Metrics for Assessing Cytoskeletal Orientational Correlations and Consistency

In biology, organization at multiple scales potentiates biological function. Current advances in staining and imaging of biological tissues provide a wealth of data, but there are few metrics to quantitatively describe these findings. In particular there is a need for a metric that would characterize the correlation and consistency of orientation of different biological constructs within a tissue. We aimed to create such a metric and to demonstrate its use with images of cardiac tissues. The co-orientational order parameter (COOP) was based on the mathematical framework of a classical parameter, the orientational order parameter (OOP). Theorems were proven to illustrate the properties and boundaries of the COOP, which was then applied to both synthetic and experimental data. We showed the COOP to be useful for quantifying the correlation of orientation of constructs such as actin filaments and sarcomeric Z-lines. As expected, cardiac tissues showed perfect correlation between actin filaments and Z-lines. We also demonstrated the use of COOP to quantify the consistency of construct orientation within cells of the same shape. The COOP provides a quantitative tool to characterize tissues beyond co-localization or single construct orientation distribution. In the future, this new parameter could be used to represent the quantitative changes during maturation of cardiac tissue, pathological malformation, and other processes.Author Summary: Biological tissues are highly organized on multiple length scales. In tissue engineering, recreating the in vivo architecture is an important aspect of in vitro experiments. An ability to quantify organization of cellular constructs, specifically the correlation in their orientations, would greatly enhance both our understanding of the function of each construct and provide a tool to evaluate engineered tissues. In this work, we have developed a parameter to evaluate the correlation and consistency of construct orientation. We have extensively characterized this co-orientational order parameter analytically, validated it using synthetic data, and demonstrated its use with experimental data of Z-lines and actin fibrils architectures in engineered cardiac tissues. As long as the orientation angles and location of constructs are known, the parameter can quantify both orientational correlation and consistency. Thus, the co-orientational order parameter has a wide scope of application both in biology and potentially outside of it.