Research lines

My research currently follows four lines. Each one lists a few key papers; the full list is on the Publications page.

1. Epithelial mechanics and rigidity transitions

Epithelial tissues switch between solid-like and fluid-like states, and that switch matters in development, wound healing and the first steps of cancer invasion. I use stochastic vertex models, in which each cell is a polygon whose junctions fluctuate, to find out which cell-level changes control the transition.

With Rubén Pérez-Carrasco I showed that the choice of friction coefficient, usually treated as a technical detail, changes how these models behave at the tissue scale. With Natalia Briñas-Pascual and Victor Manso we found that the clustering of adhesion-deficient cells controls whether an epithelium rigidifies. Experimental collaborators in Portugal and I identified the extracellular matrix and tissue architecture as major determinants of early invasion driven by E-cadherin dysfunction.

Earlier, in the vertebrate neural tube, we found that neuronal differentiation changes how progenitors arrange in the neuroepithelium. My current work asks how different sources of noise (thermal, active and tension fluctuations) affect our ability to anticipate jamming and unjamming transitions.

• Spatial clustering of adhesion-deficient cells controls epithelial rigidity transitions. J. R. Soc. Interface (2026).
• Choice of friction coefficient deeply affects tissue behaviour in stochastic epithelial vertex models. Phil. Trans. R. Soc. B 379, 20230051 (2024). DOI
• No country for old frameworks? Vertex models and their ongoing reinvention to study tissue dynamics. Biophysica 4, 586–603 (2024). DOI
• The ECM and tissue architecture are major determinants of early invasion mediated by E-cadherin dysfunction. Communications Biology 6, 1132 (2023). DOI
• Neuronal differentiation influences progenitor arrangement in the vertebrate neuroepithelium. Development 146, dev176297 (2019). DOI

2. Hybrid and multiscale methods for stochastic reaction-diffusion

Many biological systems contain regions with few molecules or cells, where noise dominates, next to regions crowded enough for deterministic equations. A fully stochastic simulation captures both but becomes too slow at tissue scale, and a continuum description discards the fluctuations that drive the behaviour.

I develop hybrid methods that couple the two descriptions, together with asymptotic and coarse-graining techniques that keep the computational cost under control. The same toolbox lets us study rare events, such as noise-induced escapes from oscillatory states, and the way intrinsic noise reshapes morphogen-controlled genetic switches in the developing neural tube.

• Hybrid methods in reaction-diffusion equations. In The Mathematics of Movement, Springer (2026). DOI · arXiv
• Minimum action path theory reveals the details of stochastic transitions out of oscillatory states. Phys. Rev. Lett. 120, 128102 (2018). DOI
• Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth. J. Comput. Phys. 350, 974–991 (2017). DOI
• Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches. PLoS Comput. Biol. 12, e1005154 (2016). DOI
• Hybrid approaches for multiple-species stochastic reaction-diffusion models. J. Comput. Phys. 299, 429–445 (2015). DOI

3. Tissue competition and travelling waves

When two cell populations share space and nutrients, the winner depends on more than growth rates. I study this competition with stochastic multiscale models and with reaction-diffusion equations, asking when one population invades the other and what sets the speed and shape of the invasion front.

Our recent work shows how competition for a shared resource gives rise to travelling wave patterns in competing tissues. This line connects with my early analytical work on travelling waves in flux-limited reaction-diffusion equations.

• Emergence of travelling wave patterns in resource-mediated tissue competition. Preprint, bioRxiv (2026), under revision.
• Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis. J. Theor. Biol. 407, 161–183 (2016). DOI
• On the analysis of travelling waves to a nonlinear flux-limited reaction-diffusion equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 30, 141–155 (2013). DOI

4. Cancer dynamics, immunotherapy and data-driven inference

Cancer was my entry point into mathematical biology, through models of angiogenesis, tumour growth and the switch between invasion and latency. I now combine stochastic models with parameter inference to study CAR-T cell therapy, with the goal of anticipating toxicities such as cytokine release syndrome and neurotoxicity from the dynamics of the engineered cells.

Inference also runs through my tissue work. With my students I train machine-learning models, including graph neural networks, to recover the mechanical parameters of vertex models from tissue configurations.

• From invasion to latency: intracellular noise and cell motility as key controls of the competition between resource-limited cellular populations. J. Math. Biol. 72, 123–156 (2016). DOI
• Deterministic and stochastic study for a microscopic angiogenesis model: applications to the Lewis lung carcinoma. PLoS ONE 11, e0155553 (2016). DOI
• Mesoscopic and continuum modelling of angiogenesis. J. Math. Biol. 70, 485–532 (2015). DOI