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Weighted gene co expression network analysis (WGCNA) with key pathways and hub-genes related to micro RNAs in ischemic stroke 加权基因共表达网络分析(WGCNA)在缺血性卒中中与微rna相关的关键途径和中心基因
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-04-20 DOI: 10.1049/syb2.12016
Xiang Qu, Shuang Wu, Jinggui Gao, Zhenxiu Qin, Zhenhua Zhou, Jingli Liu

Ischemic stroke (IS) is one of the major causes of death and disability worldwide. However, the specific mechanism of gene interplay and the biological function in IS are not clear. Therefore, more research into IS is necessary. Dataset GSE110993 including 20 ischemic stroke (IS) and 20 control specimens are used to establish both groups and the raw RNA-seq data were analysed. Weighted gene co-expression network analysis (WGCNA) was used to screen the key micro-RNA modules. The centrality of key genes were determined by module membership (mm) and gene significance (GS). The key pathways were identified by enrichment analysis with Kyoto Protocol Gene and Genome Encyclopedia (KEGG), and the key genes were validated by protein-protein interactions network. Result: Upon investigation, 1185 up- and down-regulated genes were gathered and distributed into three modules in response to their degree of correlation to clinical traits of IS, among which the turquoise module show a trait-correlation of 0.77. The top 140 genes were further identified by GS and MM. KEGG analysis showed two pathways may evolve in the progress of IS. Discussion: CXCL12 and EIF2a may be important biomarkers for the accurate diagnosis and treatment in IS.

缺血性中风(IS)是世界范围内导致死亡和残疾的主要原因之一。然而,IS中基因相互作用的具体机制和生物学功能尚不清楚。因此,有必要对IS进行更多的研究。数据集GSE110993包括20例缺血性卒中患者和20例对照标本建立两组,并分析原始RNA-seq数据。采用加权基因共表达网络分析(WGCNA)筛选关键微rna模块。关键基因的中心性通过模块隶属度(mm)和基因显著性(GS)来确定。通过京都议定书基因和基因组百科(KEGG)富集分析确定了关键通路,并通过蛋白-蛋白相互作用网络对关键基因进行了验证。结果:经调查,共收集到1185个上调和下调基因,并根据其与IS临床特征的相关程度分为三个模块,其中绿松石模块的性状相关性为0.77。通过GS和MM进一步鉴定了前140个基因。KEGG分析显示,在IS的发展过程中可能有两条途径。讨论:CXCL12和EIF2a可能是IS准确诊断和治疗的重要生物标志物。
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引用次数: 3
Fuzzy logic and Lyapunov-based non-linear controllers for HCV infection. HCV感染的模糊逻辑和基于lyapunov的非线性控制器。
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-04-01 DOI: 10.1049/syb2.12014
Ali Hamza, Iftikhar Ahmad, Muhammad Uneeb

Hepatitis C is the liver disease caused by the Hepatitis C virus (HCV) which can lead to serious health problems such as liver cancer. In this research work, the non-linear model of HCV having three state variables (uninfected hepatocytes, infected hepatocytes and virions) and two control inputs has been taken into account, and four non-linear controllers namely non-linear PID controller, Lyapunov Redesign controller, Synergetic controller and Fuzzy Logic-Based controller have been proposed to control HCV infection inside the human body. The controllers have been designed for the anti-viral therapy in order to control the amount of uninfected hepatocytes to the desired safe limit and to track the amount of infected hepatocytes and virions to their reference value which is zero. One control input is the Pegylated interferon (peg-IFN-α) which acts in reducing the infected hepatocytes and the other input is ribavirin which blocks the production of virions. By doing so, the uninfected hepatocytes increase and achieve the required safe limit. Lyapunov stability analysis has been used to prove the stability of the whole system. The comparative analysis of the proposed nonlinear controllers using MATLAB/Simulink have been done with each other and with linear PID. These results depict that the infected hepatocytes and virions are reduced to the desired level, enhancing the rate of sustained virologic response (SVR) and reducing the treatment period as compared with previous strategies introduced in the literature.

丙型肝炎是由丙型肝炎病毒(HCV)引起的肝脏疾病,可导致严重的健康问题,如肝癌。本研究考虑了HCV具有三个状态变量(未感染肝细胞、感染肝细胞和病毒粒子)和两个控制输入的非线性模型,提出了非线性PID控制器、Lyapunov再设计控制器、协同控制器和基于模糊逻辑的控制器四种非线性控制器来控制人体内HCV感染。为了将未感染肝细胞的数量控制在所需的安全限度内,并跟踪感染肝细胞和病毒粒子的数量至其参考值为零,设计了抗病毒治疗控制器。一种控制输入是聚乙二醇化干扰素(peg-IFN-α),它的作用是减少被感染的肝细胞,另一种输入是利巴韦林,它阻断病毒粒子的产生。通过这样做,未感染的肝细胞增加并达到所需的安全限度。利用李雅普诺夫稳定性分析证明了整个系统的稳定性。利用MATLAB/Simulink对所提出的非线性控制器进行了对比分析,并与线性PID进行了对比分析。这些结果表明,与文献中介绍的先前策略相比,受感染的肝细胞和病毒粒子减少到所需的水平,提高了持续病毒学应答率(SVR)并缩短了治疗时间。
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引用次数: 3
Model predictive control optimisation using the metaheuristic optimisation for blood pressure control. 使用血压控制的元启发式优化模型预测控制优化。
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-04-01 Epub Date: 2021-02-14 DOI: 10.1049/syb2.12012
Mohammad Reza Ahmadpour, Hamid Ghadiri, Saeed Reza Hajian

Given the importance of high blood pressure, it is important to control and maintain a constant blood pressure level in the normal state. The main aim of this article is to design a model predictive controller with a genetic algorithm (GA) for the regulation of arterial blood pressure. The present study is an applied cross-sectional study. In order to do this research, studies related to designing mathematical models for blood pressure regulation and mechanical models for heart muscle and pressure sensors are investigated. Then, a model predictive controller with GA is designed for blood pressure control. All control and design operations are performed in the MATLAB software. According to the viscoelasticity of blood, transducer, and injection set, we can assume the mechanical model as Mass, Spring, and Damper. Initially, the patient's blood pressure is lower than normal, and after controlling, the patient's blood pressure returned to normal. By using a GA-based model predictive control (MPC), mathematical validation, and mechanical model, the patient's blood pressure can be adjusted and maintained. The simulation result shows that the GA-based MPC offers acceptable response and speed of operation and the proposed controller can achieve good tracking and disturbance rejection.

鉴于高血压的重要性,在正常状态下控制和维持恒定的血压水平是很重要的。本文的主要目的是设计一种基于遗传算法的模型预测控制器,用于动脉血压的调节。本研究为应用横断面研究。为此,对血压调节的数学模型设计、心肌和压力传感器的力学模型设计进行了研究。然后,设计了一种基于遗传算法的模型预测控制器用于血压控制。所有的控制和设计操作都在MATLAB软件中完成。根据血液、换能器和注射装置的粘弹性,可以将其力学模型设为质量、弹簧和阻尼器。最初患者血压低于正常值,经控制后血压恢复正常。通过基于遗传算法的模型预测控制(MPC)、数学验证和力学模型,可以调节和维持患者的血压。仿真结果表明,基于遗传算法的MPC具有良好的响应性能和运行速度,具有良好的跟踪性能和抗干扰能力。
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引用次数: 3
Sliding-mode-based controllers for automation of blood glucose concentration for type 1 diabetes. 基于滑动模式的控制器,用于 1 型糖尿病患者血糖浓度的自动控制。
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-04-01 DOI: 10.1049/syb2.12015
Sheraz Ahmad Babar, Iftikhar Ahmad, Iqra Shafeeq Mughal

Destruction of β-cells in pancreas causes deficiency in insulin production that leads to diabetes in the human body. To cope with this problem, insulin is either taken orally during the day or injected into the patient's body using artificial pancreas (AP) during sleeping hours. Some mathematical models indicate that AP uses control algorithms to regulate blood glucose concentration (BGC). The extended Bergman minimal model (EBMM) incorporates, as a state variable, the disturbance in insulin level during medication due to either meal intake or burning sugar by engaging in physical exercise. In this research work, EBMM and proposed finite time robust controllers are used, including the sliding mode controller (SMC), backstepping SMC (BSMC) and supertwisting SMC (second-order SMC or SOSMC) for automatic stabilisation of BGC in type 1 diabetic patients. The proposed SOSMC diminishes the chattering phenomenon which appears in the conventional SMC. The proposed BSMC is a recursive technique which becomes robust by the addition of the SMC. Lyapunov theory has been used to prove the asymptotic stability of the proposed controllers. Simulations have been carried out in MATLAB/Simulink for the comparative study of the proposed controllers under varying data of six different type 1 diabetic patients available in the literature.

胰腺中的β细胞遭到破坏会导致胰岛素分泌不足,从而引发人体糖尿病。为了解决这个问题,胰岛素要么在白天口服,要么在睡眠时间使用人工胰腺(AP)注射到病人体内。一些数学模型表明,人工胰腺利用控制算法来调节血糖浓度(BGC)。扩展伯格曼最小模型(EBMM)将用药期间由于进餐或参加体育锻炼消耗糖分造成的胰岛素水平紊乱作为状态变量纳入其中。在这项研究工作中,使用了 EBMM 和建议的有限时间鲁棒控制器,包括滑动模式控制器(SMC)、后步 SMC(BSMC)和超扭曲 SMC(二阶 SMC 或 SOSMC),以自动稳定 1 型糖尿病患者的 BGC。拟议的 SOSMC 减少了传统 SMC 中出现的颤振现象。拟议的 BSMC 是一种递归技术,通过添加 SMC 变得更加稳健。Lyapunov 理论被用来证明拟议控制器的渐进稳定性。在 MATLAB/Simulink 中进行了仿真,以便在文献中提供的六种不同的 1 型糖尿病患者的不同数据下对所提出的控制器进行比较研究。
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引用次数: 0
Optimal control methods for drug delivery in cancerous tumour by anti-angiogenic therapy and chemotherapy. 抗血管生成治疗和化疗在肿瘤中给药的最优控制方法。
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-02-01 Epub Date: 2021-01-25 DOI: 10.1049/syb2.12010
Pariya Khalili, Sareh Zolatash, Ramin Vatankhah, Sajjad Taghvaei

There are numerous mathematical models simulating the behaviour of cancer by considering variety of states in different treatment strategies, such as chemotherapy. Among the models, one is developed which is able to consider the blood vessel-production (angiogenesis) in the vicinity of the tumour and the effect of anti-angiogenic therapy. In the mentioned-model, normal cells, cancer cells, endothelial cells, chemotherapy and anti-angiogenic agents are taking into account as state variables, and the rate of injection of the last two are considered as control inputs. Since controlling the cancerous tumour growth is a challenging matter for patient's life, the time schedule design of drug injection is very significant. Two optimal control strategies, an open-loop (calculus of variations) and a closed-loop (state-dependent Riccati equation), are applied on the system in order to find an optimal time scheduling for each drug injection. By defining a proper cost function, an optimal control signal is designed for each one. Both obtained control inputs have reasonable answers, and the system is controlled eventually, but by comparing them, it is concluded that both methods have their own benefits which will be discussed in details in the conclusion section.

有许多数学模型通过考虑不同治疗策略(如化疗)的各种状态来模拟癌症的行为。在这些模型中,我们开发了一个能够考虑肿瘤附近血管生成(血管生成)和抗血管生成治疗效果的模型。在上述模型中,将正常细胞、癌细胞、内皮细胞、化疗药物和抗血管生成药物作为状态变量,并将后两者的注射速率作为控制输入。由于控制肿瘤的生长对患者的生命是一件具有挑战性的事情,因此药物注射的时间表设计非常重要。采用开环(变分法)和闭环(状态相关Riccati方程)两种最优控制策略对系统进行优化,以找到每次药物注射的最优时间调度。通过定义合适的代价函数,为每一种情况设计最优控制信号。两种得到的控制输入都有合理的答案,系统最终都得到了控制,但通过比较,两种方法都有各自的好处,这将在结论部分详细讨论。
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引用次数: 5
Identifying the degree of genetic interactions using Restricted Boltzmann Machine-A study on colorectal cancer. 利用限制性玻尔兹曼机鉴定结直肠癌基因相互作用的程度。
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-02-01 Epub Date: 2020-12-08 DOI: 10.1049/syb2.12009
Sujay Saha, Saikat Bandopadhyay, Anupam Ghosh

The phenomenon of two or more genes affecting the expression of each other in various ways in the development of a single character of an organism is known as gene interaction. Gene interaction not only applies to normal human traits but to the diseased samples as well. Thus, an analysis of gene interaction could help us to differentiate between the normal and the diseased samples or between the two/more phases any diseased samples. At the first stage of this work we have used restricted Boltzmann machine model to find such significant interactions present in normal and/or cancer samples of every gene pairs of 20 genes of colorectal cancer data set (GDS4382) along with the weight/degree of those interactions. Later on, we are looking for those interactions present in adenoma and/or carcinoma samples of the same 20 genes of colorectal cancer data set (GDS1777). The weight/degree of those interactions represents how strong/weak an interaction is. At the end we will create a gene regulatory network with the help of those interactions, where the regulatory genes are identified by using Naïve Bayes Classifier. Experimental results are validated biologically by comparing the interactions with NCBI databases.

两个或两个以上的基因在一个生物体的单一性状的发育过程中以各种方式影响彼此的表达的现象被称为基因相互作用。基因相互作用不仅适用于正常的人类特征,也适用于患病样本。因此,基因相互作用的分析可以帮助我们区分正常和患病样本,或者区分任何患病样本的两个/多个阶段。在这项工作的第一阶段,我们使用了限制性玻尔兹曼机器模型来发现在结直肠癌数据集(GDS4382)的20个基因的每个基因对的正常和/或癌症样本中存在如此显著的相互作用,以及这些相互作用的权重/程度。随后,我们正在寻找结直肠癌数据集(GDS1777)中相同的20个基因的腺瘤和/或癌样本中存在的这些相互作用。这些相互作用的权重/程度代表了相互作用的强弱。最后,我们将在这些相互作用的帮助下创建一个基因调控网络,其中通过使用Naïve贝叶斯分类器识别调控基因。通过与NCBI数据库的相互作用比较,对实验结果进行了生物学验证。
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引用次数: 0
MiRNA-145-5p expression and prospective molecular mechanisms in the metastasis of prostate cancer. MiRNA-145-5p在前列腺癌转移中的表达及分子机制研究
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2021-02-01 DOI: 10.1049/syb2.12011
Zhi-Guang Huang, Yu Sun, Gang Chen, Yi-Wu Dang, Hui-Ping Lu, Juan He, Ji-Wen Cheng, Mao-Lin He, Sheng-Hua Li

The clinicopathological implication and prospective molecular mechanisms of miRNA-145-5p in the metastasis of prostate cancer (PCa) stand unclear. Herein, it is found that miRNA-145-5p expression was remarkably reduced in 131 cases of metastatic PCa than 1371 cases of localised ones, as the standardised mean differences (SMD) was -1.26 and the area under the curve (AUC) was 0.86, based on miRNA-chip and miRNA-sequencing datasets. The potential targets of miRNA-145-5p in metastatic PCa (n = 414) was achieved from the intersection of miRNA-145-5p transfected metastatic PCa cell line data, differential expression of metastatic PCa upregulated genes and online prediction databases. TOP2A was screened as one of the target hub genes by PPI network analysis, which was adversely related to miRNA-145-5p expression in both metastatic PCa (r = -0.504) and primary PCa (r = -0.281). Gene-chip and RNA-sequencing datasets, as well as IHC performed on clinical PCa samples, showed consistent upregulated expression of TOP2A mRNA and protein in PCa compared with non-PCa. The expression of TOP2A mRNA was also significantly higher in metastatic than localised PCa with the SMD being 1.72 and the AUC of sROC being 0.91. In summary, miRNA-145-5p may participate in PCa metastasis by binding TOP2A and be useful as a biomarker for the detection of metastatic PCa.

miRNA-145-5p在前列腺癌(PCa)转移中的临床病理意义和潜在的分子机制尚不清楚。本研究发现,基于mirna芯片和mirna测序数据集,131例转移性PCa中miRNA-145-5p的表达明显低于1371例局限性PCa,标准化平均差异(SMD)为-1.26,曲线下面积(AUC)为0.86。miRNA-145-5p在转移性PCa中的潜在靶点(n = 414)是通过miRNA-145-5p转染的转移性PCa细胞系数据、转移性PCa上调基因的差异表达和在线预测数据库的交叉分析得出的。通过PPI网络分析筛选出TOP2A作为靶枢纽基因之一,在转移性PCa (r = -0.504)和原发性PCa (r = -0.281)中,TOP2A与miRNA-145-5p表达呈负相关。基因芯片和rna测序数据集以及临床PCa样本的免疫组化显示,与非PCa相比,PCa中TOP2A mRNA和蛋白的表达一致上调。TOP2A mRNA在转移性前列腺癌中的表达也明显高于局部性前列腺癌,SMD为1.72,sROC的AUC为0.91。综上所述,miRNA-145-5p可能通过结合TOP2A参与了PCa的转移,可作为检测转移性PCa的生物标志物。
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引用次数: 9
Identification and analysis of circRNA–miRNA–mRNA regulatory network in hepatocellular carcinoma 肝细胞癌circRNA-miRNA-mRNA调控网络的鉴定与分析
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2020-11-25 DOI: 10.1049/iet-syb.2020.0061
Daxiang Zhou, Ling Dong, Lishan Yang, Qiang Ma, Feng Liu, Yanjie Li, Shu Xiong

This study was to identify important circRNA–miRNA–mRNA (ceRNAs) regulatory mechanisms in hepatocellular carcinoma (HCC). The circRNA dataset GSE97332 and miRNA dataset GSE57555 were used for analyses. Functional enrichment analysis for miRNA and target gene was conducted using cluster Profiler. Survival analysis was conducted through R package Survival. The ceRNAs and drug–gene interaction networks were constructed. The ceRNAs network contained five miRNAs including hsa-miR-25-3p, hsa-miR-3692-5p, hsa-miR-4270, hsa-miR-331-3p, and hsa-miR-125a-3p. Among the network, hsa-miR-25-3p targeted the most genes, hsa-miR-3692-5p and hsa-miR-4270 were targeted by more circRNAs than other miRNAs, hsa-circ-0034326 and hsa-circ-0011950 interacted with three miRNAs. Furthermore, target genes, including NRAS, ITGA5, SLC7A1, SEC14L2, SLC12A5, and SMAD2 were obtained in drug–gene interaction network. Survival analysis showed NRAS, ITGA5, SLC7A1, SEC14L2, SLC12A5, and SMAD2 were significantly associated with prognosis of HCC. NRAS, ITGA5, and SMAD2 were significantly enriched in proteoglycans in cancer. Moreover, hsa-circ-0034326 and hsa-circ-0011950 might function as ceRNAs to play key roles in HCC. Furthermore, miR-25-3p, miR-3692-5p, and miR-4270 might be significant for HCC development. NRAS, ITGA5, SEC14L2, SLC12A5, and SMAD2 might be prognostic factors for HCC patients via proteoglycans in cancer pathway. Taken together, the findings will provide novel insight into pathogenesis, selection of therapeutic targets and prognostic factors for HCC.

本研究旨在确定肝细胞癌(HCC)中重要的circRNA-miRNA-mRNA (ceRNAs)调控机制。使用circRNA数据集GSE97332和miRNA数据集GSE57555进行分析。利用聚类分析器对miRNA和靶基因进行功能富集分析。通过R包Survival进行生存分析。构建了cerna和药物-基因相互作用网络。ceRNAs网络包含五个mirna,包括hsa-miR-25-3p、hsa-miR-3692-5p、hsa-miR-4270、hsa-miR-331-3p和hsa-miR-125a-3p。在该网络中,hsa-miR-25-3p靶向的基因最多,hsa-miR-3692-5p和hsa-miR-4270被更多的circrna靶向,hsa-circ-0034326和hsa-circ-0011950与三个mirna相互作用。此外,在药物基因相互作用网络中获得了NRAS、ITGA5、SLC7A1、SEC14L2、SLC12A5、SMAD2等靶基因。生存分析显示NRAS、ITGA5、SLC7A1、SEC14L2、SLC12A5、SMAD2与HCC预后有显著相关性。NRAS、ITGA5和SMAD2在肿瘤蛋白聚糖中显著富集。此外,hsa-circ-0034326和hsa-circ-0011950可能作为cerna在HCC中发挥关键作用。此外,miR-25-3p、miR-3692-5p和miR-4270可能对HCC的发展具有重要意义。NRAS、ITGA5、SEC14L2、SLC12A5和SMAD2可能通过蛋白聚糖在癌通路中影响HCC患者的预后。总之,这些发现将为HCC的发病机制、治疗靶点的选择和预后因素提供新的见解。
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引用次数: 12
Petri Net modelling approach for analysing the behaviour of Wnt/ -catenin and Wnt/ Ca2+ signalling pathways in arrhythmogenic right ventricular cardiomyopathy Petri网建模方法分析Wnt/ -catenin和Wnt/ Ca2+信号通路在致心律失常右室心肌病中的行为
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2020-11-23 DOI: 10.1049/iet-syb.2020.0038
Nazia Azim, Jamil Ahmad, Nadeem Iqbal, Amnah Siddiqa, Abdul Majid, Javaria Ashraf, Fazal Jalil

Arrhythmogenic right ventricular cardiomyopathy (ARVC) is an inherited heart muscle disease that may result in arrhythmia, heart failure and sudden death. The hallmark pathological findings are progressive myocyte loss and fibro fatty replacement, with a predilection for the right ventricle. This study focuses on the adipose tissue formation in cardiomyocyte by considering the signal transduction pathways including Wnt/ -catenin and Wnt/Ca2+ regulation system. These pathways are modelled and analysed using stochastic petri nets (SPN) in order to increase our comprehension of ARVC and in turn its treatment regimen. The Wnt/ -catenin model predicts that the dysregulation or absence of Wnt signalling, inhibition of dishevelled and elevation of glycogen synthase kinase 3 along with casein kinase I are key cytotoxic events resulting in apoptosis. Moreover, the Wnt/Ca2+ SPN model demonstrates that the Bcl2 gene inhibited by c-Jun N-terminal kinase protein in the event of endoplasmic reticulum stress due to action potential and increased amount of intracellular Ca2+ which recovers the Ca2+ homeostasis by phospholipase C, this event positively regulates the Bcl2 to suppress the mitochondrial apoptosis which causes ARVC.

心律失常性右室心肌病(ARVC)是一种遗传性心肌疾病,可导致心律失常、心力衰竭和猝死。其标志性病理表现为进行性肌细胞丧失和纤维脂肪替代,以右心室为主。本研究通过考虑Wnt/ -catenin和Wnt/Ca2+调控系统等信号转导途径,重点研究心肌细胞脂肪组织的形成。使用随机petri网(SPN)对这些途径进行建模和分析,以增加我们对ARVC的理解,进而提高其治疗方案。Wnt/ -catenin模型预测,Wnt信号的失调或缺失、糖原合成酶激酶3和酪蛋白激酶I的抑制和升高是导致细胞凋亡的关键细胞毒性事件。此外,Wnt/Ca2+ SPN模型表明,在内质网动作电位应激和细胞内Ca2+量增加的情况下,C - jun n端激酶蛋白抑制Bcl2基因,通过磷脂酶C恢复Ca2+稳态,这一事件正向调节Bcl2,抑制引起ARVC的线粒体凋亡。
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引用次数: 1
Optimal minimum variance-entropy control of tumour growth processes based on the Fokker–Planck equation 基于Fokker-Planck方程的肿瘤生长过程最优最小方差熵控制
IF 2.3 4区 生物学 Q4 CELL BIOLOGY Pub Date : 2020-11-23 DOI: 10.1049/iet-syb.2020.0055
Maliheh Sargolzaei, Gholamreza Latif-Shabgahi, Mahdi Afshar

The authors demonstrated an optimal stochastic control algorithm to obtain desirable cancer treatment based on the Gompertz model. Two external forces as two time-dependent functions are presented to manipulate the growth and death rates in the drift term of the Gompertz model. These input signals represent the effect of external treatment agents to decrease tumour growth rate and increase tumour death rate, respectively. Entropy and variance of cancerous cells are simultaneously controlled based on the Gompertz model. They have introduced a constrained optimisation problem whose cost function is the variance of a cancerous cells population. The defined entropy is based on the probability density function of affected cells was used as a constraint for the cost function. Analysing growth and death rates of cancerous cells, it is found that the logarithmic control signal reduces the growth rate, while the hyperbolic tangent–like control function increases the death rate of tumour growth. The two optimal control signals were calculated by converting the constrained optimisation problem into an unconstrained optimisation problem and by using the real–coded genetic algorithm. Mathematical justifications are implemented to elucidate the existence and uniqueness of the solution for the optimal control problem.

作者展示了一种基于Gompertz模型的最佳随机控制算法,以获得理想的癌症治疗。提出了两个外力作为两个时变函数来控制冈珀兹模型漂移项的生长率和死亡率。这些输入信号分别代表外部治疗剂降低肿瘤生长速率和增加肿瘤死亡率的作用。基于Gompertz模型,同时控制癌细胞的熵和方差。他们引入了一个约束优化问题,其成本函数是癌细胞群的方差。定义的熵是基于受影响细胞的概率密度函数,并将其作为代价函数的约束。分析癌细胞的生长和死亡率,发现对数控制信号降低了肿瘤的生长速度,而双曲切线样控制函数增加了肿瘤生长的死亡率。将约束优化问题转化为无约束优化问题,采用实数编码遗传算法计算出两个最优控制信号。用数学方法证明了最优控制问题解的存在唯一性。
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引用次数: 0
期刊
IET Systems Biology
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