  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.
