Logical versus kinetic modeling of biological networks: applications in cancer research

Mathematical modeling of biological networks is a promising approach to understand the complexity of cancer progression, which can be understood as accumulated abnormalities in the kinetics of cellular biochemistry. Two major modeling formalisms (languages) have been used for this purpose in the last couple of decades: one is based on the application of classical chemical kinetics of reaction networks and the other one is based on discrete kinetics representation (called logical formalism for simplicity here), governed by logical state update rules. In this short review, we remind the reader how these two methodologies complement each other but also present the fast and recent development of semi-quantitative approaches for modeling large biological networks, with a spectrum of complementary ideas each inheriting and combining features of both modeling formalisms. We also notice an increasing influence of the recent success of machine learning and artificial intelligence onto the methodology of mathematical network modeling in cancer research, leading to appearance of a number of pragmatic hybrid approaches.To illustrate the two approaches, logical versus kinetic modeling, we provide an example describing the same biological process with different description granularity in both discrete and continuous formalisms. The model focuses on a central question in cancer biology: understanding the mechanisms of metastasis appearance.We conclude that despite significant progress in development of modeling ideas, predicting response of large biological networks involved in cancer to various perturbations remains a major unsolved challenge in cancer systems biology.