Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.PostprintPeer reviewe

Reproducibility of Molecular Phenotypes after Long-Term Differentiation to Human iPSC-Derived Neurons: A Multi-Site Omics Study.

Reproducibility in molecular and cellular studies is fundamental to scientific discovery. To establish the reproducibility of a well-defined long-term neuronal differentiation protocol, we repeated the cellular and molecular comparison of the same two iPSC lines across five distinct laboratories. Despite uncovering acceptable variability within individual laboratories, we detect poor cross-site reproducibility of the differential gene expression signature between these two lines. Factor analysis identifies the laboratory as the largest source of variation along with several variation-inflating confounders such as passaging effects and progenitor storage. Single-cell transcriptomics shows substantial cellular heterogeneity underlying inter-laboratory variability and being responsible for biases in differential gene expression inference. Factor analysis-based normalization of the combined dataset can remove the nuisance technical effects, enabling the execution of robust hypothesis-generating studies. Our study shows that multi-center collaborations can expose systematic biases and identify critical factors to be standardized when publishing novel protocols, contributing to increased cross-site reproducibility.Initiative Joint Undertaking under grant agreement no. 115439, resources of which are composed of financial contribution from the European Union's Seventh Framework Program (FP7/2007-2013) and EFPIA companies' in kind contribution. A.H., S.C., and M.Z.C. were also funded by the NIHR (Oxford BRC). K.M. and A.B. were also supported by the NIHR GOSH BRC

Stability analysis of age-structured population equations by pseudospectral differencing methods

In this paper a numerical scheme to investigate the stability of linear models of age-structured population dynamics is studied. The method is based on the discretization of the infinitesimal generator associated to the semigroup of the solution operator by using pseudospectral differencing techniques, hence following the approach recently proposed in Breda et al. [SIAM J Sci Comput 27(2): 482-495, 2005] for delay differential equations. The method computes the rightmost characteristic roots and it is shown to converge with spectral accuracy behavior

Stability analysis of age-structured population equations by pseudospectral differencing methods

In this paper a numerical scheme to investigate the stability of linear models of age-structured population dynamics is studied. The method is based on the discretization of the infinitesimal generator associated to the semigroup of the solution operator by using pseudospectral differencing techniques, hence following the approach recently proposed in Breda et al. [SIAM J Sci Comput 27(2): 482\u2013495, 2005] for delay differential equations. The method computes the rightmost characteristic roots and it is shown to converge with spectral accuracy behavior