Modeling the effect of chemotaxis on glioblastoma tumor progression

Glioblastoma-Astrocyte Connexin 43 Gap Junctions Promote Tumor Invasion

Glioblastoma multiforme (GBM), classified as World Health Organization grade IV astrocytoma, is the deadliest adult cancer of the central nervous system. An important contributing factor to poor survival rates in GBM is extensive invasion, which decreases the efficacy of resection and subsequent adjuvant therapies. These treatments could be markedly improved with increased resolution of the genetic and molecular initiators and effectors of invasion. Connexin 43 (Cx43) is the principal astrocytic gap junction (GJ) protein. Despite the heterogeneity of GBM, a subpopulation of cells in almost all GBM tumors express Cx43. Functional GJs between GBM cells and astrocytes at the tumor edge are of critical interest for understanding invasion. In this study, we find that both in vitro and in ex vivo slice cultures, GBM is substantially less invasive when placed in a Cx43-deficient astrocyte environment. Furthermore, when Cx43 is deleted in GBM, the invasive phenotype is recovered. These data strongly suggest that there are opposing roles for Cx43 in GBM migration. We find that Cx43 is localized to the tumor edge in our ex vivo model, suggesting that GBM-astrocyte GJ communication at the tumor border is a driving force for invasion. Finally, we find that by a Cx43-dependent mechanism, but likely not direct channel-mediated diffusion, miRNAs associated with cell-matrix adhesion are transferred from GBM to astrocytes and miR-19b promotes invasion, revealing a role for post-transcriptional manipulation of astrocytes in fostering an invasion-permissive peritumoral niche. IMPLICATIONS: Cx43-mediated communication, specifically miRNA transfer, profoundly impacts glioblastoma invasion and may enable further therapeutic insight.

Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution

In silico models and computer simulation are invaluable tools to better understand complex biological processes such as cancer evolution. However, the complexity of the biological environment, with many cell mechanisms in response to changing physical and chemical external stimuli, makes the associated mathematical models highly non-linear and multiparametric. One of the main problems of these models is the determination of the parameters’ values, which are usually fitted for specific conditions, making the conclusions drawn difficult to generalise. We analyse here an important biological problem: the evolution of hypoxia-driven migratory structures in Glioblastoma Multiforme (GBM), the most aggressive and lethal primary brain tumour. We establish a mathematical model considering the interaction of the tumour cells with oxygen concentration in what is called the go or grow paradigm. We reproduce in this work three different experiments, showing the main GBM structures (pseudopalisade and necrotic core formation), only changing the initial and boundary conditions. We prove that it is possible to obtain versatile mathematical tools which, together with a sound parametric analysis, allow to explain complex biological phenomena. We show the utility of this hybrid “biomimetic in vitro-in silico” platform to help to elucidate the mechanisms involved in cancer processes, to better understand the role of the different phenomena, to test new scientific hypotheses and to design new data-driven experiments.

Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study

Background

Contemporary biological observations have revealed a large variety of mechanisms acting during the expansion of a tumor. However, there are still many qualitative and quantitative aspects of the phenomenon that remain largely unknown. In this context, mathematical and computational modeling appears as an invaluable tool providing the means for conducting in silico experiments, which are cheaper and less tedious than real laboratory experiments.

Results

This paper aims at developing an extensible and computationally efficient framework for in silico modeling of tumor growth in a 3-dimensional, inhomogeneous and time-varying chemical environment. The resulting model consists of a set of mathematically derived and algorithmically defined operators, each one addressing the effects of a particular biological mechanism on the state of the system. These operators may be extended or re-adjusted, in case a different set of starting assumptions or a different simulation scenario needs to be considered.

Conclusion

In silico modeling provides an alternative means for testing hypotheses and simulating scenarios for which exact biological knowledge remains elusive. However, finer tuning of pertinent methods presupposes qualitative and quantitative enrichment of available biological evidence. Validation in a strict sense would further require comprehensive, case-specific simulations and detailed comparisons with biomedical observations.

Advances for studying clonal evolution in cancer

The "clonal evolution" model of cancer emerged and "evolved" amid ongoing advances in technology, especially in recent years during which next generation sequencing instruments have provided ever higher resolution pictures of the genetic changes in cancer cells and heterogeneity in tumors. It has become increasingly clear that clonal evolution is not a single sequential process, but instead frequently involves simultaneous evolution of multiple subclones that co-exist because they are of similar fitness or are spatially separated. Co-evolution of subclones also occurs when they complement each other's survival advantages. Recent studies have also shown that clonal evolution is highly heterogeneous: different individual tumors of the same type may undergo very different paths of clonal evolution. New methodological advancements, including deep digital sequencing of a mixed tumor population, single cell sequencing, and the development of more sophisticated computational tools, will continue to shape and reshape the models of clonal evolution. In turn, these will provide both an improved framework for the understanding of cancer progression and a guide for treatment strategies aimed at the elimination of all, rather than just some, of the cancer cells within a patient.

Non-Markovian models for migration-proliferation dichotomy of cancer cells: anomalous switching and spreading rate

Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the near-core-outer region, where biased migration away from the tumor spheroid core takes place. We suggest non-Markovian switching between the migrating and proliferating phenotypes of tumor cells. Nonlinear master equations for mean densities of cancer cells of both phenotypes are derived. In anomalous switching case we estimate the average size of the near-core-outer region that corresponds to sublinear growth (r(t)) ~ t(μ) for 0 < μ < 1. In model II we consider the outer zone, where the density of cancer cells is very low. We suggest an integrodifferential equation for the total density of cancer cells. For proliferation rate we use the classical logistic growth, while the migration of cells is subdiffusive. The exact formulas for the overall spreading rate of cancer cells are obtained by a hyperbolic scaling and Hamilton-Jacobi techniques.