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

Lineshape in Quantum Cascade Lasers - Temperature, Screening and Broadening

This dissertation deals with the optical properties of Quantum Cascade Lasers (QCLs). Studies are performed using transport calculations employing the theory of Non-Equilibrium Green's Functions, and screening is studied within the Random Phase Approximation. Focus is put on the temperature dependent effects in THz QCLs. After a popular science summary and a presentation and discussion of the theory and the methods used in this work, five original papers are presented. Paper I investigates the evolution of the optical spectra as a function of bias for a mid-infrared QCL. It is found that most spectral features can be explained by a shift of the electrons from the active region to the injection region of the laser. Paper II investigates the gain spectra of a THz QCL for increasing temperature. It is found that increased broadening, with constant population inversion, decrease the peak gain at low temperatures. The increased broadening is addressed to enhanced scattering due to reduced screening at elevated temperatures. Paper III investigates the impact of acoustic phonon scattering on the gain spectra for THz QCLs. It is found that at the temperatures of interest, acoustic phonon scattering has a marginal effect on the gain properties of THz QCLs. In Paper IV different aspects of the gain spectra are summarized with focus on the theoretical description using Non-Equilibrium Green's Functions and density matrix theory. Here, the focus lies on dispersive gain and correlations effects. Paper V investigates how the subband structure and the different subband temperatures affect screening. If is found that screening has a strong impact on scattering for increasing temperature, and that isotropic Debye screening is an excellent approximation for THz QCLs at temperatures of interest

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

Temperature Dependence and Screening Models in Quantum Cascade Structure

Different screening models in quantum cascade lasers are compared by calculating the contribution of intra-subband impurity scattering to the optical linewidth as a function of temperature. We find a strong impact of impurity scattering which is increasing substantially with temperature. A simple isotropic bulk screening model works well if the screening length is of the order or longer than the period length of the cascade structure.Comment: 7 pages, 9 figure

Temperature dependence of the gain profile for THz quantum cascade lasers

We study the rapid decrease of peak gain in resonant-phonon THz Quantum Cascade Lasers with increasing temperature. The effect of various microscopic scattering processes on the gain profile as a function of temperature is discussed. We argue that increased broadening, prim arily due to increased impurity scattering, and not diminishing population inversion, is the main reason for the reduction of peak gain

Evaluation of TH-Cre knock-in cell lines for detection and specific targeting of stem cell-derived dopaminergic neurons

The focal and progressive degeneration of dopaminergic (DA) neurons in ventral midbrain has made Parkinson's disease (PD) a particularly interesting target of cell-based therapies. However, ethical issues and limited tissue availability have so far hindered the widespread use of human fetal tissue in cell-replacement therapy. DA neurons derived from human pluripotent stem cells (hPSCs) offer unprecedented opportunities to access a renewable source of cells suitable for PD therapeutic applications. To better understand the development and functional properties of stem-cell derived DA neurons, we generated targeted hPSC lines with the gene coding for Cre recombinase knocked into the TH locus. When combined with flexed GFP, they serve as reporter cell lines able to identify and isolate TH+ neurons in vitro and after transplantation in vivo. These TH-Cre lines provide a valuable genetic tool to manipulate DA neurons useful for the design of more precise DA differentiation protocols and the study of these cells after transplantation in pre-clinical animal models of PD

Systems approaches and algorithms for discovery of combinatorial therapies

Effective therapy of complex diseases requires control of highly non-linear complex networks that remain incompletely characterized. In particular, drug intervention can be seen as control of signaling in cellular networks. Identification of control parameters presents an extreme challenge due to the combinatorial explosion of control possibilities in combination therapy and to the incomplete knowledge of the systems biology of cells. In this review paper we describe the main current and proposed approaches to the design of combinatorial therapies, including the empirical methods used now by clinicians and alternative approaches suggested recently by several authors. New approaches for designing combinations arising from systems biology are described. We discuss in special detail the design of algorithms that identify optimal control parameters in cellular networks based on a quantitative characterization of control landscapes, maximizing utilization of incomplete knowledge of the state and structure of intracellular networks. The use of new technology for high-throughput measurements is key to these new approaches to combination therapy and essential for the characterization of control landscapes and implementation of the algorithms. Combinatorial optimization in medical therapy is also compared with the combinatorial optimization of engineering and materials science and similarities and differences are delineated.Comment: 25 page

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

Tissue-specific regulatory elements in mammalian promoters

Transcription factor-binding sites and the cis-regulatory modules they compose are central determinants of gene expression. We previously showed that binding site motifs and modules in proximal promoters can be used to predict a significant portion of mammalian tissue-specific transcription. Here, we report on a systematic analysis of promoters controlling tissue-specific expression in heart, kidney, liver, pancreas, skeletal muscle, testis and CD4 T cells, for both human and mouse. We integrated multiple sources of expression data to compile sets of transcripts with strong evidence for tissue-specific regulation. The analysis of the promoters corresponding to these sets produced a catalog of predicted tissue-specific motifs and modules, and cis-regulatory elements. Predicted regulatory interactions are supported by statistical evidence, and provide a foundation for targeted experiments that will improve our understanding of tissue-specific regulatory networks. In a broader context, methods used to construct the catalog provide a model for the analysis of genomic regions that regulate differentially expressed genes