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Báo cáo khoa học: Modelling and simulating interleukin-10 production and regulation by macrophages after stimulation with an immunomodulator of parasitic nematodes potx

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IL-10 expression requires stimulation of the mitogen-activated protein kinases extracellular signal-regulated kinase ERK and p38, and we propose that a negative feedback mechanism, actin

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and regulation by macrophages after stimulation with

an immunomodulator of parasitic nematodes

Ana Sofia Figueiredo1, Thomas Ho¨fer2, Christian Klotz3, Christine Sers4, Susanne Hartmann3, Richard Lucius3and Peter Hammerstein1

1 Institute for Theoretical Biology, Humboldt University, Berlin, Germany

2 Research Group Modeling of Biological Systems, German Cancer Research Center and BioQuant Center, Heidelberg, Germany

3 Department of Parasitology, Berlin, Germany

4 Institute of Pathology, Universitaetsmedezin Charite´, Berlin, Germany

Parasitic nematodes are multicellular organisms

occupy-ing diverse niches within their hosts The economically

and medically important nematodes reside in the

intesti-nal tract, skin, muscles, blood or connective tissue of their hosts In all of these sites, nematodes are constantly exposed to various host immune responses

Keywords

autocrine crosstalk; host–parasite

interaction; regulation; signalling cascades;

systems biology

Correspondence

A S Figueiredo, Institute for Theoretical

Biology, Humboldt University,

Invalidenstrasse 43, 10115 Berlin, Germany

Fax: +49 30 20938801

Tel: +49 30 20938450

E-mail: s.figueiredo@biologie.hu-berlin.de

Note

The mathematical models described here

have been submitted to the Online Cellular

Systems Modelling Database and can be

accessed at http://jjj.biochem.sun.ac.za/

database/figueiredo1/index.html, http://jjj.

biochem.sun.ac.za/database/figueiredo2/

index.html, http://jjj.biochem.sun.ac.za/

database/figueiredo3/index.html and http://

jjj.biochem.sun.ac.za/database/figueiredo4/

index.html free of charge

(Received 5 September 2008, revised 22

February 2009, accepted 21 April 2009)

doi:10.1111/j.1742-4658.2009.07068.x

Parasitic nematodes can downregulate the immune response of their hosts through the induction of immunoregulatory cytokines such as

interleukin-10 (IL-interleukin-10) To define the underlying mechanisms, we measured in vitro the production of IL-10 in macrophages in response to cystatin from Acantho-cheilonema viteae, an immunomodulatory protein of filarial nematodes, and developed mathematical models of IL-10 regulation IL-10 expression requires stimulation of the mitogen-activated protein kinases extracellular signal-regulated kinase (ERK) and p38, and we propose that a negative feedback mechanism, acting at the signalling level, is responsible for tran-sient IL-10 production that can be followed by a sustained plateau Specifi-cally, a model with negative feedback on the ERK pathway via secreted IL-10 accounts for the experimental data Accordingly, the model predicts sustained phospho-p38 dynamics, whereas ERK activation changes from transient to sustained when the concentration of immunomodulatory protein of Acanthocheilonema viteae increases We show that IL-10 can regulate its own production in an autocrine fashion, and that ERK and p38 control IL-10 amplitude, duration and steady state We also show that p38 affects ERK via secreted IL-10 (autocrine crosstalk) These findings demonstrate how convergent signalling pathways may differentially control kinetic properties of the IL-10 signal

Abbreviations

AIC, Aikaike information criterion; AU, arbitrary units; Av17, cystatin from Acanthocheilonema viteae; ERK, extracellular signal-regulated kinase; H3, histone 3; IL-10, interleukin-10; IL-10e, extracellular interleukin-10; LPS, lipopolysaccharide; MAPK, mitogen-activated protein kinase; MKP, mitogen-activated protein kinase phosphatase; ODE, ordinary differential equation; rAV17, recombinant cystatin from

Acanthocheilonema viteae; RSS, residual sum of squares; SP1, Sp1 transcription factor; STAT3, signal transducer and activator of

transcription.

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Nevertheless, many parasitic nematode species live for

years, a fact that has recently been explained by

sophisti-cated immune evasion mechanisms deployed by the

worms For example, the species Onchocerca volvulus is

the causative agent of the tropical disease river blindness

(which afflicts about 20 million people worldwide), and

can persist in its human host for more than 10 years A

parasitic nematode of rodents, Acanthocheilonema

viteae, is used as an animal model to study basic

ques-tions of host–parasite interaction, e.g host immune

responses and parasite immune evasion mechanisms

Parasitic nematode infections induce a Th2 response,

which has the potential to trigger immune effector

mechanisms that can efficiently kill parasitic worms

However, the presence of these worms seems to blunt

this effect, and vigorous effector mechanisms do not

develop One way of interfering with immune effector

mechanisms is to stimulate the production of

anti-inflammatory cytokines such as interleukin-10 (IL-10)

As a consequence, the ability of the host to kill the

para-sites is compromised, and host pathology due to

inflam-matory reactions is minimized This balance allows

survival of parasites and hosts Blunted Th2 responses

may represent a benefit for the host, as the ensuing

downregulation of effector mechanisms decreases

auto-immune responses and allergies [1,2]

The search for molecules that modulate host immune

responses has led to the identification of A viteae

cysta-tin (Av17), a filarial protein constantly secreted by the

nematode [3] that inhibits cysteine proteases with

impor-tant functions in immune processes such as antigen

processing and presentation [4,5] Furthermore,

recom-binant Av17 (rAv17) has recently been shown to

specifi-cally inhibit allergic and inflammatory responses in mice

[6] In this scenario, rAv17 induced macrophages to

produce the anti-inflammatory cytokine IL-10 as a key

element of immunomodulation The fact that signalling

through the extracellular signal-regulated kinase (ERK)

and p38 mitogen-activated protein kinase (p38) induces

IL-10 production in macrophages [7,8] has prompted us

to model the respective signalling pathways

IL-10 is a cytokine with immunoregulatory

proper-ties It executes its functions on a wide range of cells,

macrophages being a major source of this cytokine

One major function of IL-10 is to control and reduce

excessive immune responses during infections and

auto-immunity, mainly by inhibiting the production of

pro-inflammatory cytokines in macrophages and other cell

types However, several studies show a regulatory role

of IL-10 on T-helper cell responses of different types,

e.g Th1 responses, which can lead to autoimmune

pathologies, and Th2 responses, which can lead to

aller-gies IL-10-deficient mice develop spontaneous colitis

under normal conditions and are more prone to immu-nopathology in general, being able to clear infection by intracellular pathogens more effectively than wild-type mice [6,9] This emphasizes the importance of IL-10 as

an immune regulator

The promoter region of the il-10 gene in macrophages contains binding sites for the transcription factors, e.g Sp1 transcription factor (SP1) [10–12] and signal trans-ducer and activator of transcription (STAT3) [7,8], that regulate gene expression and are controlled by ERK and p38 [13] In a sequential mechanism, the ERK signalling cascade remodels the chromatin of the il-10 promoter region by phosphorylating its histone 3 (H3) sites, and the p38 signalling pathway activates the tran-scription factors SP1 and STAT3 [7,8] These transcrip-tion factors bind to the phosphorylated H3 sites and thereby initiate il-10 gene expression [7,8,14] Macro-phages express the IL-10 receptor complex on their surface [15], suggesting feedback regulation by IL-10 A negative autoregulatory role for IL-10 is suggested for lipopolysaccharide (LPS)-stimulated or lipoprotein-stimulated IL-10 production in monocytes and mono-cyte-derived macrophages [16–19] On the basis of these findings, we assume that Av17 activates the ERK and p38 signalling pathways in macrophages, leading to IL-10 production, and we hypothesize that IL-10 is reg-ulated via a negative feedback mechanism of secreted IL-10 that binds to the macrophages and deactivates the ERK signalling pathway either by kinase inhibition

or by phosphatase activation Other ERK-induced molecules, e.g mitogen-activated protein kinase phosphatases (MKPs) can deactivate ERK and thereby regulate IL-10 induction (Fig 1)

The ERK and p38 signalling cascades are two exam-ples of MAPK cascades They are central and highly conserved, and are present in many cell types A myr-iad of stimuli can activate these kinases, which, in turn, activate many other transcription factors and regulators of transcription, controlling the expression

of many genes Although the mechanisms that control the different ERK activities are as yet unclear, diverse activation modes lead to diverging outcomes, despite the fact that the same cascade is in play [20–22]

In order to better understand the complexity of MAPK signalling pathways, many mathematical mod-els of these cascades have been developed Heinrich

et al [23] implemented mathematical models for different topologies of the receptor-stimulated kinase⁄ phosphatase signalling cascades and analysed key parameters that characterize the signalling pathways (signal amplitude, signalling time, and signal duration) Sasagawa et al [24] constructed a mathematical model

of ERK signalling based on literature findings and

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predicted ERK dynamics in response to increases in

the growth factors epidermal growth factor and nerve

growth factor Both studies show that the same

MAPK pathway can undergo a sustained or transient

activation, as experimentally shown by Marshall [20]

and Santos et al [22]

The aim of this study was to develop mathematical

models of IL-10 regulation on Av17 stimulation in

macrophages in order to understand quantitatively

whether the current qualitative knowledge of the

mecha-nism is compatible with available data Moreover, the

feedback regulation of IL-10 in macrophages is not well

understood at the moment Therefore, we implement

models distinguished by different types of regulation of

IL-10 production to test how these different hypotheses

can explain the available experimental data We select

the model that best represents the data, and analyse its

key features, such as the amplitude and duration of the

signal output On the based of the results, we provide

insights about the potential regulatory modes of IL-10

production on macrophages after Av17 stimulation

The mathematical models described here have been

submitted to the Online Cellular Systems Modelling

Database and can be accessed at http://jjj.biochem.sun

ac.za/database/figueiredo1/index.html, http://jjj.biochem

sun.ac.za/database/figueiredo2/index.html, http://jjj

biochem.sun.ac.za/database/figueiredo3/index.html and

http://jjj.biochem.sun.ac.za/database/figueiredo4/index html free of charge

Results

The model

On the basis of the experimental and literature evidence described above, we developed mathematical models of IL-10 regulation on Av17 stimulation in macrophages Model development was based on the principle of parsimony In order to keep the number

of parameters as small as possible, we included only those components and processes that we considered paramount to describe the systems dynamics and where data were available (see Fig 2 for all compo-nents and reactions included in the models)

We propose two different methods of regulation, via IL-10 (model 1 and model 2) or via an inhibitor (model 3), and compare them to a model with no feed-back (model 0) Model 1 assumes promotion of ERK dephosphorylation via IL-10 (kinase deactivation) Model 2 assumes inhibition of ERK phosphorylation via IL-10 (phosphatase activation) Model 3 assumes promotion of ERK dephosphorylation via an inhibitor (kinase deactivation) The components and reactions

of these models are described inTable 1

Fig 1 A literature-based model of IL-10 induction and regulation by the helminthic immune modulator Av17 Av17 binds to the macrophage and activates the p38 signalling pathway (which will activate the transcription factors SP1 and STAT3) and the ERK signalling pathway (which will phosphorylate the H3 site of the il-10 promoter region) These transcription factors bind to this promoter site, inducing il-10 mRNA expression [14] IL-10 protein is subsequently produced and secreted We assume that extracellular IL-10 binds to the IL-10 receptor of macrophages and deactivates phospho-ERK, either by kinase inhibition or by phosphatase activation, hence regulating its own production in

a negative feedback loop IL-10 regulation can also occur through a redundant negative feedback loop: the ERK signalling pathway induces the expression of MKPs that can deactivate ERK.

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Fig 2 Mathematical model of IL-10 production and regulation The model receives the input stimulation (Av17) as a step function (from 0 to 1), which activates ERK and p38 Phospho-ERK phosphorylates the H3 sites of the il-10 promoter region Phospho-p38 activates the set of tran-scription factors (A) necessary to induce il-10 gene expression, and il-10 mRNA expression (il-10m) and translation take place IL-10 is secreted

by the macrophage (IL-10 e ), and promotes the feedback regulation We hypothesize that extracellular IL-10 (IL-10 e ) binds to the macrophage and deactivates phospho-ERK, either by kinase deactivation (model 1) or by phosphatase activation (model 2) IL-10 regulation can also be achieved by an IL-10-independent inhibitor, X (model 3) These three models have in common the regulation by negative feedback.

Table 1 Description of reactions and its equations for the models of IL-10 production and regulation.

v1, v2 ERK phosphorylation on Av17 stimulation

and constitutive dephosphorylation

v 1 ¼ k 1  ERK t ð Þ  2 j  s t ð Þ

v 1model1 ¼ k 1  ERK t ð Þ  2 j  s t ð Þ= 1 þ k h f  IL10 e ð Þ thi

v 1model3 ¼ k 1  ERK t ð Þ  2 j  s t ð Þ= 1 þ k h f  X t ð Þ h i

v 2 ¼ k 2  ERK p ð Þ t

v 2model2 ¼ k 2  ERK p ð Þ  k t f  IL10 e ð Þ t

stimulation and constitutive dephosphorylation

v 3 ¼ k 3  2 j  s t ð Þ  p38 t ð Þ

v 4 ¼ k 4  p38 p ð Þ t

v5, v6 Transcription factor activation

and constitutive deactivation

v 5 ¼ k 5  A  p38 p ð Þ t

v6¼ k 6  A p ð Þ t

and dephosphorylation

v 7 ¼ k 7  ERK p ð Þ  H3 t t ð Þ

v 8 ¼ k 8  H3 p ð Þ t

v9, v10 Complex formation, constituting

the transcription factor bound to the phosphorylated H3 site and constitutive disaggregation

v 9 ¼ k 9  H3A p ð Þ t

v 10 ¼ k 10  H3 p ð Þ  A t p ð Þ t

IL-10 intracellular protein

v 13 ¼ k 13  IL10 m ð Þ t

v14 Degradation of IL-10 extracellular protein v14¼ k 14  IL10 e ð Þ t

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We have implemented these models using ordinary

differential equations (ODEs) (Eqns 1–10), and fitted

them to experimental data on il-10 mRNA and IL-10

protein time series, and il-10 mRNA half-life ODEs

are an effective way of mathematically describing the

dynamics of a biochemical reaction network through

its components and reactions [25,26] These equations

allow the in silico representation of qualitative

com-plex systems and the quantification of their

parame-ters, providing insights into their emergent properties

The models are also available in the SBML format,

which is a widely accepted standard of ODE models in

systems biology [27]

dERKp

dt ¼ v2 v1(reversible) ð1Þ

dp38p

dt ¼ v4 v3(reversible) ð2Þ

dAp

dt ¼ v5 v6þ v9 v10 ð3Þ

dA

dH3

dH3p

dt ¼ v7 v8þ v9 v10 ð6Þ dH3A

dIL10m

dIL10e

dX

Model fitting to the data

The different models were fitted to experimental data

on IL-10 protein and il-10 mRNA time series and il-10

mRNA half-life (for the half-life values, see

Experi-mental procedures) IL-10 protein and il-10 mRNA

time series were obtained by exposing murine

macro-phages to Av17 or NaCl⁄ Pi (as control experiment),

respectively IL-10 protein and mRNA levels were

determined after several time points by ELISA and

quantitative real-time PCR, respectively (Fig 3) For experimental details, see Experimental procedures The maximum relative il-10 mRNA expression was measured at 2 h after stimulation After 4 h, the mRNA levels reached background levels again IL-10 protein in the cell supernatant was detectable after 2–3 h, showed a steady increase over time until 8 h, and declined again after 14–24 h We observed a damped oscillation of the IL-10 mRNA between 4 and 8 h after stimulation To determine whether this was a biological effect, we repeated the same experi-ment and obtained results similar to those expected for the oscillatory effect (Fig S1) We conclude that the oscillation of the mRNA in Fig 3 represents a technical variation and is not an effect of the biolog-ical system

Model fitting was done using copasi [28] (see Exper-imental procedures for the methods used) The differ-ent regulation models fit the experimdiffer-ental data for il-10 mRNA and IL-10 secreted protein (Fig 4) Model 0 fits the data with larger error Figure 4 shows the fitting of the model of Fig 2 to IL-10 secreted protein and il-10 mRNA These data show that model

0 is not able to fit the decrease of IL-10 production observed experimentally, keeping it at a sustained level, whereas the models with regulation (model 1, model 2, and model 3) can fit the increase and decrease

in IL-10 levels For a complete listing of the best-fitting parameters, constraints and initial conditions for each model, see Doc S1

Fig 3 IL-10 protein and IL-10 mRNA kinetics after stimulation of macrophages with the helminthic immune modulator Av17 Thiogly-collate-elicited peritoneal macrophages from BALB ⁄ c mice were stimulated with 0.25 l M recombinant Av17 or with NaCl ⁄ P i for the indicated times The level of IL-10 protein in cell supernatants was quantified by ELISA Levels of il-10 mRNA were determined by real-time PCR, and are presented as expression relative to the endogenous control GAPDH All data points represent triplicates.

We show one representative experiment out of two that gave similar results.

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Model selection The fitting results allow to select models The experi-mental data (Fig 3) show that IL-10 production in macrophages after Av17 stimulation is transient This decrease in IL-10 production is evidence for its regula-tion by negative feedback Hence, we discard model 0, which includes no regulation and which presents sus-tained IL-10 production Moreover, the disagreement between fitted and experimental values is very high (Fig 4A) We calculated the Aikaike information crite-rion (AIC) and the residual sum of squares (RSS) between the estimated values and the experimental data for the four models, and model 0 yielded the highest value (compareTable 2)

It is experimentally observed that LPS-induced 10 does not reach zero in the macrophage, after

IL-10 stimulation [18] Because IL-IL-10 production in model

3 (model of regulation via an inhibitor) approximates zero, we discard model 3 and focus on the models of regulation via IL-10 (model 1 and model 2)

Simulation predicts transient phosphorylation of ERK and sustained phosphorylation of p38 after Av17 stimulation

On the basis of the estimated parameters, we predict the kinetics of phospho-ERK and phospho-p38 for model 1 (Fig 5A) and model 2 (Fig 5B) These

Fig 4 Fitted (lines) and experimental values (dots) for IL-10 secreted protein (maximum value at 8 h) and il-10 mRNA (maxi-mum value at 2 h) (A) Model 0: no feedback (B) Model 1: inhibi-tion of ERK phosphorylainhibi-tion via IL-10 (C) Model 2: activainhibi-tion of ERK dephosphorylation via IL-10 (D) Model 3: inhibition of ERK phosphorylation via another molecule; the models fit the data for the three regulation hypotheses Model 0 follows the production of IL-10, but cannot follow the decrease, because there is no regula-tion, leading to cumulative production of IL-10, which reaches a steady state.

Table 2 AIC and RSS for the four models Model 0 yields the highest value and model 3 the lowest value AIC presents a relative value that scores the model, the lowest value being the best score.

A low RSS value indicates that the difference between estimated and experimental values is low, and a high value indicates the reverse.

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models show transient phospho-ERK and sustained

phospho-p38 dynamics These predictions are

qualita-tively in accordance with experimental evidence [7,8]

These authors show that activation of macrophages by

immune complexes leads to IL-10 production through

the activation of ERK (transient) and p38 (sustained)

Both models present weak and transient ERK and

strong and sustained p38 activation

Changing the Av17 stimulus shows that both

ERK and p38 control the amplitude of IL-10

The density of the parasite population, and hence the

concentration of secreted Av17, can vary To

under-stand how this affects the system behavior, we changed the concentration of Av17 (increasing and decreasing it) and examined how this affects the dynamics of key elements of each model We implemented one-step exponential increases (from 2 to 230) and decreases (from 2)10 to 20), and compared their impacts on the dynamics of phospho-ERK (Fig 6), phospho-p38 and IL-10 (Figs 7 and 8) for kinase deactivation (model 1) and phosphatase activation (model 2)

Phospho-ERK Changing the stimulus amplitude can switch ERK acti-vation from transient to sustained Phospho-ERK of model 1 reaches maximal activation instantaneously, and the input changes affect the signal duration as well

as the amplitude (Fig 6A) The response to these input variations in model 2 is different: first, they reach maximal activation with a certain delay, which decreases as the input increases; and second, they affect only the phospho-ERK amplitude until ERK

Fig 5 Phospho-ERK (transient curve) and phospho-p38 (sustained

curve) kinetics for model 1 (A) and model 2 (B) x-axis, time (h);

y-axis, concentration (AU) On the basis of the fitted parameters for

this model, we predict the dynamic behaviour of phospho-ERK

(black) and phospho-p38 (grey) (A) Model 1: ERK activation is weak

and fast; it lasts for 1 h, and is followed by an ERK decrease At

2 h, the ERK concentration is zero, whereas the phospho-p38

con-centration is sustained (B) Model 2: ERK activation is weak and

fast; it has its peak at 1 h, and this is followed by an ERK decrease.

At 2 h, the ERK concentration is zero; the phospho-p38 increase is

slow and sustained, reaching steady state at 40 h.

Fig 6 Phospho-ERK kinetics for different input amplitudes (2)10to

2 30 ) (A) Model 1 (B) Model 2 Red line: input amplitude = 1.

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saturation, and after this level, ERK duration increases

(Fig 6B)

The mechanism of kinase inhibition (model 1) was

assumed to have a cooperative behavior (Hill

coeffi-cient of 2.5) Therefore, the inhibition has a switch-like

behavior and becomes effective only with a certain

delay, during which the phospho-ERK is maximally

active When the feedback ‘kicks in’, there is a rapid

deactivation of phospho-ERK following the plateau of

maximal activity (Fig 6A) In model 2, the inhibition

by the increase in phosphate activity is assumed to be

a linear function of IL-10, and the inhibition therefore

constantly increases, causing direct deactivation after

reaching the maximum (Fig 6B)

Phospho-p38

P38 activation is sustained for both models after

con-stant increases in the concentration of Av17 The

amplitude of phospho-p38 of both models increases

until saturation is reached [2 arbitrary units (AU)], but

as phospho-p38 activation is faster for model 1 than

for model 2, the former reaches saturation faster than the later

Extracellular IL-10 (IL-10e) Figures 7 and 8 show how the different Av17 concen-trations affect IL-10e amplitude, duration, and steady state By comparing Fig 7A with Fig 7B, we observe

a shift in IL-10e behaviour In terms of signal ampli-tude, for j = 15 (v1 and v2 in Table 1), model 1 and model 2 yield very similar maximal amplitudes For both models, a decrease in Av17 concentration shows that the macrophage produces IL-10 after a certain threshold of Av17 concentration is attained (compare

Fig 8) IL-10 production overshoots and goes down

to a steady-state level As the input concentration increases, so does the maximum value of IL-10

In terms of duration, although there is no significant difference between model 1 and model 2 for IL-10 rise time (time to reach maximum production), IL-10 downregulation is faster for the former Moreover, the

Fig 7 IL-10 e kinetics for different Av17 concentrations (1 to 215).

(A) Model 1 (B) Model 2 Red line: input amplitude = 1.

Fig 8 IL-10ekinetics for different input amplitudes (2)10to 2 0 ) (A) Model 1 (B) Model 2 The results show that there is an effective Av17 concentration level needed to start the production of IL-10 Red line: input amplitude = 1.

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difference between the maximum value and the

steady-state value is higher in model 1 than in model 2 (in this

model, the difference disappears for j = 13) These

observations correlate with phospho-ERK dynamics

(Fig 5), which show a shift from transient to sustained

in both models Model 1 shows faster activation of

ERK, followed by slower attainment of the sustained

level, which entails the same behaviour for IL-10

pro-duction with respect to increasing Av17 concentration

The different feedback mechanisms of model 1

(kinase inhibition) and model 2 (phosphatase

activa-tion) have implications for IL-10 dynamics Model 2

shows more rapid and robust IL-10 dynamics as more

phosphatase accelerates dephosphorylation, whereas

the dephosphorylation rate of the kinase inhibition

mechanism is constant

Sensitivity analysis

We performed a sensitivity analysis in order to

under-stand how perturbations in the system affect the

out-put (IL-10 production) Therefore, we perturbed, in a

systematic manner, all the parameters and checked

their influence on phospho-ERK, phospho-p38, il-10

mRNA, and IL-10 protein, in terms of amplitude and

steady state The sensitivities were calculated using the

formula:

S¼DO

O :

p Dp (O is the output and p is the perturbed parameter)

We imposed on these parameters perturbations of

10 and 0.1 The results show different behaviours for

model 1 and model 2 For model 1, the most sensitive

parameter is the Hill coefficient for the feedback

inhi-bition of ERK activation

For model 2, k9 and k12 are the most sensitive

parameters, affecting the IL-10e steady state.The

parameter k9 is associated with the production of

X2(t), which is the complex formed by the

lated transcription factors bound to the

phosphory-lated chromatin of the il-10 promoter region The

parameter k12 is the parameter associated with il-10

mRNA production, and its value is the half-life of il-10 mRNA In terms of amplitude, the system is insensitive for both models

Fig 9 Perturbations of phospho-ERK (model 1) Range of

perturba-tion: factor 10 and factor 0.1 Red line: no perturbation Green line:

factor of perturbation is 0.1 Blue line: factor of perturbation is 10.

(A) Phospho-ERK: perturbing phospho-ERK affects its duration and

amplitude, but not steady state (B) il-10 mRNA: perturbations

affect il-10 m amplitude and the duration but not the steady state.

(C) IL-10 protein: perturbations affect IL-10 e amplitude, duration and

steady state (D) Phospho-p38 is not affected at all by

phospho-ERK perturbations.

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Perturbing phospho-ERK in model 1 affects IL-10

production but has no influence on phospho-p38

Figure 9 shows the variations of parameter k1 of

model 1 In Fig 9A, we can see the imposed

perturbations of phospho-ERK and observe that these

changes affect the duration and amplitude of

phospho-ERK As the perturbation increases, the amplitude of

phospho-ERK increases and the duration decreases

These same perturbations also affect the amplitude

and the duration of il-10 mRNA (Fig 9B) and IL-10

protein (Fig 9C) The steady state of IL-10 protein is

also affected, but not the steady state of il-10 mRNA

These perturbations have no direct effect on p38,

phos-pho-p38 maintaining its curve over the whole

perturba-tion range (Fig 9D)

Perturbing phospho-p38 in model 1 affects

phospho-ERK and IL-10 production

We perturbed the phosphorylation rate constant of

p38, k3 (Fig 10A) and observed that p38 activity,

although not directly affected by the negative

feed-back, has an indirect impact on the feedback

mecha-nism by influencing the production of IL-10 and,

consequently, ERK activity This reveals autocrine

feedback between the MAPKs

In this model, secreted IL-10 binds to the

macro-phage and promotes the dephosphorylation of

phos-pho-ERK, establishing in this way a negative

feedback mechanism Hence, the production of IL-10

interferes with the ERK signalling pathway, higher

IL-10 production reflecting higher feedback strength

and lower duration of phospho-ERK (Fig 11B–D)

By comparing both perturbations on parameters k1

for phospho-ERK and k3 for phospho-p38, we can

observe that phospho-ERK has a stronger influence

on il-10 mRNA and IL-10 protein amplitude and that

phospho-p38 exerts control over the feedback

mecha-nism strength

Fig 10 Perturbations of phospho-p38 (model 1) Range of

pertur-bation: factor 10 and factor 0.1 Red line: no perturbation Green

line: factor of perturbation is 0.1 Blue line: factor of perturbation is

10 (A) Phospho-p38: perturbing phospho-p38 affects its amplitude.

(B) Phospho-ERK: phospho-ERK is sensitive to phospho-p38

pertur-bations, owing to the feedback mechanism Its amplitude maintains

a constant level, its duration increases as the perturbation

decreases, and for a perturbation factor of 0.1, its steady state

increases (C) il-10 mRNA: amplitude and duration are sensitive to

perturbations of phospho-p38, but not the steady state (D) IL-10

protein: amplitude, duration and steady state are sensitive to

per-turbations of phospho-p38.

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