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RESEARCH ARTICLEOpen Access

Kinase inhibitors can produce off-target effects

and activate linked pathways by retroactivity

Michelle L Wynn1†, Alejandra C Ventura2,5†, Jacques A Sepulchre3, Héctor J García4and Sofia D Merajver1,5*

Abstract

Background: It has been shown in experimental and theoretical work that covalently modified signaling cascades

naturally exhibit bidirectional signal propagation via a phenomenon known as retroactivity. An important

consequence of retroactivity, which arises due to enzyme sequestration in covalently modified signaling cascades,

is that a downstream perturbation can produce a response in a component upstream of the perturbation without

the need for explicit feedback connections. Retroactivity may, therefore, play an important role in the cellular

response to a targeted therapy. Kinase inhibitors are a class of targeted therapies designed to interfere with a

specific kinase molecule in a dysregulated signaling pathway. While extremely promising as anti-cancer agents,

kinase inhibitors may produce undesirable off-target effects by non-specific interactions or pathway cross-talk. We

hypothesize that targeted therapies such as kinase inhibitors can produce off-target effects as a consequence of

retroactivity alone.

Results: We used a computational model and a series of simple signaling motifs to test the hypothesis. Our results

indicate that within physiologically and therapeutically relevant ranges for all parameters, a targeted inhibitor can

naturally induce an off-target effect via retroactivity. The kinetics governing covalent modification cycles in a

signaling network were more important for propagating an upstream off-target effect in our models than the

kinetics governing the targeted therapy itself. Our results also reveal the surprising and crucial result that kinase

inhibitors have the capacity to turn “on” an otherwise “off” parallel cascade when two cascades share an upstream

activator.

Conclusions: A proper and detailed characterization of a pathway’s structure is important for identifying the

optimal protein to target as well as what concentration of the targeted therapy is required to modulate the

pathway in a safe and effective manner. We believe our results support the position that such characterizations

should consider retroactivity as a robust potential source of off-target effects induced by kinase inhibitors and

other targeted therapies.

Background

Cells propagate information through protein signaling

pathways that are part of complex signal transduction

networks [1]. The simplest view of cellular signaling

entails a cascade of molecular events initiated by the

recognition of a stimulus and culminating in the chemi-

cal alteration of an effector molecule. In the case of

covalent modification by the addition or removal of a

phosphate group, a reaction commonly found in

signaling cascades, each phosphorylated protein serves

as the kinase that activates the next cycle’s unpho-

sphorylated protein.

Targeted therapies are used to modulate disease pro-

gression by inhibiting a specific protein within a dysre-

gulated signaling pathway [2]. Kinase inhibitors are a

class of targeted therapies designed to interfere with a

specific kinase molecule. While extremely promising as

anti-cancer agents, kinase inhibitors can produce off-tar-

get effects by inducing changes in molecules other than

the one specifically targeted. Such off-target effects are

generally attributed to non-specific binding or to cross-

talk [3].

* Correspondence: smerajve@umich.edu

† Contributed equally

1Center for Computational Medicine and Bioinformatics, University of

Michigan Medical School, Ann Arbor, MI, USA

Full list of author information is available at the end of the article

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© 2011 Wynn et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons

Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in

any medium, provided the original work is properly cited.

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Recent theoretical and experimental studies have

demonstrated that covalently modified cascades also

exhibit bidirectional signal propagation via a phenom-

enon termed retroactivity [4-9]. This phenomenon arises

because cycles in a cascade are coupled, not only to the

next cycle, but also to the previous cycle (Figure 1). The

cycles can be thought of as modules where each mod-

ule’s substrate sequesters a key component of the pre-

vious module, limiting the component’s ability to

participate in the previous module and inducing a nat-

ural change in the preceding module. This change may

then propagate upstream through one or more preced-

ing modules.

While retroactivity is naturally present in covalently

modified cascades, signaling pathways likely have

evolved to propagate signals in an optimized down-

stream manner. An important consequence of retroac-

tivity, however, is that a downstream perturbation in a

signaling cascade can produce an upstream effect with-

out the need for explicit negative feedback connections

[4]. Retroactivity may, therefore, play important roles in

the dysregulated signaling networks of diseased cells as

well as the cellular response to targeted therapies

applied to dysregulated signaling networks.

Ventura, Sepulchre, and Merajver [4] demonstrated

that increasing the concentration of the inactivating

enzyme (e.g., a phosphatase) in the terminal cycle of a

cascade can decrease the concentration of the activated

protein in the previous cycle [4]. This finding led us to

hypothesize that a targeted inhibitor can produce

upstream off-target effects via retroactivity that can pro-

pagate elsewhere in the signaling network.

Off-target effects associated with targeted therapies are

often attributed to crosstalk, which refers to inter-path-

way molecular interactions arising because of explicit

regulatory feedback connections between two pathways

Figure 1 Retroactivity arises due to enzyme sequestration in covalently modified cascades. A simple signaling cascade is depicted where

each sequential cycle represents the activation (denoted by *) and inactivation of protein Yi. Y1* serves as the activating enzyme of Y2and Y2*

serves as the activating enzyme of Y3. The cycles can be thought of as modules where each module’s substrate sequesters a key component of

the previous module, limiting the component’s ability to participate in the previous module. This sequestration induces a natural change in the

preceding module which may propagate upstream through one or more preceding modules. In this example, a perturbation in the deactivation

reaction of cycle 3 induces an effect in cycle 2. If the perturbation takes the form of an increase in the concentration or activity of the enzyme

catalyzing the conversion of Y3* to Y3, more Y3will be available to react with and sequester Y2*, resulting in less Y2substrate availability for the

reaction with Y1*. Thus, a reverse response can propagate upstream to a preceding cycle or cycles. In the schematic, black arrows represent the

cell surface to nucleus direction of cellular signaling and red arrows represent the direction of retroactive signaling.

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or because two pathways share one or more molecular

components. It is well accepted that two pathways shar-

ing one or more components can exhibit cross-talk with

respect to a stimulation or perturbation above the

shared component(s). If an upstream perturbation

occurs in one of the pathways, the perturbation may

affect the other pathway via the shared downstream

component(s). Such a scenario could lead to specificity

problems [10]. Here we propose that perturbations (e.g.,

from an inhibitor) that occur downstream of a shared

component can also induce cross-talk effects without

any explicit feedback connections via the following

mechanism: the information travels upstream from the

site of the perturbation through retroactivity, reaches

the common component and then is delivered to the

parallel pathway.

To test our hypothesis, we created a computational

model that tested the application of a kinase inhibitor in

a series of simple signaling networks. The objective of

the model was to probe the effect of a targeted inhibitor

on retroactive signaling and to test whether retroactivity

is likely to contribute to measurable off-target effects

under physiological conditions. Specifically, the model

simulated the targeted inhibition of a specific kinase in

a series of multi-cycle networks. In all networks, at least

two cascades were activated by the same upstream cycle

with no explicit feedback connections between them.

Our results indicate that within physiologically and

therapeutically relevant ranges for all parameters, a tar-

geted inhibitor can naturally induce a steady state off-

target effect via retroactivity. Our results also reveal the

surprising and crucial result that a downstream kinase

inhibitor has the capacity to turn “on” an otherwise “off”

parallel cascade when two cascades share an upstream

activator.

Methods

Model development

We designed simple signaling networks to test whether

a measurable off-target effect in one cascade can occur

when a protein in another cascade is selectively inhib-

ited. In each network studied, cycle i contained the

active (phosphorylated) and inactive (unphosphorylated)

forms of protein Yi, where the active form was denoted

by Y∗

vating enzymes in a network as kinases and phospha-

tases, respectively.

Protein Y1* served as the activating kinase for all cas-

cades. Cycle 2 and cycle n were always in distinct cas-

cades (Figure 2). To determine if an off-target effect

occurred due to perturbation by the inhibitor, the steady

state concentration of the protein in cycle 2 was moni-

tored as the concentration of the drug that specifically

targeted Yn* was increased. A competitive inhibitor was

used that directly bound to Yn*, limiting its ability to

participate in the phosphatase reaction of cycle n, but

i. For simplicity, we refer to activating and inacti-

Figure 2 Topology of signaling networks studied. Two general types of network motifs consisting of covalently modified cycles were

studied: (A) the vertical case where the n-th cycle in the right hand cascade is inhibited and (B) the lateral case where the n-th single-cycle

cascade is inhibited. (C) The n = 3 network consisted of exactly 3 cycles and was the simplest form of both the vertical and lateral case. (D) An

extended n = 3 network was also studied where a fourth cycle activated by Y2* was added to the left-most cascade. In all networks, Y1* served

as the upstream activator and cycle 2 and cycle 3 were always in distinct cascades. No additional regulatory connections were included in any

network. Off-target effects in cycle 2 were monitored by measuring the steady state concentrations of Y2and Y2* as the concentration of an

inhibitory drug that specifically targeted Yn* was increased.

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did not change the rate of the phosphatase reaction in

cycle n.

Two general network types were considered: a vertical

and a lateral case (Figure 2). The vertical case consisted

of two cascades where the inhibited cascade length var-

ied (Figure 2A). This motif is similar to the upstream

activation of JUN and P53 by JNK1/2 in the mitogen-

activated protein kinase (MAPK) pathway [11]. The lat-

eral case was equivalent to a fan-out network topology

and consisted of n - 1 single cycle cascades that were all

activated by Y1* (Figure 2B). This motif is similar to the

activation of multiple cascades by p38 [11]. The n = 3

network consisted of exactly 3 cycles and represented

the simplest form of both network types studied (Figure

2C).

The general reaction scheme used for the vertical, lat-

eral, and n = 3 networks was:

Yi+ Eki

ai

←→

di

a?i

←→

d??i

Ci

ki− → Y∗

i+ Eki

Y∗

i+ Epi

C?i

ki− → Yi+ Epi

Y∗

n+ D

kon

←→

koff

CD

Where

Eki=

⎧

⎪⎪⎩

⎪⎪⎨

i = 1,

i = 2,i = 3,

i > 3 (vertical),

i > 3 (lateral),

Ek1

Y∗

1

Y∗

i−1

Y∗

1

Y∗

Yiis the inactivated protein in the ithcycle

Ekiis the kinase enzyme in the ithcycle

Epiis the phosphatase enzyme in the ithcycle

D is the inhibitory drug

Ciis the Yiand Ekicomplex in the ithcycle

iis the activated protein in the ithcycle

C?

CDis the Y∗

iis the Y∗

iand Epicomplex in the ithcycle

nand D complex in the nthcycle

Parameter definitions

In order to reduce the complexity of each network stu-

died, parameters were non-dimensionalized into 4 para-

meter types as described in Appendix A. The allowed

value of each parameter type was restricted to the

default ranges listed in Table 1. A summary of the para-

meter types is provided below.

Subscripts containing k or p indicate parameters asso-

ciated with a kinase or phosphatase reaction, respec-

tively, and subscripts containing T indicate the total

concentration of a species. Vmaxand Kmare the stan-

dard Michaelis-Menten constants representing, respec-

tively, the maximum velocity of a reaction (at a given

enzyme concentration) and the substrate concentration

necessary to achieve1

2Vmax[12].

(1) total enzyme to substrate ratio of the kinase and

phosphatase reaction, respectively, in cycle i:

Ei= EkiT/YiT

E?

i= EpiT/YiT

(2) normalized Kmof the kinase and phosphataste

reaction, respectively, in cycle i:

Ki= Kmki/YiT

K?

i= Kmpi/YiT

where Kmki=di+ ki

(3) Vmaxratio of the kinase and phosphatase reac-

tions in cycle i:

ai

and Kmpi=d?i+ k?i

a?i

Pi= Vmaxki/Vmaxpi

Table 1 The parameter space of each network consisted of a set of non-dimensional parameters, each with a

minimum and maximum allowed value.

default range

parameter

minimummaximum

description

Ei

E’i

Ki

K’i

Pi

KB

0.01

0.01

0.01

0.01

0.1

0.01

100

100

100

100

10

100

total kinase to total substrate ratio

total phosphatase to total substrate ratio

normalized Kmof kinase reaction

normalized Kmof phosphatase reaction

ratio of the kinase reaction Vmaxto the phosphatase reaction Vmax

normalized drug disassociation constant

Each cycle i consisted of 5 dimensionless parameters: Ei, E’i, Ki, K’i, and Pi. A final parameter, KB, applied to the targeted inhibitor. Randomly selected

dimensionless parameter values could not exceed the default ranges listed for each parameter type.

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where Vmaxki= kiEkiTand Vmaxpi= k?

(4) normalized disassociation constant of the inhibi-

tor binding to Yn*:

iEpiT

KB=koff/kon

YnT

Eiand E’ivalues less than 1 indicate that the enzyme

is less abundant than the substrate. Kiand K’ivalues

less than 1 indicate that the total available substrate

exceeds the concentration needed to reach Kmand,

consequently, the enzymatic reaction operates close to

or in the zero order regime [13]. In contrast, Kiand

K’ivalues greater than 1 indicate that an insufficient

amount of substrate exists to reach Kmand the enzy-

matic reaction operates in the linear regime [13]. Pi

values greater than 1 indicate that the Vmaxof the

kinase reaction exceeds the Vmaxof the phosphatase

reaction and, consequently, the cycle tends toward the

activation reaction. Likewise, Pivalues less than 1 indi-

cate that the cycle tends toward the deactivation

reaction.

Determination of off-target effects

The concentrations of species Yi, Y∗

drug D were normalized as follows:

i, and the inhibitory

yi=[Yi]

YiT

y∗

i=[Y∗

i]

YiT

I =DT

YnT

To determine if a detectable off-target effect

occurred for a specific set of parameters, changes in

the steady values of y2and y∗

model parameters were held fixed but I was varied

from 10-4to 104. If a change in the steady state value

of y2or y∗

a detection threshold of 0.10 (i.e., 10% of the total

protein in cycle 2), an off-target effect in cycle 2 was

reported. For numeric reasons, the range used for I

was intentionally larger than needed. For a given

parameter set, it was numerically more efficient to

simulate with a small (10-4) and a large (104) value

for I and then check for a change in the steady state

values of y2and y∗

values of I. In fact, the majority of off-target effects in

our model were observed as I was varied from 0.1 to

10.

When we tested the n = 3 network, we obtained the

same results when we used either I = 0.0000 or I =

0.0001 (10-4) as the minimum drug concentration. For

this reason (and because it would be experimentally

challenging to distinguish 0.0000 from 0.0001 in vivo),

we effectively considered I = 10-4to represent the

absence of the drug in the system.

2were monitored as the

2occurred that was greater than or equal to

2than it was to simulate with many

Numerical simulations

For each network tested, a system of ordinary differen-

tial equations (ODEs) was used to model the rate of

change of the reactants. Because we were only interested

in changes in steady state values as a function of I, we

first solved the system by setting the ODEs equal to

zero and generating a system of steady state equations.

As described in Appendix A, the model in this form was

the basis for the non-dimensionalization of model

parameters.

For numerical reasons, it was more efficient to solve

the ODEs over a very long time period rather than sol-

ving the system of steady state equations directly. After

randomly selecting a set of non-dimensional parameters,

the selected values were mapped to corresponding

dimensional parameter values (Additional File 1) and

the system of ODEs was solved using the Matlab

R2009b ode15s stiff solver from 0 to a maximum of

100,000 arbitrary time units. The majority (~90%) of

randomly selected parameter sets obtained steady state

within 5,000 arbitrary time units. The units are arbitrary

because we began with dimensionless parameters lack-

ing an explicit timescale. Finally, to confirm the numeri-

cal steady state solution, the original dimensionless

parameters and the final yiand yi* variable values were

substituted into the analytical steady state equations

listed in Appendix A. Matlab source code was compiled

as a C program and run on Intel Nehalem/i7 Core

processors.

Random parameter space exploration

Random parameter selection was performed via latin

hypercube sampling (LHS) to provide an efficient and

even sampling distribution across the range of allowed

values in the parameter space [14-16]. Each parameter

space exploration consisted of 5000 randomly selected

parameter sets. The number of parameter sets sampled

was determined by calculating the percent of off-target

effects in q randomly sampled parameter sets for the n

= 3 network (Figure 2C). The variation in the percent of

off-target effects stabilized when q was greater than or

equal to 5000 (Additional File 2 Figure S1). The percen-

tage of 5000 randomly selected parameter sets that pro-

duced an off-target effect provided a probability that

off-target effects would occur in a given network’s para-

meter space.

Numeric perturbation analysis

A modified perturbation method was used to probe

which model parameters were most important for pro-

ducing an off-target effect as a result of the inhibition of

Yn*. Traditional biochemical sensitivity analysis [17]

with the dimensionless parameters was not possible

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because these parameters applied to the steady state

equations and not the time dependent differential equa-

tions (Appendix A). Instead, we developed a numerical

perturbation based method that allowed us to evaluate

the parametric sensitivity of off-target effects in a net-

work’s parameter space. In the method, the value of a

single parameter was randomly selected from a

restricted range of values while all other parameter

values were randomly selected from the full range per-

mitted by the baseline parameter space. If off-target

effects are sensitive to a given parameter, we expect that

when values for the parameter under test are randomly

selected from a reduced range of values, the percentage

of off-target effects produced will differ from the per-

centage produced when values for the parameter are

instead selected from a fixed baseline range. In both

cases, all other parameter values are selected from a

fixed baseline range so that the only change in the sys-

tem is a perturbation in the allowed range of the para-

meter under test.

The reduced ranges used to perturb each parameter

were arrived at by partitioning the default range estab-

lished for each parameter type in Table 1. The default

ranges were divided into smaller perturbation sub-

ranges such that the minimum and maximum of a sub-

range was an order of magnitude larger than the mini-

mum and maximum of the previous sub-range. Because

the Ei, E’i, Ki, K’i, and KBparameters had a default

initial range of 0.01 - 100.0 (Table 1), the sub-ranges

used to perturb these parameters were: (i) 0.01 - 0.10,

(ii) 0.10 - 1.0, (iii) 1.0 - 10.0, and (iv) 10.0 - 100.0.

Because the Piparameters had a default range of 0.10 -

10.0, the sub-ranges used to perturb these parameters

were: (i) 0.10 - 1.0 and (ii) 1.0 - 10.0.

A complete numeric perturbation analysis of a para-

meter space consisted of determining the percentage of

off-target effects in 5000 randomly selected parameter

sets for each parameter’s sub-ranges. In the n = 3 net-

work (Figure 2C) there were a total of 16 parameters (5

parameters per cycle and KB). Three of the parameters

(P1, P2, and P3) had 2 perturbation sub-ranges each and

the remaining 13 parameters had 4 perturbation sub-

ranges each. In this example, the analysis consisted of a

total of 59 sets of 5000 simulations (58 sets for each

parameter sub-range and 1 set to establish the baseline

percentage of off-target effects in the parameter space

prior to perturbation).

Results

The question we wanted to answer with our models was

whether a targeted inhibitor is likely to induce a mea-

surable off-target effect due to retroactivity in a non-tar-

geted cascade under physiological conditions. In each

network, cycle n, was perturbed by an inhibitor. An off-

target effect occurred in the model if, after increasing I

(the normalized inhibitor concentration) from 10-4to

104, a change in the steady state concentration of Y2

and/or Y2* occurred that was at least 0.10 of the total

Y2protein pool. For example, a change of 0.25 in Y2

and 0.08 in Y2* would indicate that the steady state

values of Y2and Y2* changed by 25% and 8% of the

total Y2protein pool, respectively, and that a detectable

off-target effect occurred in Y2.

Specific parameter ranges promote off-target effects in

cycle 2

First, we investigated the n = 3 network (Figure 2C)

where Y3* is targeted by the inhibitor. When the full

parameter space (defined in Table 1 and depicted in Fig-

ure 3H) was used, 1.6% of the 5000 randomly selected

parameters sets produced an off-target effect in cycle 2.

This value was essentially unchanged (1.5%) when we

randomly selected 50,000 parameter sets for comparison

(Additional File 2). To identify the model parameters

that were most important for producing a cycle 2 off-

target effect, a numeric perturbation analysis was per-

formed (Figure 3A-F). The results of the analysis suggest

that the parameters controlling the activity of cycle 3

play a large role in inducing an off-target effect in cycle

2. Not surprisingly, K3(the normalized Kmof the kinase

reaction in cycle 3) had the greatest effect on off-target

effects in this network (Figure 3D). K3determines how

much sequestration of Y1* by Y3occurs and this is the

key mechanism of retroactivity. When K3was restricted

to values greater than 1, the off-target effects in the net-

work were essentially eliminated. In contrast, when K3

was restricted to values between 0.01 and 0.10, the per-

centage of off-target effects increased to 4.6%. Similarly,

K’3(the normalized Kmof the phosphatase reaction in

cycle 3) also affected the percentage of off-target effects

but to a lesser degree than K3(Figure 3E).

E3and E’3(the total kinase to substrate and the total

phosphatase to substrate ratio, respectively, in cycle 3)

also appeared to exert a large degree of control over off-

target effects (Figure 3A-B). These results indicate that

off-target effects were more likely when the kinase and

phosphatase enzymes of cycle 3 were saturated. P3, the

ratio of the Vmaxof the kinase and phosphatase reac-

tions in cycle 3, also affected the percentage of off-target

effects (Figure 3C). When P3was less than 1, cycle 3

tended toward the deactivation reaction and the percen-

tage of off-target effects increased to 2.56% from 1.6%.

Similarly, when P3was greater than 1, cycle 3 tended

toward the activation reaction and the percentage of off-

target effects was significantly reduced relative to the

baseline (0.32%).

The only parameter associated with cycle 2 that

affected the percentage of off-target effects in this

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network was K2(the normalized Kmof the kinase reac-

tion of cycle 2). K2values between 0.01 and 0.10 are

expected to produce an efficient kinase reaction

because Y2T>> Km2. The results of the numerical per-

turbation analysis indicated that when K2 was

restricted to values in this sub-range, a small percen-

tage of off-target effects was observed (Figure 3D). In

contrast, when K2was restricted to values between 1.0

and 10.00, the percentage of off-target effects increased

relative to the baseline. These results suggest that an

off-target effect in cycle 2 is more likely to occur in

the n = 3 network when the conversion of Y2to Y2*

operates in the linear regime because of substrate

constraints. This result is somewhat counter intuitive

given the fact that we are interested in measuring a

response that propagates from cycle 3 to cycle 1 and

then down to cycle 2. It is reasonable to expect that an

efficient kinase reaction in cycle 2 would be important

for recruiting Y1* to activate Y2and generate an effect

in cycle 2. If the cycle 2 kinase reaction is less efficient

than the cycle 3 kinase reaction, however, more Y1*

will be available to convert Y3to Y3*, ultimately contri-

buting to the sequestration of more Y3* into a complex

with D. Such a sequestration may give rise to a detect-

able upstream effect as a result of the reduced sub-

strate availability in cycle 3.

Figure 3 A numeric perturbation analysis revealed parameter value ranges that promote off-target effects in the n = 3 network. A

perturbation analysis of the n = 3 network (G) was performed where a single parameter’s value was randomly selected from a small range of

values, while all other parameters were selected from the larger ranges defined in Table 1. The baseline in each plot reflects the percent of off-

target effects in cycle 2 in 5000 sampled parameter sets when all parameter values were randomly selected from the ranges defined in Table 1

and depicted in (H). All other bars reflect the results of systematically perturbing each parameter (one at a time) using the given sub-ranges (A-

F). Based on this perturbation analysis, a restricted parameter space was generated (I) from which ~74% of the sampled parameter sets

produced off-target effects in cycle 2. In contrast, only ~1.6% of sampled parameter sets from the full parameter space (H) produced off-target

effects in cycle 2.

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The cycle 1 parameters with the greatest impact on

the percentage of off-target effects were K1and K’1(the

normalized Kmof the kinase and phosphatase reaction,

respectively, in cycle 1) (Figure 3D-E). Larger values of

K1acted to suppress off-target effects, while smaller

values produced an increase in off-target effects relative

to the baseline (Figure 3D). The reverse was observed

for K’1, with higher values producing a higher percen-

tage of off-target effects than smaller values (Figure 3E).

Together, the K1and K’1results suggest that off-target

effects are favored when the cycle 1 phosphatase reac-

tion tends toward inefficiency and the cycle 1 kinase

reaction tends towards efficiency. This result is not sur-

prising given that the availability of Y1* is essential for

the propagation of a signal from cycle 3 to cycle 2.

The value of KB, the normalized drug disassociation

constant, had a very slight effect on the percentage of off-

target effects. In general, KBvalues greater than 1 pro-

duced a slight decrease in the percentage of off-target

effects relative to the baseline (Figure 3F). This result

suggests that weaker binding (and larger dissociation

constants) promoted fewer off-target effects, as would be

expected given the decreased sequestration of Y3* that

would occur. The change in the percentage of off-target

effects induced by restricting KBvalues was fairly small

compared to the change induced when other model para-

meter values were restricted. This result suggests that the

activity and efficiency of component cycles in the net-

work may be more important for propagating an off-tar-

get effect than the actual kinetics of a targeted therapy.

The results of the above analysis indicate that certain

parameter value ranges are more likely to induce an off-

target effect in cycle 2 as the drug concentration is

increased. When we restricted the n = 3 parameter

space by reducing the ranges from which some key

parameters were selected (Figure 3I), the percentage of

off-target effects in 5000 randomly sampled parameter

sets increased from 1.6% to 73.9%.

A second numerical perturbation analysis was per-

formed using this new restricted n = 3 parameter space

as a baseline. In general, many of the trends observed in

the analysis of the original n = 3 parameter space

(depicted in Figure 3H) were observed in the analysis of

the restricted n = 3 parameter space (Additional File 3

Figure S3). For example, low K3values remained impor-

tant for producing off-target effects in both parameter

spaces. The effects of parameters associated with cycle

2, however, were different in the two parameter spaces.

When the original parameter space was tested, K2was

the only cycle 2 parameter found to substantially affect

the percentage of off-target effects (Figure 3D). In the

restricted parameter space, however, some ranges of E2,

E’2, and K’2produced off-target effect percentages that

differed substantially from the baseline. For example, E2

values between 10 and 100 produced off-target effects in

92.1% of sampled parameter sets, the largest percentage

of off-target effects observed in any of our analyses

(Additional File 3 Figure S3A). Because E2is the total

enzyme to substrate ratio of the kinase reaction (Y1T/

Y2T), this result suggests when more total protein exists

in cycle 1 compared to cycle 2, off-target effects in cycle

2 are more likely in this network.

While some parameters associated with cycle 2 were

able to effect the percentage of off-target effects, the

parameters associated with cycle 3 continued to have

the greatest effect on off-target effects in the restricted n

= 3 parameter space. Only parameters in cycle 3 had the

ability to effectively eliminate (or substantially reduce)

the percentage of off-target effects within specific

reduced ranges. Values between 10 and 100 for E3, E’3,

K3and K’3produced off-target effect percentages of 0%,

3.24%, 0% and 3.20%, respectively. In addition, P3values

greater than 1 produced off-target effects in 18.24% of

sampled parameter sets which, compared to the baseline

of 73.9%, represents a large decrease in off-target effects

(Additional File 3 Figure S3).

Varying a single parameter can produce a large change

in the size of the off-target effect

The magnitude of off-target effects produced by para-

meter sets randomly sampled from the original n = 3

parameter space (depicted in Figure 3H) generally fell

between .10 and .30 of the total Y2protein pool (Figure

4A). In contrast, the magnitude of off-target effects pro-

duced by parameter sets randomly sampled from the

restricted n = 3 parameter space (depicted in Figure 3I)

were more uniformly distributed across a range of

values (Figure 4B). These results suggest that when con-

ditions in a network are favorable for off-target effects,

the size of an off-target effect is highly variable.

We used stimulus response curves to examine how a

change in a single parameter value may affect the size of

an off-target effect in Y2* as a function of the normal-

ized inhibitor concentration (Figure 5). A randomly

selected parameter set and a parameter set derived from

a Xenopus MAPK model [18] were used (refer to Addi-

tional File 4 for the derivation of the Xenopus parameter

values). In each parameter set, either E2or K3was var-

ied, while all other parameter values were fixed to the

values listed in Table 2.

The randomly selected parameter set produced a base-

line off-target response of 0.19 in Y2* (Figure 5A-B) and

of 0.40 in Y2(data not shown). In this parameter set the

original E2value was 32.56 and the original K3value

was 0.04 (Table 2). Increasing E2to 326.61 substantially

decreased the response in Y2* and decreasing E2to 3.26

increased the response in Y2* from 0.19 to 0.27 (Figure

5A). Similarly, increasing K3 to 0.41 reduced the

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response in Y2* to 0.07 (below the detection threshold)

and decreasing K3to 0.004 increased the response in

Y2* to 0.26 (Figure 5B).

The parameter set derived from the MAPK Xenopus

model [18] produced a baseline response of 0.08 (below

the detection threshold) in both Y2* (Figure 5C-D) and

Y2(data not shown). In this parameter set the original

E2value was 0.0025 and the original K3value was 0.25

(Table 2). While changing E2did not alter the response

(Figure 5C), increasing K3to 2.5 completely eliminated

the response in Y2* and decreasing K3to 0.025 substan-

tially increased the response in Y2* to 0.60 (Figure 5D).

These results suggest that when using physiologically

realistic parameter values, changing one kinetic para-

meter or species concentration by an order of magni-

tude has the capacity to dramatically alter whether a

targeted inhibitor induces an off-target effect.

A few of the enzyme to substrate ratios in the Xenopus

parameter set (E2= 0.0025, E’2= 0.00025, and E3=

0.0025) were outside the limits of parameter ranges

allowed in our random parameter space explorations

(Table 1 and Figure 3H), suggesting that off-target effects

are possible for a larger range of parameter values than

we specifically tested. While we may have been too con-

servative in the estimation of the ranges defined in Table

1, this finding supports the position that a targeted inhi-

bitor can naturally induce an off-target effect via retroac-

tivity over a range of physiologically relevant conditions.

The percentage of off-target effects decreased as the size

of the vertical and lateral networks increased

We next investigated networks with more than 3 cycles

by randomly exploring the parameter spaces of the

vertical (Figure 2A) and lateral (Figure 2B) cases using n

= 5 and n = 7 cycles. As before, we measured the steady

state change in cycle 2 as the normalized concentration

of the drug that targeted cycle n was increased. The

restricted parameter space depicted in Figure 3I (from

which 73.9% of sampled parameter sets produced off-

target effects in cycle 2) was used for this analysis. Net-

works were analyzed using homogenous parameter

values in cycles 4, 5, 6 and 7 that equalled the corre-

sponding parameter values randomly selected for cycle 3

(e.g., in the n = 5 case, E3= E4= E5). This allowed us

to keep the size of the parameter space fixed so that

5000 parameter sets remained a reasonable number to

sample from each network’s parameter space.

In the vertical case, the percentage of off-target effects

in the n = 5 and n = 7 networks were 27.92% and

13.50%, respectively (Table 3). The reduced probability

of off-target effects as the cascade lengthened suggests

that applying a targeted inhibitor near the bottom of a

long cascade can produce a detectable off-target

response but the signal may attenuate as it travels up

the cascade. This conclusion is in agreement with a

recent work that investigated retroactivity in long signal-

ing cascades [9] and found that retroactive signals are

likely to attenuate as they travel up long cascades.

In the lateral case, the drop in the percentage of off-

target effects was more dramatic than in the vertical

case, with the n = 5 and n = 7 networks producing 6%

and 0% off-target effects, respectively (Table 3). This

result suggests applying a targeted inhibitor to a cycle

that is activated by a signaling molecule involved in the

simultaneous activation of many other cycles decreases

the likelihood of off-target effects. This conclusion is

Figure 4 Distribution of the size of off-target effects in the n = 3 network. Histograms of the size of off-target effects in n = 3 network

(Figure 3D) are plotted for two different parameter spaces. The y-axis on each plot represents the proportion of all parameter sets that

produced off-target effects in 5000 randomly selected parameter sets. The x-axis on each plot represents the size of an off-target effect in cycle

2 as a proportion of Y2Tsuch that each value indicates a response that was at least as big as the given value but less than the next sequential

value. For example, a value of .30 indicates that the magnitude of the response was greater than or equal to .30 but less than 0.40. (A) The

majority of off-target effects in the original n = 3 parameter space (depicted in Figure 3H) were less than 0.30. (B) In contrast, the distribution of

the size of off-target effects in the restricted n = 3 parameter space (depicted in Figure 3I) was more uniform.

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based on a limited exploration of the parameter space

(due to the homogenous parameter selection used for

cycles 3 and greater) but is in agreement with a model

proposed by Kim et al. [8] that showed retroactivity (or

what they referred to as subsrate-dependent control) is

attenuated by the number of substrates available.

Off-target effects from retroactivity can propagate down

a non-targeted cascade

Our results suggest that, under appropriate conditions,

it is possible for a downstream perturbation from a tar-

geted inhibitor to transmit up a cascade resulting in a

detectable off-target effect near the top of another cas-

cade. Because signal amplification is an important cellu-

lar sensory mechanism [19], we next investigated

whether off-target effects from targeted inhibitors are

likely to amplify down a non-targeted cascade.

To test for downstream propagation of off-target

effects from cycle 2, we created an extended n = 3 net-

work by adding a 4thcycle activated by Y2* (Figure 2D).

If a change in the steady state concentration of Y4and/

or Y4* occurred that was at least 0.10 of the total Y4

protein pool, then an off-target effect was considered to

have occurred in cycle 4. If an off-target effect occurred

in cycle 4 and the size of the response in cycle 4

exceeded the size of the response in cycle 2, then an

off-target effect with amplification was considered to

have occurred in cycle 4.

When the default parameter ranges defined in Table 1

were used for all cycles in the extended n = 3 network,

the percentage of off-targets in cycle 2 and cycle 4,

respectively, was 1.78% and 0.03%. We next tested the

extended n = 3 network using the restricted n = 3 para-

meter space (depicted in Figure 3I) for cycles 1 - 3 and

Figure 5 Varying a single parameter value can produce a large change in the off-target response. Stimulus response curves were plotted

for the n = 3 network using a randomly selected parameter set and a parameter set derived from a Xenopus model [18] (all parameters values

are listed in Table 2). For each parameter set, E2and K3were increased or decreased by 1 order of magnitude and the resulting stimulus

response curves were plotted. (A-B) The random parameter set produced an off-target effect in Y2of 0.40 (data not shown) and in Y2* of 0.19.

(A) Increasing E2from 32.56 to 325.61 substantially decreased the off-target effect in Y2*, while decreasing E2to 3.26 increased the off-target

effect in Y2* to 0.27. (B) Increasing K3from 0.04 to 0.41 reduced the response in Y2* below the detection threshold to 0.07, while decreasing K3

to 0.004 increased the off-target response to 0.26. (C-D) A second parameter set was derived from the literature using MAPK parameters from a

Xenopus model. This parameter set did not initially produce an off-target effect because the response in both Y2* and Y2was 0.08, which was

below the detection threshold. (C) Increasing or decreasing E3to 0.025 or 0.00025, respectively, from 0.0025 had no effect on the response to

the targeted inhibitor. (D) In contrast, increasing K3from 0.25 to 2.5 eliminated the original response completely, while decreasing K3from 0.25

to 0.025 produced a large off-target response of 0.60. Original parameter values prior to variation are indicated by‡on the plots (see also Table

2).

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the default parameter ranges from Table 1 for cycle 4.

In this partially restricted parameter space (depicted in

Additional File 3 Figure S4H), the percentage of off-tar-

get effects in cycle 2 and cycle 4 were 75.3% and 35.5%,

respectively, and amplification contributed to cycle 4

off-target effects in 23.3% of the sampled parameter sets

(representing more than half of the off-target effects in

the sampled parameter sets). The remaining off-target

effects in cycle 4 occurred in 12.2% of the sampled para-

meter sets and had a response size that was either atte-

nuated relative to cycle 2 or equal to the cycle 2

response (Table 4).

To identify the parameters that were most important

for amplifying an off-target effect from cycle 2 to cycle

4 in the extended n = 3 network, we performed a

numeric perturbation analysis (as previously described)

on the partially restricted parameter space depicted in

Additional File 3 Figure S4H. From these results, we

generated a new parameter space (Additional File 3 Fig-

ure S4I) which produced off-target effects of 45.3% and

67.4% in cycle 2 and cycle 4, respectively. Amplification

contributed to cycle 4 off-target effects in 61.9% of the

sampled parameter sets. The remaining off-target effects

in cycle 4 occurred in 5.5% of the sampled parameter

sets and had a response size that was either attenuated

relative to cycle 2 or equal to the cycle 2 response

(Table 4).

Discussion

We developed a computational model to test whether

targeted therapies, such as kinase inhibitors, can pro-

duce off-target effects in upstream pathways as a conse-

quence of retroactivity alone. Using a numeric

perturbation method, we identified specific conditions

(Figure 6) that favored the promotion of steady state

off-target effects via retroactivity when a targeted inhibi-

tor was applied to cycle n in a series of simple signaling

networks (Figure 2).

Our investigation considered only the effect of retro-

activity and targeted inhibitors on the individual motifs

we studied in the absence of genetic and/or other regu-

latory 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

Table 2 Parameter sets used in stimulus response curves.

Random set

Xenopus set

E1

E2

E3

E’1

E’2

E’3

K1

K2

K3

K’1

K’2

K’3

P1

P2

P3

KB

4.87

32.56

0.28

0.05

1.26

0.29

5.07

28.18

0.04

66.34

9.33

0.59

0.21

3.43

0.42

0.05

0.1

0.0025

0.0025

0.1

0.00025

0.1

100

0.25

0.25

100

0.25

0.25

1

1

0.025

0.0833

The two parameters sets used in Figure 5 are summarized in the table. The

Random set refers to a randomly selected parameter set and the Xenopus set

refers to a parameter set derived from a Xenopus MAPK model (Additional File

4). Bolded values represent the original parameter values varied in Figure 5.

Table 3 The percentage of off-target effects decreased as

the network size increased.

n Off Target Effects

3 73.9

verticallateral

5

7

27.9

13.5

6.0

0.0

The n = 3 network’s restricted parameter space produced 73.9% off-target

effects. The n = 5 and n = 7 vertical case networks produced 27.9% and

13.5% off-target effects, respectively, using the same parameter space. In the

lateral case the drop was more dramatic with the n = 5 and n = 7 networks

producing 6% and 0% off-target effects, respectively. Parameter values used

in cycles 4, 5, 6 or 7 were homogenous with cycle 3. All percentages are out

of 5000 randomly selected parameter sets using the parameter space

depicted in Figure 3I.

Table 4 Off-target effects can amplify downstream of

cycle 2.

Cycle 2Cycle 4

Cycles 1-3 with restricted ranges and cycle 4 with default ranges

% Off Target Effects

75.3

–

–

35.5

23.4

12.1

% Off Target Effects with Amplification

% Off Target Effects without Amplification

Cycles 1- 4 with restricted ranges

% Off Target Effects

45.3

–

–

67.4

61.9

5.5

% Off Target Effects with Amplification

% Off Target Effects without Amplification

To test for downstream propagation of off-target effects from cycle 2, the

extended n = 3 network was used. If an off-target effect occurred in cycle 4

and the size of the response in cycle 4 exceeded the size of the response in

cycle 2, then an off-target effect with amplification was reported for cycle 4.

First, the n = 3 restricted parameter space was used for cycles 1 - 3 and the

default parameter ranges from Table 1 were used for cycle 4 (Additional File 3

Figure S4H). Next, cycles 2 - 4 were further restricted to ranges which favor

off-target effect propagation from cycle 2 to 4 (Additional File 3 Figure S4I).

Values listed in the table are percentages out of 5000 randomly selected

parameter sets.

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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 trans-

duction networks can be modulated by important oscil-

latory behavior, for example, from the P53/MDM2

regulatory feedback loop [20,21]. 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-tar-

get 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 5 (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 net-

work 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. More-

over, 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 compo-

nent cycles in the network were more important for

increasing the likelihood of off-target effects (Figure 3

and Additional File 3 Figure S3, S4). In general, off-tar-

get effects were more likely to occur in the networks

studied when the targeted cycle n favored the deactiva-

tion reaction because the Vmaxof the deactivation reac-

tion was larger than the Vmaxof 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 2D), 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 activa-

tion. 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 Vmaxof the deactivation

reaction was generally larger than the Vmaxof the acti-

vation reaction. Thus, off-target effects were promoted

when cycle 2 was “off” and not consuming significant

amounts of the shared upstream activator, Y1*.

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) the

extended n = 3 network were favored when cycle 3 tended toward deactivation and cycle 1 tended toward activation. Off-target effects were

favored in cycle 4 of (B) the extended n = 3 network when cycle 2 tended toward deactivation and cycle 4 tended toward activation. Blue

arrows in a cycle indicate which Vmaxis larger when off-target effects are favored. (C) A summary of the specific conditions in each cycle found

to favor off-target effects in the n = 3 network, in the extended n = 3 network, or in both networks is also provided.

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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 (Enand E’n, respectively) were less than 1. In the

n = 3 network, this meant that there was less total pro-

tein in cycle 1 than in cycle 3 because E3< 1 implies

Y1T<Y3T. The reason for this is that the smaller the

Y1T/Y3Tratio, 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

Y3Tis in the inactive Y3form, promoting the binding of

Y3to Y1*.

The immediate experimental implications of this result

is that, in the absence of kinetic information, the likeli-

hood of off-target effects may potentially be estimated

for a network configuration of this type (Figure 2A,C-D)

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 [8,9],

we found the probability of off-target effects attenu-

ated 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

3). Our results also suggest that within physiologically

realistic parameter ranges, changing a single kinetic

parameter or species concentration by 1 order of mag-

nitude 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 5).

Conclusions

Off-target drug effects in vivo are typically attributed to

cross-talk arising from a feedback connection in a sig-

naling network or to non-specific interactions with

other proteins. In this work we have demonstrated that

off-target drug effects can also arise naturally from ret-

roactivity in a covalently modified signaling network.

This view of signaling challenges the widespread notion

that information in signaling cascades only flows from

the cell surface to the nucleus and, consequently, this

work has far reaching implications for targeted cancer

therapies.

A crucial finding of this work is that the kinetics

governing the covalently modified cycles in a signaling

network are likely to be far more important for propa-

gating an off-target effect due to retroactive signaling

than the binding affinity of the drug for the targeted

protein, which is a commonly optimized property in

drug development. Another particularly paramount

finding is that an off-target effect due to retroactive

signaling is more likely when the first cycle in a non-

inhibited cascade is “off” and essentially inactive. This

suggests that, in the motifs we studied, a targeted ther-

apy has the capacity to turn “on” an otherwise “off” tri-

butary cascade.

To emphasize, it is entirely possible for a branch of a

signaling network that is “off” to become activated or

“on” due to the inhibition of another protein in the net-

work based on retroactivity alone, suggesting an inher-

ent opportunity for negative therapeutic effects. Our

findings, therefore, have implications for somatic evolu-

tion in cancer and the onset of therapeutic resistance,

which has been widely reported for many targeted can-

cer therapeutics [25], most notably for the targeted inhi-

bition of BCR-ABL by imatinib [26]. Moreover, a single

mutation could conceivably give rise to a spontaneous

off-target effect without the need for any direct regula-

tory connections between the targeted protein and the

effected protein.

While our approach does not definitively establish that

the predicted responses will occur in vivo, our results

demonstrate that off-target effects are indeed possible in

the absence of direct regulatory relationships and sug-

gest that additional (and more specific) experimental

and theoretical investigations are warranted. A proper

characterization of a pathway’s structure is important

for identifying the optimal protein to target as well as

what concentration of the targeted therapy is required

to modulate the pathway in a safe and effective manner.

We believe our results strongly support the position

that such characterizations should consider retroactivity

as a potential source of off-target effects induced by

kinase inhibitors and other targeted therapies. This

work has also provided an initial roadmap for how to

assess the likelihood of off-target effects in a signaling

network.

Appendix A - Non-dimensionalization of the n = 3

network

In order to reduce the complexity of the networks stu-

died, model parameters were non-dimensionalized. The

following explains the non-dimensionalization of the n

= 3 network. The dimensionless parameters of the n = 5

and n = 7 vertical and lateral networks’ were obtained

in a similar manner.

The ODEs and conservation laws governing the n = 3

network (Figure 2C) at steady state are:

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d[Y∗

dt

1]

= k1[C1] − a?1[Y∗

− a2[Y2][Y∗

− a3[Y3][Y∗

i][Ep1] + d?1[C?1]

1] + (d2+ k2)[C2]

1] + (d3+ k3)[C3] = 0

d[C1]

dt

= a1[Y1][Ek1] − (d1+ k1)[C1] = 0

d[C?1]

dt

= a?

1[Y∗

i][Ep1] − (d?

1+ k?

1)[C?

1] = 0

d[Y∗

dt

2]

= −a?

2[Y∗

2][Ep2] + d?

2[C?

2] + k2[C2] = 0

d[C2]

dt

= a2[Y2][Y∗

1] − (d2+ k2)[C2] = 0

d[C?2]

dt

= a?

2[Y∗

2][Ep2] − (d?

2+ k?

2)[C?

2] = 0

d[Y∗

dt

3]

= −a?3[Y∗

− kon[Y∗

3][Ep3] + d?3[C?3] + k3[C3]

3][D] + koff[CD] = 0

d[C3]

dt

= a3[Y3][Y∗

1] − (d3+ k3)[C3] = 0

d[C?3]

dt

= a?

3[Y∗

3][Ep3] − (d?

3+ k?

3)[C?

3] = 0

d[CD]

dt

= kon[Y∗

3][D] − koff[CD] = 0

Y1T= [Y1] + [Y∗

1] + [C1] + [C?

1] + [C2] + [C3]

Y2T= [Y2] + [Y∗

2] + [C2] + [C?

2]

Y3T= [Y3] + [Y∗

3] + [C3] + [C?

3] + [CD]

Ek1T= [Ek1] + [C1]

Ep1T= [Ep1] + [C?

1]

Ep2T= [Ep2] + [C?

2]

Ep3T= [Ep3] + [C?

3]

DT= [D] + [CD]

Dimensionless Parameters

Pi=kiEkiT

k?

iEpiT

=

Vmaxki

Vmaxpi

Ei=EkiT

YiT

E’i=EpiT

YiT

Ki=di+ ki

aiYiT

=

Kmki

YiT

K?

i=d?i+ k?i

a?iYiT

=

Kmpi

YiT

KB=koff/kon

Y3T

(forn = 3)

KB=koff/kon

YnT

(foralln)

I =DT

Y3T(for n = 3)

I =DT

YnT(for alln)

where EkiT=

⎧

⎪⎪⎩

⎪⎪⎨

i = 1,

i = 2, i = 3,

i > 3 (vertical),

i > 3 (lateral),

Ek1T

Y1T

Y(i−1)T

Y1T

Dimensionless Variables

yi=[Yi]

YiT

y∗

i=[Y∗

i]

YiT

Algebraic rearrangement and substitution yield the

following dimensionless steady state equations:

y1

y1+ K1

y∗

1

?

+E1

y1+ K1

y∗

(3) P2y2y∗

K2

y∗

2

?

+E?

2

y∗

2

(5) P3y3y∗

K3

y∗

3

y∗

1

K3) + y∗

y∗

3

y∗

3

y∗

(1) P1

−

y∗

1

1+ K?

1 +y2

= 0

(2)

−1 + y1+ y∗

1

K2

+y3

K3

y∗

1

1+ K?

?

= 0

y1

+ E?

1

1

1

−

y∗

2

2+ K?

= 0

?

(4)

−1 + y2

1 + E2

y∗

K2

1

+ y∗

2

y∗

2

2+ K?

= 0

1

−

y∗

3

3+ K?

= 0

(6)

−1 + y3(1 + E3

3

+E?

3

3+ K?

+ I

y∗

3

3+ KB

= 0

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Additional material

Additional file 1: Mapping dimensionless parameters to

dimensional parameters. This file describes how randomly sampled

dimensionless parameter values were mapped to dimensional parameter

values prior to numeric simulation.

Additional file 2: Parameter space sampling to estimate the

probability of off-target effects. This file describes how the parameter

space of a network was sampled to provide an estimate of the

probability of off-target effects due to retroactivity alone.

Additional file 3: Additional analysis of the n = 3 and extended n =

3 networks. This file provides additional results from the numeric

perturbation analyses of the n = 3 and extended n = 3 networks.

Additional file 4: Xenopus MAPK Model Parameters [18,27,28]. This

file explains how the Xenopus model parameters listed in Table 2 were

derived.

Acknowledgements

MLW was supported by the Rackham Merit Fellowship, NIH T32 CA140044,

and the Breast Cancer Research Foundation. ACV is a member of the Carrera

del Investigador Científico (CONICET) and was supported by the Department

of Defense Breast Cancer Research Program, the Center for Computational

Medicine and Bioinformatics (University of Michigan), and the Agencia

Nacional de Promoción Científica y Tecnológica (Argentina). SDM was

supported by the Burroughs Wellcome Fund, NIH CA77612, the Avon

Foundation, and the Breast Cancer Research Foundation. ACV thanks Dr. Bob

Ziff for helpful discussions and MLW thanks Dr. Santiago Schnell for helpful

discussions and computing resources.

Author details

1Center for Computational Medicine and Bioinformatics, University of

Michigan Medical School, Ann Arbor, MI, USA.2Laboratorio de Fisiología y

Biología Molecular, Departamento de Fisiología, Biología Molecular y Celular,

IFIBYNE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de

Buenos Aires, Ciudad Universitaria, Pabellón 2, Buenos Aires, Argentina.

3Institut Non Linéaire de Nice, Université de Nice Sophia-Antipolis, UMR

CNRS 6618, Valbonne, France.4Electrical Engineering and Computer Science,

University of Michigan, Ann Arbor, MI, USA.5Department of Internal

Medicine, Division of Hematology and Oncology and Comprehensive Cancer

Center, University of Michigan Medical School, Ann Arbor, MI, USA.

Authors’ contributions

ACV and SDM conceived the study. ACV and JAS created the general model.

ACV and MLW designed the experiments and analyzed results. MLW, HJG,

and ACV wrote codes for numerical simulations. MLW wrote the manuscript

and SDM, ACV, and JAS edited the manuscript. All authors read and

approved the final manuscript.

Received: 24 June 2011 Accepted: 4 October 2011

Published: 4 October 2011

References

1.Kholodenko BN: Cell-signalling dynamics in time and space. Nat Rev Mol

Cell Biol 2006, 7:165-176.

2.Sawyers C: Targeted cancer therapy. Nature 2004, 432:294-297.

3.Kumar N, Afeyan R, Kim HD, Lauffenburger DA: Multipathway model

enables prediction of kinase inhibitor cross-talk effects on migration of

Her2-overexpressing mammary epithelial cells. Mol Pharmacol 2008,

73:1668-1678.

4. Ventura AC, Sepulchre JA, Merajver SD: A hidden feedback in signaling

cascades is revealed. PLoS Comput Biol 2008, 4:e1000041.

5. Del Vecchio D, Ninfa AJ, Sontag ED: Modular cell biology: retroactivity

and insulation. Mol Syst Biol 2008, 4:161.

6.Ventura AC, Jackson TL, Merajver SD: On the role of cell signaling models

in cancer research. Cancer Res 2009, 69:400-402.

7.Ventura AC, Jiang P, Van Wassenhove L, Del Vecchio D, Merajver SD,

Ninfa AJ: Signaling properties of a covalent modification cycle are

altered by a downstream target. Proc Natl Acad Sci USA 2010,

107:10032-10037.

Kim Y, Paroush Z, Nairz K, Hafen E, Jimenez G, Shvartsman SY: Substrate-

dependent control of MAPK phosphorylation in vivo. Mol Syst Biol 2011,

7:467.

Ossareh HR, Ventura AC, Merajver SD, Del Vecchio D: Long signaling

cascades tend to attenuate retroactivity. Biophys J 2011, 100:1617-1626.

Komarova NL, Zou X, Nie Q, Bardwell L: A theoretical framework for

specificity in cell signaling. Mol Syst Biol 2005, 1:2005 0023.

Wagner EF, Nebreda AR: Signal integration by JNK and p38 MAPK

pathways in cancer development. Nat Rev Cancer 2009, 9:537-549.

Cornish-Bowden A: Fundamentals of enzyme kinetics. 3 edition. London:

Portland Press; 2004.

Goldbeter A, Koshland DE Jr: An amplified sensitivity arising from

covalent modification in biological systems. Proc Natl Acad Sci USA 1981,

78:6840-6844.

Marino S, Hogue IB, Ray CJ, Kirschner DE: A methodology for performing

global uncertainty and sensitivity analysis in systems biology. J Theor Biol

2008, 254:178-196.

McKay MD, Beckman RJ, Conover WJ: A Comparison of Three Methods for

selecting Values of Input Variables in the Analysis of Output from a

Computer Code. Technometrics 2000, 42:55-61.

Tsai TY, Choi YS, Ma W, Pomerening JR, Tang C, Ferrell JE Jr: Robust,

tunable biological oscillations from interlinked positive and negative

feedback loops. Science 2008, 321:126-129.

Varma A, Morbidelli M, Wu H: Parametric sensitivity in chemical systems

Cambridge ; New York: Cambridge University Press; 2005.

Huang CY, Ferrell JE Jr: Ultrasensitivity in the mitogen-activated protein

kinase cascade. Proc Natl Acad Sci USA 1996, 93:10078-10083.

Koshland DE, Goldbeter A, Stock JB: Amplification and adaptation in

regulatory and sensory systems. Science 1982, 217:220-225.

Lahav G, Rosenfeld N, Sigal A, Geva-Zatorsky N, Levine AJ, Elowitz MB,

Alon U: Dynamics of the p53-Mdm2 feedback loop in individual cells.

Nat Genet 2004, 36:147-150.

Ciliberto A, Novak B, Tyson JJ: Steady states and oscillations in the p53/

Mdm2 network. Cell Cycle 2005, 4:488-493.

Siddiquee K, Zhang S, Guida WC, Blaskovich MA, Greedy B, Lawrence HR,

Yip ML, Jove R, McLaughlin MM, Lawrence NJ, et al: Selective chemical

probe inhibitor of Stat3, identified through structure-based virtual

screening, induces antitumor activity. Proc Natl Acad Sci USA 2007,

104:7391-7396.

Rawlings JS, Rosler KM, Harrison DA: The JAK/STAT signaling pathway. J

Cell Sci 2004, 117:1281-1283.

Rhodes N, Heerding DA, Duckett DR, Eberwein DJ, Knick VB, Lansing TJ,

McConnell RT, Gilmer TM, Zhang SY, Robell K, et al: Characterization of an

Akt kinase inhibitor with potent pharmacodynamic and antitumor

activity. Cancer Res 2008, 68:2366-2374.

Astsaturov I, Ratushny V, Sukhanova A, Einarson MB, Bagnyukova T, Zhou Y,

Devarajan K, Silverman JS, Tikhmyanova N, Skobeleva N, et al: Synthetic

lethal screen of an EGFR-centered network to improve targeted

therapies. Sci Signal 2010, 3:ra67.

Azam M, Latek RR, Daley GQ: Mechanisms of autoinhibition and STI-571/

imatinib resistance revealed by mutagenesis of BCR-ABL. Cell 2003,

112:831-843.

Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E,

Henry A, Stefan MI, et al: BioModels Database: An enhanced, curated and

annotated resource for published quantitative kinetic models. BMC Syst

Biol 2010, 4:92.

Bluthgen N, Herzel H: How robust are switches in intracellular signaling

cascades? J Theor Biol 2003, 225:293-300.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

doi:10.1186/1752-0509-5-156

Cite this article as: Wynn et al.: Kinase inhibitors can produce off-target

effects and activate linked pathways by retroactivity. BMC Systems

Biology 2011 5:156.

Wynn et al. BMC Systems Biology 2011, 5:156

http://www.biomedcentral.com/1752-0509/5/156

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