title: Theoretical knock-outs on biological networks.
abstract: In this work we redefine the concept of biological importance and how to compute it, based on a model of complex networks and random walk. We call this new procedure, theoretical knock-out (KO). The proposed method generalizes the procedure presented in a recent study about Oral Tolerance. To devise this method, we make two approaches: algebraically and algorithmically. In both cases we compute a vector on an asymptotic state, called flux vector. The flux is given by a random walk on a directed graph that represents a biological phenomenon. This vector gives us the information about the relative flux of walkers on a vertex which represents a biological agent. With two vector of this kind, we can calculate the relative mean error between them by averaging over its coefficients. This quantity allows us to assess the degree of importance of each vertex of a complex network that evolves in time and has experimental background. We find out that this procedure can be applied in any sort of biological phenomena in which we can know the role and interrelationships of its agents. These results also provide experimental biologists to predict the order of importance of biological agents on a mounted complex network.
authors.affiliation: Department of Physics, State University of Ponta Grossa, Paraná, Brazil. Electronic address: pedrojemiranda@hotmail.com.
authors.forename: Pedro J
authors.initials: PJ
authors.lastname: Miranda
authors.affiliation: Department of Physics, State University of Ponta Grossa, Paraná, Brazil.
authors.forename: Sandro E
authors.initials: SE
authors.lastname: de S Pinto
authors.affiliation: Institute for Complex System and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen, United Kingdom.
authors.forename: Murilo S
authors.initials: MS
authors.lastname: Baptista
authors.affiliation: Department of Mathematics and Statistics, State University of Ponta Grossa, Paraná, Brazil.
authors.forename: Giuliano G
authors.initials: GG
authors.lastname: La Guardia
mesh_terms: D000465:Algorithms; D055786:Gene Knockout Techniques; D053263:Gene Regulatory Networks; D008962:Models, Theoretical
keywords: (M, R)-system; Complex networks; Random walks; Relational biology; Theoretical KOs