Logical modeling vs. rule-based modeling

Cell signaling systems have been modeled using logical and rule-based approaches. What's the difference? A rule-based model is similar to a logical model, in that both types of models involve rules. However, the rules are usually rather different in character. In a typical logical model, rules define state transitions of biomolecules, including conditions on these transitions. They have an "if-then" flavor. The rules operate on variables representing states of whole biomolecules, and they define when and how such state variables change their values. Biomolecules in logical models are often characterized by state variables that take one of two values, e.g., 0 or 1. Such variables are introduced to represent "on" and "off" states. More than two states can be considered, but there is a limit to what's tractable, as the reachable state space tends to grow exponentially with the number of possible states. As more states are considered, there are more and more transitions between these states, each of which is usually considered explicitly when specifying a logical model. The behavior of a logical model can sometimes depend on the algorithmic protocol used for changing states in a simulation. This seems undesirable. In a rule-based model, the amount of an activated protein can be continuous or discrete, from 0 copies to all copies of the protein. This is because a rule-based model is based on the principles of chemical kinetics. The state variables implicitly defined by rules capture numbers of biomolecules in particular states and/or complexes. Rules are associated with rate laws, which govern the rates or probabilities of transitions of biomolecular site states, not the state transitions of whole molecules. With a physicochemical foundation, it is relatively easy to capture certain phenomena found in cell signaling systems, such as competition, feedback, and crosstalk. These phenomena are more difficult to capture in a logical model. At least, it seems that way to me. With model-specification languages such as BNGL (http://bionetgen.org), a set of rules can be used to perform different tasks: stochastic or deterministic simulation, via a direct or indirect method. Is it possible to modify BNGL to enable logical modeling? Although typical logical models are different from typical rule-based models, it does not seem that the rules used in the two types of models, although usually different, are necessarily fundamentally different, so my answer is a tentative "yes." What do you think?