Travelling waves in a model of quasi-active dendrites with active spines

Dendrites, the major components of neurons, have many different types of branching structures and are involved in receiving and integrating thousands of synaptic inputs from other neurons. Dendritic spines with excitable channels can be present in large densities on the dendrites of many cells. The recently proposed Spike-Diffuse-Spike (SDS) model that is described by a system of point hot-spots (with an integrate-and-fire process) embedded throughout a passive tree has been shown to provide a reasonable caricature of a dendritic tree with supra-threshold dynamics. Interestingly, real dendrites equipped with voltage-gated ion channels can exhibit not only supra-threshold responses, but also sub-threshold dynamics. This sub-threshold resonant-like oscillatory behaviour has already been shown to be adequately described by a quasi-active membrane. In this paper we introduce a mathematical model of a branched dendritic tree based upon a generalisation of the SDS model where the active spines are assumed to be distributed along a quasi-active dendritic structure. We demonstrate how solitary and periodic travelling wave solutions can be constructed for both continuous and discrete spine distributions. In both cases the speed of such waves is calculated as a function of system parameters. We also illustrate that the model can be naturally generalised to an arbitrary branched dendritic geometry whilst remaining computationally simple. The spatio-temporal patterns of neuronal activity are shown to be significantly influenced by the properties of the quasi-active membrane. Active (sub- and supra-threshold) properties of dendrites are known to vary considerably among cell types and animal species, and this theoretical framework can be used in studying the combined role of complex dendritic morphologies and active conductances in rich neuronal dynamics

Expression of basic fibroblast growth factor, FGFR1 and FGFR2 in normal and malignant human breast, and comparison with other normal tissues.

The expression of basic fibroblast growth factor (bFGF) and two of its receptors, FGFR1 and FGFR2, was detected using the polymerase chain reaction, and quantified by comparison to the relative amount of product obtained following co-amplification of the ubiquitous glyceraldehyde phosphate dehydrogenase transcript. Varying levels were found in the vast majority of both cancer and non-malignant breast biopsies as well as in samples of several other normal human tissues. Significantly less bFGF was present in cancers (P less than 0.0001). Similarly, FGFR2 product was also much less in cancer tissues (P = 0.0078), as was FGFR1 (P = 0.002). FGFR1 levels in cancers tended to be higher in those which were oestrogen receptor positive (P less than 0.06). Amplification of different coding regions showed evidence of variant forms of FGFR1 RNA. Cancers appeared to have a significantly greater proportion of PCR product corresponding to the region between the third immunoglobulin like domain and the tyrosine kinase domain (P = 0.046). Differential expression was observed in breast cell lines, with bFGF in the normal derived HBL100, HBR SV1.6.1 and 184A1 but little or none in ZR-75-1, MCF-7, T47D and MDA-MB-231. FGFR1 was present in most of these but FGFR2 was absent from T47D, MDA-MB-231 and HBL100. ZR-75-1 cells had a marked preponderance of FGFR1 variants lacking part of the coding sequence. Aberrant receptor processing may provide clues concerning the role of FGF's and their potential involvement in malignancy

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem

Transcripts for transforming growth factors in human breast cancer: clinical correlates.

The levels of mRNA for transforming growth factors (TGF alpha and beta) and the epidermal growth factor receptor (EGFR) were determined in 69 human breast carcinomas and 20 biopsies of non-neoplastic breast tissue by dot blot hybridisation analysis. TGF alpha mRNA was detected in 42% of cancers and 44% of non-neoplastic breast tissue at low levels. TGF beta mRNA was found in all breast cancers and non-neoplastic breast tissues, but the levels of TGF beta mRNA were found to be higher in breast cancers (P = 0.01). EGFR mRNA was detected in 55% of breast cancers and in all non-neoplastic breast tissue tested. The presence of EGFR mRNA was inversely related to oestrogen receptor (ER) status (P = 0.0001). Coexpression of TGF alpha and EGFR was observed in 28% of the carcinomas, and significantly more commonly in ER negative tumours (P = 0.01). No significant relationship was found between histological grade, tumour cellularity or tumour desmoplasia and expression of either the TGFs or of EGFR mRNA. High levels of TGF beta were, however, associated with the absence of lymph node metastases at presentation (P = 0.05). Levels of TGF alpha and beta and EGFR mRNA were analysed in relationship to the relapse-free and overall survival of patients with breast cancer, but none was found to predict significantly the outcome in these patients. Longer clinical follow-up and larger numbers of patients are required to determine whether TGFs will prove a useful marker for prognosis in breast cancer patients

Robustness and Enhancement of Neural Synchronization by Activity-Dependent Coupling

We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the coupling between neurons produces enlarged frequency locking zones and results in synchronization that is more rapid and much more robust against noise than classical synchronization arising from connections with constant strength. We also present a simple discrete map model that demonstrates the generality of the phenomenon.Comment: 4 pages, accepted for publication in PR

Nicastrin and Notch4 drive endocrine therapy resistance and epithelial to mesenchymal transition in MCF7 breast cancer cells

Introduction Resistance to anti-estrogen therapies is a major cause of disease relapse and mortality in estrogen receptor alpha (ERα)-positive breast cancers. Tamoxifen or estrogen withdrawal increases the dependence of breast cancer cells on Notch signalling. Here, we investigated the contribution of Nicastrin and Notch signalling in endocrine-resistant breast cancer cells. Methods We used two models of endocrine therapies resistant (ETR) breast cancer: tamoxifen-resistant (TamR) and long-term estrogen-deprived (LTED) MCF7 cells. We evaluated the migratory and invasive capacity of these cells by Transwell assays. Expression of epithelial to mesenchymal transition (EMT) regulators as well as Notch receptors and targets were evaluated by real-time PCR and western blot analysis. Moreover, we tested in vitro anti-Nicastrin monoclonal antibodies (mAbs) and gamma secretase inhibitors (GSIs) as potential EMT reversal therapeutic agents. Finally, we generated stable Nicastrin overexpessing MCF7 cells and evaluated their EMT features and response to tamoxifen. Results We found that ETR cells acquired an epithelial to mesenchymal transition (EMT) phenotype and displayed increased levels of Nicastrin and Notch targets. Interestingly, we detected higher level of Notch4 but lower levels of Notch1 and Notch2 suggesting a switch to signalling through different Notch receptors after acquisition of resistance. Anti-Nicastrin monoclonal antibodies and the GSI PF03084014 were effective in blocking the Nicastrin/Notch4 axis and partially inhibiting the EMT process. As a result of this, cell migration and invasion were attenuated and the stem cell-like population was significantly reduced. Genetic silencing of Nicastrin and Notch4 led to equivalent effects. Finally, stable overexpression of Nicastrin was sufficient to make MCF7 unresponsive to tamoxifen by Notch4 activation. Conclusions ETR cells express high levels of Nicastrin and Notch4, whose activation ultimately drives invasive behaviour. Anti-Nicastrin mAbs and GSI PF03084014 attenuate expression of EMT molecules reducing cellular invasiveness. Nicastrin overexpression per se induces tamoxifen resistance linked to acquisition of EMT phenotype. Our finding suggest that targeting Nicastrin and/or Notch4 warrants further clinical evaluation as valid therapeutic strategies in endocrine-resistant breast cancer

Spearhead Nanometric Field-Effect Transistor Sensors for Single-Cell Analysis.

Nanometric field-effect-transistor (FET) sensors are made on the tip of spear-shaped dual carbon nanoelectrodes derived from carbon deposition inside double-barrel nanopipettes. The easy fabrication route allows deposition of semiconductors or conducting polymers to comprise the transistor channel. A channel from electrodeposited poly pyrrole (PPy) exhibits high sensitivity toward pH changes. This property is exploited by immobilizing hexokinase on PPy nano-FETs to give rise to a selective ATP biosensor. Extracellular pH and ATP gradients are key biochemical constituents in the microenvironment of living cells; we monitor their real-time changes in relation to cancer cells and cardiomyocytes. The highly localized detection is possible because of the high aspect ratio and the spear-like design of the nano-FET probes. The accurately positioned nano-FET sensors can detect concentration gradients in three-dimensional space, identify biochemical properties of a single living cell, and after cell membrane penetration perform intracellular measurements