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We present the statistical method to study the interaction between a chosenprotein and another molecule (e.g., both being components of lubricin found insynovial fluid) in a water environment. The research is performed on theexample of univariate time series of chosen features of the dynamics of mucin,which interact with chondroitin sulfate (4 and 6) in four different salinesolutions. Our statistical approach is based on recurrence methods to analyzechosen features of molecular dynamics. Such recurrence methods are usuallyapplied to reconstruct the evolution of a molecular system in its reduced phasespace, where the most important variables in the process are taken intoaccount. In detail, the analyzed time-series are spitted onto sub-series ofrecords that are expected to carry meaningful information about the system ofmolecules. Elements of sub-series are splinted by the constant delay-time lag(that is the parameter determined by statistical testing in our case), and thelength of sub-series is the embedded dimension parameter (using the Caomethod). We use the recurrent plots approach combined with the Shannon entropyapproach to analyze the robustness of the sub-series determination. Wehypothesize that the robustness of the sub-series determines some specifics ofthe dynamics of the system of molecules. We analyze rather highly noisedfeatures to demonstrate that such features lead to recurrence plots thatgraphically look similar. From the recurrence plots, the Shannon entropy hasbeen computed. We have, however, demonstrated that the Shannon entropy value ishighly dependent on the delay time value for analyzed features. Hence,elaboration of a more precise method of the recurrence plot analysis isrequired. For this reason, we suggest the random walk method that can beapplied to analyze the recurrence plots automatically.

Statistical method for analysis of interactions between chosen protein and chondroitin sulfate in an aqueous environment