Metrics for Assessing Cytoskeletal Orientational Correlations and Consistency

Abstract

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.

Multiscale Characterization of Engineered Cardiac Tissue Architecture

“…Standard methods were used to prepare cells and tissues for structure characterization [17,37]. Here, we describe them briefly.…”

“…Transactions of the ASME software (MathWorks, Natick, MA) as previously described [12,33,37] to determine orientation of structures and metrics. One of the metrics, the orientation order parameter has been commonly used for over 40 yr [28,40].…”

“…Conversely, if the COOP is identical to the uncorrelated COOP, the two structures are as uncorrelated as possible [37]. The COOP ranges from 0 to 1, and its limits (i.e., uncorrelated and correlated COOPs) can also vary from 0 to 1 with the corresponding orientational order in the two structures.…”

“…The heart architecture has been extensively studied for decades [1,12,16,33,[35][36][37]. However, the complex nature of the structures that form the heart makes it challenging to quantitatively describe architecture in a consistent manner.…”

“…In order to both understand and rebuild the threedimensional (3D) myocardium, it is necessary to fully understand the 2D sheets. To this end, we demonstrate how a collection of order parameters [28,29,33,37] can be used to elucidate cardiac cell and tissue architecture over multiple scales that span from subcellular to tissue scale. The qualitative observation of consistent self-assembly as a function of cellular shape was tested over multiple subcellular length-scales and was found to have implications on these cells contractile function.…”