The application of thermodynamic principles to histochemical and morphometric tissue research: principles and practical outline with focus on the glycosciences.

Physicochemical terms such as entropy or current of entropy are commonly used to refer solely to the description of reactions in the realm of chemistry and physics. Since these thermodynamic terms have a predictive value for the further course of development of such reactions, e.g., extent of a chemical reaction or affinity of molecular interactions, it is tempting to introduce the respective algorithms to biological problems. By combining quantitative morphology with the histochemical visualization of distinct cellular and textural properties such as nuclear DNA contents or intensity of histochemical staining, equations from the general theory of thermodynamics can be adapted. They permit appropriate calculations to be performed which introduce the entropy concept to the processing of the information collected by analysis of structures formed by histochemically labeling cells. The theory of weighted graphs offers the appropriate mathematical tools. Nuclei are defined as vertices. Their DNA contents measured by the integrated optical density or additional cellular features (for example staining intensity of applied immuno-/ligandohistochemical probes) define the associated weights and the minimum spanning tree as a derivative from Voronoi's theorem for the definition of the geometrical neighborhood. This technique is equivalent to syntactic structure analysis as developed by Lu and Fu (1978), Sanfeliu et al. (1981), Kayser and Schlegel (1982), and Kayser (1988). Assuming that the texture of a healthy tissue is displayed in the energetically most efficient and stable manner to perform the required biological functions, i.e., to maintain the lowest level of entropy, deviations from this level are reflected in differences in distances and weights between neighboring nuclei or cells. The measure of textural differences in relation to the normal appearance of an organ or tissue is denoted as structural entropy. Since organisms or their compartments are thermodynamically open systems, they are insufficiently described by the (structural) entropy. This parameter only provides a snapshot, with no information about the status of entropy changes from a directed exchange with the environment. The current of entropy, which is equivalent to the amount of entropy exported or imported through a boundary, is an appropriate measure of the "thermodynamic distance" of the system under consideration from its environment, as is readily appreciated for tumors. A solid tumor is a biological system embedded in another one (healthy tissue). Its current of entropy can be calculated if its boundary and proliferative activity are known. This parameter can be measured by histochemical methods (Ki-67 antibody) or from the cytometric characteristics (percentage of S-phase-related tumor cells), and the boundary can be measured by the volume fraction of the internal vessels and the size of the external surface of the tumor. Since biochemical factors will contribute to the generation and establishment of these structural and thermodynamic features at the level of tissue organization, histochemical studies can uncover the correlation with these parameter alterations. Taking glycohistochemical determinants as an example for this hypothesis, the potential value of combining the results of immuno-/ligandohistochemistry with the data derived from the cytometric or syntactic structure analysis measurements and from the calculations based on thermodynamic theorems is illustrated.