Model Fitting And Clustering Analysis Of Bacterial Growth Curve

In both industrial and medical fields,bacteria are important microorganisms.The study of bacterial growth curve is helpful to understand and utilize microorganisms.The analysis of growth curve is usually to use mathematical model to fit the growth of bacteria,to estimate various growth parameters and to describe the growth regulation of microorganisms.It is found that even if some bacterial strains have similar growth trends,there are usually potential growth differences among different strains,so it is necessary to optimize and improve existing mathematical models or to develop new models during analysis processes for further obtaining meaningful results in the biological sense.In addition,due to the development of artificial intelligence in recent years,machine learning algorithms have been widely employed in many fields of scientific research,especially in the biological category.In this context,this paper makes use of clustering analysis algorithm in machine learning to preliminarily explore the feasibility of cluster analysis of growth curve of E.coli(Escherichia coli)and its genomic variant strains as model microorganisms under different medium conditions.Firstly,this study collects a series of growth curves based on two variables.The first variable parameter is the genome mutations of the strain.In this paper,a series of mutant strains with decreasing genome length were selected to explore the influence of genome changes on strain growth patterns.The second parameter is the culture medium of the strain.Three kinds of medium were selected to investigate the effect of different nutrient components on the growth patterns of the bacteria.Secondly,the growth curves of different genome-mutated bacteria under each medium condition were fitted by Logistic model,and the biological significance of each parameter obtained in the model fitting was analyzed as well.Due to the decay period of growth curve,a new parameter(decay rate)is introduced into the Logistic model,which makes the improved Logistic model moresuitable for fitting the shape of gained growth curve.Compared with the original Logistic model,the modified model has better goodness of fit and also lower error sum of squares.Moreover,the modified logistic model was subsequently applied to the growth curve data of E.coli in this study,and the negative correlation between the decay rate and the length of E.coli genome was discovered.Taken together,our findings provide a better methodology for new model fitting to study the growth patterns of bacteria.Moreover,in order to explore the relationship between the shape of growth curve and the culture medium and/or genome structure,time series clustering analysis was utilized to cluster the growth curve of E.coli for the first time.The similarity between the growth curves of E.coli strains was calculated by Dynamic Time Warping(DTW)and Derivative Dynamic Time Warping(DDTW).According to the similarity,the hierarchical clustering is carried out from bottom to top.Four commonly used clustering evaluation algorithms are used to evaluate the clustering results and then the best clustering results were evaluated.The results showed that the same growth curve of medium could be divided into the same clusters.In addition,in order to make the optimal clustering result of clustering evaluation index accord with the biological characteristics of growth curve,a new evaluation standard is proposed.According to the new standard,the clustering results have higher accuracy.The reasonable clustering of growth curve shows that DTW and DDTW combined with hierarchical clustering algorithm can be better used for bacterial growth analysis.The clustering results from this study demonstrated that the culture medium determined some specific growth patterns of E.coli.Compared with the parameter of genome,the influence of the culture medium on the growth curve seems to have a higher priority in some conditions.Collectively,this study presents the feasibility of methodology for clustering bacterial growth curves,which provides a technical reference for bacterial growth in the future.