Nonlocal and local models for taxis in cell migration: a rigorous limit procedure

A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the involved nonlocalities in terms of integral operators applied directly to the gradients of signal-dependent quantities. The proposed approach handles both model types in a unified way and extends the previous mathematical framework to settings that allow for general solution-dependent coefficient functions. The previous forms of nonlocal operators are compared with the new ones introduced in this paper and the advantages of the latter are highlighted by concrete examples. Numerical simulations in 1D provide an illustration of some of the theoretical findings.

BCAP31, a cancer/testis antigen-like protein, can act as a probe for non-small-cell lung cancer metastasis

Non-small-cell lung cancer (NSCLC) represents most of lung cancers, is often diagnosed at an advanced metastatic stage. Therefore, exploring the mechanisms underlying metastasis is key to understanding the development of NSCLC. The expression of B cell receptor-associated protein 31 (BCAP31), calreticulin, glucose-regulated protein 78, and glucose-regulated protein 94 were analyzed using immunohistochemical staining of 360 NSCLC patients. It resulted that the high-level expression of the four proteins, but particularly BCAP31, predicted inferior overall survival. What’s more, BCAP31 was closely associated with histological grade and p53 status, which was verified by seven cohorts of NSCLC transcript microarray datasets. Then, three NSCLC cell lines were transfected to observe behavior changes BCAP31 caused, we found the fluctuation of BCAP31 significantly influenced the migration, invasion of NSCLC cells. To identify the pathway utilized by BCAP31, Gene Set Enrichment Analysis was firstly performed, showing Akt/m-TOR/p70S6K pathway was the significant one, which was verified by immunofluorescence, kinase phosphorylation and cellular behavioral observations. Finally, the data of label-free mass spectroscopy implied that BCAP31 plays a role in a fundamental biological process. This study provides the first demonstration of BCAP31 as a novel prognostic factor related to metastasis and suggests a new therapeutic strategy for NSCLC.

Mathematical Models of Cancer Cell Plasticity

Quantitative modelling is increasingly important in cancer research, helping to integrate myriad diverse experimental data into coherent pictures of the disease and able to discriminate between competing hypotheses or suggest specific experimental lines of enquiry and new approaches to therapy. Here, we review a diverse set of mathematical models of cancer cell plasticity (a process in which, through genetic and epigenetic changes, cancer cells survive in hostile environments and migrate to more favourable environments, respectively), tumour growth, and invasion. Quantitative models can help to elucidate the complex biological mechanisms of cancer cell plasticity. In this review, we discuss models of plasticity, tumour progression, and metastasis under three broadly conceived mathematical modelling techniques: discrete, continuum, and hybrid, each with advantages and disadvantages. An emerging theme from the predictions of many of these models is that cell escape from the tumour microenvironment (TME) is encouraged by a combination of physiological stress locally (e.g., hypoxia), external stresses (e.g., the presence of immune cells), and interactions with the extracellular matrix. We also discuss the value of mathematical modelling for understanding cancer more generally.

Non-local Parabolic and Hyperbolic Models for Cell Polarisation in Heterogeneous Cancer Cell Populations

Tumours consist of heterogeneous populations of cells. The sub-populations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell–cell interactions, i.e. attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell–cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.