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Mathematical and Computational Methods in Systems Biology
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Mathematical and Computational Methods in Systems Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 18786

Special Issue Editor

Dr. Sergey A. Lashin

E-Mail Website
Guest Editor
Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences (SB RAS), 630090 Novosibirsk, Russia
Interests: computational biology; mathematical biology; bioinformatics; gene networks; agent-based models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Biological systems are complex hierarchical systems functioning at different levels of biological organization, from molecular–genetic to ecological. Mathematical modeling is one of the main approaches to the comprehensive study of biological systems. In light of the recent advances in experimental biology, in particular, the development of omics technologies that have led to a massive accumulation of data on the functioning of molecular genetic systems, mathematical modeling in a number of cases remains the only means of integrating them at the system level.

The purpose of this Special Issue is to present recent advances in mathematical modeling in systems biology with a particular focus on methods of the building and analysis of hierarchically organized complex models of biological systems. We welcome you to submit original research articles and reviews on the variety of aspects of modeling in systems biology, which include, but are not limited to, ordinary differential equations, partial differential equations, graph and network models, machine learning, and deep learning.

Dr. Sergey A. Lashin
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (12 papers)

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21 pages, 3146 KiB  
Article
Multicompartmental Mathematical Model of SARS-CoV-2 Distribution in Human Organs and Their Treatment
by Vasiliy N. Afonyushkin, Ilya R. Akberdin, Yulia N. Kozlova, Ivan A. Schukin, Tatyana E. Mironova, Anna S. Bobikova, Viktoriya S. Cherepushkina, Nikolaj A. Donchenko, Yulia E. Poletaeva and Fedor A. Kolpakov
Mathematics 2022, 10(11), 1925; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111925 - 04 Jun 2022
Cited by 5 | Viewed by 2301
Abstract
Patients with COVID-19 can develop pneumonia, severe symptoms of acute respiratory distress syndrome, and multiple organ failure. Nevertheless, the variety of forms of this disease requires further research on the pathogenesis of this disease. Based on the analysis of published data and original [...] Read more.
Patients with COVID-19 can develop pneumonia, severe symptoms of acute respiratory distress syndrome, and multiple organ failure. Nevertheless, the variety of forms of this disease requires further research on the pathogenesis of this disease. Based on the analysis of published data and original experiments on the concentrations of SARS-CoV-2 in biological fluids of the nasopharynx, lungs, and intestines and using a developed modular model of the virus distribution in human tissue and organs, an assessment of the SARS-CoV-2 reproduction in various compartments of the body is presented. Most of the viral particles can transport to the esophagus from the nasopharynx. The viral particles entering the gastrointestinal tract will obviously be accompanied by the infection of the intestinal epithelium and accumulation of the virus in the intestinal lumen in an amount proportional to their secretory and protein-synthetic activities. The relatively low concentration of SARS-CoV-2 in tissues implies an essential role of transport processes and redistribution of the virus from the nasopharynx and intestines to the lungs. The model simulations also suppose that sanitation of the nasopharynx mucosa at the initial stage of the infectious process has prospects for the use in medical practice. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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24 pages, 1882 KiB  
Article
Analysis of the In-Host Dynamics of Tuberculosis and SARS-CoV-2 Coinfection
by Ahmed M. Elaiw and Afnan D. Al Agha
Mathematics 2023, 11(5), 1104; https://0-doi-org.brum.beds.ac.uk/10.3390/math11051104 - 22 Feb 2023
Cited by 1 | Viewed by 1158
Abstract
The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection [...] Read more.
The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection with other infectious diseases. Tuberculosis (TB) is a bacterial disease caused by Mycobacterium tuberculosis (Mtb). SARS-CoV-2 coinfection with TB has been recorded in many countries. It has been suggested that the coinfection is associated with severe disease and death. Mathematical modeling is an effective tool that can help understand the dynamics of coinfection between new diseases and well-known diseases. In this paper, we develop an in-host TB and SARS-CoV-2 coinfection model with cytotoxic T lymphocytes (CTLs). The model investigates the interactions between healthy epithelial cells (ECs), latent Mtb-infected ECs, active Mtb-infected ECs, SARS-CoV-2-infected ECs, free Mtb, free SARS-CoV-2, and CTLs. The model’s solutions are proved to be nonnegative and bounded. All equilibria with their existence conditions are calculated. Proper Lyapunov functions are selected to examine the global stability of equilibria. Numerical simulations are implemented to verify the theoretical results. It is found that the model has six equilibrium points. These points reflect two states: the mono-infection state where SARS-CoV-2 or TB occurs as a single infection, and the coinfection state where the two infections occur simultaneously. The parameters that control the movement between these states should be tested in order to develop better treatments for TB and COVID-19 coinfected patients. Lymphopenia increases the concentration of SARS-CoV-2 particles and thus can worsen the health status of the coinfected patient. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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21 pages, 9653 KiB  
Article
Computational Human Nasal Reconstruction Based on Facial Landmarks
by Ho Nguyen Anh Tuan and Nguyen Truong Thinh
Mathematics 2023, 11(11), 2456; https://0-doi-org.brum.beds.ac.uk/10.3390/math11112456 - 25 May 2023
Viewed by 1303
Abstract
This research presented a mathematical-based approach to the computational reconstruction of the human nose through images with anthropometric characteristics. The nasal baselines, which were generated from facial aesthetic subunits combined with the facial landmarks, were reconstructed using interpolation and Mesh adaptive direct search [...] Read more.
This research presented a mathematical-based approach to the computational reconstruction of the human nose through images with anthropometric characteristics. The nasal baselines, which were generated from facial aesthetic subunits combined with the facial landmarks, were reconstructed using interpolation and Mesh adaptive direct search algorithms to generate points that would serve as the support for the layer-by-layer reconstruction. The approach is proposed as the basis for nasal reconstruction in aesthetics or forensics rather than focusing on the applications of image processing or deep learning. A mathematical model for the computational reconstruction was built, and then volunteers were the subjects of nasal reconstruction experiments. The validations based on the area errors—which are based on four samples and eight sub-regions with different values depending on the regions C1, C2, and C3 and nasal shapes of the volunteers—were measured to prove the results of the mathematical model. Evaluations have demonstrated that the computer-reconstructed noses fit the original ones in shape and with minimum area errors. This study describes a computational reconstruction based on a mathematical approach directly to facial anthropometric landmarks to reconstruct the nasal shape. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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19 pages, 4637 KiB  
Article
Classification of Fruit Flies by Gender in Images Using Smartphones and the YOLOv4-Tiny Neural Network
by Mikhail A. Genaev, Evgenii G. Komyshev, Olga D. Shishkina, Natalya V. Adonyeva, Evgenia K. Karpova, Nataly E. Gruntenko, Lyudmila P. Zakharenko, Vasily S. Koval and Dmitry A. Afonnikov
Mathematics 2022, 10(3), 295; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030295 - 18 Jan 2022
Cited by 12 | Viewed by 2709
Abstract
The fruit fly Drosophila melanogaster is a classic research object in genetics and systems biology. In the genetic analysis of flies, a routine task is to determine the offspring size and gender ratio in their populations. Currently, these estimates are made manually, which [...] Read more.
The fruit fly Drosophila melanogaster is a classic research object in genetics and systems biology. In the genetic analysis of flies, a routine task is to determine the offspring size and gender ratio in their populations. Currently, these estimates are made manually, which is a very time-consuming process. The counting and gender determination of flies can be automated by using image analysis with deep learning neural networks on mobile devices. We proposed an algorithm based on the YOLOv4-tiny network to identify Drosophila flies and determine their gender based on the protocol of taking pictures of insects on a white sheet of paper with a cell phone camera. Three strategies with different types of augmentation were used to train the network. The best performance (F1 = 0.838) was achieved using synthetic images with mosaic generation. Females gender determination is worse than that one of males. Among the factors that most strongly influencing the accuracy of fly gender recognition, the fly’s position on the paper was the most important. Increased light intensity and higher quality of the device cameras have a positive effect on the recognition accuracy. We implement our method in the FlyCounter Android app for mobile devices, which performs all the image processing steps using the device processors only. The time that the YOLOv4-tiny algorithm takes to process one image is less than 4 s. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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7 pages, 1048 KiB  
Article
A Procedure for Modeling Genetic Diversity Distortions in Populations of Organisms with Mixed Reproductive Strategies
by Anastasiya Poroshina and Dmitry Sherbakov
Mathematics 2023, 11(13), 2985; https://0-doi-org.brum.beds.ac.uk/10.3390/math11132985 - 04 Jul 2023
Viewed by 617
Abstract
We propose an approach for modeling the pattern of the genetic diversity of microsatellite markers in a population with a mixed breeding strategy. Part of the population is reproduced sexually, and part is produced asexually. The method of the proposed simulation is different [...] Read more.
We propose an approach for modeling the pattern of the genetic diversity of microsatellite markers in a population with a mixed breeding strategy. Part of the population is reproduced sexually, and part is produced asexually. The method of the proposed simulation is different from others in that it produces a set of microsatellite markers as the outcome of a computer simulation of processes in a fixed-size population. These markers can be utilized with the assistance of available software to calculate various metrics of genetic diversity. Our approach is implemented in Python 3.10 and is accompanied by additional scripts that ensure result compatibility with programs that calculate different population characteristics. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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9 pages, 1229 KiB  
Article
Algorithm for the Reconstruction of Mathematical Frame Models of Bacterial Transcription Regulation
by Tatiana N. Lakhova, Fedor V. Kazantsev, Aleksey M. Mukhin, Nikolay A. Kolchanov, Yury G. Matushkin and Sergey A. Lashin
Mathematics 2022, 10(23), 4480; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234480 - 28 Nov 2022
Viewed by 1195
Abstract
Transcription regulation plays an important role in bacterial activity. The operon concept coined by François Jacob and Jacques Monod has had a considerable effect on investigations into gene expression regulation, including modeling. However, most such studies have considered the regulation models devised manually [...] Read more.
Transcription regulation plays an important role in bacterial activity. The operon concept coined by François Jacob and Jacques Monod has had a considerable effect on investigations into gene expression regulation, including modeling. However, most such studies have considered the regulation models devised manually for one or several operons. For that reason, the objective of the present study was automated genome model reconstruction for different bacteria. The suggested algorithm accounted for all possible interactions of transcription factors and their binding sites in an operon’s promoter region. Transcription factor enumeration was performed using the deep-first search technique. The obtained models are of interest for those involved in the research of transcription factor regulatory effects on bacterial gene expression in microbiology and biotechnology. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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14 pages, 2102 KiB  
Article
Long-COVID Inducement Mechanism Based on the Path Module Correlation Coefficient
by Ziqi Liu, Ziqiao Yin, Zhilong Mi and Binghui Guo
Mathematics 2023, 11(6), 1368; https://0-doi-org.brum.beds.ac.uk/10.3390/math11061368 - 11 Mar 2023
Cited by 1 | Viewed by 1115
Abstract
As the number of COVID-19 cases increases, the long-COVID symptoms become the focus of clinical attention. Based on the statistical analysis of long-COVID symptoms in European and Chinese populations, this study proposes the path module correlation coefficient, which can estimate the correlation between [...] Read more.
As the number of COVID-19 cases increases, the long-COVID symptoms become the focus of clinical attention. Based on the statistical analysis of long-COVID symptoms in European and Chinese populations, this study proposes the path module correlation coefficient, which can estimate the correlation between two modules in a network, to evaluate the correlation between SARS-CoV-2 infection and long-COVID symptoms, providing a theoretical support for analyzing the frequency of long-COVID symptoms in European and Chinese populations. The path module correlation coefficients between specific COVID-19-related genes in the European and Chinese populations and genes that may induce long-COVID symptoms were calculated. The results showed that the path module correlation coefficients were completely consistent with the frequency of long-COVID symptoms in the Chinese population, but slightly different in the European population. Furthermore, the cathepsin C (CTSC) gene was found to be a potential COVID-19-related gene by a path module correlation coefficient correction rate. Our study can help to explore other long-COVID symptoms that have not yet been discovered and provide a new perspective to research this syndrome. Meanwhile, the path module correlation coefficient correction rate can help to find more species-specific genes related to COVID-19 in the future. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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11 pages, 346 KiB  
Article
Mathematical Model of Hepatitis B Virus Treatment with Support of Immune System
by Irina Volinsky
Mathematics 2022, 10(15), 2821; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152821 - 08 Aug 2022
Cited by 3 | Viewed by 1579
Abstract
In the current paper, the classification of the equilibrium points of an HBV mathematical model with combined therapy is presented. The influence of right-hand side changes on solution behavior is estimated, and regulation with delays in upper- and lower-bound integral limits that presents [...] Read more.
In the current paper, the classification of the equilibrium points of an HBV mathematical model with combined therapy is presented. The influence of right-hand side changes on solution behavior is estimated, and regulation with delays in upper- and lower-bound integral limits that presents a time period with IL-2 support therapy are researched. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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19 pages, 6195 KiB  
Article
A New Visualization and Analysis Method for a Convolved Representation of Mass Computational Experiments with Biological Models
by Alexandra I. Klimenko, Diana A. Vorobeva and Sergey A. Lashin
Mathematics 2023, 11(12), 2783; https://0-doi-org.brum.beds.ac.uk/10.3390/math11122783 - 20 Jun 2023
Viewed by 823
Abstract
Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties [...] Read more.
Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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18 pages, 5566 KiB  
Article
New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments
by Nasser H. Sweilam, Seham M. AL-Mekhlafi, Saleh M. Hassan, Nehaya R. Alsenaideh and Abdelaziz Elazab Radwan
Mathematics 2022, 10(23), 4579; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234579 - 02 Dec 2022
Cited by 3 | Viewed by 1068
Abstract
A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter μ is presented. The boundedness, existence, and positivity of the solutions [...] Read more.
A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter μ is presented. The boundedness, existence, and positivity of the solutions for the proposed model are discussed. Two improved numerical methods are presented in this paper. The Caputo proportional constant nonstandard modified Euler–Maruyama method is introduced to study the fractional stochastic model, and the Grünwald–Letnikov nonstandard finite difference method is presented to study the hybrid fractional order deterministic model. Comparative studies with real data from Spain and Wuhan are presented. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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20 pages, 83453 KiB  
Article
Modular Representation of Physiologically Based Pharmacokinetic Models: Nanoparticle Delivery to Solid Tumors in Mice as an Example
by Elena Kutumova, Ilya Akberdin, Ilya Kiselev, Ruslan Sharipov and Fedor Kolpakov
Mathematics 2022, 10(7), 1176; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071176 - 04 Apr 2022
Cited by 1 | Viewed by 1989
Abstract
Here we describe a toolkit for presenting physiologically based pharmacokinetic (PBPK) models in a modular graphical view in the BioUML platform. Firstly, we demonstrate the BioUML capabilities for PBPK modeling tested on an existing model of nanoparticles delivery to solid tumors in mice. [...] Read more.
Here we describe a toolkit for presenting physiologically based pharmacokinetic (PBPK) models in a modular graphical view in the BioUML platform. Firstly, we demonstrate the BioUML capabilities for PBPK modeling tested on an existing model of nanoparticles delivery to solid tumors in mice. Secondly, we provide guidance on the conversion of the PBPK model code from a text modeling language like Berkeley Madonna to a visual modular diagram in the BioUML. We give step-by-step explanations of the model transformation and demonstrate that simulation results from the original model are exactly the same as numerical results obtained for the transformed model. The main advantage of the proposed approach is its clarity and ease of perception. Additionally, the modular representation serves as a simplified and convenient base for in silico investigation of the model and reduces the risk of technical errors during its reuse and extension by concomitant biochemical processes. In summary, this article demonstrates that BioUML can be used as an alternative and robust tool for PBPK modeling. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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17 pages, 4483 KiB  
Article
A Fractional Order Model to Study the Effectiveness of Government Measures and Public Behaviours in COVID-19 Pandemic
by Meghadri Das, Guruprasad Samanta and Manuel De la Sen
Mathematics 2022, 10(16), 3020; https://0-doi-org.brum.beds.ac.uk/10.3390/math10163020 - 22 Aug 2022
Cited by 4 | Viewed by 1453
Abstract
In this work, we emphasise the dynamical study of spreading COVID-19 in Bangladesh. Considering the uncertainty caused by the limited coronavirus (COVID-19) information, we have taken the modified Susceptible-Asymptomatic-Infectious-Hospitalised-Recovered (SAIHR) compartmental model in a Caputo fractional order system. We have also introduced public [...] Read more.
In this work, we emphasise the dynamical study of spreading COVID-19 in Bangladesh. Considering the uncertainty caused by the limited coronavirus (COVID-19) information, we have taken the modified Susceptible-Asymptomatic-Infectious-Hospitalised-Recovered (SAIHR) compartmental model in a Caputo fractional order system. We have also introduced public behavioural and government policy dynamics in our model. The dynamical nature of the solutions of the system is analysed and we have also calculated the sensitivity index of different parameters. It has been observed that public behaviour and government measures play an important role in controlling the pandemic situation. The government measures (social distance, vaccination, hospitalisation, awareness programme) are more helpful than only public responses to the eradication of the COVID-19 pandemic. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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