Effects of ordered mutations on dynamics in signaling networks

Abstract

Background: Many previous clinical studies have found that accumulated sequential mutations are statistically related to tumorigenesis. However, they are limited in fully elucidating the significance of the ordered-mutation because they did not focus on the network dynamics. Therefore, there is a pressing need to investigate the dynamics characteristics induced by ordered-mutations.

Methods: To quantify the ordered-mutation-inducing dynamics, we defined the mutation-sensitivity and the order-specificity that represent if the network is sensitive against a double knockout mutation and if mutation-sensitivity is specific to the mutation order, respectively, using a Boolean network model.

Results: Through intensive investigations, we found that a signaling network is more sensitive when a double-mutation occurs in the direction order inducing a longer path and a smaller number of paths than in the reverse order. In addition, feedback loops involving a gene pair decreased both the mutation-sensitivity and the order-specificity. Next, we investigated relationships of functionally important genes with ordered-mutation-inducing dynamics. The network is more sensitive to mutations subject to drug-targets, whereas it is less specific to the mutation order. Both the sensitivity and specificity are increased when different-drug-targeted genes are mutated. Further, we found that tumor suppressors can efficiently suppress the amplification of oncogenes when the former are mutated earlier than the latter.

Conclusion: Taken together, our results help to understand the importance of the order of mutations with respect to the dynamical effects in complex biological systems.

Keywords: Boolean dynamics; Mutation-sensitivity; Order-specificity; Ordered-mutations; Signaling networks.

Fig. 1

An example of mutation-sensitivity and order-specificity computation. Given a network G(V, A) with a set of wild-type update rules F, let v₃ and v₄ be a pair of nodes subject to a double-mutation with a time gap T, and 0100 ∈ S an initial state. F^W denotes a W-mutant update rule set where every gene in W ⊆ V is frozen. In this example, the wild-type attractor (Att1) is computed by applying F all the time. On the other hand, a (v₃, v₄)-ordered (or (v₄, v₃)-ordered) mutant attractor denoted by Att2 (resp. Att3) is computed by assuming that $F^{\left\{v_3\right\}}$ (resp. $F^{\left\{v_4\right\}}$) and $F^{\left\{v_3,v_4\right\}}$ apply for 0 ≤ t < T and T ≤ t, respectively. The mutation-sensitivity of (v₃, v₄)-ordered (or (v₄, v₃)-ordered) double-mutation is computed by comparing Att1 and Att2 (resp. Att3). The order-specificity is computed by comparing Att2 and Att3

Fig. 2

Cumulative probability distributions of mutation-sensitivity and order-specificity values in signaling networks. Mutation-sensitivity and order-specificity of ordered gene pairs were examined. (a-c) Results in HCS, KEGG, and TGL, respectively. The time gap (T) was set to 20 in (a) and (b), and 10 in (c)

Fig. 3

Relations of structural properties with the ordered-mutation-inducing dynamics in signaling networks. (a-c) Mutation-sensitivity results with respect to the path length in HCS, KEGG, and TGL, respectively. All pairs of nodes involving an FBL were classified into ‘Shorter-path direction’ and ‘Longer-path direction’ groups where l(v_i, v_j) is smaller and larger than l(v_j, v_i), respectively. (d-f) Mutation-sensitivity results with respect to the number of paths in HCS, KEGG, and TGL, respectively. All pairs of nodes were classified into ‘More-paths direction’ and ‘Fewer-paths direction’ groups such that n(v_i, v_j) is smaller and larger than n(v_j, v_i), respectively. (g-i) Mutation-sensitivity results with respect to of the FBLs in HCS, KEGG, and TGL, respectively. All pairs of nodes were classified into ‘FBL’ and ‘Non-FBL’ groups such that any gene in the pair is involved in an FBL or not. (j-l) Order-specificity results with respect to the feedback loops in HCS, KEGG, and TGL, respectively. Time gap (T) was set to 2–20 in HCS and KEGG networks, and 1–10 in TGL networks. The error bar represents the standard error deviation

Fig. 4

Analysis of ordered-mutation-inducing dynamics with respect to drug-targets in signaling networks. (a-c) Mutation-sensitivity results in HCS, KEGG, and TGL, respectively. All genes were specified by ‘Drug-target (DT)’ and ‘Non-drug-target (Non-DT)’, and every gene pair was classified into four groups, ‘DT → DT’, ‘DT → Non-DT’, ‘Non-DT → DT’, and ‘Non-DT → Non-DT’. (d-f) Order-specificity results in HCS, KEGG, and TGL, respectively. Time gap (T) was set to 2–20 in HCS and KEGG networks, and 1–10 in TGL networks. The error bar represents the standard error deviation

Fig. 5

Comparison of ordered-mutation-inducing dynamics between gene pairs targeting same and different drugs in signaling networks. All pairs of genes were classified into ‘Same-drug’ or ‘Different-drug’ groups if the two genes in a pair target a same drug or different drugs, respectively. (a-b) Mutation-sensitivity results in HCS and KEGG, respectively. (c-d) Order-specificity results in HCS and KEGG, respectively. All time gap (T) was set to 2–20. The error bar represents the standard error deviation. Note that TGL network was excluded from analysis, because there was no pair of genes belonging to ‘Same-drug’ group

Fig. 6

Analysis of ordered-mutation-inducing dynamics with respect to tumor suppressors and oncogenes in signaling networks. (a-c) Mutation-sensitivity results in HCS, KEGG, and TGL, respectively. All genes were specified by ‘Tumor suppressor gene (TSG)’ and ‘Oncogene (OCG)’ groups, and every ordered gene pair was classified into ‘TSG → OCG’ and ‘OCG → TSG’ groups. (d-f) Order-specificity results in HCS, KEGG, and TGL, respectively. Time gap (T) was set to 2–20 in HCS and KEGG networks, and 1–10 in TGL networks. The error bar represents the standard error deviation