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Trans-heteroclinic bifurcation: a novel type of catastrophic shift.

ABSTRACT: Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth transitions involve a continuous change in the steady state of the system until the bifurcation value is crossed, giving place to a second-order phase transition. Catastrophic transitions involve a discontinuity of the steady state at the bifurcation value, giving place to first-order phase transitions. Examples of catastrophic shifts can be found in ecosystems, climate, economic or social systems. Here we report a new type of global bifurcation responsible for a catastrophic shift. This bifurcation, identified in a family of quasi-species equations and named as trans-heteroclinic bifurcation, involves an exchange of stability between two distant and heteroclinically connected fixed points. Since the two fixed points interchange the stability without colliding, a catastrophic shift takes place. We provide an exhaustive description of this new bifurcation, also detailing the structure of the replication-mutation matrix of the quasi-species equation giving place to this bifurcation. A perturbation analysis is provided around the bifurcation value. At this value the heteroclinic connection is replaced by a line of fixed points in the quasi-species model. But it is shown that, if the replication-mutation matrix satisfies suitable conditions, then, under a small perturbation, the exchange of heteroclinic connections is preserved, except on a tiny range around the bifurcation value whose size is of the order of magnitude of the perturbation. The results presented here can help to understand better novel mechanisms behind catastrophic shifts and contribute to a finer identification of such transitions in theoretical models in evolutionary biology and other dynamical systems.

SUBMITTER: Sardanyes J

PROVIDER: S-EPMC5792914 | biostudies-literature | 2018 Jan

REPOSITORIES: biostudies-literature

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Project description:Background: Microcephalic osteodysplastic primordial dwarfism type II (MOPD II) is an autosomal recessive and skeletal disorder included wide spectrum of clinical abnormalities such as fetal growth restriction, disproportionate face, microcephaly, post-natal growth retardation, adult height under 100 cm, abnormal skin pigmentation, insulin resistance, and susceptibility to cerebrovascular and hematologic abnormalities. Due to heterogeneous feature of MOPDs diseases and common clinical features among the different subtypes, mutation analysis can be considered as fundamental in the accurate diagnosis and confirmation of the MOPD II disease. Some studies revealed that, variants of gene encoding Pericentrin protein, PCNT, were associated with MOPD II. Methods: We performed whole exome sequencing based on the next generation sequencing (Illumina platform), to perform correct diagnosis in a 17-year-old girl with an unknown disease who was referred to the Diabetes Research Center in Yazd, Iran. The clinical features of the patient were short stature, generalized brachydactyly, gradual deterioration of brain functioning, menstrual irregularity, clitoromegaly, acanthosis nigricans, diabetes mellitus, hyperinsulinemia, insulin resistance, and dyslipidemia. Accordingly, her parents were also first cousin with no background disease. After identifying the novel variant, it was confirmed in the proband and her family using bi-directional Sanger sequencing, and its pathogenicity was also checked by different online tools. Results: Our study revealed a novel frame-shift variant in PCNT gene (c.7511delA, p.K2504Sfs*27), which causes premature termination of Pericentrin protein. The result disclosed that, the proband was affected by MOPD II disease. In addition, the Sanger sequencing confirmed the novel homozygote variant in the proband and heterozygote one in her parents, and the extended family perfectly segregated among them. Online tools such as Varsome and MutationTaster also showed a high level of pathogenicity for the variant identified. Conclusion: A novel variant was identified in the proband and her extended family, which emphasized the importance of PCNT gene mutations analysis in the screening and accurate identification of MOPD II disease, especially in prenatal diagnosis.

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Trans-heteroclinic bifurcation: a novel type of catastrophic shift.

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