Effects of multiple parameter variations on biological system behaviors

Biological networks often involve many parameters, and the importance of these parameters in determining system behaviors must be assessed in order to gain deep insight into designing principles of living organisms. However, many parameters cause the biological system behaviors vary extensively, therefore it is difficult to analyze the effect of individual parameters in a systematic way. In this paper, we show the effects of multiple parameter variations on bistability (or multistability) of positive feedback loop networks and further on oscillations in interlocked feedback loop networks by extending the techniques from the recently developed theory of monotone systems. This approach is based on decomposing a closed loop system into some open loops. The main ideas are illustrated through a positive feedback loop system and another system with a negative feedback loops, meanwhile, the proposed technique is valid for a general class of biological systems.