Travelling wave analysis of a mathematical model of glioblastoma growth

In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, PLoS Comp. Bio., 8(6) 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered.Comment: Corrected error in the equation for the Jacobia

The Impact of Phenotypic Switching on Glioblastoma Growth and Invasion

The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma tumour is determined by two key factors: the cell proliferation rate and the cell migration speed. At the microscopic level, however, proliferation and migration appear to be mutually exclusive phenotypes, as indicated by recent in vivo imaging data. Here, we develop a mathematical model to analyse how the phenotypic switching between proliferative and migratory states of individual cells affects the macroscopic growth of the tumour. For this, we propose an individual-based stochastic model in which glioblastoma cells are either in a proliferative state, where they are stationary and divide, or in motile state in which they are subject to random motion. From the model we derive a continuum approximation in the form of two coupled reaction-diffusion equations, which exhibit travelling wave solutions whose speed of invasion depends on the model parameters. We propose a simple analytical method to predict progression rate from the cell-specific parameters and demonstrate that optimal glioblastoma growth depends on a non-trivial trade-off between the phenotypic switching rates. By linking cellular properties to an in vivo outcome, the model should be applicable to designing relevant cell screens for glioblastoma and cytometry-based patient prognostics

An improved method for detecting and delineating genomic regions with altered gene expression in cancer

A method is presented for identifying genomic regions with altered gene expression in gene expression maps

Optimal Sparsity Selection Based on an Information Criterion for Accurate Gene Regulatory Network Inference

Accurate inference of gene regulatory networks (GRNs) is important to unravel unknown regulatory mechanisms and processes, which can lead to the identification of treatment targets for genetic diseases. A variety of GRN inference methods have been proposed that, under suitable data conditions, perform well in benchmarks that consider the entire spectrum of false-positives and -negatives. However, it is very challenging to predict which single network sparsity gives the most accurate GRN. Lacking criteria for sparsity selection, a simplistic solution is to pick the GRN that has a certain number of links per gene, which is guessed to be reasonable. However, this does not guarantee finding the GRN that has the correct sparsity or is the most accurate one. In this study, we provide a general approach for identifying the most accurate and sparsity-wise relevant GRN within the entire space of possible GRNs. The algorithm, called SPA, applies a “GRN information criterion” (GRNIC) that is inspired by two commonly used model selection criteria, Akaike and Bayesian Information Criterion (AIC and BIC) but adapted to GRN inference. The results show that the approach can, in most cases, find the GRN whose sparsity is close to the true sparsity and close to as accurate as possible with the given GRN inference method and data. The datasets and source code can be found at https://bitbucket.org/sonnhammergrni/spa/

Прикладна механіка і основи конструювання: навчально-методичний посібник

Розроблено відповідно до навчальної програми і призначено для виконання розрахунково-графічної роботи з дисципліни «Прикладна механіка і основи конструювання» студентам напряму підготовки 6.050202 «Автоматизація та компютерно-ігрегровані технології» денної та заочної форм навчання. Посібник рекомендовано також для самостійної роботи студентів, оскільки він вміщує короткі теоретичні викладки основного матеріалу дисципліни «Прикладна механіка і основи конструювання», умови завдань, приклади їх розв’язування, необхідні довідкові дані

Monotherapy efficacy of blood-brain barrier permeable small molecule reactivators of protein phosphatase 2A in glioblastoma

Glioblastoma is a fatal disease in which most targeted therapies have clinically failed. However, pharmacological reactivation of tumour suppressors has not been thoroughly studied as yet as a glioblastoma therapeutic strategy. Tumour suppressor protein phosphatase 2A is inhibited by non-genetic mechanisms in glioblastoma, and thus, it would be potentially amendable for therapeutic reactivation. Here, we demonstrate that small molecule activators of protein phosphatase 2A, NZ-8-061 and DBK-1154, effectively cross the in vitro model of blood-brain barrier, and in vivo partition to mouse brain tissue after oral dosing. In vitro, small molecule activators of protein phosphatase 2A exhibit robust cell-killing activity against five established glioblastoma cell lines, and nine patient-derived primary glioma cell lines. Collectively, these cell lines have heterogeneous genetic background, kinase inhibitor resistance profile and stemness properties; and they represent different clinical glioblastoma subtypes. Moreover, small molecule activators of protein phosphatase 2A were found to be superior to a range of kinase inhibitors in their capacity to kill patient-derived primary glioma cells. Oral dosing of either of the small molecule activators of protein phosphatase 2A significantly reduced growth of infiltrative intracranial glioblastoma tumours. DBK-1154, with both higher degree of brain/blood distribution, and more potent in vitro activity against all tested glioblastoma cell lines, also significantly increased survival of mice bearing orthotopic glioblastoma xenografts. In summary, this report presents a proof-of-principle data for blood-brain barrier-permeable tumour suppressor reactivation therapy for glioblastoma cells of heterogenous molecular background. These results also provide the first indications that protein phosphatase 2A reactivation might be able to challenge the current paradigm in glioblastoma therapies which has been strongly focused on targeting specific genetically altered cancer drivers with highly specific inhibitors. Based on demonstrated role for protein phosphatase 2A inhibition in glioblastoma cell drug resistance, small molecule activators of protein phosphatase 2A may prove to be beneficial in future glioblastoma combination therapies.Peer reviewe

Network modeling of the transcriptional effects of copy number aberrations in glioblastoma

DNA copy number aberrations (CNAs) are a characteristic feature of cancer genomes. In this work, Rebecka Jörnsten, Sven Nelander and colleagues combine network modeling and experimental methods to analyze the systems-level effects of CNAs in glioblastoma

Increasing the accuracy of glioblastoma subtypes : Factoring in the tumor's cell of origin

The transcriptional classification of glioblastoma has proven to be a complex issue. In the absence of strong correlations between underlying genomic lesions and transcriptional subtype, there is a need to systematically understand the origins of the glioblastoma subtypes. A recent integrated analysis of data from both mouse models and patient-derived cells supports that the glioblastoma's cell of origin is important in shaping transcriptional diversity and tumor cell malignancy

A genomic approach to smooth muscle differentiation and diversity

Smooth muscle cells (SMCs) are a broad class of contractile cells that are found in a number of organs systems, including the vasculature, the urogenital system, the bronchi and the gastrointestinal tract. The two main functions exerted by SMCs are to provide contractile force and to synthesize structural components of the extracellular matrix. SMCs are not terminally differentiated, but have a capacity to adjust their cellular phenotype to meet crucial physiological needs. Examples include repair of blood vessels, and uterine growth during pregnancy. In addition, SMC plasticity may be important in human diseases such as asthma, pre-term delivery, atherosclerosis, and hypertension. A great challenge in smooth muscle biology is therefore to identify molecular mechanisms that mediate SMC phenotypic differences. The aim of the present study is to examine SMC differentiation and diversity in terms of global gene expression. In general terms, we ask how genome sequences and large-scale observations of gene expression patterns together can be used to define and understand SMC differentiation and diversity. Three lines of investigation are followed. First, we examine gene expression patterns of SMC subpopulations using gene chip technology, which results in a transcription atlas of SMC diversity (I, IV). Second, we propose a general approach to the functional and regulatory interpretation of such data, based on the biological concept of gene batteries defined as sets of genes that are co-regulated and functionally linked (II, III). This approach is general, and applicable beyond SMC biology. Third, we use this framework to interpret our exploration of SMC phenotypes, and to postulate regulators of SMC phenotypic diversity (III, IV). We find evidence that that several gene batteries are synchronously regulated during vascular SMC maturation and neointima formation, suggesting that distinct features of the vascular SMC phenotype are encoded by individual gene batteries (IV). Among regulated gene batteries, a lipid metabolism battery and a vascular-selective extracellular matrix battery are found. Regulatory sequence analysis was performed on a whole-genome scale with respect to 266 DNA-binding transcription factors, and results were used to predict cis regulatory elements of importance for gene batteries and vascular SMC marker genes (III, IV). Specific findings include novel SMC differentiation markers, including LPP, a potential SMC-selective transcriptional regulator (II). In summary, the work provides a genomic formulation of the SMC differentiation and diversity problem, and proposes a model for the SMC phenotype which is based on explicitly defined groups of genes