Abstract
Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.
Highlights
When cells are unable to adhere to the extracellular matrix (ECM), they modify their shape and squeeze through the ECM pores by using the amoeboid migration, which is very efficient—rapid cell locomotion—and it is observed in cells such as neutrophils and T cells (Beauchemin et al, 2007; Lämmermann et al, 2008; Swaney et al, 2010)
Whenever cells adhesion to the ECM is high, they degrade the ECM to pass through by using the mesenchymal migration mode, which is very inefficient—cell displacement is very slow—and it is observed in cells such as fibroblast and osteoblasts (Friedl and Wolf, 2010)
We propose to establish a new strategy based on the Bayesian optimization (BO) technique, which combines numerical simulations relied on a mathematical model and in vitro experiments in order to calibrate the model’s parameters
Summary
Cell migration is a fundamental event in a wide variety of physiological processes, spanning from embryogenesis (Knecht and Bronner-Fraser, 2002; Martin and Parkhurst, 2004), angiogenesis (Lamalice et al, 2007; Spill et al, 2015), osteogenesis (Reina-Romo et al, 2012), inflammatory response (Luster et al, 2005), immune response (Bogle and Dunbar, 2010), and wound healing (Shaw and Martin, 2009; Valero et al, 2014a), to develop diseases such as cancer and metastasis formation (Franz et al, 2002; Condeelis et al, 2005; Condeelis and Pollard, 2006).Cell migration can present different characteristics according to the dimensionality in which it is produced. Whenever cells adhesion to the ECM is high, they degrade the ECM to pass through by using the mesenchymal migration mode, which is very inefficient—cell displacement is very slow (cell speed < 1 μm/min)—and it is observed in cells such as fibroblast (wound healing) and osteoblasts (bone formation) (Friedl and Wolf, 2010). This mesenchymal migration mode is investigated in this paper
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