Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Neural stem cell characteristics affected by oncogenic pathways and in a human motoneuron disease

Neural stem cell characteristics affected by oncogenic pathways and in a human motoneuron disease Stem cells provide the self-renewing cell pool for developing or regenerating organs. The mechanisms underlying the decisions of a stem or progenitor cell to either self-renew and maintain multipotentiality or alternatively to differentiate are incompletely understood. In this thesis work, I have approached this question by investigating the role of the proto-oncogene Myc in the regulatory functions of neural progenitor cell (NPC) self-renewal, proliferation and differentiation. By using a retroviral transduction technique to create overexpression models in embryonic NPCs cultured as neurospheres, I show that activated levels of Myc increase NPC self-renewal. Furthermore, several mechanisms that regulate the activity of Myc were identified. Myc induced self-renewal is signalled through binding to the transcription factor Miz-1 as shown by the inhibited capacity of a Myc mutant (MycV394D), deficient in binding to Miz-1, to increase self-renewal in NPCs. Furthermore, overexpression of the newly identified proto-oncogene CIP2A recapitulates the effects of Myc overexpression in NPCs. Also the expression levels and in vivo expression patterns of Myc and CIP2A were linked together. CIP2A stabilizes Myc protein levels in several cancer types by inhibiting its degradation and our results suggest the same function for CIP2A in NPCs. Our results also support the conception of self-renewal and proliferation being two separately regulated cellular functions. Finally, I suggest that Myc regulates NPC self-renewal by influencing the way stem and progenitor cells react to the environmental cues that normally dictate the cellular identity of tissues containing self-renewing cells. Neurosphere cultures were also utilised in order to characterise functional defects in a human disease. Neural stem cell cultures obtained post-mortem from foetuses of lethal congenital contracture syndrome (LCCS) were used to reveal possible cell autonomous differentiation defects of patient NPCs. However, LCCS derived NPCs were able to differentiate normally in vitro although several transcriptional differences were identified by using microarray analysis. Proliferation rate of the patient NPCs was also increased as compared to NPCs of age-matched control foetuses.

Stem Cell Markers in Cancer: Do They Have Clinical Significance?

In cancer, a subpopulation of malignant cells expresses markers of normal stem cells. These cells have the potential of initiating tumor growth and therefore also tumor recurrence. Thus, these cells are called cancer stem cells. A myriad of markers have been applied to identify these cells, but no single marker can be found exclusively in cancer stem cells. In many types of cancer, clinical recurrence and tumor progression are the main causes of mortality, despite intense oncological treatment. It has been proposed that the presence of cancer stem cells causes this resistance to therapy. The scope of this thesis is to investigate the role of stem cell markers and genes in the clinical setting. Especially, the aim was to elucidate the clinical significance of stem cell markers as novel prognostic and diagnostic tools in cancer. Tumor biopsy material from central nervous system tumors (oligodendroglioma, astrocytoma and glioblatoma), neural crest derived tumors (pheochromocytomas) and oral carcinoma was screened for stem cell markers. Initially, 15 stem cell markers were screened in a test series of gliomas. The markers applied for expanded tumor analyses (in 305 cases of glioma, 42 cases of pheochromocytoma, and 73 cases of oral carcinoma) were BMI-1, Snail, p16, mdm2, and c-Myc. Data on marker expression was compared with clinical and pathological parameters. In gliomas, BMI-1 expression was found in nearly all tumors analyzed, but the frequency of BMI-1 expressing cells was highly variable, ranging from 1 to 100%. In oligodendroglioma, BMI-1 expression was identified as a prognostic marker independent of tumor grade and clinical parameters. In pheochromocytoma, Snail expression was shown to distinguish between the metastatic and non-metastatic forms of the tumor. Snail expression was seen only in metastatic tumors, whereas non-metastatic tumors did not commonly express Snail. Finally, in oral carcinoma, BMI-1 expression was seen in roughly 80% of tumors, and Snail expression was high or very high in all cases. The lack of BMI-1 expression was associated with early relapse in oral carcinoma.

Magnetic resonance microimaging of cancer cell spheroid constructs

BACKGROUND Hydrogel-based cell cultures are excellent tools for studying physiological events occurring in the growth and proliferation of cells, including cancer cells. Diffusion magnetic resonance is a physical technique that has been widely used for the characterisation of biological systems as well as hydrogels. In this work, we applied diffusion magnetic resonance imaging (MRI) to hydrogel-based cultures of human ovarian cancer cells. METHODS Diffusion-weighted spin-echo MRI measurements were used to obtain spatially-resolved maps of apparent diffusivities for hydrogel samples with different compositions, cell loads and drug (Taxol) treatment regimes. The samples were then characterised using their diffusivity histograms, mean diffusivities and the respective standard deviations, and pairwise Mann-Whitney tests. The elastic moduli of the samples were determined using mechanical compression testing. RESULTS The mean apparent diffusivity of the hydrogels was sensitive to the polymer content, cell load and Taxol treatment. For a given sample composition, the mean apparent diffusivity and the elastic modulus of the hydrogels exhibited a negative correlation. CONCLUSIONS Diffusivity of hydrogel-based cancer cell culture constructs is sensitive to both cell proliferation and Taxol treatment. This suggests that diffusion-weighted imaging is a promising technique for non-invasive monitoring of cancer cell proliferation in hydrogel-based, cellularly-sparse 3D cell cultures. The negative correlation between mean apparent diffusivity and elastic modulus suggests that the diffusion coefficient is indicative of the average density of the physical microenvironment within the hydrogel construct.

General properties of electrochemical capacitors

The use of capacitors for electrical energy storage actually predates the invention of the battery. Alessandro Volta is attributed with the invention of the battery in 1800, where he first describes a battery as an assembly of plates of two different materials (such as copper and zinc) placed in an alternating stack and separated by paper soaked in brine or vinegar [1]. Accordingly, this device was referred to as Volta’s pile and formed the basis of subsequent revolutionary research and discoveries on the chemical origin of electricity. Before the advent of Volta’s pile, however, eighteenth century researchers relied on the use of Leyden jars as a source of electrical energy. Built in the mid-1700s at the University of Leyden in Holland, a Leyden jar is an early capacitor consisting of a glass jar coated inside and outside with a thin layer of silver foil [2, 3]. With the outer foil being grounded, the inner foil could be charged with an electrostatic generator, or a source of static electricity, and could produce a strong electrical discharge from a small and comparatively simple device.

The mechanisms of human renal epithelial cell modulation of autologous dendritic cell phenotype and function

Proximal tubule epithelial cells (PTEC) of the kidney line the proximal tubule downstream of the glomerulus and play a major role in the re-absorption of small molecular weight proteins that may pass through the glomerular filtration process. In the perturbed disease state PTEC also contribute to the inflammatory disease process via both positive and negative mechanisms via the production of inflammatory cytokines which chemo-attract leukocytes and the subsequent down-modulation of these cells to prevent uncontrolled inflammatory responses. It is well established that dendritic cells are responsible for the initiation and direction of adaptive immune responses. Both resident and infiltrating dendritic cells are localised within the tubulointerstitium of the renal cortex, in close apposition to PTEC, in inflammatory disease states. We previously demonstrated that inflammatory PTEC are able to modulate autologous human dendritic cell phenotype and functional responses. Here we extend these findings to characterise the mechanisms of this PTEC immune-modulation using primary human PTEC and autologous monocyte-derived dendritic cells (MoDC) as the model system. We demonstrate that PTEC express three inhibitory molecules: (i) cell surface PD-L1 that induces MoDC expression of PD-L1; (ii) intracellular IDO that maintains the expression of MoDC CD14, drives the expression of CD80, PD-L1 and IL-10 by MoDC and inhibits T cell stimulatory capacity; and (iii) soluble HLA-G (sHLA-G) that inhibits HLA-DR and induces IL-10 expression by MoDC. Collectively the results demonstrate that primary human PTEC are able to modulate autologous DC phenotype and function via multiple complex pathways. Further dissection of these pathways is essential to target therapeutic strategies in the treatment of inflammatory kidney disorders.

Electrochemical phase formation (ECPF) and macrogrowth Part I. Hemispherical models

The phenomenological theory of hemispherical growth is generalised to time-dependent nucleation and growth-rates. Special cases, which include models with diffusion-controlled rates, are analysed. Expressions are obtained for small and large time behaviour and peak characteristics of potentiostatic transients, and their use in model parameter estimation is discussed. Two earlier equations are corrected. Numerically calculated transients which are presented exhibit some interesting features such as a maximum preceding the steady state, oscillations and shoulder.