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Fractional unstable patterns of energy in α−helix proteins with long-range interactions

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  • Tabi, Conrad Bertrand

Abstract

Energy transport and storage in α−helix proteins, in the presence of long-range intermolecular interactions, is addressed. The modified discrete Davydov model is first reduced to a space-fractional nonlinear Schrödinger (NLS) equation, followed by the stability analysis of its plane wave solution. The phenomenon is also known as modulational instability and relies on the appropriate balance between nonlinearity and dispersion. The fractional-order parameter (σ), related to the long-range coupling strength, is found to reduce the instability domain, especially in the case 1 ≤ σ < 2. Beyond that interval, i.e., σ > 2, the fractional NLS reduces to the classical cubic NLS equation, whose dispersion coefficient depends on σ. Rogue waves solution for the later are proposed and the biological implications of the account of fractional effects are discussed in the context of energy transport and storage in α−helix proteins.

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  • Tabi, Conrad Bertrand, 2018. "Fractional unstable patterns of energy in α−helix proteins with long-range interactions," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 386-391.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:386-391
    DOI: 10.1016/j.chaos.2018.09.037
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    References listed on IDEAS

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    1. C.B. Tabi & J.C. Mimshe Fewu & H.P. Ekobena Fouda & A. Mohamadou & T.C. Kofané, 2013. "Nonlinear wave trains in three-strand α-helical protein models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(9), pages 1-8, September.
    2. R. Ondoua & C. Tabi & H. Ekobena Fouda & A. Mohamadou & T. Kofané, 2012. "Discrete energy transport in the perturbed Ablowitz-Ladik equation for Davydov model of α-helix proteins," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(9), pages 1-6, September.
    3. Tabi, C.B. & Dang Koko, A. & Oumarou Doko, R. & Ekobena Fouda, H.P. & Kofané, T.C., 2016. "Modulated charge patterns and noise effect in a twisted DNA model with solvent interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 498-509.
    4. Daniel, M. & Deepamala, K., 1995. "Davydov soliton in alpha helical proteins: higher order and discreteness effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 241-255.
    5. Etémé, Armand S. & Tabi, Conrad B. & Mohamadou, Alidou, 2017. "Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 813-826.
    6. Tabi, C.B. & Maïna, I. & Mohamadou, A. & Ekobena, H.P.F. & Kofané, T.C., 2015. "Long-range intercellular Ca2+ wave patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 1-14.
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    Cited by:

    1. Tabi, C.B. & Ndjawa, P.A.Y. & Motsumi, T.G. & Bansi, C.D.K. & Kofané, T.C., 2020. "Magnetic field effect on a fractionalized blood flow model in the presence of magnetic particles and thermal radiations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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