# Circuit topology

The **circuit topology** of a linear polymer refers to arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. For defining the circuit topology, contacts are defined depending on the context. For proteins with disulfide bonds, these bonds could be considered as contacts. In a context where beta-beta interactions in proteins are more relevant, these interactions are used to define the circuit topology. As such, circuit topology framework can be applied to a wide range of applications including protein folding and analysis of genome architecture.^{[1]} In particular, data from Hi-C and related technologies can be readily analysed using circuit topology framework.

For a chain with two binary contacts, three arrangements are available: parallel, series and crossed. For a chain with n contacts, the topology can be described by an n by n matrix in which each element illustrates the relation between a pair of contacts and may take one of the three states, P, S and X.

Multi-valent intra chain interactions can often be structurally decomposed into binary interactions and then be subjected to similar analysis.

Circuit topology has implications for folding kinetics and molecular evolution. Circuit topology along with contact order and size are determinants of folding rate of linear polymers.^{[2]} The topology of the cellular proteome and natural RNA reflect evolutionary constraints on biomolecular structures.^{[3]} Topology landscape of biomolecules can be characterized and evolution of molecules can be studied as transition pathways within the landscape.^{[4]}

## References[edit]

**^**Mashaghi, Alireza; van Wijk, Roeland J.; Tans, Sander J. (2014). "Circuit Topology of Proteins and Nucleic Acids".*Structure*.**22**: 1227–1237. doi:10.1016/j.str.2014.06.015.**^**Mugler, Andrew; Tans, Sander J.; Mashaghi, Alireza (2014). "Circuit topology of self-interacting chains: implications for folding and unfolding dynamics".*Phys. Chem. Chem. Phys*.**16**: 22537–22544. Bibcode:2014PCCP...1622537M. doi:10.1039/C4CP03402C.**^**Mashaghi, Alireza; Ramezanpour, Abolfazl (2015). "Circuit topology of linear polymers: a statistical mechanical treatment".*RSC Adv*.**5**: 51682–51689. arXiv:1509.00432 . doi:10.1039/C5RA08106H.**^**Mashaghi, Alireza; Ramezanpour, Abolfazl (2015). "Distance measures and evolution of polymer chains in their topological space".*Soft Matter*.**11**: 6576–6585. arXiv:1509.00444 . Bibcode:2015SMat...11.6576M. doi:10.1039/C5SM01482D.