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Symmetry
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Mathematical Modeling in Biology and Life Sciences
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Mathematical Modeling in Biology and Life Sciences

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 5735

Special Issue Editors

Dr. Yueping Dong

E-Mail Website
Guest Editor
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
Interests: mathematical modelling; numerical analysis; engineering, applied and computational; mathematics; nonlinear dynamics
Prof. Dr. Wanbiao Ma

E-Mail Website
Guest Editor
Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Interests: differential equation models in epidemiology; virology and mirobiology and population biology; stability and bifurcation of ordinary/delayed differential equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yasuhiro Takeuchi

E-Mail Website
Guest Editor
Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan
Interests: infection; mathematical models; avian influenza; HIV; functional equations; infectious disease epidemiology; immunology of infectious diseases; emerging infectious diseases; infectious disease control and prevention; analysis; ecology; stability; epidemiological modeling; neural networks; vaccination

Special Issue Information

Dear Colleagues,

The progress in biology and life sciences over the last several decades has been revolutionary. However, many aspects of the biological mechanisms remain unclear due to complex interactions at the molecular, cellular, individual and population levels. As modern biology and life science research become more quantitative, mathematical modeling becomes increasingly important. These methods have been widely used to study complex biological processes and phenomena, test biological hypotheses, answer questions that cannot be tackled in clinical research alone, and provide both qualitative and quantitative findings.

Symmetry permeates all aspects of life sciences, from biological molecules to ecosystems and biomes, which has a strict mathematical interpretation: invariance under transformation. It plays an important role in the construction and analysis of mathematical models of biological forms and processes. More evidence is beginning to show that taking an interdisciplinary approach has the potential to lead to breakthroughs in the study of biology and life sciences.

This Special Issue welcomes all contributions on the recent advances in the study of biology and life sciences by means of mathematical modeling and methods.

Dr. Yueping Dong
Prof. Dr. Wanbiao Ma
Prof. Dr. Yasuhiro Takeuchi
Guest Editors

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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.

Keywords

  • population dynamics
  • infectious disease modelling
  • complex network
  • virus dynamics and mutation
  • cancer immune modelling
  • potential symmetries
  • differential equations
  • dynamical systems

Published Papers (5 papers)

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Research

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16 pages, 5602 KiB  
Article
Molecular-Memory-Induced Counter-Intuitive Noise Attenuator in Protein Polymerization
by Xiaojun Bai, Sizhe Wang, Xin Zhang and Haohua Wang
Symmetry 2024, 16(3), 315; https://doi.org/10.3390/sym16030315 - 06 Mar 2024
Viewed by 618
Abstract
Gene expression comprises many asymmetric and complex processes. Transcriptional details revealed by the whole genome indicate that genes resort to transcriptional bursting and accumulate molecular memory. However, it is still unclear how the interplay of transcriptional bursting and memory regulates robustness and expression [...] Read more.
Gene expression comprises many asymmetric and complex processes. Transcriptional details revealed by the whole genome indicate that genes resort to transcriptional bursting and accumulate molecular memory. However, it is still unclear how the interplay of transcriptional bursting and memory regulates robustness and expression noise. Here, we consider a model of multiple coupled processes of protein polymerization to focus on decoding the effect of molecular memory. Using non-Markovian transformation technology, we first define the memory index to measure the correlation window of expression to decipher the mechanism of regulation. The results indicate that memory from synthesis can amplify expression noise, while memory originating from polymerization can reduce the lower bound of the noise of gene products; that is, the memory from different sources plays distinct regulatory roles to induce non-symmetry. Moreover, it is counterintuitive that the dual regulation from memory and bursting expression can directly suppress system noise, violating the principle that transcriptional bursting enhances noise. Our results not only provide a theoretical framework for investigating the function of memory but also imply that expression noise is not part of a half-power relationship with, nor mediated by, memory. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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13 pages, 916 KiB  
Article
Steady State Kinetics for Enzymes with Multiple Binding Sites Upstream of the Catalytic Site
by Manuel I. Osorio, Mircea Petrache, Dino G. Salinas, Felipe Valenzuela-Ibaceta, Fernando González-Nilo, William Tiznado, José M. Pérez-Donoso, Denisse Bravo and Osvaldo Yáñez
Symmetry 2023, 15(12), 2176; https://doi.org/10.3390/sym15122176 - 08 Dec 2023
Viewed by 1497
Abstract
The Michaelis–Menten mechanism, which describes the binding of a substrate to an enzyme, is a simplification of the process on a molecular scale. A more detailed model should include the binding of the substrate to precatalytic binding sites (PCBSs) prior to the transition [...] Read more.
The Michaelis–Menten mechanism, which describes the binding of a substrate to an enzyme, is a simplification of the process on a molecular scale. A more detailed model should include the binding of the substrate to precatalytic binding sites (PCBSs) prior to the transition to the catalytic site. Our work shows that the incorporation of PCBSs, in steady-state conditions, generates a Michaelis–Menten-type expression, in which the kinetic parameters KM and Vmax adopt more complex expressions than in the model without PCBSs. The equations governing reaction kinetics can be seen as generalized symmetries, relative to time translation actions over the state space of the underlying chemical system. The study of their structure and defining parameters can be interpreted as looking for invariants associated with these time evolution actions. The expression of KM decreases as the number of PCBSs increases, while Vmax reaches a minimum when the first PCBSs are incorporated into the model. To evaluate the trend of the dynamic behavior of the system, numerical simulations were performed based on schemes with different numbers of PCBSs and six conditions of kinetic constants. From these simulations, with equal kinetic constants for the formation of the Substrate/PCBS complex, it is observed that KM and Vmax are lower than those obtained with the Michaelis–Menten model. For the model with PCBSs, the Vmax reaches a minimum at one PCBS and that value is maintained for all of the systems evaluated. Since KM decreases with the number of PCBSs, the catalytic efficiency increases for enzymes fitting this model. All of these observations are consistent with the general equation obtained. This study allows us to explain, on the basis of the PCBS to KM and Vmax ratios, the effect on enzyme parameters due to mutations far from the catalytic site, at sites involved in the first enzyme/substrate interaction. In addition, it incorporates a new mechanism of enzyme activity regulation that could be fundamental to search for new activity-modulating sites or for the design of mutants with modified enzyme parameters. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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17 pages, 369 KiB  
Article
Dynamics of Competitive Two-Strain Stochastic SIR Epidemics on Heterogeneous Networks
by Xiaojie Jing and Guirong Liu
Symmetry 2023, 15(10), 1813; https://doi.org/10.3390/sym15101813 - 23 Sep 2023
Viewed by 624
Abstract
Mathematical modeling in epidemiology, biology, and life sciences requires the use of stochastic models. In this paper, we derive a competitive two-strain stochastic SIR epidemic model by considering the change in state of the epidemic process due to an event. Based on the [...] Read more.
Mathematical modeling in epidemiology, biology, and life sciences requires the use of stochastic models. In this paper, we derive a competitive two-strain stochastic SIR epidemic model by considering the change in state of the epidemic process due to an event. Based on the density-dependent process theory, we construct a six-dimensional deterministic model that can be used to describe the diffusion limit of the stochastic epidemic on a heterogeneous network. Furthermore, we show the explicit expressions for the variances of infectious individuals with strain 1 and strain 2 when the level of infection is increasing exponentially. In particular, we find that the expressions of the variances are symmetric. Finally, simulations for epidemics spreading on networks are performed to confirm our analytical results. We find a close agreement between the simulations and theoretical predictions. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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11 pages, 1715 KiB  
Article
Stability Analysis of a Mathematical Model for Adolescent Idiopathic Scoliosis from the Perspective of Physical and Health Integration
by Yuhua Zhang and Haiyin Li
Symmetry 2023, 15(8), 1609; https://doi.org/10.3390/sym15081609 - 20 Aug 2023
Viewed by 770
Abstract
In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a [...] Read more.
In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a positive equilibrium under the delays of τ=0 and τ≠0. Furthermore, through numerical simulation, it has been verified the delay, τ, exceeds a critical value, the positive equilibrium loses its stability and Hopf bifurcation occurs. Lastly, we determine that sports have a positive effect on adolescent idiopathic scoliosis, directly reducing the number of people with adolescent idiopathic scoliosis. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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Review

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23 pages, 402 KiB  
Review
Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology
by Vasyl’ Davydovych, Vasyl’ Dutka and Roman Cherniha
Symmetry 2023, 15(11), 2025; https://doi.org/10.3390/sym15112025 - 07 Nov 2023
Viewed by 1115
Abstract
The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most [...] Read more.
The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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