Quantitative modeling in systems biology can be difficult due to the scarcity of quantitative details about biological phenomenons, especially at the subcellular scale. An alternative to escape this difficulty is qualitative modeling since it requires few to no quantitative information. Among the qualitative modeling approaches , the Boolean network formalism is one of the most popular . However, Boolean models allow variables to be valued at only true or false , which can appear too simplistic when modeling biological processes. Consequently, this work proposes a modeling approach derived from Boolean networks where fuzzy operators are used and where edges are tuned. Fuzzy operators allow variables to be continuous and then to be more finely valued than with discrete modeling approaches, such as Boolean networks, while remaining qualitative. Moreover, to consider that in a given biological network some interactions are slower and/or weaker relative to other ones, edge states are  computed in order to modulate in speed and strength the signal they convey. The proposed formalism is illustrated through its implementation on a tiny sample of the epidermal growth factor receptor signaling pathway. The obtained simulations show that continuous results are produced, thus allowing finer analysis , and that modulating the signal conveyed by the edges allows their tuning according to knowledge about the modeled interactions , thus incorporating more knowledge. The proposed modeling approach is expected to bring enhancements in the ability of qualitative models to simulate the dynamics of biological networks while not requiring quantitative information.
Due to the scarcity of quantitative details about biological phenomena, quantitative modeling in systems biology can be compromised, especially at the subcellular scale. One way to get around this is qualitative modeling because it requires few to no quantitative information. One of the most popular qualitative modeling approaches is the Boolean network formalism . However, Boolean models allow variables to take only two values , which can be too simplistic in some cases. The present work proposes a modeling approach derived from Boolean networks where continuous logical operators are used and where edges can be tuned. Using continuous logical operators allows variables to be more finely valued while remaining qualitative. To consider that some biological interactions can be slower or weaker than other ones, edge states are also computed in order to modulate in speed and strength the signal they convey. The proposed formalism is illustrated on a toy network coming from the epidermal growth factor receptor signaling pathway. The obtained simulations show that continuous results are produced, thus allowing finer analysis . The simulations also show that modulating the signal conveyed by the edges allows to incorporate knowledge about the interactions they model. The goal is to provide enhancements in the ability of qualitative models to simulate the dynamics of biological networks while limiting the need of quantitative information.
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