text: Biological signaling networks incorporate a wide array of reversible interactions, post-translational modifications and conformational changes. Furthermore, it is common for a protein to be composed of several - identical or nonidentical - subunits, and for several proteins and/or nucleic acid species to assemble into larger complexes. A molecular species with several of those features can therefore exist in a large number of possible states.
  For instance, it has been estimated that the yeast scaffold protein Ste5 can be a part of 25666 unique protein complexes. In E. coli, chemotaxis receptors of four different kinds interact in groups of three, and each individual receptor can exist in at least two possible conformations and has up to eight methylation sites, resulting in billions of potential states. The protein kinase CaMKII is a dodecamer of twelve catalytic subunits, arranged in two hexameric rings.  Each subunit can exist in at least two distinct conformations, and each subunit features various phosphorylation and ligand binding sites. A recent model incorporated conformational states, two phosphorylation sites and two modes of binding calcium/calmodulin, for a total of around one billion possible states per hexameric ring. A model of  coupling of the EGF receptor to a MAP kinase cascade presented by Danos and colleagues accounts for  distinct molecular species, yet the authors note several points at which the model could be further extended. A more recent model of ErbB receptor signalling even accounts for more than one googol () distinct molecular species. The problem of combinatorial explosion is also relevant to synthetic biology, with a recent model of a relatively simple synthetic eukaryotic gene circuit featuring 187 species and 1165 reactions.
  Of course, not all of the possible states of a multi-state molecule or complex will necessarily be populated. Indeed, in systems where the number of possible states is far greater than that of molecules in the compartment (e.g. the cell), they cannot be. In some cases, empirical information can be used to rule out certain states if, for instance, some combinations of features are incompatible. In the absence of such information, however, all possible states need to be considered a priori. In such cases, computational modeling can be used to uncover to what extent the different states are populated.
  The existence (or potential existence) of such large numbers of molecular species is a combinatorial phenomenon: It arises from a relatively small set of features or modifications (such as post-translational modification or complex formation) that combine to dictate the state of the entire molecule or complex, in the same way that the existence of just a few choices in a coffee shop (small, medium or large, with or without milk, decaf or not, extra shot of espresso) quickly leads to a large number of possible beverages (24 in this case; each additional binary choice will double that number). Although it is difficult for us to grasp the total numbers of possible combinations, it is usually not conceptually difficult to understand the (much smaller) set of features or modifications and the effect each of them has on the function of the biomolecule. The rate at which a molecule undergoes a particular reaction will usually depend mainly on a single feature or a small subset of features. It is the presence or absence of those features that dictates the reaction rate. The reaction rate is the same for two molecules that differ only in features which do not affect this reaction. Thus, the number of parameters will be much smaller than the number of reactions. (In the coffee shop example, adding an extra shot of espresso will cost 40 cent, no matter what size the beverage is and whether or not it has milk in it). It is such "local rules" that are usually discovered in laboratory experiments. Thus, a multi-state model can be conceptualised in terms of combinations of modular features and local rules. This means that even a model that can account for a vast number of molecular species and reactions is not necessarily conceptually complex.