In vitro effects and mathematical modelling of CTCE-9908 (a chemokine receptor 4 antagonist) on melanoma cell survival.

CTCE-9908, a CXC chemokine receptor 4 (CXCR4) antagonist, prevents CXCR4 phosphorylation and inhibits the interaction with chemokine ligand 12 (CXCL12) and downstream signalling pathways associated with metastasis. This study evaluated the in vitro effects of CTCE-9908 on B16 F10 melanoma cells with the use of mathematical modelling. Crystal violet staining was used to construct a mathematical model of CTCE-9908 B16 F10 (melanoma) and RAW 264.7 (non-cancerous macrophage) cell lines on cell viability to predict the half-maximal inhibitory concentration (IC50). Morphological changes were assessed using transmission electron microscopy. Flow cytometry was used to assess changes in cell cycle distribution, apoptosis via caspase-3, cell survival via extracellular signal-regulated kinase1/2 activation, CXCR4 activation and CXCL12 expression. Mathematical modelling predicted IC50 values from 0 to 100 h. At IC50, similar cytotoxicity between the two cell lines and ultrastructural morphological changes indicative of cell death were observed. At a concentration 10 times lower than IC50, CTCE-9908 induced inhibition of cell survival (p = 0.0133) in B16 F10 cells but did not affect caspase-3 or cell cycle distribution in either cell line. This study predicts CTCE-9908 IC50 values at various time points using mathematical modelling, revealing cytotoxicity in melanoma and non-cancerous cells. CTCE-9908 significantly inhibited melanoma cell survival at a concentration 10 times lower than the IC50 in B16 F10 cells but not RAW 264.7 cells. However, CTCE-9908 did not affect CXCR4 phosphorylation, apoptosis,\ or cell cycle distribution in either cell line.

Quantifying assays: inhibition of signalling pathways of cancer.

Inhibiting a signalling pathway concerns controlling the cellular processes of a cancer cell's viability, cell division and death. Assay protocols created to see if the molecular structures of the drugs being tested have the desired inhibition qualities often show great variability across experiments, and it is imperative to diminish the effects of such variability while inferences are drawn. In this paper, we propose the study of experimental data through the lenses of a mathematical model depicting the inhibition mechanism and the activation-inhibition dynamics. The method is exemplified through assay data obtained from an experimental study of the inhibition of the chemokine receptor 4 (CXCR4) and chemokine ligand 12 (CXCL12) signalling pathway of melanoma cells. The quantitative analysis is conducted as a two step process: (i) deriving theoretically from the model the cell viability as a function of time depending on several parameters; (ii) estimating the values of the parameters by using the experimental data. The cell viability is obtained as a function of concentration of the inhibitor and time, thus providing a comprehensive characterization of the potential therapeutic effect of the considered inhibitor, e.g. $IC_{50}$ can be computed for any time point.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

Dynamics of SI epidemic with a demographic Allee effect.

In this paper, we present an extended SI model of Hilker et al. (2009). In the presented model the birth rate and the death rate are both modeled as quadratic polynomials. This approach provides ample opportunity for taking into account the major contributors to an Allee effect and effectively captures species' differential susceptibility to the Allee effects. It is shown that, the behaviors (persistence or extinction) of the model solutions are characterized by the two essential threshold parameters λ0 and λ1 of the transmissibility λ and a threshold quantity µ(∗) of the disease pathogenicity µ. If λ<λ0, the model is bistable and a disease cannot invade from arbitrarily small introductions into the host population at the carrying capacity, while it persists when λ>λ0 and µ<µ(∗). When λ>λ1 and µ>µ(∗), the disease derives the host population to extinction with origin as the only global attractor. For the special cases of the model, verifiable conditions for host population persistence (with or without infected individuals) and host extinction are derived. Interestingly, we show that if the values of the parameters α and ß of the extended model are restricted, then the two models are similar. Numerical simulations show how the parameter ß affects the dynamics of the model with respect to the host population persistence and extinction.

LULU operators and discrete pulse transform for multi-dimensional arrays.

The LULU operators for sequences, that is L(n), U(n) and their compositions, are extended to multidimensional arrays in a way which preserves their essential properties, e.g., consistent separation, total variation and shape preservation. The power of the operators is demonstrated by deriving the discrete pulse transform (DPT), which is a hierarchical decomposition of the input array into pulses. Similar to its 1-D counterpart this transform satisfies a basic consistency property.

Survival motor neuron protein regulates apoptosis in an in vitro model of spinal muscular atrophy.

Progressive spinal muscular atrophy (SMA), the most prevalent hereditary lower motor neuron disease, is caused by mutations in the telomeric copy of the survival of motor neuron (SMN1) gene. Unlike other cells, lower motor neurons cannot tolerate low levels of smn protein. However, it is unclear as to the nature of the cell death involved. There is evidence that lower motor neurons undergo apoptosis in SMA, leading to muscle weakness and wasting. This study investigated whether SMN1 regulation in a motor neuron model affected indices of apoptotic cell death. Decreased smn expression in neuroblastoma hybrid (NSC-34) cell lines by small interfering RNA (siRNA) was demonstrated at the mRNA and protein level. Smn-depleted cells showed elevated caspase-3 activity, decreased cell viability and increased percentage of TUNEL positive cells. Conversely, NSC-34 cell smn overexpression by adenoviral gene transfer decreased staurosporine-induced caspase-3 elevation and mitigated induced cell toxicity as assessed by 3-(4,5-dimethyl thiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) assay. However, increased smn expression by itself did not increase cell viability. These data suggest not only that decreased smn levels increase apoptosis in an in vitro model of SMA, but also that increased smn can protect against neural injury.

Gene transfer of glial cell-derived neurotrophic factor and cardiotrophin-1 protects PC12 cells from injury: involvement of the phosphatidylinositol 3-kinase and mitogen-activated protein kinase kinase pathways.

Gene therapy for neurodegenerative diseases may utilize the expression of neurotrophic factors because of their potential to promote survival and regeneration of injured neuronal cells. Increasing numbers of these factors are being considered for gene transfer, but their specificity and efficacy in neuroprotection are greatly variable. The major aims of this study were to carry out gene transfer of various neurotrophic factors and investigate their mechanisms of action as well as their protective effects on the viability of rat pheochromocytoma (PC12) cells. We used glutamate, S-nitroso-N-acetyl-DL-penicillamine (SNAP), and staurosporine to induce excitatory damage, oxidative stress, and apoptosis, respectively, because these mechanisms are thought to participate in various disease processes leading to degeneration of cells. We utilized adenovirus vectors for efficient gene transfer of trophic factors (glial-cell derived neurotrophic factor [GDNF] and cardiotrophin-1 [CT-1]) or calbindin-D28k. We found that GDNF and CT-1 gene transfers were equally effective in saving PC12 cells from injury, but calbindin expression did not show any beneficial effects. GDNF gene transfer was much more efficient in protecting PC12 cells from damage than direct GDNF administration. The protection by GDNF expression against staurosporine was mediated through both phosphatidylinositol 3-kinase (PI3K) and mitogen-activated protein kinase kinase (MAPK kinase; MEK) pathways, but only the MEK pathway was involved in the protection against SNAP. In contrast, the protective effect of GDNF against glutamate toxicity was independent of these RET-dependent signal transduction pathways.

Increased survival and function of SOD1 mice after glial cell-derived neurotrophic factor gene therapy.

Amyotrophic lateral sclerosis (ALS) is caused by a progressive degeneration of motor neurons. The cause of sporadic ALS is not known, but 1-2% of all cases are familial and caused by mutations in the copper-zinc superoxide dismutase (SOD1) gene. Transgenic SOD1 mice serve as a transgenic mouse model for these cases. Glial cell-derived neurotrophic factor (GDNF) has a potent trophic effect on motor neurons. Clinical trials in which growth factors have been systemically administered to ALS patients have not been effective, owing in part to the short half-life of these factors and their low concentrations at target sites. Gene transfer of therapeutic factors to motor neurons and/or their target cells, such as muscle, may overcome these problems. Previously, we and others have shown that intramuscularly administered adenovirus vector (AVR) results in foreign gene expression not only in muscle cells, but also in relevant motor neurons in the spinal cord, because of retrograde axonal transport. In this study we utilized an AVR to introduce GDNF into muscles of neonatal SOD1 mice. We showed that AVR-mediated GDNF expression delayed the onset of disease by 7 +/- 8 days (mean +/- SD), prolonged survival by 17 +/- 10 days, and delayed the decline in motor functions (as determined on a rotating rod) by 7-14 days. These results demonstrate that gene delivery to muscle and motor neurons has the potential to treat devastating neurodegenerative diseases such as ALS.