Modeling positive regulatory feedbacks in cell-cell interactions.

Our current understanding of molecular mechanisms of cellular regulation still does not support quantitative predictions of the overall growth kinetics of normal or malignant tissues. However, discernment of the role of growth-factor mediated cell-cell communication in tissue kinetics is possible by the use of simple mathematical models. Here we discuss the design and use of mathematical models in quantifying the contribution of autocrine and paracrine (i.e., humoral) interactions to the kinetics of tissue growth. We present models that include a humorally mediated regulatory feedback among cells built into phenomenological mathematical models of growth. Application of these models to data exemplifies the finite contributions of positive feedback in cell-cell interactions to the overall tissue growth. In addition, we propose a perturbation approach to allow separation of cell-cell interactions dependent on the perturbing agent (such as hormone antagonists in hormone-dependent tissues) from cell-cell interactions independent of it.