Pub Date : 2023-10-17DOI: 10.55630/j.biomath.2023.08.047
Oleh Pundyak
This article proposes a model for swimming of red algae spores. The model considers a released spore in unbound water as a spherical particle enclosing a liquid incompressible cytosol, in which oscillates a solid spherical organelle. An analysis of the solutions of the Navier-Stokes equations for the cytosol flow caused by the organelle motion within the cell is presented in the limit of small Reynolds number. It is shown that in the case when the cytosol has Newtonian or Maxwell properties, the spore may swim only when the forward and backward trajectories of the organelle are different. In the case of the shear thinning cytosol properties the spore may swim also when the organelle trajectories are the same, but the velocities of forward and backward movements of the organelle should differ. Such a cell may swim in a straight line. The swimming of the model spores completely satisfies experimental data.
{"title":"Possible means of swimming of red algae spores","authors":"Oleh Pundyak","doi":"10.55630/j.biomath.2023.08.047","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.08.047","url":null,"abstract":"This article proposes a model for swimming of red algae spores. The model considers a released spore in unbound water as a spherical particle enclosing a liquid incompressible cytosol, in which oscillates a solid spherical organelle. An analysis of the solutions of the Navier-Stokes equations for the cytosol flow caused by the organelle motion within the cell is presented in the limit of small Reynolds number. It is shown that in the case when the cytosol has Newtonian or Maxwell properties, the spore may swim only when the forward and backward trajectories of the organelle are different. In the case of the shear thinning cytosol properties the spore may swim also when the organelle trajectories are the same, but the velocities of forward and backward movements of the organelle should differ. Such a cell may swim in a straight line. The swimming of the model spores completely satisfies experimental data.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033236","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}
Pub Date : 2023-07-28DOI: 10.55630/j.biomath.2023.07.207
José Paulo Carvalho dos Santos, Evandro Monteiro, J. C. Ferreira, Nelson Henrique Teixeira Lemes, D. S. Rodrigues
In this paper, we study the well-posedness and the qualitative behavior of equilibria of a SEIR epidemic models with spatial diffusion for the spreading of COVID-19. The well-posedness of the model is proved using both the Semigroup Theory of sectorial operators and existence results for abstract parabolic differential equations. The asymptotical local stability of both disease-free and endemic equilibria are established using standard linearization theory, and confirmed by illustrative numerical simulations. The asymptotical global stability of both disease-free and endemic equilibria are established using a Lyapunov function.
{"title":"Well-posedness and qualitative analysis of a SEIR model with spatial diffusion for COVID-19 spreading","authors":"José Paulo Carvalho dos Santos, Evandro Monteiro, J. C. Ferreira, Nelson Henrique Teixeira Lemes, D. S. Rodrigues","doi":"10.55630/j.biomath.2023.07.207","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.07.207","url":null,"abstract":"In this paper, we study the well-posedness and the qualitative behavior of equilibria of a SEIR epidemic models with spatial diffusion for the spreading of COVID-19. The well-posedness of the model is proved using both the Semigroup Theory of sectorial operators and existence results for abstract parabolic differential equations. The asymptotical local stability of both disease-free and endemic equilibria are established using standard linearization theory, and confirmed by illustrative numerical simulations. The asymptotical global stability of both disease-free and endemic equilibria are established using a Lyapunov function.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47202347","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}
Pub Date : 2023-04-28DOI: 10.55630/j.biomath.2023.01.307
Lingga Sanjaya Putra Mahardhika, F. Adi-Kusumo, D. Ertiningsih
In this paper is considered a microalgae growth model under the influence of sunlight. The model is a two-dimensional system of the first order Ordinary Differential Equations (ODE) with a ten-dimensional parameter space. For this model, we study the existence of equilibrium points and their stability, and determine a bifurcation of the system when the value of some parameters is varied. The Lambert w function is used to calculate equilibrium points and apply the linearization technique to provide their stabilities. By varying the value of some parameters numerically, we found a transcritical bifurcation of the system and show stability regions of the equilibrium points in parameter diagrams. The bifurcation shows that the microalgae have a minimum sustainable nutrition supply and have a minimum light intensity that plays an important role for survival in a chemostat which has a certain depth. The results can be used to design a chemostat in optimizing the growth of microalgae.
{"title":"Bifurcation analysis of a mathematical model of microalgae growth under the influence of sunlight","authors":"Lingga Sanjaya Putra Mahardhika, F. Adi-Kusumo, D. Ertiningsih","doi":"10.55630/j.biomath.2023.01.307","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.01.307","url":null,"abstract":"\u0000\u0000\u0000In this paper is considered a microalgae growth model under the influence of sunlight. The model is a two-dimensional system of the first order Ordinary Differential Equations (ODE) with a ten-dimensional parameter space. For this model, we study the existence of equilibrium points and their stability, and determine a bifurcation of the system when the value of some parameters is varied. The Lambert w function is used to calculate equilibrium points and apply the linearization technique to provide their stabilities. By varying the value of some parameters numerically, we found a transcritical bifurcation of the system and show stability regions of the equilibrium points in parameter diagrams. The bifurcation shows that the microalgae have a minimum sustainable nutrition supply and have a minimum light intensity that plays an important role for survival in a chemostat which has a certain depth. The results can be used to design a chemostat in optimizing the growth of microalgae.\u0000\u0000\u0000","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49030421","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}
Pub Date : 2023-01-27DOI: 10.55630/j.biomath.2022.12.207
Julien Arino, khalid el hail, M. Khaladi, A. Ouhinou
We investigate a model of the early stage of the COVID-19 epidemic comprising undetected infected individuals as well as behavioural change towards the use of self-protection measures. The model is fitted to China data reported between 22 January and 29 June 2020. Using fitting results, we then consider model responses to varying screening intensities.
{"title":"A model for the early COVID-19 outbreak in China with case detection and behavioural change","authors":"Julien Arino, khalid el hail, M. Khaladi, A. Ouhinou","doi":"10.55630/j.biomath.2022.12.207","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.12.207","url":null,"abstract":"We investigate a model of the early stage of the COVID-19 epidemic comprising undetected infected individuals as well as behavioural change towards the use of self-protection measures. The model is fitted to China data reported between 22 January and 29 June 2020. Using fitting results, we then consider model responses to varying screening intensities.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46797874","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}
Pub Date : 2022-12-22DOI: 10.55630/j.biomath.2022.12.149
K. Al-Maqrashi, F. Al-Musalhi, I. Elmojtaba, N. Al-Salti
A mathematical model of Zika virus transmission, incorporating human movement between rural areas and nearby forests, is presented to investigate the role of human movement in the spread of Zika virus infections in human and mosquito populations. Proportions of both susceptible and infected humans living in rural areas are assumed to move to nearby forest areas. Direct, indirect, and vertical transmission routes are incorporated for all populations. A mathematical analysis of the proposed model is presented. The analysis starts with normalizing the proposed model. The positivity and boundedness of solutions to the normalized model are then addressed. The basic reproduction number is calculated using the next-generation matrix method and its relation to the three routes of disease transmission has been presented. The sensitivity analysis of the basic reproduction number to all model parameters is investigated. The analysis also includes the existence and stability of disease-free and endemic equilibrium points. Bifurcation analysis is also carried out. Finally, numerical solutions to the normalized model are obtained to confirm the theoretical results and demonstrate human movement's role in disease transmission in human and mosquito populations.
{"title":"Investigating the Role of Mobility between Rural Areas and Forests on the Spread of Zika","authors":"K. Al-Maqrashi, F. Al-Musalhi, I. Elmojtaba, N. Al-Salti","doi":"10.55630/j.biomath.2022.12.149","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.12.149","url":null,"abstract":"A mathematical model of Zika virus transmission, incorporating human movement between rural areas and nearby forests, is presented to investigate the role of human movement in the spread of Zika virus infections in human and mosquito populations. Proportions of both susceptible and infected humans living in rural areas are assumed to move to nearby forest areas. Direct, indirect, and vertical transmission routes are incorporated for all populations. A mathematical analysis of the proposed model is presented. The analysis starts with normalizing the proposed model. The positivity and boundedness of solutions to the normalized model are then addressed. The basic reproduction number is calculated using the next-generation matrix method and its relation to the three routes of disease transmission has been presented. The sensitivity analysis of the basic reproduction number to all model parameters is investigated. The analysis also includes the existence and stability of disease-free and endemic equilibrium points. Bifurcation analysis is also carried out. Finally, numerical solutions to the normalized model are obtained to confirm the theoretical results and demonstrate human movement's role in disease transmission in human and mosquito populations.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44144790","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}
Pub Date : 2022-11-14DOI: 10.55630/j.biomath.2022.10.119
Z. Ivanova, Tihomir Ivanov
In the present work, we propose a new integrated mathematical model of neuromuscular activation. It combines the Izhikevich model of neural activity with the Williams model of calcium activity inside the muscle cell and a Hill-type model for the resultant muscle force. The coupling is done using a heuristic approach. The aim is to construct a simple model, which has biophysically meaningful parameters and is applicable to the study of neuromuscular diseases. Then, we study numerically the properties of the model solutions with respect to the main parameters. To that end, we study the effect of various firing patterns of the motoneuron, variations in the properties of the end-plate as well as the rates, corresponding to the calcium dynamics inside the muscle cell.
{"title":"A Simple Integrated Mathematical Model of Neuromuscular Activation","authors":"Z. Ivanova, Tihomir Ivanov","doi":"10.55630/j.biomath.2022.10.119","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.10.119","url":null,"abstract":"In the present work, we propose a new integrated mathematical model of neuromuscular activation. It combines the Izhikevich model of neural activity with the Williams model of calcium activity inside the muscle cell and a Hill-type model for the resultant muscle force. The coupling is done using a heuristic approach. The aim is to construct a simple model, which has biophysically meaningful parameters and is applicable to the study of neuromuscular diseases. Then, we study numerically the properties of the model solutions with respect to the main parameters. To that end, we study the effect of various firing patterns of the motoneuron, variations in the properties of the end-plate as well as the rates, corresponding to the calcium dynamics inside the muscle cell.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45294741","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}
Pub Date : 2022-10-14DOI: 10.55630/j.biomath.2022.08.319
Erick Manuel Delgado Moya, Diego Samuel Rodrigues, A. Piétrus, Aymee Marrero Severo
HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adherence to treatment, and prevention are important factors in controlling the epidemic in the population. In this paper, we present a new mathematical model for the study of HIV/AIDS transmission. Our model is stratified in men and women, to account for the main forms of sexual transmission homosexual and heterosexual relationships, and infectiousness in the HIV and AIDS stages. In addition, in the construction of the model, we take into account the influence of Pre-Exposure Prophylaxis (PrEP) and Post-Exposure Prophylaxis (PEP) to study the impact of these implementations, diagnosis, and effectiveness of treatment based on viral load undetectability. We study the basic reproduction number by subpopulation (men and women) and general. Working by subpopulations allows us to study men who have sex with men who have a strong impact on virus transmission. Also, we study the infection-free equilibrium points due to their relationship with the basic reproduction number and demonstrate the global stability by subpopulation and general. To explore our model, we performed computational simulations on a scenario designed with data from the literature and assumed, studying the influence of the parameters associated with the use of PrEP, PEP, and undetectability on the basic reproduction number by varying them individually and jointly. We concluded that in women the basic reproduction number is always lower than unity and that in men the parameter associated with the undetectability of the viral load in HIV men has a strong influence on the dynamics. We also address the impact of PrEP, PEP, and undetectability in HIV and AIDS on the compartments, considering different scenarios varying the parameters jointly and independently and by sex which show difficulty in reducing women with AIDS. The scenario that showed the best results in the reduction of the number of HIV and AIDS cases was when the parameters associated with undetectability in HIV and AIDS men and women take the 90-90-90 that is proposed in the World Health Organization (WHO) strategy.
{"title":"A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis","authors":"Erick Manuel Delgado Moya, Diego Samuel Rodrigues, A. Piétrus, Aymee Marrero Severo","doi":"10.55630/j.biomath.2022.08.319","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.08.319","url":null,"abstract":"HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adherence to treatment, and prevention are important factors in controlling the epidemic in the population. In this paper, we present a new mathematical model for the study of HIV/AIDS transmission. Our model is stratified in men and women, to account for the main forms of sexual transmission homosexual and heterosexual relationships, and infectiousness in the HIV and AIDS stages. In addition, in the construction of the model, we take into account the influence of Pre-Exposure Prophylaxis (PrEP) and Post-Exposure Prophylaxis (PEP) to study the impact of these implementations, diagnosis, and effectiveness of treatment based on viral load undetectability. We study the basic reproduction number by subpopulation (men and women) and general. Working by subpopulations allows us to study men who have sex with men who have a strong impact on virus transmission. Also, we study the infection-free equilibrium points due to their relationship with the basic reproduction number and demonstrate the global stability by subpopulation and general. To explore our model, we performed computational simulations on a scenario designed with data from the literature and assumed, studying the influence of the parameters associated with the use of PrEP, PEP, and undetectability on the basic reproduction number by varying them individually and jointly. We concluded that in women the basic reproduction number is always lower than unity and that in men the parameter associated with the undetectability of the viral load in HIV men has a strong influence on the dynamics. We also address the impact of PrEP, PEP, and undetectability in HIV and AIDS on the compartments, considering different scenarios varying the parameters jointly and independently and by sex which show difficulty in reducing women with AIDS. The scenario that showed the best results in the reduction of the number of HIV and AIDS cases was when the parameters associated with undetectability in HIV and AIDS men and women take the 90-90-90 that is proposed in the World Health Organization (WHO) strategy.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48317619","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}
Pub Date : 2022-08-11DOI: 10.55630/j.biomath.2022.07.158
Edison Mayanja, L. Luboobi, Juma Kasozi, R. Nsubuga
In this work, we formulated and analysed a deterministic model to study the HIV-HCV co-infection dynamics in presence of HIV therapy. The HCV chronic stage was split into two periods: the period before and the period after onset of cirrhosis. This was done because the HCV chronic stage of infection is long, asymptomatic and infectious. The effective reproduction numbers, one of our outcome measures, were computed using the next generation matrix method. Numerical simulations were performed to support the analytical results from the model. The different parameters in the model were subjected to a sensitivity analysis to determine their relative importance on the HIV-HCV co-infection dynamics. The results indicated that both HIV and HCV infections enhance each other; and in the long run, increasing the rates at which people are put on HIV treatment reduces the prevalence of HCV in the community; however, it increases the prevalence of HIV. Therefore, there should be increased safer sexual behaviour campaigns among individuals on HIV treatment.
{"title":"Mathematical Modelling of HIV-HCV Co-infection Dynamics in Presence of HIV Therapy","authors":"Edison Mayanja, L. Luboobi, Juma Kasozi, R. Nsubuga","doi":"10.55630/j.biomath.2022.07.158","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.07.158","url":null,"abstract":"In this work, we formulated and analysed a deterministic model to study the HIV-HCV co-infection dynamics in presence of HIV therapy. The HCV chronic stage was split into two periods: the period before and the period after onset of cirrhosis. This was done because the HCV chronic stage of infection is long, asymptomatic and infectious. The effective reproduction numbers, one of our outcome measures, were computed using the next generation matrix method. Numerical simulations were performed to support the analytical results from the model. The different parameters in the model were subjected to a sensitivity analysis to determine their relative importance on the HIV-HCV co-infection dynamics. The results indicated that both HIV and HCV infections enhance each other; and in the long run, increasing the rates at which people are put on HIV treatment reduces the prevalence of HCV in the community; however, it increases the prevalence of HIV. Therefore, there should be increased safer sexual behaviour campaigns among individuals on HIV treatment.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43115224","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}
Pub Date : 2022-05-30DOI: 10.55630/j.biomath.2022.03.068
Dessislava Jereva, M. Angelova, I. Tsakovska, P. Alov, I. Pajeva, M. Miteva, T. Pencheva
The experimental procedures of drug design, proven to be time-consuming and costly, are successfully complemented with computer-aided (in silico) approaches nowadays. Virtual ligand screening (VLS) is one of the most promising approaches when searching for new hit compounds. The efficiency of VLS procedures might be improved via post-docking optimization. In the focus of this investigation is AMMOS (Automatic Molecular Mechanics Optimization for in silico Screening) developed as multi-step structure-based procedure for efficient computational refinement of protein-ligand complexes at different levels of protein flexibility. Their performance has been assessed by the recently developed InterCriteria analysis (ICrA), elaborated as multi-criterion decision-making approach to reveal possible relations in the behavior of pairs of criteria when multiple objects are considered. The capacity of ICrA as a supporting tool to assess the effect of applying different levels of protein flexibility in the post-docking optimization via AMMOS has been investigated and analyzed.
{"title":"An Application of InterCriteria Analysis Approach to Assess the AMMOS Software Platform Outcomes","authors":"Dessislava Jereva, M. Angelova, I. Tsakovska, P. Alov, I. Pajeva, M. Miteva, T. Pencheva","doi":"10.55630/j.biomath.2022.03.068","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.03.068","url":null,"abstract":"The experimental procedures of drug design, proven to be time-consuming and costly, are successfully complemented with computer-aided (in silico) approaches nowadays. Virtual ligand screening (VLS) is one of the most promising approaches when searching for new hit compounds. The efficiency of VLS procedures might be improved via post-docking optimization. In the focus of this investigation is AMMOS (Automatic Molecular Mechanics Optimization for in silico Screening) developed as multi-step structure-based procedure for efficient computational refinement of protein-ligand complexes at different levels of protein flexibility. Their performance has been assessed by the recently developed InterCriteria analysis (ICrA), elaborated as multi-criterion decision-making approach to reveal possible relations in the behavior of pairs of criteria when multiple objects are considered. The capacity of ICrA as a supporting tool to assess the effect of applying different levels of protein flexibility in the post-docking optimization via AMMOS has been investigated and analyzed.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47555474","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}
Pub Date : 2022-05-16DOI: 10.55630/j.biomath.2022.03.288
A. A. Mohamad, T. Yashiro
A DNA replicon is modeled by a special type of 2-component link, called a DNA-link, in which two circles form a double helix around a trivial center core curve. The DNA replication process is semi-conservative, which is interpreted as a splitting process of the DNA-link. To split this non-trivial link, the linking number must become zero, and thus an unknotting operation is necessary. Some families of enzymes act as the unknotting operation. The present paper considers two topological problems; one is to know how the linking number is reduced and the other, how the enzymes are allocated at appropriate places. For the first problem, we suggest a reduction system of the linking number of a DNA-link. From this system, the number of repetitions of the procedure is obtained and this could be reduced when the DNA is previously relaxed by type I topoisomerases. For the second problem, we propose a possible conformation of the DNA-link in which the unknotting operation does not change the knot type of the core curve but decreases the writhe. This conformation could allocate type II topoisomerases to appropriate places. These models suggest that the combination of type I and type II topoisomerases efficiently reduces the linking number and it is possible to allocate enzymes by the conformation of DNA strands.
{"title":"Topological Process of Splitting DNA-Links","authors":"A. A. Mohamad, T. Yashiro","doi":"10.55630/j.biomath.2022.03.288","DOIUrl":"https://doi.org/10.55630/j.biomath.2022.03.288","url":null,"abstract":"A DNA replicon is modeled by a special type of 2-component link, called a DNA-link, in which two circles form a double helix around a trivial center core curve. The DNA replication process is semi-conservative, which is interpreted as a splitting process of the DNA-link. To split this non-trivial link, the linking number must become zero, and thus an unknotting operation is necessary. Some families of enzymes act as the unknotting operation. The present paper considers two topological problems; one is to know how the linking number is reduced and the other, how the enzymes are allocated at appropriate places. For the first problem, we suggest a reduction system of the linking number of a DNA-link. From this system, the number of repetitions of the procedure is obtained and this could be reduced when the DNA is previously relaxed by type I topoisomerases. For the second problem, we propose a possible conformation of the DNA-link in which the unknotting operation does not change the knot type of the core curve but decreases the writhe. This conformation could allocate type II topoisomerases to appropriate places. These models suggest that the combination of type I and type II topoisomerases efficiently reduces the linking number and it is possible to allocate enzymes by the conformation of DNA strands.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47833602","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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