Fig. 1

An illustrative example of computing the gene-gene dynamics influence value. a An example GMI network. Given a network G(V, A) with a set of update rules F, let v ₃ a node subjected to the knockout mutation for t ≤ T. The knockout mutation changes F into F ^′ where the state value of v ₃ is frozen to 0 for t ≤ T. b Identification of wild-type and mutant attractors. Let [0000] ∈ S be an initial state considered in this example. By examining two state trajectories along with F and F ^′, respectively, we obtain two corresponding attractors, 〈G, F, v(0)〉 and 〈G, F ^′, v(0)〉 of which the least common multiple of the lengths is four. c Computation of a distance between wild-type and mutant attractors. Since the greatest common divisor of the lengths of two attractors is two, we examine two different alignments of the state sequences of v ₁ in those attractors. The number of different bits between [0101] and [0001] is 1 in case 1 (m = 0), whereas that between [1010] and [0001] is 3 in case 2 (m = 1). Accordingly, the minimum bitwise difference is 1, and hence \( d\left(\mathbf{v}(0),{v}_3,{v}_1\right)=\frac{1}{4} \). We can compute μ(v ₃, v ₁) by averaging out d(v(0), v ₃, v ₁) over the set of initial states. d The resultant GDI network. The left matrix shows the dynamics influence value for every ordered pair of genes, and the right graph shows the resultant GDI network with nine positive dynamics influence relations