We developed a computational model to test whether targeted therapies, such as kinase inhibitors, can produce off-target effects in upstream pathways as a consequence of retroactivity alone. Using a numeric perturbation method, we identified specific conditions (Figure ) that favored the promotion of steady state off-target effects via retroactivity when a targeted inhibitor was applied to cycle n in a series of simple signaling networks (Figure ).
Figure 6 A summary of conditions that favor off-target effects in the n = 3 and the extended n = 3 networks. The conditions that promoted off-target effects in our model are summarized for two network types. Off-target effects in (A) the n = 3 network and (B) (more ...)
Our investigation considered only the effect of retroactivity and targeted inhibitors on the individual motifs we studied in the absence of genetic and/or other regulatory relationships. This allowed us to investigate whether such motifs have the capacity to produce off-target effects without regulatory feedback connections. In addition, the present study only considered the steady state response to a targeted therapy. The primary reason we considered only steady state responses was because it provided us with an objective measure that could be used to compare the effect of a targeted inhibitor across many different parameter sets. It is important to note that the dynamics of a retroactive signaling process are likely to induce transient changes in the levels of key signaling molecules. These transient changes, which are not observable at steady state, may lead to important in vivo responses.
It is also well known that the dynamics of signal transduction networks can be modulated by important oscillatory behavior, for example, from the P53/MDM2 regulatory feedback loop [20
]. Because we have not considered transient dynamics, our approach cannot be assumed to apply to all signaling networks. Nevertheless, we expect conditions that favor the induction of off-target effects at steady state to also favor the induction of detectable transient changes associated with the steady state response. In fact, this is what we observed when we plotted the time-course of the cycle 2 proteins with the parameter sets used in Figure (data not shown).
This work has led to very interesting and somewhat surprising results. A major importance of this work is that it did not investigate off-target effects related to a specific therapeutic intervention. There are, however, examples of targeted inhibitors of great clinical interest that are involved in signaling motifs similar to the network motifs we examined. The drug NSC 74859 [22
], for example, is a selective inhibitor that targets STAT3. JAK is an upstream activator of both STAT3 and PI3K [23
], thus when NSC 74859 inhibits STAT3, JAK could potentially facilitate the propagation off-target effects due to retroactive signaling from STAT3 to PI3K. Moreover, the inhibitor GSK690693 [24
] targets AKT and could potentially give rise to a retroactive signal that propagates upstream to a common activator of either the MAPK or STAT3 cascades, generating off-target effects in these pathways.
The binding affinity of the inhibitor for its target did not play a substantial role in the promotion of off-target effects in our model. Instead, the kinetics of the component cycles in the network were more important for increasing the likelihood of off-target effects (Figure and Additional File 3
Figure S3, S4). In general, off-target effects were more likely to occur in the networks studied when the targeted cycle n
favored the deactivation reaction because the Vmax
of the deactivation reaction was larger than the Vmax
of the activation reaction and/or both enzymatic reactions in cycle n
operated in or near the zero order regime. Off-target effects were also more likely when cycle 1 (the source of the shared activator in our models) favored the activation reaction and its kinase reaction operated in or near the zero order regime.
If cycle 2's cascade was extended to include cycle 4 (Figure ), which was activated by Y2*, off-target effects were more likely to propagate to cycle 4 when cycle 2 favored deactivation and cycle 4 favored activation. In cycle 2 this meant that the kinetics of the kinase reaction were generally inefficient (operating in or near the linear regime) and that the Vmax of the deactivation reaction was generally larger than the Vmax of the activation reaction. Thus, off-target effects were promoted when cycle 2 was "off" and not consuming significant amounts of the shared upstream activator, Y1*.
The results also indicate that off-target effects were more likely when the total kinase to substrate and the total phosphatase to substrate ratios in the inhibited cycle (En and E'n, respectively) were less than 1. In the n = 3 network, this meant that there was less total protein in cycle 1 than in cycle 3 because E3 < 1 implies Y1T <Y3T. The reason for this is that the smaller the Y1T/Y3T ratio, the stronger the sequestration of Y1* will be. The impact of this ratio increases if cycle 3 favors the deactivation reaction such that a large fraction of Y3T is in the inactive Y3 form, promoting the binding of Y3 to Y1*.
The immediate experimental implications of this result is that, in the absence of kinetic information, the likelihood of off-target effects may potentially be estimated for a network configuration of this type (Figure ) based on the ratio of the concentrations of components in the inhibited cycle and the preceding cycle (using, for example, proteomic or gene expression data). While this ratio would not be an absolute predictor, the presence of this condition would suggest an increased probability of off-target effects.
In agreement with the work of other groups [8
], we found the probability of off-target effects attenuated when the targeted cycle was near the bottom of a long cascade or when there were many substrates competing for a common upstream activator (Table ). Our results also suggest that within physiologically realistic parameter ranges, changing a single kinetic parameter or species concentration by 1 order of magnitude has the capacity to dramatically alter whether an off-target effect occurs as a direct result of targeted inhibition. It is also worth noting that, even though we varied the normalized drug concentration over a very large range, in general, the normalized inhibitor concentration needed to change by only 2 orders of magnitude to induce an off-target effect (see, for example, Figure ).