The work focuses on mathematical modeling of linear growth marine red algae Porphyridium purpureum batch culture under various surface irradiation. Before starting the batch culture P. purpureum was maintained for 3–5 days in turbidostat, which allowed the culture to adapt to a given light intensity. On each batch curve the maximum specific growth rate and maximum productivity are determined by approximating the exponential and linear growth phases with the appropriate equations. It is taken into account that at the beginning of the linear growth phase the integral light absorption coefficient, calculated from the true absorption spectrum in PAR range, exceeded 50 %. It is shown that with light intensity increase from 15 to 227 µmol photons m–2·s–1 the maximum specific growth rate increased from 0.31 to 1 day–1, the maximum productivity increased from 1.32 to 16.38 g DW m–2·day–1. Mathematical modeling of the linear growth of P. purpureum batch culture have showed that at any light intensity the specific growth rate is determined by the surface illumination, the light absorption coefficient and chlorophyll a concentration. The concept of reduced irradiation – the amount of absorbed light energy per chlorophyll a – was introduced. A linear dependence of the specific growth rate on reduced irradiation is given. The tangent of the angle of line slope is determined by the organization of the key multi-enzyme complex («metabolism bottleneck»). Parameters of this complex depend on the cells photoadaptation degree. For the first time a quantitative relationship between multi-enzyme complex parameters, light intensity and the chlorophyll / P700 ratio was established.
{"title":"Modeling Growth and Photoadaptation of Porphyridium purpureum Batch Culture","authors":"A. Lelekov, V. Klochkova","doi":"10.17537/2024.19.169","DOIUrl":"https://doi.org/10.17537/2024.19.169","url":null,"abstract":"\u0000 The work focuses on mathematical modeling of linear growth marine red algae Porphyridium purpureum batch culture under various surface irradiation. Before starting the batch culture P. purpureum was maintained for 3–5 days in turbidostat, which allowed the culture to adapt to a given light intensity. On each batch curve the maximum specific growth rate and maximum productivity are determined by approximating the exponential and linear growth phases with the appropriate equations. It is taken into account that at the beginning of the linear growth phase the integral light absorption coefficient, calculated from the true absorption spectrum in PAR range, exceeded 50 %. It is shown that with light intensity increase from 15 to 227 µmol photons m–2·s–1 the maximum specific growth rate increased from 0.31 to 1 day–1, the maximum productivity increased from 1.32 to 16.38 g DW m–2·day–1. Mathematical modeling of the linear growth of P. purpureum batch culture have showed that at any light intensity the specific growth rate is determined by the surface illumination, the light absorption coefficient and chlorophyll a concentration. The concept of reduced irradiation – the amount of absorbed light energy per chlorophyll a – was introduced. A linear dependence of the specific growth rate on reduced irradiation is given. The tangent of the angle of line slope is determined by the organization of the key multi-enzyme complex («metabolism bottleneck»). Parameters of this complex depend on the cells photoadaptation degree. For the first time a quantitative relationship between multi-enzyme complex parameters, light intensity and the chlorophyll / P700 ratio was established.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"122 50","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141362595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.
本文提出了一个数学模型，描述了 HIV-1 感染在感染者单个淋巴结中传播的初始阶段。模型变量为病毒颗粒、CD4+ T 淋巴细胞和抗原递呈细胞的数量。在建立模型时，使用了一个带有延迟的高维微分方程系统，并补充了初始数据。其中一些模型方程考虑到了病毒粒子和参与感染过程的细胞的中间发展阶段。在初始数据为非负的情况下，确定了模型解在半轴上的分量的存在性、唯一性和非负性。此外，还获得了被解释为淋巴结中不存在 HIV-1 感染的平衡状态的渐进稳定性条件。为了对模型进行数值求解，采用了半隐式欧拉方案。对淋巴结中 HIV-1 感染的衰减和感染者机体内感染开始全身扩散的条件进行了分析和数值计算。
{"title":"Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node","authors":"N. Pertsev, G. Bocharov, K. Loginov","doi":"10.17537/2024.19.112","DOIUrl":"https://doi.org/10.17537/2024.19.112","url":null,"abstract":"\u0000 A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"20 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140707584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Model of closed microecosystem “algae - heterotrophic bacteria” is proposed in this paper. Mathematical model is the Cauchy problem for system of nonlinear ordinary differential equations. To develop the model the Liebig’s law of the minimum is consistently used for both specific rate of biomass growth and specific death rate of algae and bacteria cells. To describe the specific rate of substrate utilization by algae and bacteria the Andrew’s model (substrate inhibition) is used. It is assumed that specific death rate of algae and bacteria cells increases with decreasing substrate concentration. It is also assumed that carbon and nitrogen are main biogenic elements, and in the system they are in the form of mineral substrate (CO2, NO2, NO3, NH4) and biological substrate (proteins, lipids and carbohydrates). Mathematical model describing time variations in concentration of elements of microecosystem is formulated under the following assumptions: 1) stoichiometric coefficients of algae and bacteria cells are constant in the development of microecosystem; 2) utilization of carbon and nitrogen by algae and bacteria occurs independently; 3) oxygen produced by algae cells during photosynthesis completely covers the demand for oxygen for algae and bacteria cells. To verify the proposed model experimental data for microecosystems «Clorella vulgaris – Pseudomonas sp.» и «Scenedesmus obliquus – Pseudomonas sp.» are used. These systems were studied in laboratory conditions, and concentrations of elements of microecosystems in stationary state were obtained. Parameters of functions describing specific rate of utilization of biogenic elements were derived from experimental data for growth kinetics of algae and bacteria. Concentration of the biomass in stationary state obtained with the use of the proposed model is in reasonable agreement with experimental data.
{"title":"Mathematical Model of Closed Microecosystem “Algae – Heterotrophic Bacteria”","authors":"V. Zalizniak, O. A. Zolotov","doi":"10.17537/2024.19.96","DOIUrl":"https://doi.org/10.17537/2024.19.96","url":null,"abstract":"\u0000 Model of closed microecosystem “algae - heterotrophic bacteria” is proposed in this paper. Mathematical model is the Cauchy problem for system of nonlinear ordinary differential equations. To develop the model the Liebig’s law of the minimum is consistently used for both specific rate of biomass growth and specific death rate of algae and bacteria cells. To describe the specific rate of substrate utilization by algae and bacteria the Andrew’s model (substrate inhibition) is used. It is assumed that specific death rate of algae and bacteria cells increases with decreasing substrate concentration. It is also assumed that carbon and nitrogen are main biogenic elements, and in the system they are in the form of mineral substrate (CO2, NO2, NO3, NH4) and biological substrate (proteins, lipids and carbohydrates). Mathematical model describing time variations in concentration of elements of microecosystem is formulated under the following assumptions: 1) stoichiometric coefficients of algae and bacteria cells are constant in the development of microecosystem; 2) utilization of carbon and nitrogen by algae and bacteria occurs independently; 3) oxygen produced by algae cells during photosynthesis completely covers the demand for oxygen for algae and bacteria cells. To verify the proposed model experimental data for microecosystems «Clorella vulgaris – Pseudomonas sp.» и «Scenedesmus obliquus – Pseudomonas sp.» are used. These systems were studied in laboratory conditions, and concentrations of elements of microecosystems in stationary state were obtained. Parameters of functions describing specific rate of utilization of biogenic elements were derived from experimental data for growth kinetics of algae and bacteria. Concentration of the biomass in stationary state obtained with the use of the proposed model is in reasonable agreement with experimental data.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"20 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140746323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Using a drug repurposing strategy, virtual screening of potential inhibitors of the NHR domain of the HIV-1 gp41 protein, a conserved region critical for the virus-cell membrane fusion and viral infectivity, was carried out. The used computational approach included: (1) molecular docking of this functionally significant region of the HIV-1 envelope with compounds from a library of bioactive molecules containing clinically approved drugs, experimental drugs, and investigational drug candidates; (2) assessing the binding affinity of these compounds to the therapeutic target; (3) molecular dynamics simulations of ligand/NHR-gp41 complexes; (4) calculations of the binding free energy followed by the analysis of molecular dynamics trajectories and selection of compounds promising to test for anti-HIV-1 activity. As a result, six compounds that exhibited the high binding affinity to the NHR domain of the HIV-1 gp41 protein and showed acceptable pharmacological properties were identified. The predicted compounds are assumed to form a promising basis for the development of new, effective and safe broad-spectrum antiviral agents able to inhibit the HIV-1 entry into the host cell.
{"title":"Using a Drug Repurposing Strategy to Virtually Screen Potential HIV-1 Entry Inhibitors That Block the NHR Domain of the Viral Envelope Protein gp41","authors":"A. Andrianov, Y.V. Laykov, A. Tuzikov","doi":"10.17537/2024.19.77","DOIUrl":"https://doi.org/10.17537/2024.19.77","url":null,"abstract":"\u0000 Using a drug repurposing strategy, virtual screening of potential inhibitors of the NHR domain of the HIV-1 gp41 protein, a conserved region critical for the virus-cell membrane fusion and viral infectivity, was carried out. The used computational approach included: (1) molecular docking of this functionally significant region of the HIV-1 envelope with compounds from a library of bioactive molecules containing clinically approved drugs, experimental drugs, and investigational drug candidates; (2) assessing the binding affinity of these compounds to the therapeutic target; (3) molecular dynamics simulations of ligand/NHR-gp41 complexes; (4) calculations of the binding free energy followed by the analysis of molecular dynamics trajectories and selection of compounds promising to test for anti-HIV-1 activity. As a result, six compounds that exhibited the high binding affinity to the NHR domain of the HIV-1 gp41 protein and showed acceptable pharmacological properties were identified. The predicted compounds are assumed to form a promising basis for the development of new, effective and safe broad-spectrum antiviral agents able to inhibit the HIV-1 entry into the host cell.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"43 34","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140752122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper delves into the application of fractional calculus, with a focus on Caputo derivatives, in epidemiological models using ordinary differential equations. It highlights the critical role Caputo derivatives play in modeling intricate systems with memory effects and assesses various epidemiological models, including SIR variants, demonstrating how Caputo derivatives capture fractional-order dynamics and memory phenomena found in real epidemics. The study showcases the utility of Laplace transformations for analyzing systems described by ordinary differential equations with Caputo derivatives. This approach facilitates both analytical and numerical methods for system analysis and parameter estimation. Additionally, the paper introduces a tabular representation for epidemiological models, enabling a visual and analytical exploration of variable relationships and dynamics. This matrix-based framework permits the application of linear algebra techniques to assess stability and equilibrium points, yielding valuable insights into long-term behavior and control strategies. In summary, this research underscores the significance of Caputo derivatives, Laplace transformations, and matrix representation in epidemiological modeling. We assume that by using this type of methodology we can get analytic solutions by hand when considering a function as constant in certain cases and it will not be necessary to search for numerical methods.
本文深入探讨了分数微积分在使用常微分方程的流行病学模型中的应用，重点是卡普托导数。它强调了卡普托导数在模拟具有记忆效应的复杂系统中发挥的关键作用，并评估了各种流行病学模型，包括 SIR 变体，展示了卡普托导数如何捕捉真实流行病中的分数阶动态和记忆现象。这项研究展示了拉普拉斯变换在分析由带有卡普托导数的常微分方程描述的系统时的实用性。这种方法有助于采用分析和数值方法进行系统分析和参数估计。此外，论文还介绍了流行病学模型的表格表示法，从而能够对变量关系和动态进行可视化和分析性探索。这种基于矩阵的框架允许应用线性代数技术来评估稳定性和平衡点，从而为长期行为和控制策略提供有价值的见解。总之，这项研究强调了卡普托导数、拉普拉斯变换和矩阵表示法在流行病学建模中的重要性。我们假定，在某些情况下，将函数视为常数时，通过使用这类方法，我们可以用手得到解析解，而无需寻找数值方法。
{"title":"Applying Laplace Transformation on Epidemiological Models as Caputo Derivatives","authors":"Nikolaos Gkrekas","doi":"10.17537/2024.19.61","DOIUrl":"https://doi.org/10.17537/2024.19.61","url":null,"abstract":"\u0000 This paper delves into the application of fractional calculus, with a focus on Caputo derivatives, in epidemiological models using ordinary differential equations. It highlights the critical role Caputo derivatives play in modeling intricate systems with memory effects and assesses various epidemiological models, including SIR variants, demonstrating how Caputo derivatives capture fractional-order dynamics and memory phenomena found in real epidemics. The study showcases the utility of Laplace transformations for analyzing systems described by ordinary differential equations with Caputo derivatives. This approach facilitates both analytical and numerical methods for system analysis and parameter estimation. Additionally, the paper introduces a tabular representation for epidemiological models, enabling a visual and analytical exploration of variable relationships and dynamics. This matrix-based framework permits the application of linear algebra techniques to assess stability and equilibrium points, yielding valuable insights into long-term behavior and control strategies. In summary, this research underscores the significance of Caputo derivatives, Laplace transformations, and matrix representation in epidemiological modeling. We assume that by using this type of methodology we can get analytic solutions by hand when considering a function as constant in certain cases and it will not be necessary to search for numerical methods.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"89 26","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140377673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fatimah A. Abdul Jabbar, R. AlChalabi, Ahmed Yaseen AL-Tarboolee, S.A. Shaban, Ahmed A.J. Suleiman
Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal malignancy that poses a significant global health threat, marked by a substantial increase in prevalence and mortality rates. Accounting for 90 % of pancreatic cancer cases, PDAC carries a dismal prognosis, and current therapeutic approaches, including immunotherapy, face challenges due to poor immunogenicity. This study aimed to discover differentially expressed immune genes shared between PDAC and normal samples from two datasets obtained from the NCBI GEO Dataset. The RNA-seq pipeline was employed for gene expression analysis, and enrichR facilitated functional enrichment analysis of biologically and statistically significant genes. Predictions of immune infiltration cells and corresponding genes, along with their immune responses, were made using the ScType database and the immunedeconv package, respectively. Verification of gene expression levels was conducted through GEPIA2, Expression Atlas, and literature review. Additionally, isoform-switching analysis of dysregulated genes aimed to uncover alternatively spliced pathogenic isoforms in PDAC. Notably, four immune genes (EPHA2 upregulated, GNG11, CRHBP, and FCER1A downregulated) were found to be common in both datasets and were highly implicated in PDAC. The dysregulated immune genes influenced molecular functions, including protein binding, transmembrane receptor protein tyrosine kinase activity, protein tyrosine kinase activity, and cadherin binding for upregulated genes. Downregulated genes were associated with GTPase activity and ribonucleoside triphosphate phosphatase activity. This study suggests these immune genes as potential prognostic biomarkers for effective PDAC treatment. However, further investigations are essential to unravel the functional perspectives of potential isoforms.
{"title":"Alternative Splicing in Pancreatic Ductal Adenocarcinoma Leads to Dysregulated Immune System","authors":"Fatimah A. Abdul Jabbar, R. AlChalabi, Ahmed Yaseen AL-Tarboolee, S.A. Shaban, Ahmed A.J. Suleiman","doi":"10.17537/2024.19.15","DOIUrl":"https://doi.org/10.17537/2024.19.15","url":null,"abstract":"\u0000 Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal malignancy that poses a significant global health threat, marked by a substantial increase in prevalence and mortality rates. Accounting for 90 % of pancreatic cancer cases, PDAC carries a dismal prognosis, and current therapeutic approaches, including immunotherapy, face challenges due to poor immunogenicity. This study aimed to discover differentially expressed immune genes shared between PDAC and normal samples from two datasets obtained from the NCBI GEO Dataset. The RNA-seq pipeline was employed for gene expression analysis, and enrichR facilitated functional enrichment analysis of biologically and statistically significant genes. Predictions of immune infiltration cells and corresponding genes, along with their immune responses, were made using the ScType database and the immunedeconv package, respectively. Verification of gene expression levels was conducted through GEPIA2, Expression Atlas, and literature review. Additionally, isoform-switching analysis of dysregulated genes aimed to uncover alternatively spliced pathogenic isoforms in PDAC. Notably, four immune genes (EPHA2 upregulated, GNG11, CRHBP, and FCER1A downregulated) were found to be common in both datasets and were highly implicated in PDAC. The dysregulated immune genes influenced molecular functions, including protein binding, transmembrane receptor protein tyrosine kinase activity, protein tyrosine kinase activity, and cadherin binding for upregulated genes. Downregulated genes were associated with GTPase activity and ribonucleoside triphosphate phosphatase activity. This study suggests these immune genes as potential prognostic biomarkers for effective PDAC treatment. However, further investigations are essential to unravel the functional perspectives of potential isoforms.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"20 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140427227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. A. Grigoriev, E. A. Isaev, D. Pervukhin, V. N. Petrushin, F. Doronin, Y. Rudyak, G. Rytikov, V. Nazarov
The work is devoted to the use of methods of applied mathematics and statistics for the formalization and mathematical modeling of the structure of shark skin as a prototype of new polymer materials for shipbuilding purposes. A technique for mathematical modeling of biological objects is described, and a method for using a biomimetic approach for the design of planar composite polymer materials with improved lyophilic adhesion properties is proposed. Because of studying images of shark skin obtained using high-resolution optical (HRO) and scanning electron (SEM) microscopy, we found that its texture is anisotropic. Quantitative analysis of BOM and SEM images made it possible to rationalize the choice of synthetic digital models intended for simulation prototyping of maximally and minimally texturally isotropic polymer samples using 3D printing and gas-phase surface modification.
该研究致力于利用应用数学和统计学方法，对鲨鱼皮的结构进行形式化和数学建模，将其作为造船用新型聚合物材料的原型。文中介绍了一种生物物体数学建模技术，并提出了一种利用仿生方法设计具有更好冻干粘附性能的平面复合聚合物材料的方法。通过研究使用高分辨率光学显微镜（HRO）和扫描电子显微镜（SEM）获得的鲨鱼皮图像，我们发现鲨鱼皮的纹理是各向异性的。通过对 BOM 和 SEM 图像进行定量分析，我们可以合理地选择合成数字模型，以便利用三维打印和气相表面改性技术模拟制作最大和最小各向同性聚合物样品的原型。
{"title":"A Biomimetic Approach to the Creation of Polymer Materials with Improved Tribological Properties","authors":"A. A. Grigoriev, E. A. Isaev, D. Pervukhin, V. N. Petrushin, F. Doronin, Y. Rudyak, G. Rytikov, V. Nazarov","doi":"10.17537/2024.19.1","DOIUrl":"https://doi.org/10.17537/2024.19.1","url":null,"abstract":"\u0000 The work is devoted to the use of methods of applied mathematics and statistics for the formalization and mathematical modeling of the structure of shark skin as a prototype of new polymer materials for shipbuilding purposes. A technique for mathematical modeling of biological objects is described, and a method for using a biomimetic approach for the design of planar composite polymer materials with improved lyophilic adhesion properties is proposed. Because of studying images of shark skin obtained using high-resolution optical (HRO) and scanning electron (SEM) microscopy, we found that its texture is anisotropic. Quantitative analysis of BOM and SEM images made it possible to rationalize the choice of synthetic digital models intended for simulation prototyping of maximally and minimally texturally isotropic polymer samples using 3D printing and gas-phase surface modification.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"30 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140510290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V.S. Bystrov, E. Paramonova, S.V. Filippov, L. Avakyan, M. Chaikina, N. V. Eremina, S.V. Makarova, N. Bulina
The results of calculations of the substitution of calcium atoms for zinc in the structure of hydroxyapatite using density functional theory methods using hybrid functionals in the supercell model are presented. Changes in the parameters and volume of the unit cell, energy bands and energy of formation of substitutions with increasing number of substitutions in different positions of calcium (Ca1 and Ca2) are analyzed in comparison with experimental data. A proportional decrease in the parameters and volume of the cell with an increase in the number of substitutions has been established, and a more complex behavior of various cell parameters has been revealed, which is a consequence of the violation of the original symmetry. Electronic energy levels were found to depend on the zinc concentration and the positions of the calcium ions being replaced. In this case, the band gap Eg of hydroxyapatite experiences a jump of 0.6–0.8 eV with the introduction of one zinc ion per supercell, and then decreases and reaches values below the initial Eg value by 0.5–0.6 eV for substitutions in Ca1 positions, and by 0.8–0.9 eV for substitutions in Ca2 positions. It has been shown that the energy of substitution has a complex dependence on the concentration of the substituent and the replacement of calcium ions with zinc occurs predominantly in the Ca2 position over the entire concentration range. An analysis of changes in interatomic distances during the process of relaxation to the equilibrium state at different zinc concentrations was carried out. We revealed formation of bonds between zinc atoms and nearby oxygen anions, which violates the original symmetry of hydroxypatite structures. The data obtained are important for understanding the structural changes that occur during substitution, as well as for understanding and predicting the properties of synthesized biocompatible materials.
{"title":"Zinc-Substituted Structures of Hydroxyapatite: Modeling and Experiment","authors":"V.S. Bystrov, E. Paramonova, S.V. Filippov, L. Avakyan, M. Chaikina, N. V. Eremina, S.V. Makarova, N. Bulina","doi":"10.17537/2023.18.580","DOIUrl":"https://doi.org/10.17537/2023.18.580","url":null,"abstract":"\u0000 The results of calculations of the substitution of calcium atoms for zinc in the structure of hydroxyapatite using density functional theory methods using hybrid functionals in the supercell model are presented. Changes in the parameters and volume of the unit cell, energy bands and energy of formation of substitutions with increasing number of substitutions in different positions of calcium (Ca1 and Ca2) are analyzed in comparison with experimental data. A proportional decrease in the parameters and volume of the cell with an increase in the number of substitutions has been established, and a more complex behavior of various cell parameters has been revealed, which is a consequence of the violation of the original symmetry. Electronic energy levels were found to depend on the zinc concentration and the positions of the calcium ions being replaced. In this case, the band gap Eg of hydroxyapatite experiences a jump of 0.6–0.8 eV with the introduction of one zinc ion per supercell, and then decreases and reaches values below the initial Eg value by 0.5–0.6 eV for substitutions in Ca1 positions, and by 0.8–0.9 eV for substitutions in Ca2 positions. It has been shown that the energy of substitution has a complex dependence on the concentration of the substituent and the replacement of calcium ions with zinc occurs predominantly in the Ca2 position over the entire concentration range. An analysis of changes in interatomic distances during the process of relaxation to the equilibrium state at different zinc concentrations was carried out. We revealed formation of bonds between zinc atoms and nearby oxygen anions, which violates the original symmetry of hydroxypatite structures. The data obtained are important for understanding the structural changes that occur during substitution, as well as for understanding and predicting the properties of synthesized biocompatible materials.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138948677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The phytoplankton in an aquatic ecosystem is the basis of its life activity and the main producing link. The functioning of phytoplankton in same time depends on environmental factors: mineral nutrition, photosynthetically active solar radiation, water temperature and other less significant ones. Sunlight is a stable factor, varying predictably over time and space. The water temperature is the small regulatory factor. Concentrations of mineral substances can change quite quickly and significantly, this much influences on plant organisms. Thus, mineral nutrition is a basic environmental factor of influence to phytoplankton. On the other hand, in large aquatic basin such as seas and oceanic areas the distribution of living organisms is very heterogeneous in space. These two aspects – nutrient and spatial heterogeneity – are the focus of this article. A model of competitive interaction is considered using the example of two species of phytoplankton. The phytoplankton move passively in water what is simulated by the diffusion process. The model contains one non-trivial stationary and spatially homogeneous equilibrium and two trivial ones, i.e. degenerate in at least one species of phytoplankton. Trivial equilibria are stable only in some “degenerate” situations. The non-trivial equilibrium in “normal” conditions is stable to temporal and spatial disturbances. The behavior of solutions near a nontrivial equilibrium for a stationary living environment and in cases of its nonstationary is studied. Perturbation of a nontrivial equilibrium in a stationary environment leads to relatively long-term deviations from equilibrium and a slow return to it. The instability of trivial equilibria increases the spatial heterogeneity of solutions. At the same time, the nontrivial equilibrium computationally demonstrates weak properties of global stability in time. The unsteadiness of the environment is simulated by the unsteadiness of the influx of nutrients. It has been shown that the distribution of nutrients can lead to significant heterogeneity in the distribution of individuals across the spatial habitat.
{"title":"Mathematical Model of Phytoplankton Interspecific Competition for Food Resource","authors":"A. Abakumov, I.S. Kozitskaya","doi":"10.17537/2023.18.568","DOIUrl":"https://doi.org/10.17537/2023.18.568","url":null,"abstract":"\u0000 The phytoplankton in an aquatic ecosystem is the basis of its life activity and the main producing link. The functioning of phytoplankton in same time depends on environmental factors: mineral nutrition, photosynthetically active solar radiation, water temperature and other less significant ones. Sunlight is a stable factor, varying predictably over time and space. The water temperature is the small regulatory factor. Concentrations of mineral substances can change quite quickly and significantly, this much influences on plant organisms. Thus, mineral nutrition is a basic environmental factor of influence to phytoplankton. On the other hand, in large aquatic basin such as seas and oceanic areas the distribution of living organisms is very heterogeneous in space. These two aspects – nutrient and spatial heterogeneity – are the focus of this article. A model of competitive interaction is considered using the example of two species of phytoplankton. The phytoplankton move passively in water what is simulated by the diffusion process. The model contains one non-trivial stationary and spatially homogeneous equilibrium and two trivial ones, i.e. degenerate in at least one species of phytoplankton. Trivial equilibria are stable only in some “degenerate” situations. The non-trivial equilibrium in “normal” conditions is stable to temporal and spatial disturbances. The behavior of solutions near a nontrivial equilibrium for a stationary living environment and in cases of its nonstationary is studied. Perturbation of a nontrivial equilibrium in a stationary environment leads to relatively long-term deviations from equilibrium and a slow return to it. The instability of trivial equilibria increases the spatial heterogeneity of solutions. At the same time, the nontrivial equilibrium computationally demonstrates weak properties of global stability in time. The unsteadiness of the environment is simulated by the unsteadiness of the influx of nutrients. It has been shown that the distribution of nutrients can lead to significant heterogeneity in the distribution of individuals across the spatial habitat.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a systematic approach to modelling the responses of the immune system to virus infections. Two continuous-discrete stochastic models arising in mathematical immunology are developed and computationally implemented. The variables of the models are integer random variables that denote the quantity of individuals (cells and viral particles), and sets of unique types of individuals that take into account the current state and history of stay of individuals in some stages of their development. The distribution laws of the durations of the mentioned stages are different from exponential or geometric. A probabilistic description of a one-stage stochastic model of population dynamics is presented. A stochastic model of the development of HIV-1 infection in the lymph node in the initial period after infection of a healthy person is formulated. A computational algorithm based on the Monte Carlo method is given. Each of the stochastic models is complemented by a deterministic analogue in the form of integral and delay differential equations. The results of numerical simulation are presented.
{"title":"Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics","authors":"N. Pertsev, K. Loginov","doi":"10.17537/2023.18.543","DOIUrl":"https://doi.org/10.17537/2023.18.543","url":null,"abstract":"\u0000 We present a systematic approach to modelling the responses of the immune system to virus infections. Two continuous-discrete stochastic models arising in mathematical immunology are developed and computationally implemented. The variables of the models are integer random variables that denote the quantity of individuals (cells and viral particles), and sets of unique types of individuals that take into account the current state and history of stay of individuals in some stages of their development. The distribution laws of the durations of the mentioned stages are different from exponential or geometric. A probabilistic description of a one-stage stochastic model of population dynamics is presented. A stochastic model of the development of HIV-1 infection in the lymph node in the initial period after infection of a healthy person is formulated. A computational algorithm based on the Monte Carlo method is given. Each of the stochastic models is complemented by a deterministic analogue in the form of integral and delay differential equations. The results of numerical simulation are presented.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"137 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139003979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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