MATHEMATICAL MODELING OF CIRCULAR DORSAL RUFFLES AND LAMELLIPODIAL DYNAMICS IN SINGLE AND COLLECTIVE CELL MIGRATION LAI TAN LEI B.Eng.(Hons.),NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NUS GRADUATE SCHOOL FOR INTEGRATIVE SCIENCES AND ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 Acknowledgements Many thanks to the Biophysics Team at the Institute of High Performance Computing for their valuable insights and criticisms of this work, especially my co-supervisor Dr Chiam Keng Hwee, who has been extremely patient and whose guidance has been invaluable. I would also like to thank my collaborators, Mr Zeng Yukai, Mr Leong Man Chun, Dr Vedula Sri Ram Krishna, Asst Prof Koh Cheng Gee, Prof Philip R. LeDuc and Prof Benoit Ladoux who provided the experimental expertise cited in this thesis, and my main supervisor Prof Lim Chwee Teck for his support of my work. Thank you to my beloved family for their continual support these years. Last but not least, my husband who has been very encouraging through these difficult times. i Contents Acknowledgements Summary i vii List of Tables x List of Figures xi List of Abbreviations Introduction and Literature Review xiii 1.1 The impact of cell migration: why study it? . . . . . . . . . . 1.2 Structural ingredients for cell motility . . . . . . . . . . . . . . 1.2.1 Actin, its polymer and associated proteins . . . . . . . 1.2.2 Myosin: powering motility . . . . . . . . . . . . . . . . 1.2.3 Integrins provide the foothold . . . . . . . . . . . . . . 1.3 Achieving single cell motility . . . . . . . . . . . . . . . . . . . 10 1.3.1 Beginning with protrusion: lamellipodium, filopodium, circular dorsal ruffles and blebbing . . . . . . . . . . . 10 1.3.2 Stabilising protrusions with adhesions . . . . . . . . . . 12 ii 1.3.3 Deadhering the rear . . . . . . . . . . . . . . . . . . . . 14 1.3.4 Experimental models used for the study of single cell migration - keratocytes and fibroblasts . . . . . . . . . 15 1.3.5 1.4 1.5 Theoretical models developed for single cell motility . . 17 Collective cell migration . . . . . . . . . . . . . . . . . . . . . 23 1.4.1 Migration in three dimensions (3D) . . . . . . . . . . . 23 1.4.2 Migration of sheets . . . . . . . . . . . . . . . . . . . . 25 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.5.1 Part I: Investigating actin dynamics in circular dorsal ruffles . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5.2 Part II: A mechano-chemical study of lamellipodial dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5.3 Part III: Collective migration on a contrained substrate 31 1.5.4 What have we learnt? . . . . . . . . . . . . . . . . . . 32 1.5.5 Publications . . . . . . . . . . . . . . . . . . . . . . . . 33 Part I: Investigating the effect of substrate stiffness on circular dorsal ruffles through mathematical modeling 2.1 35 Circular dorsal ruffles: overview and biological impact . . . . . 35 iii 2.1.1 2.2 Motivation and objectives . . . . . . . . . . . . . . . . 37 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 37 2.2.1 Preparation and characterization of elastic substrates . 38 2.2.2 Cell culture . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.3 Fluorescent staining and visualization . . . . . . . . . . 39 2.2.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.5 Results from experiments: CDR size is independent of substrate stiffness but CDR lifetime increases with substrate stiffness . . . . . . . . . . . . . . . . . . . . . 41 2.3 Development and results of mathematical model . . . . . . . . 42 2.3.1 Development of mathematical model . . . . . . . . . . 42 2.3.2 Rac-Rho antagonism tunes the level of actin available for stress fibers and CDRs . . . . . . . . . . . . . . . . 58 2.3.3 Negative feedback by WGAP results in actin ring instead of actin patch formation . . . . . . . . . . . . . . 61 2.4 2.3.4 Multiple CDRs spread and merge into a single CDR . . 62 2.3.5 CDR actin propagates as an excitable wave . . . . . . 64 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 iv Part II: Mechanochemical model of lamellipodial dynamics during cell migration 3.1 75 The lamellipodium: experiments and models . . . . . . . . . . 75 3.1.1 Objective of model . . . . . . . . . . . . . . . . . . . . 78 3.2 Model to describe lamellipodial fluctuations . . . . . . . . . . 79 3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 89 3.3.1 Periodic protrusion-retraction cycles observed in simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.3.2 Periodic protrusion-retraction requires sufficiently stiff substrate . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.3.3 Periodic protrusion-retraction requires sufficient activation of integrins . . . . . . . . . . . . . . . . . . . . . 92 3.3.4 Excessive activation of focal adhesions, coupled with stiff substrates, leads to continuous protrusion . . . . . 94 3.3.5 Phase diagram and relation to experimental observations 95 3.3.6 Period of protrusion-retraction cycle is only affected by the time delay in signal propagation . . . . . . . . . . . 98 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Part III: Collective migration of epithelial cells in constrained v environment 4.1 Collective migration of 2D sheets: an introduction . . . . . . . 100 4.1.1 4.2 4.3 100 Objective of study . . . . . . . . . . . . . . . . . . . . 105 Methods and analysis . . . . . . . . . . . . . . . . . . . . . . . 106 4.2.1 Development of Cellular Potts Model . . . . . . . . . . 106 4.2.2 Analysis of results: calculating correlation . . . . . . . 115 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 118 4.3.1 The migration of the cell sheet is stalled by low cellsubstrate adhesion coupled with the absence of cell polarization . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.3.2 Migration velocity and correlated movement are controlled by extent of polarization and geometrical constraints 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Conclusion 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 124 131 Future work: where can we go next? . . . . . . . . . . . . . . 139 References 143 vi Summary Cell motility is a phenomenon that has intrigued scientists for many years. Increasingly, researchers realize the need for quantitative analysis of both the mechanical as well as the biochemical aspects at multiple scales. The objective of this thesis is therefore to use mathematical and computational modeling to quantitatively study several specific processes in cell motility. The reorganization of actin, being the building block of the cell cytoskeleton, is crucial in driving cell movement. A good appreciation of the biochemical nature of actin dynamics is essential in the understanding of cell migration. This was achieved by studying the dynamics of circular dorsal ruffles (CDR), an actin-based structure often seen in growth-factor stimulated migrating cells. The presence of CDRs has been shown to be the precursor to lamellipodia generation and cell motility. Experimentalists have found that the appearance of CDRs is often accompanied by the disappearance of actin-rich stress fibers. While the generation of CDRs can been attributed to the activation of the Rac, stress fibers have been shown to be stabilized by the presence of active Rho. I therefore represented the formation of CDRs, starting from growth factor induced Rac activation interacting with pre-existing Rho and the associated stress fibers, using a system of partial differential equations. The numerical simulation results showed that increasing the substrate stiffness, which led to increased stress fiber formation prior to stimulation, increased the lifetime of the CDR without altering the size of these structures. A simplified model, which involved Rac and a Rac inactivator, showed that vii the dynamics of CDRs can be likened to wave propagation in an excitable medium. The study of CDRs showed that the actin cytoskeleton is highly dynamic, with many proteins regulating its activity. Yet, cell migration cannot be reenacted without considering the interaction of forces that drive motion. An important part of a migrating cell is the lamellipodium, a thin protrusive portion at the front of the migrating cell. I developed a model of lamellipodial dynamics that incorporated actin polymerization and forces exerted on the actin cytoskeleton. Through the use of a stretch-sensitive protein that responded to substrate stiffness, the model showed that the lamellipodium can exhibit periodic protrusion-retraction cycles, continuous protrusion and unstable retraction, depending on the substrate stiffness and the relative amounts of integrin and myosin activation. In particular, periodic behavior similar to that seen in recent experiments can be achieved when the substrate is sufficiently stiff. Studying cell migration is incomplete without looking at how cells move when interacting with one another, which is usually the case in vivo. Therefore, I investigated the collective migration of cells on constrained substrates. Using a lattice-based computational method known as the Cellular Potts Model, I studied the collective migration of cells as a function of the substrate channel width and found that the collective migration velocity decreased with increasing channel width. Analysis of the velocity field showed that the component of the cell velocities perpendicular to the channel’s long axis demonstrated increasing correlation length with channel width whereas the parallel comviii ponent was unaffected. The decrease in velocity as the adhesive substrate channel width was increased was found to be a consequence of the ability of the cell to polarize during motion. This study showed that the study of collective cell migration can reveal long range migratory behaviour within tissues which single cell migration would not elucidate. 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Biophys J, 66:2210–2216, 1994. 190 [...]... front of the cell, therefore regulating directed cell motility The formation and regulation of circular dorsal ruffles will be further investigated in this thesis In another mode of cell protrusion known as blebbing, the cell membrane is pushed outwards by an increase in hydrostatic pressure in the cell, often 11 achieved by increase in contractility in the actin cytoskeleton, also known as the actin cortex,... adenosine triphosphate (ATP), the source of energy in the cell 3 1.2.1 Actin, its polymer and associated proteins Apart from the organelles mentioned above, the cytoplasm of the cell contains a vast array of other proteins and structures which maintain the everyday activities of the cell In cell migration, the skeleton of the cell, known as the cytoskeleton, is arguably the structure in the center of. .. complex and its nucleation promoting factors (NPF) The Arp2/3 complex is made up of seven subunits which activate upon binding to NPFs and the sides of existing actin filaments at an angle of 70◦ [85] This forms a branching network of actin filaments usually seen at the front of migrating cells [1, 16, 15] On the other hand, formins, a separate class of actin-nucleating proteins, do not require pre-existing... which prevents the capping of the barbed ends of the actin filaments and also binds to profilin, therefore increasing the local concentration of actin monomers and heightening the rate of actin polymerization The lamellipodium and filopodia work in concert to generate effective cell protrusion: while the lamellipodium can push a long stretch of the cell membrane and induce growth in a particular direction... implicated in various cellular processes which includes cell migration [136] A study by Suetsugu et al showed that circular dorsal ruffles require the activation of WAVE complexes, which are involved in the activation of Arp2/3 [235] This suggests a possible role for circular dorsal ruffles in affecting actin-based cell migration It is likely that circular dorsal ruffles can tune the level of actin monomers in the... of the Cellular Potts Model setup 108 19 Initial setup of simulations of cell sheet migration 114 20 Experimental setup of MDCK cell sheet migration 117 21 MDCK cell sheet migration when PDMS slab was removed 119 22 Time lapse of CPM simulation of migrating cell sheet 120 23 CPM simulation of collective cell migration 121 24 Cell migration stalls when the cell- substrate... meshwork of actin filaments, microtubules and intermediate filaments, the actin cytoskeleton has been identified as the main player in cell migration The actin cytoskeleton is generated from the actin monomer, which is a 42 kDa globular protein (G-actin) that binds ATP and is highly conserved in the eukaryotic kingdom [193] The polymerization of actin into filamentous structures (F-actin) form the actin cytoskeleton... located Actin elongation is a tightly regulated process which requires coordination among a vast array of actin binding proteins For instance, capping proteins prevent the elongation of actin filaments by blocking the addition of new monomers at the barbed end [264] Gelsolin, on the other hand, can sever actin filaments, therefore regulating the length of actin filaments but at the same time increasing the... filopodium, circular dorsal ruffles and blebbing To successfully create motion of the cell, the different ingredients must assemble at the right locations and at the right time, as illustrated in Figure 3 Cell protrusion at the front can be achieved by a combination of actin-nucleating factors and actin, both monomeric and filamentous Depending on the nucleating proteins present, different types of actin protrusion... localization of Arp2/3 complexes, filopodia can extend and probe the extracellular environment, serving as sensors to provide feedback to the cell in order to guide the direction of cell migration [206] Another interesting phenomenon seen in migrating cells are circular dorsal ruffles, which form ridges on the surface of cells and have been shown to be actin-rich [31] While the exact function of these structures . MATHEMATICAL MODELING OF CIRCULAR DORSAL RUFFLES AND LAMELLIPODIAL DYNAMICS IN SINGLE AND COLLECTIVE CELL MIGRATION LAI TAN LEI B.Eng.(Hons.),NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF. building block of the cell cytoskeleton, is crucial in driving cell movement. A good appreciation of the biochemical nature of actin dynamics is essential in the understanding of cell migration. This. proteins Apart from the organelles mentioned above, the cytoplasm of the cell contains a vast array of other proteins and structures which maintain the everyday activities of the cell. In cell migration,