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A farey wavelet-based mathematical model for biological series

Department of Mathematics, Faculty of Sciences, University of Tabuk, King Faisal Road, 47512 Tabuk, Saudi Arabia.

Laboratory of Algebra, Number Theory and Nonlinear Analysis Lr18es15, Department of Mathematics, Faculty of Sciences, University of Monastir, Boulevard of the Environment, 5000 Monastir, Tunisia.

Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Street of Assad Ibn Al Fourat, Kairouan 3100, Tunisia.

* Corresponding Author
Annals of Communications in Mathematics 2023
, 6 (3),
Received: 25 June 2023 |
Accepted: 25 September 2023 |
Published: 31 October 2023

This work lies in the whole biomathematics framework which has as general goal the solving of biological problems with mathematical tools. The main objective of the present paper is to predict the transmembrane helices of proteins using wavelet denoising techniques. As a case of matter, we particularly highlight the interest in solving the problem of localizing these helices. Indeed, these helices play a vital role in the human body, notably in photosynthesis, respiration, neuronal signaling, immune response, absorption of nutrition, and have an important link with drugs as receptors coupled to many proteins. However, due to technical constraints, the crystallization of these helices remains very complex, which limits the exploration of their structure [27]. To overcome these difficul- ties, different prediction tools have been developed, initially based on hydrophobicity. In this paper, we serve the Farey wavelet as a last alternative mother wavelet constructed in [4] to develop a mathematical model suitable for protein series description. We precisely apply a new type of wavelets constructed recently in [4] to localize the and/or predict the position of the transmembrane proteins alpha-helices in a coronavirus strain. The results are compared to existing works for performance, accuracy, and efficiency.


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A farey wavelet-based mathematical model for biological series.

Annals of Communications in Mathematics,

6 (3):
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


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