# High-order fractional partial differential equation transform for molecular surface construction

Langhua Hu; Duan Chen; Guo-Wei Wei

Molecular Based Mathematical Biology (2013)

- Volume: 1, page 1-25
- ISSN: 2299-3266

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topLanghua Hu, Duan Chen, and Guo-Wei Wei. "High-order fractional partial differential equation transform for molecular surface construction." Molecular Based Mathematical Biology 1 (2013): 1-25. <http://eudml.org/doc/267473>.

@article{LanghuaHu2013,

abstract = {Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.},

author = {Langhua Hu, Duan Chen, Guo-Wei Wei},

journal = {Molecular Based Mathematical Biology},

keywords = {Molecular surface generation; High order fractional derivatives; Fractional calculus; Fractional PDE transform; molecular surface generation; high order fractional derivatives; fractional calculus; fractional PDE transform},

language = {eng},

pages = {1-25},

title = {High-order fractional partial differential equation transform for molecular surface construction},

url = {http://eudml.org/doc/267473},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Langhua Hu

AU - Duan Chen

AU - Guo-Wei Wei

TI - High-order fractional partial differential equation transform for molecular surface construction

JO - Molecular Based Mathematical Biology

PY - 2013

VL - 1

SP - 1

EP - 25

AB - Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

LA - eng

KW - Molecular surface generation; High order fractional derivatives; Fractional calculus; Fractional PDE transform; molecular surface generation; high order fractional derivatives; fractional calculus; fractional PDE transform

UR - http://eudml.org/doc/267473

ER -

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