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

Limits and dynamics of stochastic neuronal networks with random heterogeneous delays

Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the delays distributions, a quenched or averaged propagation of chaos takes place in these networks, and that the network equations converge towards a delayed McKean-Vlasov equation with distributed delays. Our approach is mostly fitted to neuroscience applications. We instantiate in particular a classical neuronal model, the Wilson and Cowan system, and show that the obtained limit equations have Gaussian solutions whose mean and standard deviation satisfy a closed set of coupled delay differential equations in which the distribution of delays and the noise levels appear as parameters. This allows to uncover precisely the effects of noise, delays and coupling on the dynamics of such heterogeneous networks, in particular their role in the emergence of synchronized oscillations. We show in several examples that not only the averaged delay, but also the dispersion, govern the dynamics of such networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and clarified a regularity hypothesis (remark 1

Clinical translation of [18F]ICMT-11 for measuring chemotherapy-induced caspase 3/7 activation in breast and lung cancer

Background: Effective anticancer therapy is thought to involve induction of tumour cell death through apoptosis and/or necrosis. [18F]ICMT-11, an isatin sulfonamide caspase-3/7-specific radiotracer, has been developed for PET imaging and shown to have favourable dosimetry, safety, and biodistribution. We report the translation of [18F]ICMT-11 PET to measure chemotherapy-induced caspase-3/7 activation in breast and lung cancer patients receiving first-line therapy. Results: Breast tumour SUVmax of [18F]ICMT-11 was low at baseline and unchanged following therapy. Measurement of M30/M60 cytokeratin-18 cleavage products showed that therapy was predominantly not apoptosis in nature. While increases in caspase-3 staining on breast histology were seen, post-treatment caspase-3 positivity values were only approximately 1%; this low level of caspase-3 could have limited sensitive detection by [18F]ICMT-11-PET. Fourteen out of 15 breast cancer patients responded to first–line chemotherapy (complete or partial response); one patient had stable disease. Four patients showed increases in regions of high tumour [18F]ICMT-11 intensity on voxel-wise analysis of tumour data (classed as PADS); response was not exclusive to patients with this phenotype. In patients with lung cancer, multi-parametric [18F]ICMT-11 PET and MRI (diffusion-weighted- and dynamic contrast enhanced-MRI) showed that PET changes were concordant with cell death in the absence of significant perfusion changes. Conclusion: This study highlights the potential use of [18F]ICMT-11 PET as a promising candidate for non-invasive imaging of caspase3/7 activation, and the difficulties encountered in assessing early-treatment responses. We summarize that tumour response could occur in the absence of predominant chemotherapy-induced caspase-3/7 activation measured non-invasively across entire tumour lesions in patients with breast and lung cancer

Neural field models with threshold noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches

Mass spectrometry data processing using zero-crossing lines in multi-scale of Gaussian derivative wavelet

Motivation: Peaks are the key information in mass spectrometry (MS) which has been increasingly used to discover diseases-related proteomic patterns. Peak detection is an essential step for MS-based proteomic data analysis. Recently, several peak detection algorithms have been proposed. However, in these algorithms, there are three major deficiencies: (i) because the noise is often removed, the true signal could also be removed; (ii) baseline removal step may get rid of true peaks and create new false peaks; (iii) in peak quantification step, a threshold of signal-to-noise ratio (SNR) is usually used to remove false peaks; however, noise estimations in SNR calculation are often inaccurate in either time or wavelet domain. In this article, we propose new algorithms to solve these problems. First, we use bivariate shrinkage estimator in stationary wavelet domain to avoid removing true peaks in denoising step. Second, without baseline removal, zero-crossing lines in multi-scale of derivative Gaussian wavelets are investigated with mixture of Gaussian to estimate discriminative parameters of peaks. Third, in quantification step, the frequency, SD, height and rank of peaks are used to detect both high and small energy peaks with robustness to noise

Inhibition of γ-secretase induces G2/M arrest and triggers apoptosis in breast cancer cells

γ-Secretase activity is vital for the transmembrane cleavage of Notch receptors and the subsequent migration of their intracellular domains to the nucleus. Notch overexpression has been associated with breast, colon, cervical and prostate cancers. We tested the effect of three different γ-secretase inhibitors (GSIs) in breast cancer cells. One inhibitor (GSI1) was lethal to breast cancer cell lines at concentrations of 2 μM and above but had a minimal effect on the non-malignant breast lines. GSI1 was also cytotoxic for a wide variety of cancer cell lines in the NCI60 cell screen. GSI1 treatment resulted in a marked decrease in γ-secretase activity and downregulation of the Notch signalling pathway with no effects on expression of the γ-secretase components or ligands. Flow cytometric and western blot analyses indicated that GSI1 induces a G2/M arrest leading to apoptosis, through downregulation of Bcl-2, Bax and Bcl-XL. GSI1 also inhibited proteasome activity. Thus, the γ-secretase inhibitor GSI1 has a complex mode of action to inhibit breast cancer cell survival and may represent a novel therapy in breast cancer

Kernel reconstruction for delayed neural field equations

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Frechet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience