6 papers
Multiscale modelling, analysis and simulation of cancer invasion mediated by bound and soluble enzymes
Mariya Ptashnyk, Chandrasekhar Venkataraman
We formulate a cell-scale model for the degradation of the extra-cellular matrix by membrane-bound and soluble matrix degrading enzymes produced by cancer cells. Based on the micro…
Mathematical models for the EP2 and EP4 signaling pathways and their crosstalk
Alessandra Cambi, Diane S Lidke, Mariya Ptashnyk +2
The G-protein coupled receptors EP2 and EP4 both transduce the signal of the lipid messenger Prostaglandin E2 (PGE2). Changes in the cell response to PGE2 can have important effect…
Trait-structured chemotaxis: Exploring ligand-receptor dynamics and travelling wave properties in a Keller-Segel model
Viktoria Freingruber, Tommaso Lorenzi, Kevin J. Painter +1
A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derive…
Mathematical Modelling of Mechanotransduction via RhoA Signalling Pathways
Sofie Verhees, Chandrasekhar Venkataraman, Mariya Ptashnyk
We derive and simulate a mathematical model for mechanotransduction related to the Rho GTPase signalling pathway. The model addresses the bidirectional coupling between signalling…
Fast numerical solvers for parameter identification problems in mathematical biology
Karolína Benková, John W. Pearson, Mariya Ptashnyk
In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models for pattern evolution within biological proce…
A biased random walk approach for modeling the collective chemotaxis of neural crest cells
Viktoria Freingruber, Kevin J. Painter, Mariya Ptashnyk +1
Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. "Collectiveness" can be promoted by cel…