{"title":"Improvement and Evaluation of a Mathematical Model for Fertilization Calcium Waves in Caenorhabditis Elegans","authors":"Momoko Imakubo, Jun Takayama, Shuichi Onami","doi":"10.2197/IPSJTBIO.11.24","DOIUrl":null,"url":null,"abstract":"Ca2+ waves propagate through the oocyte during fertilization, activate the oocyte and induce embryonic development. Ca2+-induced Ca2+-release (CICR) is a mechanism of Ca2+ wave formation. We previously quantified the Ca2+ waves in the nematode Caenorhabditis elegans by using high-speed imaging and image analysis. We found that the waves consist of a rapid local rise at the point of sperm entry and a slow global wave. We demonstrated that the Nagumo model, which models the CICR by a reaction–diffusion equation, can produce a similar biphasic waveform. However, the model cannot represent the observed gradual decrease in maximum Ca2+ concentration with increasing distance from the point of sperm entry. In this study, we introduced a linear monotonically decreasing function into the reaction part of the Nagumo model. We demonstrated that our new model can produce the gradual decrease in maximum Ca2+ concentration with increasing distance from the point of sperm entry and a biphasic waveform simultaneously.","PeriodicalId":38959,"journal":{"name":"IPSJ Transactions on Bioinformatics","volume":"11 1","pages":"24-30"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IPSJ Transactions on Bioinformatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2197/IPSJTBIO.11.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Biochemistry, Genetics and Molecular Biology","Score":null,"Total":0}
引用次数: 0
Abstract
Ca2+ waves propagate through the oocyte during fertilization, activate the oocyte and induce embryonic development. Ca2+-induced Ca2+-release (CICR) is a mechanism of Ca2+ wave formation. We previously quantified the Ca2+ waves in the nematode Caenorhabditis elegans by using high-speed imaging and image analysis. We found that the waves consist of a rapid local rise at the point of sperm entry and a slow global wave. We demonstrated that the Nagumo model, which models the CICR by a reaction–diffusion equation, can produce a similar biphasic waveform. However, the model cannot represent the observed gradual decrease in maximum Ca2+ concentration with increasing distance from the point of sperm entry. In this study, we introduced a linear monotonically decreasing function into the reaction part of the Nagumo model. We demonstrated that our new model can produce the gradual decrease in maximum Ca2+ concentration with increasing distance from the point of sperm entry and a biphasic waveform simultaneously.