Quantitative assessment of the microstructure of rat behavior: I, f(d), the extension of the scaling hypothesis

Previous studies demonstrated that drug effects on the movement sequences of rats in unconditioned motor activity paradigms can be quantified by scaling measures that describe the average relationship between a variable of interest and an experimental parameter. However, rats engage in a wide variety of geometrically distinct movements that can be influenced differentially by drugs. In this investigation, the extended scaling approach is presented to capture quantitatively the relative contributions of geometrically distinct movement sequences to the overall path structure. The calculation of the spectrum of local spatial scaling exponents, f(d), is based on ensemble methods used in statistical physics. Results of the f(d) analysis confirm that the amount of motor activity is not correlated with the geometrical structure of movement sequences. Changes in the average spatial scaling exponent, d, correspond to shifting the entire f(d) function, and indicate overall changes in path structure. With the extended scaling approach, straight movement sequences are assessed independently from highly circumscribed movements. Thus, the f(d) function identifies drug effects on particular ranges of movement sequences as defined by the geometrical structure of movements. More generally, the f(d) function quantifies the relationship between microscopically recorded variables, in this paradigm consecutive (x,y) locations, and the macroscopic behavioral patterns that constitute the animal's response topography.