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In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which the FitzHugh-Nagumo (FHN) kinetics, in its excitable regime, is coupled to linear cross-diffusion terms. In (Gambino et al. in Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), we proved that the model supports the emergence of cross-Turing patterns, i.e., close-to-equilibrium structures occurring as an effect of cross-diffusion. Here, we shall construct the cross-Turing patterns close to equilibrium on 1-D and 2-D rectangular domains. Through this analysis, we shall show that the species are out-of-phase spatially distributed and derive the amplitude equations that govern the pattern dynamics close to criticality. Moreover, we shall classify the bifurcation in the parameter space, distinguishing between super-and sub-critical transitions. In the final part of the paper, we shall numerically investigate the impact of the cross-diffusion terms on large-amplitude pulse-like solutions existing outside the cross-Turing regime, showing their emergence also in the case of lateral activation and short-range inhibition. [ABSTRACT FROM AUTHOR]

In this paper, we shall study a spatially extended version of the FitzHugh-Nagumo model, where one describes the motion of the species through cross-diffusion. The motivation comes from modeling biological species where reciprocal interaction influences spatial movement. We shall focus our analysis on the excitable regime of the system. In this case, we shall see how cross-diffusion terms can destabilize uniform equilibrium, allowing for the formation of close-to-equilibrium patterns; the species are out-of-phase spatially distributed, namely high concentration areas of one species correspond to a low density of the other (cross-Turing patterns). Moreover, depending on the magnitude of the inhibitor's cross-diffusion, the pattern's development can proceed in either case of the inhibitor/activator diffusivity ratio being higher or smaller than unity. This allows for spatial segregation of the species in both cases of short-range activation/long-range inhibition or long-range activation/short-range inhibition. [ABSTRACT FROM AUTHOR]

Purpose: In order to better define the breast cancer (BC) genetic risk factors in men, a germline investigation was carried out on 81 Male BC cases by screening the 24 genes involved in BC predisposition, genome stability maintenance and DNA repair mechanisms by next-generation sequencing. Methods: Germline DNAs were tested in a custom multi-gene panel focused on all coding exons and exon–intron boundaries of 24 selected genes using two amplicon-based assays on PGM-Ion Torrent (ThermoFisher Scientific) and MiSeq (Illumina) platforms. All variants were recorded and classified by using a custom pipeline. Results: Clinical pathological data and the family history of 81 Male BC cases were gathered and analysed, revealing the average age of onset to be 61.3 years old and that in 35 cases there was a family history of BC. Our genetic screening allowed us to identify a germline mutation in 22 patients (23%) in 4 genes: BRCA2, BRIP1, MUTYH and PMS2. Moreover, 12 variants of unknown clinical significance (VUS) in 9 genes (BARD1, BRCA1, BRIP1, CHEK2, ERCC1, NBN, PALB2, PMS1, RAD50) were predicted as potentially pathogenic by in silico analysis bringing the mutation detection rate up to 40%. Conclusion: As expected, a positive family history is a strong predictor of germline BRCA2 mutations in male BC. Understanding the potential pathogenicity of VUS represents an extremely urgent need for the management of BC risk in Male BC cases and their own families. [ABSTRACT FROM AUTHOR]

We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper the Turing pattern formation mechanism of a two components reaction-diffusion system modeling the Schnakenberg chemical reaction is considered. In Ref. (Madzavamuse et al., J Math Biol 70(4):709-743, 2015) it was shown how the presence of linear cross-diffusion terms favors the destabilization of the constant steady state. We perform the weakly nonlinear multiple scales analysis to derive the equations for the amplitude of the Turing patterns and to show how the cross-diffusion coefficients influence the occurrence of super-critical or sub-critical bifurcations. We present a numerical exploration of far from equilibrium regimes and prove the existence of multistable stationary solutions. [ABSTRACT FROM AUTHOR]

Five viroid species have been reported from grapevine. Hop stunt viroid (HSVd) and Grapevine yellow speckle viroid 1 (GYSVd-1) are distributed worldwide, whereas Grapevine yellow speckle viroid 2 (GYSVd-2), Australian grapevine viroid (AGVd) and Citrus exocortis viroid (CEVd) are found only sporadically. However, the presence of AGVd and GYSVd-2 in several countries, including China, Turkey and Tunisia, suggests a wider dissemination, possibly also in Europe, where AGVd has never been found and GYSVd-2 has been occasionally identified in Italy. Taking advantage of a multiplex RT-PCR assay recently developed for detecting simultaneously these five viroids, vines growing in Italy in commercial vineyards and germplasm collections were surveyed. Besides confirming the widespread presence of HSVd and GYSVd-1 in the field, GYSVd-2 and/or AGVd were identified in two grapevine table cultivars (Sultanina Bianca and Red Globe) from germplasm collections. Tests extended to vines cultivated in southern Italy confirmed the presence of both viroids, which were further characterized. No major sequence divergences between the AGVd and GYSVd-2 variants from Italy and those previously described from other countries were observed. Phylogenetic analysis supported the close relationships among AGVd variants from Italy, Tunisia and Australia. To our knowledge this is the first report of AGVd in Europe and the first molecular characterization of GYSVd-2 isolates from a European country. [ABSTRACT FROM AUTHOR]

In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel-Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal modulation of the phase and amplitude of the homogeneous oscillatory solution. [ABSTRACT FROM AUTHOR]

In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many important non-linear PDEs or PDE systems, for which these analytical solutions would correspond to regular or localized pulses of the PDE. As such, the homoclinic solutions derived here are clearly topical, and they are shown to match closely to earlier results obtained by homoclinic numerical shooting. In addition, the results for the non-reversible case go beyond those that have been typically considered in analyses conducted within bifurcation-theoretic settings. We also comment on generalizing the treatment here to parameter regimes where solutions homoclinic to exponentially small periodic orbits are known to exist, as well as another possible extension placing the solutions derived here within the framework of a comprehensive categorization of ALL possible traveling-wave solutions, both smooth and non-smooth, for our governing ODE. [ABSTRACT FROM AUTHOR]

In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control. [ABSTRACT FROM AUTHOR]

In order to understand the onset of hyperchaotic behavior recently observed in many systems, we study bifurcations in the modified Chen system leading from simple dynamics into chaotic regimes. In particular, we demonstrate that the existence of only one fixed point of the system in all regions of parameter space implies that this simple point attractor may only be destabilized via a Hopf or double Hopf bifurcation as system parameters are varied. Saddle-node, transcritical and pitchfork bifurcations are precluded. The normal form immediately following double Hopf bifurcations is constructed analytically by the method of multiple scales. Analysis of this generalized double Hopf normal form along standard lines reveals possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. However, considering these more carefully, we find that only certain combinations or sequences of these dynamical regimes are possible, while others derived and considered in earlier work are in fact mathematically impossible. We also discuss the post-bifurcation dynamics in the context of two intermittent routes to chaos (routes following either (i) subcritical or (ii) supercritical Hopf or double Hopf bifurcations). In particular, the route following supercritical bifurcations is somewhat subtle. Such behavior following repeated Hopf bifurcations is well-known and widely observed, including in the classical Ruelle-Takens and quasiperiodic routes to chaos. However, to the best of our knowledge, it has not been considered in the context of the double-Hopf normal form, although it has been numerically observed and tracked in the post-double Hopf regime. Numerical simulations are employed to corroborate these various predictions from the normal form. They reveal the existence of stable periodic and toroidal attractors in the post-supercritical-Hopf cases, and either attractors at infinity or bounded chaotic dynamics following subcritical Hopf bifurcations. Future work will map out the remainder of the routes into the chaotic regimes, including further bifurcations of the post-supercritical-Hopf two- and three-tori via either torus doubling or breakdown. [ABSTRACT FROM AUTHOR]

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The Microphthalmia basic-Helix – Loop – Helix-Leucine Zipper (bHLH-LZ) transcription factor plays a crucial role in the genesis of melanocytes; mice deficient for a functional microphthalmia gene product lack all pigment cells. We show here that the Mi activation domain resides N-terminal to the DNA-binding domain and that as little as 18 amino acids are sufficient to mediate transcription activation. The minimal activation region of Mi is highly conserved in the related transcription factor TFE3 and is predicted to adopt an amphipathic alpha-helical conformation. This region of Mi is also highly conserved with a region of E1A known to be essential for binding the CBP/p300 transcription cofactor. Consistent with these observations, the Mi activation domain can interact in vitro with CBP specifically through a region of CBP required for complex formation with E1A, P/CAF and c-Fos, and anti p300 antibodies can co-immunoprecipitate Mi from both melanocyte and melanoma cell lines. In addition, co-transfection of a vector expressing CBP2 fused to the VP16 activation domain potentiated the ability of Mi to activate transcription, confirming the significance of the CBP-Mi interaction observed in vitro. These data suggest that transcription activation by Mi is achieved at least in part by recruitment of CBP. The parallels between transcription regulation by Microphthalmia in melanocytes and MyoD in muscle cells are discussed. [ABSTRACT FROM AUTHOR]

The mutation analysed in HOXA1 is a base transition from 'A' to 'G' at position 218 of mRNA. In the HOXB1 gene, the 'at risk' allele consists of a 9-base insertion (INS), the other allele is named ('+'). In order to verify the existence of LD between these mutations and autism, researchers have used TDT analysis in a group of 85 complete trios families and a conventional 'case-control' study with an ethnically matched sample as reference population. Deviation from Hardy-Weinberg equilibrium was detected for none of the four gene sample-of-individuals combinations tested. Comparison of the 'at risk' alleles for both HOXA1 (allele 'G') and HOXB1 (allele 'INS') genes, between cases and ethnically matched controls, did not reveal statistically significant differences. For HOXB1, from 52 heterozygote parents 30 transmissions and 22 non-transmissions were scored for allele 'INS'.