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mathematical modeling of the Dimerization of EGFR and ErbB3 in Lung Adenocarcinoma

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Mathematical Modeling of the Dimerization of EGFR and ErbB3 ...

International Symposium on Fusion of Mathematics and Biology, 2020

作者： Ito, Takeshi Suzuki, Takashi Murakami, Yoshinori Division of Molecular Pathology The Institute of Medical Science The University of Tokyo 4-6-1 Shirokanedai Minato-ku Tokyo108-8639 Japan Center for Mathematical Modeling and Data Science Osaka University 1-3 Machikaneyama Toyonaka Osaka560-8531 Japan

ISBN: (纸本)9789811648656

The most common driver mutations in lung adenocarcinoma occur in the EGFR gene. Gefitinib, an EGFR tyrosine kinase inhibitor, is an effective therapy for lung adenocarcinoma with EGFR mutations. However, resistant tumors inevitably arise. One of the mechanisms conferring gefitinib resistance is the amplification of the MET gene, which is observed in 5–22% of all cases. A previous study suggested that MET overexpression may cause gefitinib resistance through ErbB3, and most likely through the formation of EGFR-ErbB3 heterodimers. In this study, we focused on the dimer formation of EGFR and ErbB3 in lung adenocarcinoma cells and built a mathematical model using ordinary differential equations. To simulate the dimerization process of EGFR and ErbB3, we determined the molecular concentrations of each on the cell surface by flow cytometry and estimated unknown reaction constants by dimensional analysis. Our mathematical model would provide a quantitative understanding of dimer formation, one which cannot be obtained by a molecular biology methods. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Dimerization

NON-SPLITTING EULERIAN-LAGRANGIAN WENO SCHEMES FOR TWO-DIMENSIONAL NONLINEAR CONVECTION-DIFFUSION EQUATIONS

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arXiv 2024年

作者： Zheng, Nanyi Cai, Xiaofeng Qiu, Jing-Mei Qiu, Jianxian Department of Mathematical Sciences University of Delaware NewarkDE19716 United States Research Center for Mathematics Advanced Institute of Natural Sciences Beijing Normal University Zhuhai519087 China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College Zhuhai519087 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed EL-RK-FV-WENO scheme defines modified characteristic lines and evolves the solution along them, significantly relaxing the time-step constraint for the convection term. The main algorithm design challenge arises from the complexity of constructing accurate and robust reconstructions on dynamically varying Lagrangian meshes. This reconstruction process is needed for flux evaluations on time-dependent upstream quadrilaterals and time integrations along moving characteristics. To address this, we propose a strategy that utilizes a WENO reconstruction on a fixed Eulerian mesh for spatial reconstruction, and updates intermediate solutions on the Eulerian background mesh for implicit-explicit RK temporal integration. This strategy leverages efficient reconstruction and remapping algorithms to manage the complexities of polynomial reconstructions on time-dependent quadrilaterals, while ensuring local mass conservation. The proposed scheme ensures mass conservation due to the flux-form semi-discretization and the mass-conservative reconstruction on both background and upstream cells. Extensive numerical tests have been performed to verify the effectiveness of the proposed scheme. © 2024, CC BY.

关键词： Mesh generation

Lectures on the Error Analysis of Interpolation on Simplicial Triangulations without the Shape-Regularity Assumption, Part 2: Lagrange Interpolation on Tetrahedrons

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arXiv 2021年

作者： Kobayashi, Kenta Tsuchiya, Takuya Graduate School of Bussiness Administration Hitotsubashi University Kunitachi Japan Center for Mathematical Modeling and Data Science Osaka University Toyonaka Japan

This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption 1. In this manuscript, we explain the error analysis of Lagrange interpolation on (possibly anisotropic) tetrahedrons. This topic is hardly explained in standard textbooks of the mathematical theory of finite element methods. The authors hope that this manuscript will be merged into a new textbook in future. Therefore, this manuscript is not intended to be a research paper. Supposed readers are students and researchers who are familiar with the mathematical theory of the finite element methods. © 2021, CC BY-NC-ND.

关键词： Interpolation

Securing the light escaping in a Li-Fi network environment

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Procedia Computer science 2022年 201卷 684-689页

作者： D.D. Diambeki R.E. Mandiya K. Kyamakya S.K. Kasereka University of Kinshasa Mathematics and Computer Science Department Kinshasa DR Congo Artificial intelligence Big data and modeLing simulation research center (ABIL) Kinshasa Democratic Republic of the Congo Alpen-Adria-Universitaet Klagenfurt Institute of Smart Systems Technologies Department of Mathematical Sciences Klagenfurt Austria

Nowadays, everyone knows Wi-Fi. The technology that ensures connection of computer equipment. It is now positioned as the easiest way to interconnect multiple end users because It allows user mobility in workspaces, avoids cable clutter within the network coverage, such as offices, homes and so on. Despite these advantages, several scientific studies have shown that this technology can raise security and safety issues and is dangerous to human health, and therefore not suitable for hospital networks. In an attempt to overcome these difficulties, Li-Fi technology based on visible light is beginning to interest researchers. This technology is considered more secure than Wi-Fi because the light can be contained in a physical space and waves can’t pass through walls and other objects. Unfortunately, when the physical environment contains spaces that can escape light to the outdoors, this can be a security risk for Li-Fi because it uses light sources to transmit data. That why, in this paper, the main differences between Wi-Fi and Li-Fi technologies are explained, and a Li-Fi architecture provided with an authentification captive portal and a data transfer security mechanism between end users based on the AES algorithm is proposed. The developed prototype and the architecture proposed guarantee the security of the Li-Fi network even if the physical environment is provided with multiple light escape spaces.

关键词： Li-Fi (Light-Fidelity) VLC (Visible Light Communication) LED (Light Emitting Diode) Photodetector LDR (Light Dependent Resistor) Arduino AES algorithm Captive portal

mathematical modelling and simulation of invadopodia formation due to ligand and transmembrane protein binding

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AIP Conference Proceedings 2024年第1期2895卷

作者： Muhammad Amsyar Hamidi Nur Azura Noor Azhuan Noorehan Yaacob Takashi Suzuki Mohd Ariff Admon Department of Mathematical Sciences Faculty of Science Universiti Teknologi Malaysia Skudai 81310 Johor Bahru Johor Malaysia Center for Mathematical Modeling and Data Science Osaka University Osaka Japan

Cancer cells have the ability to infect nearby tissue and spread to other parts of the body. This process is known as metastasis, and it is widely recognised as the primary source of cancer cell invasion and the leading cause of death in cancer patients. We discovered specialised cellular membrane structures in invasive cancer cells that carry out a crucial phase in cancer invasion known as invadopodia. Actin rearrangement, extracellular matrix degradation, signalling transduction via membrane receptors such as the epidermal growth factor receptor and matrix metalloproteinase combination, and distribution to the invading front are all required for the creation of invadopodia. In this study, a mathematical model of invadopodia formation associated with binding of ligand and epidermal growth factor receptor (EGFR) that stimulates signal transduction is investigated. The ligand and signal equations are considered as heat equations with initial and free boundary conditions. The concentrations of signal and ligand are assumed to be equivalent to the concentration of EGFR on the plasma membrane (interface). Furthermore, the EGFR equation is derived from material derivatives of the reaction between ligand and EGFR that occurs at the interface. The EGFR velocity is equivalent to the ligand gradient. To detect the movement of the moving interface, the level set method is highlighted by designating the interface as the zero-level set function. In addition, the regular and nearby points are solved using the second-order centred difference and the ghost fluid with linear extrapolation methods, respectively. The velocity is calculated using the gradient difference between the intracellular signal and the extracellular ligand, which moves the interface. The results demonstrated that protrusions or invadopodia are produced on the plasma membrane using Matlab software.

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Time Changes in the VEGF-A Concentration Gradient Lead Neovasculature to Engage in Stair-Like Growth

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Time Changes in the VEGF-A Concentration Gradient Lead Neova...

International Symposium on Fusion of Mathematics and Biology, 2020

作者： Ito, Yukinobu Minerva, Dhisa Tasaki, Sohei Yoshida, Makoto Suzuki, Takashi Goto, Akiteru Department of Cellular and Organ Pathology Graduate School of Medicine Akita University 1-1-1 Hondo Akita Akita010-8543 Japan Center for Mathematical Modeling and Data Science Osaka University Osaka Japan Institute for the Advanced Study of Human Biology Kyoto University Kyoto Japan

ISBN: (纸本)9789811648656

Arteriovenous malformations consist of tangles of arteries and veins that are often connected by a fistula. The causes of and mechanisms underlying the development of these clinical entities are not fully understood. We previously reported a novel in vivo angiogenesis model as a useful disease model of arteriovenous malformation. With this model, the arterial graft was collected from the left carotid artery and sutured to the left jugular vein as a patchwork. The neovasculature extended from the branch of the subclavian artery toward the arterial graft. We measured the neovasculature, which had sprouted from arterioles, in the tissue samples. In the present study, we collected the arterial patch graft and adipose tissue surrounding the arterial graft and examined the distribution of the VEGF concentration by an enzyme-linked immunosorbent assay. At the area most distant from the arterial graft, the VEGF-A concentration changed over time in a sine wave pattern that gradually attenuated. A mathematical model was then constructed using the results, and a mathematical simulation of the neovasculature growth was performed. The new vessels grew in a stair-like pattern in this simulation, a result that matched those obtained through histological measurements. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Tissue

Bayesian Nonparametric Clustering with Feature Selection for Spatially Resolved Transcriptomics data

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arXiv 2023年

作者： Zhu, Bencong Hu, Guanyu Xie, Yang Xu, Lin Fan, Xiaodan Li, Qiwei Department of Statistics The Chinese University of Hong Kong Hong Kong Department of Biostatistics and Data Science Center for Spatial Temporal Modeling for Applications in Population Sciences The University of Texas Health Science Center Houston United States School of Public Health The University of Texas Southwestern Medical Center United States Department of Statistics The Chinese University of Hong Kong Hong Kong Department of Mathematical Sciences The University of Texas Dallas United States

The advent of next-generation sequencing-based spatially resolved transcriptomics (SRT) techniques has reshaped genomic studies by enabling high-throughput gene expression profiling while preserving spatial and morphological context. Nevertheless, there are inherent challenges associated with these new high-dimensional spatial data, such as zero-inflation, over-dispersion, and heterogeneity. These challenges pose obstacles to effective clustering, which is a fundamental problem in SRT data analysis. Current computational approaches often rely on heuristic data preprocessing and arbitrary cluster number prespecification, leading to considerable information loss and consequently, suboptimal downstream analysis. In response to these challenges, we introduce BNPSpace, a novel Bayesian nonparametric spatial clustering framework that directly models SRT count data. BNPSpace facilitates the partitioning of the whole spatial domain, which is characterized by substantial heterogeneity, into homogeneous spatial domains with similar molecular characteristics while identifying a parsimonious set of discriminating genes among different spatial domains. Moreover, BNPSpace incorporates spatial information through a Markov random field prior model, encouraging a smooth and biologically meaningful partition pattern. We assess the performance of BNPSpace utilizing both simulated and real SRT data. In the application to the human dorsolateral prefrontal cortex (DLPFC) 10x Visium data, comprising 4, 788 spots and 33, 538 genes with a 95% sparsity, BNPSpace outperforms existing methods by identifying more coherent spatial domain patterns and achieving the best clustering performance. Furthermore, the discriminating genes identified by BNPSpace showed significant enrichment with odd ratio = 1.877 (p-value = 0.00162) in DLPFC gene sets validated by real biological experiments, underscoring its effectiveness in revealing biologically relevant insights. Copyright © 2023, The Authors. All ri

关键词： Gene expression

ROTA-BAXTER OPERATORS, DIFFERENTIAL OPERATORS, PRE- AND NOVIKOV STRUCTURES ON GROUPS AND LIE ALGEBRAS

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arXiv 2024年

作者： Gao, Xing Guo, Li Han, Zongjian Zhang, Yi School of Mathematics and Statistics Lanzhou University Lanzhou730000 China Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics Lanzhou730070 China Department of Mathematics and Computer Science Rutgers University NewarkNJ07102 United States School of Mathematical Sciences Tonji University Shanghai200092 China School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis NUIST Jiangsu Nanjing210044 China

Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota-Baxter operators on Lie algebras are closely related to pre-Lie algebras and post-Lie algebras. Some of their group counterparts have been introduced to study post-groups, skew left braces and set-theoretic solutions of Yang-Baxter equations, but searching suitable notions of relative Rota-Baxter operators on groups with weight zero and pre-groups has been challenging and has been the focus of recent studies, by provisionally imposing an abelian condition. Arising from the works of Balinsky-Novikov and Gelfand-Dorfman, Novikov algebras and their constructions from differential commutative algebras have led to broad applications. Finding their suitable counterparts for groups and Lie algebras has also attracted quite much recent attention. This paper uses one-sided-inverse pairs of maps to give a perturbative approach to a general notion of relative Rota-Baxter operators and differential operators on a group and a Lie algebra with limit-weight. With the extra condition of limit-abelianess on the group or Lie algebra, we give an interpretation of relative Rota-Baxter and differential operators with weight zero. These operators motivate us to define pre-groups and Novikov groups respectively as the induced structures. The tangent maps of these operators are shown to give Rota-Baxter and differential operators with weight zero on Lie algebras. The tangent spaces of the pre-Lie and Novikov Lie groups are pre-Lie algebras and Novikov Lie algebras, fulfilling the expected property. Furthermore, limit-weight relative Rota-Baxter operators on groups give rise to skew left braces and then set-theoretic solutions of the Yang-Baxter *** Codes 22E60, 17B38, 17B40, 16W99, 45N05 Copyright © 2024, The Authors. All rights reserved.

关键词： Lie groups

Quasilinear reaction diffusion systems with mass dissipation

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arXiv 2021年

作者： Latos, Evangelos Suzuki, Takashi Institut für Mathematik und Wissenschaftliches Rechnen Heinrichstraße 36 Graz8010 Austria Center for Mathematical Modeling and Data Science Osaka University Japan

We study quasilinear reaction diffusion systems relative to the Shigesada-Kawasaki-Teramoto model. Nonlinearity standing for the external force is provided with mass dissipation. Estimate in several norms of the solution is provided under the restriction of diffusion coefficients, growth rate of reaction, and space dimension. © 2021, CC BY.

关键词： Dynamic models