplasms • Diabetic Retinopathy • For tumors • Altered vessel network • Dense, no hierarchical structure • Capillaries are fragile, permeable, with variable diameter • Capillary network carries both nutrients and drugs

27. Gerhardt et al, Cell (2003) Gerhardt et al, Cell (2003) Two types of cells • Tip cells are special • Have filopodia • Follow gradients of VEGF • Produce MMPs which degrade ECM • Construct path • Do not proliferate • Stalk cells • Proliferation regulated by VEGF • Not diggers • Follow tip cell created pathway Agent Based Component Phase-field Component

28. Endothelial cells Pericites, smooth muscle cells… VEGF Meyer et al, Am.J.Path. (1997) Angiogenesis in a Nutshell • Capillaries are constituted by • Endothelial cells • Pericites, muscle cells VEGF weakens capillary wall  Endothelial cells may divide Cells follow VEGF gradient  The first cell is activated and opens way in ECM Cells organize to form lumen Blood flows when capillaries form loops  Blood reorganizes network

29. Ginzburg-Landau free energy Chemical potential Cahn-Hilliard dynamics Surface tension driven, bulk material conservation T The Model • Two equations • Diffusion: concentration of VEGF, T • Phase-Field: order parameter dynamics • Tip cell • Characteristic radius Rc • Perfect Notch signaling • Introduced when T > Tc • Velocity: •  regulates the proliferation and D the chemotaxis The penetration length of T inside the capillary is given by D  = 1 inside capillary  = -1 outside capillary

30. Capillary Cells in hypoxia Simulation • Starting configuration • Capillary close to tissue in hypoxia • Concentration of VEGF at hypoxic cells constant Blood vessel network emerge

31. Low Proliferation High Proliferation Proliferation • Higher proliferation rate leads to thicker and ramified vessels

32. Low Chemotaxis High Chemotaxis Chemotaxis Response • Higher tip cell velocity leads to thinner and more ramified vessels

33. Low VEGF High VEGF VEGF Prodution • Higher production of VEGF leads to more vessels but not thicker vessels Gerhardt et al., Develop. Biol. (2003)

34. low cMMP D high cMMP Th Matrix Metalloproteinase • MMPs implementation: • Heavy VEGF isoforms getbound to matrix if cMMP high • cMMP high in a radius RMMP of tumor cell • Diffusion in function of Th • Formation of thick vessels • Thin vessel merging MMP-9 Inhibition MMP-9 Overexpressed Rodriguez-Manzaneque et al, PNAS (2001)

35. Insight is important but not sufficient • Taxa de proliferação • Dependente do meio (VEGF, Ang-2)? Como? • Propriedades dos tecidos • Tecido como meio viscoelástico • Permeabilidade e elasticidade dos vasos • Metabolismo das células • Possibilidade de respiração anaeróbia? Em que circunstâncias? • Influencia do meio ácido na viabilidade das células • Transporte de proteínas • Reacções químicas • As células tumorais são de diferentes tipos • Dinâmica de populações • Evolução

36. Simulação • Morfogénese • Tumores • Pólipos • Retinopatia termos relevantes in vivo medição exp. de parâmetros previsões decrescimentovascular novas hipótesese experiências Lab in vitro Lab in vivo observaçõesclínicas acompanhamento clínico individualizado Dados Clínicos Interdisciplinaridade • A Física poderá ajudar, mas como um elemento de um esforço interdisciplinar • Integração de técnicas e métodos de diferentes disciplinas

37. Gerhardt et al, Cell (2003) High Pressure Conclusion • Physics required to tackle problems in Biology • New insights • New therapies • Interdisciplinary context • Modeling tumor growth • Variety of modeling techniques • Hybrid models are able to integrate in a continuous description cell based processes essential in tumor growth and angiogenesis • Hybrid model for angiogenesis with phase-field component • Proliferation rate and matrix dependent tip cell velocity regulate capillary network morphology • High production VEGF levels lead to increased vessel density • Bio-avaibility of VEGF determines network

38. A Pretty One