Research On Identification Of Fractional Order Adjacency Function For Optimized Tuning Method Of WGCNA

The weighted network co-expression analysis(WGCNA)method has been applied in medical subdivisions such as disease typing,pathogenesis,drug research,evolutionary mechanisms,and gene function annotation for more than ten years after birth.At the same time,the research results of network science in the past 30 years have also been applied in many fields such as economy,communication,control,and biomedicine.It shows its wide application prospect.The WGCNA method reveals the relationship between the expression of highly relevant gene clusters and clinical indications through a scale-free network.However,the existing WGCNA method has some inconsistencies in the tuning criteria,and the results are obviously different.The reason is that the WGCNA tuning method under the existing integer-order framework is not optimized enough,and its ability to describe intermediate processes and complex phenomena is limited.As an effective tool to solve abnormal problems,fractional calculus has been successfully applied in many fields such as science,engineering,agriculture,commerce,medicine,etc.,especially its application in biomedicine has become a frontier.In this paper,the Mittag-Leffler function was introduced into the WGCNA method,which improved the self-similarity of the generated scale-free network and realized the selection of core genes affecting the formation of Helicobacter pylori biofilm.In particular,the effects of fractional order adjacency functions on Helicobacter pylori resistance,diffusion between cell membranes and other microscopic states were explored.Firstly,the existing WGCNA adjacency function can not effectively build the scale-free networks with high enough self-similarity,and the fractional-order generalized adjacency function of Mittag-Leffler function is proposed in this paper.The Stejiglitz-Mcbride algorithm is used to solve the problem of digital realization of fractional model.The fast calculation method based on Gauss-Kronrod numerical integration method is used to solve the problem of large amount of calculation using Mittag-Leffler function directly.The parameters in Mittag-Leffler function are used as input.The iterative learning method for self-similarity of the scale-free network is used to solve the parameter identification problem.In this way,the fractional-order WGCNA optimization tuning method is proposed,and the advantages and disadvantages of the fractional-order WGCNA method and the original WGCNA method are compared.Subsequently,according to the source and characteristics of biofilm data related to Helicobacter pylori resistance used in this paper,the application points of the fractional WGCNA method in this data set were analyzed.The scale-free network is constructed by the fractional-order adjacency function proposed,and various indicators and methods such as gene module,module clustering result,multi-dimensional scale map and related parameters in clinical indication and module relationship chart are formed by clustering method.analysis.The correctness of the fractional-order WGCNA method was verified by cross-checking the distribution of genes in each module,the degree of correlation with clinical indications,and the analysis results of individual modules.Finally,Cytoscape was used to visualize all of the genes in the clinically relevant module,clearly and visually representing and selecting the core genes most relevant to the clinical indications for H.pylori.