Dynamics of cell-mediated aggregation Cristóvão Dias Centro de Física Teórica e Computacional, Universidade de Lisboa, Portugal Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Portugal Encontro CIÊNCIA 2017 Lisboa, Portugal 4/Julho/2017

Regenerative Medicine Morphogenesis Genetics 156, 1671 (2000) Wound healing http://www.biophysics.com/healingmodule.php 3D models National Geographics Regenerative Medicine Andrew Pelling (http://www.pellinglab.net)

Scaffolds 3D printing flat substrates self-assembly http://www.wakehealth.edu/ flat substrates Soft Matter 9, 2985 (2013) self-assembly Biomaterials 43, 23 (2015)

Cell-mediated self-assembled scaffolds chitosan particles: 120 micron (diameter) cells: 10-20 micron in the bulk (diameter) and 50 micron flat on the substrate C. A. Custódio, M. T. Cerqueira, A. P. Marques, R. L. Reis, and J. F. Mano, Biomaterials 43, 23 (2015)

Aggregation dynamics particle-based simulations n sites on the surface (n = 6); one site only adheres to one cell; cell-site interaction is attractive; colloid-colloid interaction is repulsive. cell-mediated particle-particle bond Cell adheres to the particle

Aggregation dynamics particle-based simulations Stochastic force Cell/colloid interaction Cell/Cell-colloid interaction Langevin Dynamics:   Stochastic force drag term inter-particle force

Aggregation dynamics particle-based simulations (results) 512 particles total time = 100 Dcell/Dparticle = 10 10 samples particle-based simulations (results) Size of the largest aggregate cell/site ratio

Aggregation dynamics particle-based simulations (results) 512 particles total time = 100 Dcell/Dparticle = 10 10 samples particle-based simulations (results) with and with cell-cell

Particle-cell-particle Aggregation dynamics Free cell mean-field approximation Cell-particle Cell adheres to the particle Particle-cell-particle \dot{C}_0=-k_0C_0P \\ \dot{C}_1=+k_0C_0P-k_1C_1P \\ \dot{C}_2=+k_1C_1P cell-mediated particle-particle bond

Aggregation dynamics mean-field approximation 512 particles total time = 100 Dcell/Dparticle = 10 10 samples mean-field approximation mean field grasps the cell dynamics \dot{C}_0=-k_0C_0P \\ \dot{C}_1=+k_0C_0P-k_1C_1P \\ \dot{C}_2=+k_1C_1P

Aggregation dynamics mean-field approximation k1/k0=1 k1/k0=10-1 bond probability strongly depends on the kinetics for high \Phi \dot{C}_0=-k_0C_0P \\ \dot{C}_1=+k_0C_0P-k_1C_1P \\ \dot{C}_2=+k_1C_1P 5 k1/k0=10-1 k1/k0=10-2

Aggregation dynamics lattice model (without loops)

Aggregation dynamics lattice model (without loops)

Aggregation dynamics lattice model (without loops) without loops all particles belong to the giant component

Future… Spatial correlations competing timescales aggregation dynamics Lattice model Molecular dynamics Spatial correlations competing timescales aggregation dynamics size distribution Aggregates loops diffusion coefficient mechanical properties Proliferation model Cell dynamics adhesion chemotaxis division extrusion

Margarida Telo da Gama Nuno Araújo Gonçalo Antunes Universidade de Aveiro João Mano Catarina Custódio Financial support from the Portuguese Foundation for Science and Technology (FCT) under Contracts nos. EXCL/FIS-NAN/0083/2012.