Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behaviour of biological molecules or complexes that can adopt a large number of possible functional states. Biological signaling systems often rely on complexes of biological macromolecules that can undergo several functionally significant modifications that are mutually compatible. Thus, they can exist in a very large number of functionally different states. Modeling such multi-state systems poses two problems: The problem of how to describe and specify a multi-state system (the "specification problem") and the problem of how to use a computer to simulate the progress of the system over time (the "computation problem"). To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states, and towards rule-based modeling that allow for implicit model specification, including the κ-calculus, BioNetGen, the Allosteric Network Compiler and others. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm. Given current computing technology, particle-based methods are sometimes the only possible option. Particle-based simulators further fall into two categories: Non-spatial simulators such as StochSim, DYNSTOC, RuleMonkey, and NFSim and spatial simulators, including Meredys, SRSim and MCell. Modelers can thus choose from a variety of tools; the best choice depending on the particular problem. Development of faster and more powerful methods is ongoing, promising the ability to simulate ever more complex signaling processes in the future.
Introduction
Multi-state biomolecules in signal transduction In living cells, signals are processed by networks of proteins that can act as complex computational devices. These networks rely on the ability of single proteins to exist in a variety of functionally different states achieved through multiple mechanisms, including post-translational modifications, ligand binding, conformational change, or formation of new complexes. Similarly, nucleic acids can undergo a variety of transformations, including protein binding, binding of other nucleic acids, conformational change and DNA methylation. In addition, several types of modifications can co-exist, exerting a combined influence on a biological macromolecule at any given time. Thus, a biomolecule or complex of biomolecules can often adopt a very large number of functionally distinct states. The number of states scales exponentially with the number of possible modifications, a phenomenon known as "combinatorial explosion". This is of concern for computational biologists who model or simulate such biomolecules, because it raises questions about how such large numbers of states can be represented and simulated.
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![Multi-state modeling of biomolecules: Screenshot from an MCell simulation of calcium signaling within the spine. Although other types of calcium-regulated molecules were included in the simulations, only CaMKII molecules are visualized. They are shown in red when bound to calmodulin and in black when unbound. The simulation compartment is a reconstruction of a dendritic spine.[54] The area of the postsynaptic density is shown in red, the spine head and neck in gray, and the parent dendrite in yellow. The figure was generated by visualizing the simulation results in Blender.](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bd/CaMKII_spine.png/500px-CaMKII_spine.png?utm_source=en.wikipedia.org&utm_campaign=parser&utm_content=thumbnail)
