The Study Of The Role Of Feedback Loop In The Oscillation Behavior Of Feedforward Loop Motif

Both feedforward loop(FFL)and feedback loop(FBL)exist widely in biological networks.The simplest FFL is a loop which is composed of three substances.In this study,these three substances are assumed to be X,Y,and Z,where X is the signal input end,Z is the signal output end,and Y is the intermediate substance connecting the two.The loop contains two paths: a direct path from X to Z,and an indirect path from X through Y to Z.When the direct and indirect effects of X on Z are coherent,the feedforward loop is called a coherent FFL.According to the difference of integration manner of direct path and indirect path at the output end,the coherent FFL are further divided into "AND" type coherent FFL and "OR" type coherent FFL.Feedback refers to the process in which the output of the system is returned to the input through a specific path and superimposed with the original input,thereby affecting the system function.According to the influence of feedback on output,feedback can be divided into positive feedback and negative feedback.The former enhances the output of the system,while the latter weakens it.Due to a closed loop will be formed between the substances that have feedback effects,the motif often be called FBL.The existence of feedback loop will make the system produce complex dynamic behavior,such as oscillation behavior.The motifs represented by feedforward loop and feedback loop exist widely in biological networks,and the researches on the dynamics of these have attracted wide attention.However,it is still lacking that the systematic researches on the dynamics of FFLFBL coupled network at present.In order to study the role of FBL in the oscillation behavior of FFL,firstly 729 topological structures are generated by enumeration method and converted into differential equations model.Then,latin hypercube sampling is performed on the parameters of differential equations model and numerical solutions are obtained through numerical simulation to determine whether oscillation behavior occurs.Thus,the probability of oscillating behavior of each topology structure is obtained.Then the probability is used to carry out K-means clustering and calculate the evaluation index.The clustering analysis results are used to construct the decision tree model and calculate the evaluation index.The classification number is selected by combining the two evaluation indexes.Finally,through K-means clustering analysis,decision tree model important node analysis and topology evolution analysis,the role of feedback loop in the oscillation behavior of feedforward loop module was found.The results show that the positive feedback of X to itself and the negative feedback of Z to X play a key role in the oscillation behavior of the "AND" type coherent FFL.For the "OR" type coherent FFL,the positive feedback of X to itself and the negative feedback of Z to X and the negative feedback of Y to X play a key role in the oscillation behavior.In addition,the parameters,amplitudes and periods of the equation that generate the topology of oscillating behavior are analyzed statistically and repeated by simple random sampling to verify the reliability and robustness of the results.This study,for the first time,systematically study the oscillation behavior of the coherent FFL-FBL coupled network,which reveals the important factors of the oscillation of the network and expands the research on the dynamic model of biological networks.