  A dynamic logic method was developed to analyze molecular networks of cells
by combining Kauffman and Thomas's logic operations with molecular interaction
parameters. The logic operations characterize the discrete interactions between
biological components. The interaction parameters (e.g. response times)
describe the quantitative kinetics. The combination of the two quantitatively
characterizes the discrete biological interactions. A number of simple networks
were analyzed. The main results include: we proved the theorems to determine
bistable states and oscillation behaviors of networks, we showed that time
delays are essential for oscillation structures, we proved that single variable
networks do not have chaotic behaviors, and we explained why one signal can
have multiply responses. In addition, we applied the present method to the
analysis of the MAPK cascade, feed-forward loops, and mitosis cycle of budding
yeast cells.
