Abstract: P. Weber, P. Beldowski, A. Gadomski, K. Domino, P. Sionkowski, D. Ledziński (2024)

In: Perspectives in Dynamical Systems II – Numerical and Analytical Approaches, 454, Eds.: J. Awrejcewicz, Springer, Cham (Switzerland), 697–714p. (2024) DOI:10.1007/978-3-031-56496-3_45

Statistical Method for Analysis of Interactions Between Chosen Protein and Chondroitin Sulfate in an Aqueous Environment

We present the statistical method to study the interaction between a chosen protein and another molecule (e.g., both being components of lubricin found in synovial fluid) in a water environment. The research is performed on the example of univariate time series of chosen features of the dynamics of mucin, which interact with chondroitin sulfate (4 and 6) in four different saline solutions. Our statistical approach is based on recurrence methods to analyze chosen features of molecular dynamics. Such recurrence methods are usually applied to reconstruct the evolution of a molecular system in its reduced phase space, where the most important variables in the process are taken into account. In detail, the analyzed time-series are spitted onto sub-series of records that are expected to carry meaningful information about the system of molecules. Elements of sub-series are splinted by the constant delay-time lag (that is the parameter determined by statistical testing in our case), and the length of sub-series is the embedded dimension parameter (using the Cao method). We use the recurrent plots approach combined with the Shannon entropy approach to analyze the robustness of the sub-series determination. We hypothesize that the robustness of the sub-series determines some specifics of the dynamics of the system of molecules. We analyze rather highly noised features to demonstrate that such features lead to recurrence plots that graphically look similar. From the recurrence plots, the Shannon entropy has been computed. We have, however, demonstrated that the Shannon entropy value is highly dependent on the delay time value for analyzed features. Hence, elaboration of a more precise method of the recurrence plot analysis is required. For this reason, we suggest the random walk method that can be applied to analyze the recurrence plots automatically.

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