Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry
share announcement

Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry

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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 19602

Special Issue Editor

Prof. Dr. Eugene Postnikov

E-Mail Website
Guest Editor
Theoretical Physics Department of the Research Center for Condensed Matter Physics, Kursk State University, Radishcheva St. 33, 305000 Kursk, Russia
Interests: mathematical and theoretical physics; biophysics

Special Issue Information

Dear Colleagues,

Mathematical modeling is an important tool that can lead us to a deeper understanding of biological and chemical processes on various levels of a system’s organization: from the kinetics of individual chemical and biochemical reactions and genetic and metabolic networks to neuronal and population dynamics. This Special Issue will focus on a wide variety of such systems as unified by the application of modern mathematical tools for their analytical and numerical treatment. Potential submissions should report novel results and approaches that combine both a mathematical technique (including numerical simulations) and clear examples of its application to a particular problem of biology, biophysics/biochemistry, or physical chemistry, where the proposed model gives prospective insights into the principles of a system's functioning.

Prof. Dr. Eugene Postnikov
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.

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (8 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

17 pages, 4882 KiB  
Article
Mathematical and Experimental Model of Neuronal Oscillator Based on Memristor-Based Nonlinearity
by Ivan Kipelkin, Svetlana Gerasimova, Davud Guseinov, Dmitry Pavlov, Vladislav Vorontsov, Alexey Mikhaylov and Victor Kazantsev
Mathematics 2023, 11(5), 1268; https://doi.org/10.3390/math11051268 - 6 Mar 2023
Cited by 5 | Viewed by 2086
Abstract
This article presents a mathematical and experimental model of a neuronal oscillator with memristor-based nonlinearity. The mathematical model describes the dynamics of an electronic circuit implementing the FitzHugh–Nagumo neuron model. A nonlinear component of this circuit is the Au/Zr/ZrO2(Y)/TiN/Ti memristive device. [...] Read more.
This article presents a mathematical and experimental model of a neuronal oscillator with memristor-based nonlinearity. The mathematical model describes the dynamics of an electronic circuit implementing the FitzHugh–Nagumo neuron model. A nonlinear component of this circuit is the Au/Zr/ZrO2(Y)/TiN/Ti memristive device. This device is fabricated on the oxidized silicon substrate using magnetron sputtering. The circuit with such nonlinearity is described by a three-dimensional ordinary differential equation system. The effect of the appearance of spontaneous self-oscillations is investigated. A bifurcation scenario based on supercritical Andronov–Hopf bifurcation is found. The dependence of the critical point on the system parameters, particularly on the size of the electrode area, is analyzed. The self-oscillating and excitable modes are experimentally demonstrated. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

12 pages, 1874 KiB  
Article
Modeling the Kinetics of the Singlet Oxygen Effect in Aqueous Solutions of Proteins Exposed to Thermal and Laser Radiation
by Alexey V. Shkirin, Sergey N. Chirikov, Nikolai V. Suyazov, Veronika E. Reut, Daria V. Grigorieva, Irina V. Gorudko, Vadim I. Bruskov and Sergey V. Gudkov
Mathematics 2022, 10(22), 4295; https://doi.org/10.3390/math10224295 - 16 Nov 2022
Viewed by 1292
Abstract
A system of kinetic equations describing the changes in the concentration of reactive oxygen species (ROS) in aqueous solutions of proteins was obtained from the analysis of chemical reactions involving singlet oxygen. Applying the condition of the stationarity of the intermediate products to [...] Read more.
A system of kinetic equations describing the changes in the concentration of reactive oxygen species (ROS) in aqueous solutions of proteins was obtained from the analysis of chemical reactions involving singlet oxygen. Applying the condition of the stationarity of the intermediate products to the system, we determined the functional dependence of the hydrogen peroxide concentration on the protein concentration under the action of thermal and laser radiation. An approximate analytical solution to the nonlinear system of differential equations that define the ROS concentration dynamics was found. For aqueous solutions of bovine serum albumin (BSA) and bovine gamma globulin (BGG), the orders and rate constants of the reactions describing the ROS conversions were determined by minimizing the sum of squared deviations of the functions found by solving both the static and dynamic problems from experimentally measured dependences. When solving the optimization problem, the Levenberg–Marquardt algorithm was used. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

14 pages, 1735 KiB  
Article
Modeling the Cognitive Activity of an Individual Based on the Mathematical Apparatus of Self-Oscillatory Quantum Mechanics
by Alexandr Yurevich Petukhov and Yury Vasilevich Petukhov
Mathematics 2022, 10(22), 4215; https://doi.org/10.3390/math10224215 - 11 Nov 2022
Viewed by 1284
Abstract
The goal of this research is to design a model of cognitive activity in the human brain. The fundamental component of such a model is the mathematical apparatus of self-oscillating quantum mechanics considered through the theory of information images/representations. Methods. This article provides [...] Read more.
The goal of this research is to design a model of cognitive activity in the human brain. The fundamental component of such a model is the mathematical apparatus of self-oscillating quantum mechanics considered through the theory of information images/representations. Methods. This article provides a brief description of the proposed theory and highlights remarkable similarities between information images/representations and certain elementary particles, in particular—virtual Feynman particles. Following this principle, the human mind is considered as a one-dimensional potential hole with finite walls of different sizes. The internal potential barrier in this model represents the border between consciousness and subconsciousness. The authors carried out parametrization, taking into account the proposed theory. This allowed authors to lay down the foundations of the mathematical apparatus, viewing the proposed model both from the standpoint of classical quantum mechanics and through the mathematical apparatus of self-oscillatory quantum mechanics. The findings could open a way to the prediction of certain cognitive functions of the human brain. Additionally, the authors formulated the equation, which describes the state function of the information image during the cognitive activity of an individual. Conclusions. The key outcome of this research are the primary calculations of the state functions of information images/representations on the computer model, as well as the patterns of movement of the information image into and out of the human consciousness. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

18 pages, 1110 KiB  
Article
Contribution of Cardiorespiratory Coupling to the Irregular Dynamics of the Human Cardiovascular System
by Yurii M. Ishbulatov, Tatiana S. Bibicheva, Vladimir I. Gridnev, Mikhail D. Prokhorov, Marina V. Ogneva, Anton R. Kiselev and Anatoly S. Karavaev
Mathematics 2022, 10(7), 1088; https://doi.org/10.3390/math10071088 - 28 Mar 2022
Cited by 6 | Viewed by 1933
Abstract
Irregularity is an important aspect of the cardiovascular system dynamics. Numerical indices of irregularity, such as the largest Lyapunov exponent and the correlation dimension estimated from interbeat interval time series, are early markers of cardiovascular diseases. However, there is no consensus on the [...] Read more.
Irregularity is an important aspect of the cardiovascular system dynamics. Numerical indices of irregularity, such as the largest Lyapunov exponent and the correlation dimension estimated from interbeat interval time series, are early markers of cardiovascular diseases. However, there is no consensus on the origin of irregularity in the cardiovascular system. A common hypothesis suggests the importance of nonlinear bidirectional coupling between the cardiovascular system and the respiratory system for irregularity. Experimental investigations of this theory are severely limited by the capabilities of modern medical equipment and the nonstationarity of real biological systems. Therefore, we studied this problem using a mathematical model of the coupled cardiovascular system and respiratory system. We estimated and compared the numerical indices of complexity for a model simulating the cardiovascular dynamics in healthy subjects and a model with blocked regulation of the respiratory frequency and amplitude, which disturbs the coupling between the studied systems. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

14 pages, 779 KiB  
Article
The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
by Eugene B. Postnikov, Elena A. Lebedeva, Andrey Yu. Zyubin and Anastasia I. Lavrova
Mathematics 2021, 9(21), 2802; https://doi.org/10.3390/math9212802 - 4 Nov 2021
Cited by 6 | Viewed by 1969
Abstract
Raman spectra of biological objects are sufficiently complex since they are comprised of wide diffusive spectral peaks over a noisy background. This makes the resolution of individual closely positioned components a complicated task. Here we propose a method for constructing an approximation of [...] Read more.
Raman spectra of biological objects are sufficiently complex since they are comprised of wide diffusive spectral peaks over a noisy background. This makes the resolution of individual closely positioned components a complicated task. Here we propose a method for constructing an approximation of such systems by a series, respectively, to shifts of the Gaussian functions with different adjustable dispersions. It is based on the coordination of the Gaussian peaks’ location with the zeros of the signal’s Hilbert transform. The resolution of overlapping peaks is achieved by applying this procedure in a hierarchical cascade way, subsequently excluding peaks of each level of decomposition. Both the mathematical rationale for the localization of intervals, where the zero crossing of the Hilbert-transformed uni- and multimodal mixtures of Gaussians occurs, and the step-by-step outline of the numerical algorithm are provided and discussed. As a practical case study, we analyze results of the processing of a complicated Raman spectrum obtained from a strain of Mycobacterium tuberculosis. However, the proposed method can be applied to signals of different origins formed by overlapped localized pulses too. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

13 pages, 1062 KiB  
Article
Toward Minimalistic Model of Cellular Volume Dynamics in Neurovascular Unit
by Robert Loshkarev and Dmitry Postnov
Mathematics 2021, 9(19), 2407; https://doi.org/10.3390/math9192407 - 27 Sep 2021
Cited by 2 | Viewed by 1820
Abstract
The neurovascular unit (NVU) concept denotes cells and their communication mechanisms that autoregulate blood supply in the brain parenchyma. Over the past two decades, it has become clear that besides its primary function, NVU is involved in many important processes associated with maintaining [...] Read more.
The neurovascular unit (NVU) concept denotes cells and their communication mechanisms that autoregulate blood supply in the brain parenchyma. Over the past two decades, it has become clear that besides its primary function, NVU is involved in many important processes associated with maintaining brain health and that altering the proportion of the extracellular space plays a vital role in this. While biologists have studied the process of cells swelling or shrinking, the consequences of the NVU’s operation are not well understood. In addition to direct quantitative modeling of cellular processes in the NVU, there is room for developing a minimalistic mathematical description, similar to how computational neuroscience operates with very simple models of neurons, which, however, capture the main features of dynamics. In this work, we have developed a minimalistic model of cell volumes regulation in the NVU. We based our model on the FitzHugh–Nagumo model with noise excitation and supplemented it with a variable extracellular space volume. We show that such a model acquires new dynamic properties in comparison with the traditional neuron model. To validate our approach, we adjusted the parameters of the minimalistic model so that its behavior fits the dynamics computed using the high-dimensional quantitative and biophysically relevant model. The results show that our model correctly describes the change in cell volume and intercellular space in the NVU. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

25 pages, 1012 KiB  
Article
Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability
by Haiyue Chen, Benedikt Haus and Paolo Mercorelli
Mathematics 2021, 9(17), 2076; https://doi.org/10.3390/math9172076 - 27 Aug 2021
Cited by 13 | Viewed by 3235
Abstract
Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of [...] Read more.
Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of different considered populations as Susceptible, Exposed, Infected and Recovered compartments (SEIR). This study derives control-oriented compartmental models of the pandemic, together with constructive control laws based on the Lyapunov theory. The paper presents the derivation of new vaccination and quarantining strategies, found using compartmental models and design methods from the field of Lyapunov theory. The Lyapunov theory offers the possibility to track desired trajectories, guaranteeing the stability of the controlled system. Computer simulations aid to demonstrate the efficacy of the results. Stabilizing control laws are obtained and analyzed for multiple variants of the model. The stability, constructivity, and feasibility are proven for each Lyapunov-like function. Obtaining the proof of practical stability for the controlled system, several interesting system properties such as herd immunity are shown. On the basis of a generalized SEIR model and an extended variant with additional Protected and Quarantined compartments, control strategies are conceived by using two fundamental system inputs, vaccination and quarantine, whose influence on the system is a crucial part of the model. Simulation results prove that Lyapunov-based approaches yield effective control of the disease transmission. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

14 pages, 454 KiB  
Article
A Review of Matrix SIR Arino Epidemic Models
by Florin Avram, Rim Adenane and David I. Ketcheson
Mathematics 2021, 9(13), 1513; https://doi.org/10.3390/math9131513 - 28 Jun 2021
Cited by 11 | Viewed by 4064
Abstract
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call [...] Read more.
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-8
Back to TopTop