Cell-based modeling of angiogenic blood vessel sprouting

Transcription

1 Cell-based modeling of angiogenic blood vessel sprouting Roeland Merks Biomodeling & Biosystems Analysis Centrum Wiskunde & Informatica - Life Sciences Netherlands Institute for Systems Biology Netherlands Consortium for Systems Biology

2 Angiogenesis Growth of new blood vessels Wound healing, tumor growth, etc. Source: Genentech

3 Controlling angiogenesis Tumor growth Stop (or normalize) blood vessel growth Wound healing Stimulate blood vessel growth: promote healing Tissue engineering Build blood vessels: blood supply is key to growing large organs in vitro

4 State-of-the-art: intercepting signals Therapies inhibit the signals that tumors secrete Limited success. Why? Mechanisms are poorly understood Blood vessel growth is a multiscale process Too much focus on the molecules: cells build blood vessels Our approach: Systems biology Computer models and lab experiments can unravel angiogenesis mechanistically Identify controlling factors of system

5 Simplified experimental system Human umbilical vein endothelial cells (HUVEC) in Matrigel Movie: courtesy Luigi Preziosi, Politecnico di Torino, Italy

6 Hypothesis: Chemotaxis (Gamba et al. 2003; Serini et al., 2003) Observation: cells migrate to higher concentrations of cells

7 Cell-based modeling (Merks and Glazier, Phys. A 2005) Input at microscale: behavior of endothelial cells (EC) Output at macroscale: Emergent tissue shapes and patterns Change in cell behavior alters tissue shape Cell-based models analyze: How cells build blood vessels How tissue structure feeds back on cell behavior

8 How much detail is required? 1.How does genetics regulate cell behaviors? 2.How do collective cell behaviors follow from behaviors of individual cells?

9 How much detail is required? 1.How does genetics regulate cell behaviors? 2.How do collective cell behaviors follow from behaviors of individual cells?

10 How much detail is required? 1.How does genetics regulate cell behaviors? 2.How do collective cell behaviors follow from behaviors of individual cells? Experiments in cell cultures and in vivo Cell-based, computational modeling

11 Cell-based simulation methods!"#$%&'()*+",%& -.%+"(%&'()*+",%& 76"#+8()*+",%&1 8-)118()*+",%&1 /)++",&'0)1&2 344'%)++",& 5%%"(16" #2)*:8()*+",%&1 Membrane movements and cell shape are crucial Multi-particle method required

12 Multi-particle, lattice-based method Cellular Potts Model (Graner and Glazier, 1992; Glazier and Graner, 1993) Cellular automata model: cells live on grid A cluster of CA sites represents the biological cell Metropolis algorithm: Generalized energy represents balance of forces in cell community: cell size, cell adhesion, chemotaxis, etc. Cells attempt to copy their state into neighboring sites: accepted if copy reduces energy

13 Derives from Ising spin model Cellular Potts Model ( Lattice of spins σ( x) σ( x) [0,n] with n number of cells (each spin identifies a bio-cell) H defines cell behaviors Each cell has a type τ; identifies parameter set defining a biological cell type J: diagonal matrix of adhesion energies x, x ': pair of adjacent lattice sites Area/volume constraint:, actual area; A σ, resting area, cell elasticity a σ λ

14 Derives from Ising spin model Cellular Potts Model ( Lattice of spins σ( x) σ( x) [0,n] with n number of cells (each spin identifies a bio-cell) H defines cell behaviors Each cell has a type τ; identifies parameter set defining a biological cell type J: diagonal matrix of adhesion energies x, x ': pair of adjacent lattice sites Area/volume constraint:, actual area; A σ, resting area, cell elasticity a σ λ

15 Cellular Potts Model Cell adhesion Volume conservation

16 Cellular Potts Model Pick random site Cell adhesion Volume conservation

17 Cellular Potts Model Pick random neighbor Cell adhesion Volume conservation

18 Cellular Potts Model Consider energy change ΔH if we accepted this copying Cell adhesion Volume conservation

19 Cellular Potts Model ΔH < 0? Accept always Cell adhesion Volume conservation

20 Cellular Potts Model ΔH > 0? Accept with Cell adhesion Volume conservation

21 Cellular Potts Model Repeat Cell adhesion Volume conservation

22 Homotypic adhesion (yellow adheres to yellow, red to red)

23 Homotypic adhesion (yellow adheres to yellow, red to red)

24 Initial configuration Sorting Jyellow, yellow = Jred,red < Jyellow, red Mixing Jyellow, red > Jyellow, yellow = Jred,red Engulfment Jyellow, red < Jyellow, medium Jred,medium < Jyellow, medium No cell-cell adhesion Jcell, cell > 2 Jcell, medium

25 Chemotaxis Modify the energy term to bias pseudopod extensions according to chemical gradient (algorithm by Savill and Hogeweg 1997)

26 Chemotaxis Pseudopods extend more likely up chemical gradient µ=100 c(x )=0.5 c(x)=1 H -= 50

27 Chemotaxis Pseudopods extend more likely up chemical gradient µ=100 c(x )=0.5 c(x)=1 H -= 50

28 Chemotaxis Pseudopods extend more likely up chemical gradient µ=100 c(x )=0.5 c(x)=1 H -= 50

29 Chemotaxis Pseudopods retract more likely up chemical gradient µ=100 c(x)=1.0 c(x )=0.5 Savill and Hogeweg, J Theor Biol 1997 H -= 50

30 Chemotaxis Pseudopods retract more likely up chemical gradient µ=100 c(x)=1.0 c(x )=0.5 Savill and Hogeweg, J Theor Biol 1997 H -= 50

31 Chemotaxis Pseudopods retract more likely up chemical gradient µ=100 c(x)=1.0 c(x )=0.5 Savill and Hogeweg, J Theor Biol 1997 H -= 50

32 Cell-based model of endothelial cell behavior Grey-scale indicates chemoattractant concentration chemoattractant concentration isoline Endothelial cell Endothelial cells Probe environment with filopodia Secrete chemoattractants Move up chemoattractant gradients Chemoattractant Diffuses through extracellular matrix Rapidly degrades in ECM

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34 Hypothesis I: cell elongation L 100 µm A 400 µm 2 Merks et al. Dev. Biol. 2006

35 Cell shape suffices for network formation: no chemotaxis required Margriet Palm

36 Hypothesis II: Contact-inhibited motility Cell contact suppresses response to chemoattractant? Context-dependent effect of VEGF (VEGF = growth factor stimulating blood vessel growth) Dejana, Nat. Rev. MCB, 2004

37 Contact-inhibited motility with Erica Perryn, Abbas Shirinifard and James Glazier Indiana University Bloomington and Kansas University Medical Center Merks, Perryn, Shirinifard and Glazier, PLoS Comp. Biol., 2008 Merks & Glazier (2006). Nonlinearity 19, C1-C10

38 Vasculogenesis and sprouting: two sides of the same coin? Same mechanism also drives sprouting Merks & Glazier (2006). Nonlinearity 19, C1-C10 Merks, Perryn, Shirinifard and Glazier, PLoS Comp. Biol., 2008, e

39 Contact-inhibited chemotaxis Buckling instability? A. B. C. A. Only peripheral cells chemotact to center B. Invading surface cells displace interior cells Only possible with contact inhibition C. Resulting pressure pushes peripheral cells further outwards

40 Chemotactic pushing required for buckling instability? Eliminate pushing: extension-only chemotaxis µ=100 c(x )=0.5 c(x)=1 H -= 50

41 Chemotactic pushing required for buckling instability? Eliminate pushing: extension-only chemotaxis µ=100 c(x )=0.5 c(x)=1 H -= 50

42 Chemotactic pushing required for buckling instability? Eliminate pushing: extension-only chemotaxis µ=100 c(x )=0.5 c(x)=1 H -= 50

43 Extension-only chemotaxis Pseudopod retraction energetically neutral µ=100 c(x)=1.0 c(x )=0.5 H -= 0

44 Extension-only chemotaxis Pseudopod retraction energetically neutral µ=100 c(x)=1.0 c(x )=0.5 H -= 0

45 Extension-only chemotaxis Pseudopod retraction energetically neutral µ=100 c(x)=1.0 c(x )=0.5 H -= 0

46 No sprouting T=50

47 Random motility drives sprouting T=200

48 Chemoattractant inhibits pseudopod extension most strongly at concavities At high motility (T): many pseudopod extensions, which the chemical gradients counteracts Gradient is most shallow at convexities Cells at sprout tips move faster than those between branches Note: chemoattractant here also acts as an inhibitor of cell motility!

49 Cell-based models ignore key component: Extracellular matrix (ECM) Extracellular matrix: materials that cells produce Mechanical support Signaling Signals in ECM can be long-lived and long-distance ECM binds chemical signals Cells respond to strains in ECM Mol. Biol. Cell Thus: ECM is key to tissue growth

50 Unraveling cell-ecm interactions starts with simplified system Cells grown on purified matrix endothelial cells isolated from foreskins extracellular matrix blood-vessel-like structure Collaboration with Koolwijk and Van Hinsbergh, VUMC Amsterdam

51 Cell culture model Sprout formation in fibrin Pieter Koolwijk (VUMC)

52 In silico model Stalk cell Tip cell Pressure BM Fibrin Sonja Boas 15/41

53 Basement membrane degradation 16/41 Sonja Boas

54 Basement membrane degradation Tip cell secretes proteolytic enzymes to degrade the basement membrane 16/41 Sonja Boas

55 Cell migration 17/41 Sonja Boas

56 Cell migration Tip cell secretes proteolytic enzymes to degrade fibrin 17/41 Sonja Boas

57 Sprouting in fibrin Sonja Boas

58 3D sprout and lumen 38 Sonja Boas

59 Cell velocity Cells move fastest at optimal ECM concentration Area Cell area Velocity Collagen (ECM) density on substrate Gaudet et al. Biophys J Fibroblasts move fastest at intermediate ECM concentrations Also true for endothelial cells (cf. Yin et al. MSB 2008)

60 Cells also deposit ECM and respond to it ECs secrete and degrade ECM Source of angiogenic factor (VEGF) ECs follow ECM paths of optimal concentration ECs stimulated by VEGF degrade collagen Extracellular matrix (cf. Yin et al. 2008) Josephine Daub Endothelial cells

61 Mechanotaxis Alternative hypothesis for network formation (cf. Manoussaki 1996) cells contract and pull on extracellular matrix, producing strains Perimeter nodes pull on one another; force depends distance resultant force applied to ECM Finite Element model calculates strains in ECM cells follow strains in matrix René van Oers

62 Why use models? Test hypotheses for logical consistency Do you have sufficient knowledge of the system to reconstruct it? Suggests functional role of key genes Input: cell behavior output: blood vessel level Models help design experiments Parameters correspond to key players Sweeps predict controlling handles of system

63 Open questions Several models explain network formation Chemotaxis, crystallization, mechanotaxis What data is needed to choose between mechanisms? Experimental bifurcation analysis E.g., system change after experimental manipulation and corresponding parameter change Precise measurements of cell behavior Quantitative predictions of tissue level properties and time scales

64 Quantifying cell behavior Microfluidics e.g., movement in precisely defined molecular gradients Traction force microscopy displacement due to cell forces can be measured Yin et al. Mol. Sys. Biol Reinhart-King et al. Biophys. J. 2005

65 Multiscale models Filling in the details Genetic networks inside each cells Cell differentiation (e.g. tip cell vs. stalk cell) Will allow us to use the model to guide experimental research Explain sequence of events between change at genetic level, to a change in cell behavior, to a change in collective behavior

66 Acknowledgements Funding: CWI Margriet Palm Sonja Boas Josephine Daub Erik van Dijk Ioana Niculescu VUMC, Amsterdam Pieter Koolwijk Victor van Hinsbergh Indiana University Bloomington Abbas Shirinifard James Glazier New York Medical College Sergey Brodsky Stuart Newman Michael Goligorsky Kansas University Medical Center Erica Perryn Charles D. Little Politecnico di Torino, Italy Luigi Preziosi