Czirok, A.

Garay, T.

Hegedus, B.

Szabó, A. (Andras)

Varga, K.

English

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Invasion from a cell aggregate: the roles of active cell motion and mechanical equilibrium1. IntroductionCell invasion from an aggregate into a surrounding extracellular matrix is an important process during development and disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by extracellular matrix filaments, we propose a suitably modified cellular Potts model. By comparing our simulations to a widely used in vitro experimental setup we argue that both the invasion morphology and kinetics is well reproduced for the first few days without assuming cell proliferation or chemotactic guidance within the model. Instead, we consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements. This mechanism can result in highly persistent motion when constrained by an oriented extracellular matrix structure. Furthermore, ensuring proper mechanical relaxation of the aggregate is of key importance to model how cells leave the aggregate and enter the extracellular matrix. [1] Hegedűs B, Marga F, Jakab K, Sharpe-Timms KL, Forgacs G: The interplay of cell-cell and cell-matrix interactions in the invasive properties of brain tumors. Biophysical Journal, 91(7):2708-16, 2006 [2] Szabó A, Varga K, Garay T, Hegedűs B, Czirók A: Invasion from a cell aggregate -- the roles of active cell motion and mechanical equilibrium. Submitted to Physical Biology.[3] Szabó A, Ünnep R, Méhes E, Twal WO, Argraves WS, Cao Y, Czirók A: Collective cell motion in endothelial monolayers. Physical Biology, 7(1):046007, 20102. Experimental observations3. ECM in the Potts 4. Modeling ECM fibers5. Mechanical equilibrium6. Invasion by haptotaxis7. Active cell motion8. Invasion by active motion and haptotaxis9. Outlook: matrix degradation ReferencesInvasion can occur with and without degrading the ECM. In the former case, cells may create tunnels but fail to follow them. When combined with active cell motion, a leading cell degrades the matrix and others follow. Initiating of new sidebranches is determined by the balance between matrix degradation and the persistent cell motion.Image from [2]Repeated experiments in the presence of cell division inhibitor Q50 showed that cell division is not neccessary for the invasive behavior.the speed of invasion was found to be approximately constant (200 μm/day)cells left the aggregates  in multicellular, linear structures, oriented radially outwards. cells with minimal matrix degrading enzyme production were also able to invade the matrix.In this study we focus on the experimental observations of [1]: aggregates of various cell lines were cultured in collagen I gels and were charaterized by their ability to invade the matrix:In our model, the matrix is represented as a static object. Adhesion to the matrix is defined by a surface tension-like parameter, γ, and cell-cell and cell-medium contact parameters are α and β, respectively. Depending on their relative values, these parameters define the behaviour of single cells. Motion of cells is constrained by the ECM: cells stepping onto a matrix site are penalized, thus lessening the probability of these steps. Adhesion parameters define the morphology of a cell aggregate surrounded by an impenetrable ECM. (α=1)Image from [2]Image modified from [2]Image from [2]The random but possibly oriented structure of ECM fibers is constructed using a Markov chain process. This way the matrix geometry is defined by two parameters controling the fiber density and the fiber length. fiber densityfiber lengthDuring invasion, cells enter the gel and adhere to the filaments. As a result, the interface between the cell aggregate and the matrix is depopulated, as the bulk cannot react to the changes fast enough. This leads to the unrealistic separation of the bulk and We introduce additional timesteps between the conventional Monte Carlo steps (MCS) in which the passive forces are allowed to equilibrate the system and drive it to a mechanical equilibrium. For demonstration, we simulate a bulk of cells attached to a slowly moving surface (piston). Cells in mechanical equilibrium follow the piston without changing the overall shape of the aggregate.Piston test: cells follow a moving surface without (A) and with (B) additional steps.Active cell motion in the model is represented by a positive feedback between cell  displacements and cell polarization [3]. We investigated the effect of constrained motion on this mechanism: we simulated the motion of cells in a single cell-wide tunnel and in the unconstrained plane. The comparison of cell displacements showed that the constraint might increase the motion persistence of cells, depending on the characteristic time T needed to change the polarization direction of a cell.Displacement of constrained (solid line) and unconstrained (dotted line) cells. By fitting the persistent diffusion formula, the persistece time Tp is determined as the function of T and the geometry. Image from [2]if the matrix is adhesive, cells move into the matrix by haptotaxisthe invasion is driven by a cell density gradient inside the matrixadhesive matrix can organize otherwise non-adhesive cells along the ECM filamentsincreasing cell-cell adhesion smoothens the surface and slows down the invasionthe speed of invasion decreases as the invasion depth increasesImage from [2]repulsive ECMadhesive ECMrepulsive cells adhesive cellsImage modified  from [2]Cell density along invasion axisImage modified from [2]cell invasion speed is constant throughout the simulated time-scales invasion speed is 130 μm/day, comparable with the experimental findingsinvasion is substantially faster than with spontaneously moving cells: cells cover 200 μm over 33h (2000MCS)Cell density along invasion axis10.000 MCSthe matrix. We argue, that this effect is the result of the inherent  effective friction with the CPM grid.GELAGGREGATEAGGREGATEPISTONAGGREGATEPISTON50 MCS 103 MCS 104 MCS0 MCS  1000   3000   5000 0 MCS  1000   3000   5000500 μm2.000 MCS500 μmA. Szabó1,5,6, K. Varga1,2, T. Garay2, B. Hegedűs2,3, A. Czirók1,41Dept. of Biological Physics, Eötvös University, Budapest, Hungary 22nd Dept. of Pathology, Semmelweis University, Budapest, Hungary 3Dept. of Thoracic Surgery, Medical University of Vienna, Vienna, Austria 4Dept. of Anatomy and Cell Biology, University of Kansas Medical Center, Kansas City, KS, USA 5MAC4, Centrum Wiskunde en Informatica, Amsterdam, The Netherlands 6Life Sciences Group, NISB, NCSB

Invasion from a cell aggregate: the roles of active cell motion and mechanical equilibrium

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