Time-delayed feedback in neurosystems

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns, or amplitude death.Comment: 13 pages, 13 figure

Control of unstable steady states in neutral time-delayed systems

We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between the control strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can successfully stabilize an otherwise unstable steady state.Comment: 11 pages, 8 figure

Asymptotic properties of the spectrum of neutral delay differential equations

Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time delay, and the inclusion of a time-delayed velocity feedback improves this agreement for small delays. Theoretical results are complemented by a numerically computed spectrum of the corresponding characteristic equations.Comment: 14 pages, 6 figure

Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities

The effects of nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. Earlier investigations have demonstrated that non-local and hierarchical network connectivity often induces complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are non-locally linked with positive diffusive coupling in a ring architecture the system splits into a number of alternating domains. Half of these domains contain elements, whose potential stays near the threshold, while they are interrupted by active domains, where the elements perform regular LIF oscillations. The active domains move around the ring with constant velocity, depending on the system parameters. The idea of introducing reflecting non-local coupling in LIF networks originates from signal exchange between neurons residing in the two hemispheres in the brain. We show evidence that this connectivity induces novel complex spatial and temporal structures: for relatively extensive ranges of parameter values the system splits in two coexisting domains, one domain where all elements stay near-threshold and one where incoherent states develop with multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure

Claudin-1, -3 and -4 proteins and mRNA expression in benign and malignant breast lesions: a research study

INTRODUCTION: We compared levels of protein and mRNA expression of three members of the claudin (CLDN) family in malignant breast tumours and benign lesions. METHODS: Altogether, 56 sections from 52 surgically resected breast specimens were analyzed for CLDN1, CLDN3 and CLDN4 expression by immunohistochemistry. mRNA was also analyzed using real-time PCR in 17 of the 52 cases. RESULTS: CLDNs were rarely observed exclusively at tight junction structures. CLDN1 was present in the membrane of normal duct cells and in some of the cell membranes from ductal carcinoma in situ, and was frequently observed in eight out of nine areas of apocrine metaplasia, whereas invasive tumours were negative for CLDN1 or it was present in a scattered distribution among such tumour cells (in 36/39 malignant tumours). CLDN3 was present in 49 of the 56 sections and CLDN4 was present in all 56 tissue sections. However, CLDN4 was highly positive in normal epithelial cells and was decreased or absent in 17 out of 21 ductal carcinoma grade 1, in special types of breast carcinoma (mucinous, papillary, tubular) and in areas of apocrine metaplasia. CLDN1 mRNA was downregulated by 12-fold in the sample (tumour) group as compared with the control group using GAPDH as the reference gene. CLDN3 and CLDN4 mRNA exhibited no difference in expression between invasive tumours and surrounding tissue. CONCLUSIONS: The significant loss of CLDN1 protein in breast cancer cells suggests that CLDN1 may play a role in invasion and metastasis. The loss of CLDN4 expression in areas of apocrine metaplasia and in the majority of grade 1 invasive carcinomas also suggests a particular role for this protein in mammary glandular cell differentiation and carcinogenesis

Cancer Biomarker Discovery: The Entropic Hallmark

Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases