A Dual Negative Regulation Model of Toll-Like Receptor 4 Signaling for Endotoxin Preconditioning in Human En Do Toxemia

8/2/2019 A Dual Negative Regulation Model of Toll-Like Receptor 4 Signaling for Endotoxin Preconditioning in Human En Do T

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2 A dual negative regulation model of Toll-like receptor 4 signaling3 for endotoxin preconditioning in human endotoxemia

4 Qian Yang a , Steven E. Calvano b , Stephen F. Lowry b , Ioannis P. Androulakis a ,b ,c,

5 a Chemical Engineering, Rutgers University, 98 Brett Road, Piscataway, NJ 08854, USA6 b Department of Surgery, UMDNJ-Robert Wood Johnson Medical School, New Brunswick, NJ 08901, USA7 c Biomedical Engineering, Rutgers University, 599 Taylor Road, Piscataway, NJ 08854, USA

89

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a r t i c l e i n f o

2 Article history:3 Received 9 September 20104 Received in revised form 10 May 20115 Accepted 16 May 20116 Available online xxxx

7 Keywords:8 Mathematical modeling9 Lipopolysaccharide0 Endotoxin1 Potentiation2 Tolerance3 Humans4

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a b s t r a c t

We discuss a model illustrating how the outcome of repeated endotoxin administration experiments canemerge as a natural consequence of the tightly regulated signaling pathways and also highlight theimportance of a dual negative feedback regulation including PI3K/Akt and IRAK-M (IRAK3). We identifythe relative time scales of the onset andthe magnitude of the stimulus as key determinants of outcome inrepeated administration experiments. The results of our simulations involve potentiated response, toler-ance, and protective tolerance. Moreover, the knockout of negative regulators shows that IRAK-M is anecessary and sufcient factor for generation of endotoxin tolerance (ET). The effects of the knockoutof IRAK-M gene or administration of PI3K inhibitor do yield predictions that have been veried experi-mentally. Finally, the pretreatment with PI3K inhibitor reveals the interaction between these two nega-tive regulations.

2011 Published by Elsevier Inc.

89 1. Introduction

0 Endotoxin (LPS), a membrane glycolipid of Gram-negative bac-1 teria, is a potent inducer of pro-inammatory responses in mono-2 cytes, macrophages, and neutrophils and is widely accepted model3 for the study of inammatory responses [1] . While immune cells4 exposure to LPS induces the release of both pro- and anti-inam-5 matory cytokines (small proteins that are the principal mediators6 of inammation), repeated treatment with LPS can lead to7 enhancement or desensitization of subsequent pro-inammatory8 cytokine responses [2] so-called potentiation or tolerance, respec-9 tively [3] . Potentiation is dened as the enhanced response to a0 secondary LPS administration [4] whereas endotoxin tolerance1 (ET) is dened as a diminished secondary response to LPS activa-2 tion following a primary exposure. LPS tolerance has also been3 termed hyporesponsiveness, refractoriness, adaptation, deactiva-4 tion, desensitization, immunoparalysis or reprogramming [2,5] .5 Studies of ET induced in vitro [6,7] and in vivo [8] have shown a de-6 crease in the production of several cytokines by macrophages;7 including IL-1 b , TNF-a , and IL-6. In the extreme, endotoxin

tolerance was initially depicted when animals survived a lethaldose of bacterial endotoxin if they had been previously treatedwith sublethal stimulus [4] .

In an attempt to interpret LPS preconditioning, model-based ap-proaches have been proposed to explore potential underlyingmechanisms and to establish relationships between the variousLPS preconditioning strategies and the alternative outcomes. Anumber of excellent prior studies [3,913] have investigated pre-conditioning phenomena while evaluating alternative computa-tional models. The central signaling receptor for LPS is Toll-likereceptor 4 (TLR4), and all previous work address preconditioningas it relates to TLR4 signaling. Day et al. [9] construct a four-dimen-sional model whose key feature is the presence of anti-inamma-tory factors in the system suppressing the growth of inammatorycytokines in response to the secondary stimulus. Similarly, Vasile-scu et al. [10] build a two differential equation model describingthe dynamics of TNF- a concentration and the brake system, andassumed that the generation of ET is induced by the suppressioneffect by the brake system. More recently, Rivieres work [3] sug-gests that preconditioning is controlled by the regeneration rate of TLR4 without invoking a specic signaling inhibition mechanism.Finally, negative feedback regulation by specic proteins consid-ered as mechanism is also used to induce ET in an agent basedmodel proposed by An and coworkers [11,12] .

Our fundamental understanding of LPS signaling has improveddramatically over the recent years as new experimental evidenceemerges. Thus it is believed that ET may not be solely induced by

0025-5564/$ - see front matter 2011 Published by Elsevier Inc.doi: 10.1016/j.mbs.2011.05.005

Corresponding author at: Biomedical Engineering, Rutgers University, 599Taylor Road, Piscataway, NJ 08854, USA. Tel.: +1 (732) 445 0099; fax: +1 (732) 44537534.

E-mail addresses: [email protected] (Q. Yang), [email protected] (S.E.Calvano), [email protected] (S.F. Lowry), [email protected] (I.P. Androula-kis).

Mathematical Biosciences xxx (2011) xxxxxx

Contents lists available at ScienceDirect

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Please cite this article in press as: Q. Yang et al., A dual negative regulation model of Toll-like receptor 4 signaling for endotoxin preconditioning in humanendotoxemia, Math. Biosci. (2011), doi: 10.1016/j.mbs.2011.05.005
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suppression of anti-inammatory mediators [14] , nor through theexclusive down-regulation of cell surface receptors [15] . Further-more, simple feedback control mechanisms could not explainwhy immune responses are not suppressed simultaneously underET condition [16] . Thus, the complexity of the response to LPS pre-conditioning implies the possibility of multilevel regulation requir-ing the development of more elaborate underlying mechanisms.

Recently a number of studies focusing on quantifying proteinsor enzymes in TLR4 signaling pathways have suggested that thedifferent results following preconditioning are related to thecomplex and tightly regulated molecular mechanisms within thissignaling pathway. TLR4 is involved in host defense against invad-ing pathogens, functioning as the primary sensor of microbialproducts andactivating signaling pathways that induce the expres-sion of immune and pro-inammatory genes [17] . Due to thishighly signicant biological role, the TLR4 signaling pathway istightly regulated [18] . Thus, it is not surprising to nd that variousnegative regulatory mechanisms have evolved to control TLR4 sig-naling in order to maintain immunological balance. Several mole-cules which are identied as potential negative regulators of theLPS-induced TLR4 signaling pathway are highly likely to play a rolein the signal transduction alterations associated with endotoxintolerance based on recent in vitro and murine in vivo studies. Neg-ative regulators such as intracellular molecules myeloid-differenti-ation-88-short (MyD88s) [19,20] , IL-1R-associated-kinase-M(IRAK-M) [21] , Toll interacting protein (TOLLP) [22] and suppres-sor-of-cytokine signaling 1 (SOCS1) [23,24] have been shown toplay a vital role in endotoxin tolerance. Moreover, additional sig-naling pathways which are triggered by LPS are found to be ableto negatively regulate TLR4 signaling. Phosphatidylinositol 3-ki-nase (PI3K), a family of intracellular signal transducer enzymes,has been linked to an extraordinarily diverse group of cellularfunctions including cell growth proliferation, differentiation,motility, survival and intracellular trafcking [25] which could beactivated in many ways, directly by integrins [26] , by growth fac-tors [27] , by G-protein coupled receptors [28] . Many of these func-tions relate to the ability of PI3K to activate protein kinase B (Akt).Recent data indicate that these molecules are also integral playersin coordinating defense mechanisms in the innate immune systemwhich could also be stimulated in diverse manners, by cytokinesvia JAK1 [29] , by antigen via BCAP [30] . It has been reported thatthe LPS-induced activation of PI3K/Akt limits lipopolysaccharideactivation of TLR4 signaling pathways and expression of inamma-tory mediators in human monocytic cells [31] . These mechanismspoint to the possibility of a dual-phase mechanism of negative reg-ulation associated with innate immune response. Though bothPI3K/Akt and IRAK-M have roles in the gate-keeping system, pre-venting excessive innate immune response [32] , there is a criticaldifference between PI3K/Akt- and IRAK-M-dependent negativeregulatory mechanisms. Unlike IRAK-M that is induced by TLR sig-

naling and functions during the second or continuous exposure tostimulation, PI3K/Akt acts at the rst phase of TLR signaling andmodulate the magnitude of the primary activation. Therefore,PI3K/Akt functions as a negative controller in the early (or pri-mary) phase of the innate immune response by inhibiting someof the shared signaling pathways downstream of TLR4, whereasIRAK-M acts in the late (or second) phase of the innate immuneresponse [32] .

The work to be discussed in this paper aims to develop a modelbased on the molecular mechanisms of the TLR4 signaling pathwayexploring the synergies between these two negative feedbackregulations in order to describe the complex dynamics of theLPS-induced inammation and investigate different scenarios of preconditioning. Our model describes the interaction between

the ligand (LPS) and the transmembrane signaling receptor(TLR4) coupled with the recruitment of kinase (IRAK) and the

15activation of transcriptional factor (NF- j B) which triggers the15stimulation of expression of essential leukocyte-specic transcrip-15tional dynamics. Simultaneously, the indirect activation of the15PI3K/Akt signaling pathway by TLR4 which suppresses the NF- j B15activity develops a short loop. On the other hand, the suppression15of kinase IRAK by its specic inhibitor IRAK-M whose transcription15is stimulated by the activation of PI3K/Akt signaling pathway cre-15ates a longer loop. Such dual negative inhibition can potentially15emerge as a critical enabler towards understanding the connectiv-16ity and relationship of critical components in the innate immune16system. In addition, our model offers opportunity for unraveling16the multiple outcomes associated with endotoxin preconditioning.16The capability of describing both potentiation and tolerance using16a single model illustrates how the outcomes of endotoxin adminis-16tration experiments can emerge as a natural consequence of the16tightly regulated signaling pathway in acute inammatory re-16sponse. Moreover, our model predicts that the relative time scales16of the onset are key determinants of the outcome in repeated16administration experiments. In addition, the in silico knockout of 17the negative regulator IRAK-M induces a lack of endotoxin toler-17ance and demonstrates that IRAK-M is a necessary and sufcient17factor for this complex behavior. In silico knockout of irak -M or17administration of PI3K inhibitors respectively predicts experimen-17tally veried responses highlighting the importance of a dual neg-17ative feedback regulation in the model with both the PI3K/Akt and17IRAK-M. Finally, the pretreatment with PI3K inhibitor reveals the17crosstalk between these two negative regulations.

172. Materials and methods

17 2.1. Human endotoxin model

18Gene expression data used herein were obtained from the18Inammation and Host Response to Injury Large Scale Collabora-18tive Project funded by the USPHS, U54 GM621119 [33] . Human

18subjects were treated by intravenous injection with endotoxin 18(CC-RE, lot 2) at a dose of 2-ng/kg body weight (endotoxin treated18subjects) or 0.9% sodium chloride (placebo treated subjects). After18the lysis of erythrocytes and isolation of total RNA from leukocyte18pellets [34] , biotin-labeled cRNA was hybridized to the HU133A18and HU133B arrays which contain a total of 44,924 probes for test-18ing the expression level of genes whose expression can be altered19in response to endotoxin. A set of 5093 probe sets were character-19ized by signicant variation (corresponding to 0.2% false discovery19rate) across the time course of the experiment using the SAM soft-19ware [35] . The data are publicly available with accession number19GSE3284 at the Gene Omnibus Database ( http://www.ncbi.nlm.-19nih.gov/geo/ ). Blood samples were also extracted and analyzed to19determine the plasma concentration of stress hormones including19cortisol and epinephrine [36,37] . Specically, cortisol levels were19tested at 0, 0.5, 1, 1.5, 2, 3, 4, 6, and 24 h in response to endotoxin19administration [36] while the study period for epinephrine levels20was 0, 2, 4 and 6 h following endotoxin administration [37] .

20 2.2. An LPS-Induced acute inammation model

20We have previously [38] , proposed a quantitative model of an20endotoxin induced inammatory response. The activation process20involves the induction of a signal transduction cascade that trig-20gers transcriptional initiation of inammatory genes [39] . The20model describes the kinetic interaction between the ligand (LPS)20and its signaling receptor (TLR4) coupled with their activation of 20kinase activity (IKK) which induces the phosphorylation and deg-

20radation of I j Ba and then the release of the transcriptional factor 21(NF- j B). NF- j B translocates into the nucleus and initiates the

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expression of inammatory response related genes including P ,the pro-inammatory component, A, the anti-inammatory com-ponent, and E , the energetic component. Moreover, the critical as-pects of the neuro-endocrine immune crosstalk connecting thecellular response level were also described. These responses wereintegrated into a mathematical model using the basic principlesof an Indirect Response Model (IDR) [40] that bridges the extracel-lular signal (LPS) with the downstream activation of the majortranscriptional responses activation and neuro-endocrine systeminteraction. The model is succinctly presented in Eqs. (1)(5) andis described in great detail in [38]

2

LPS kineticsdLPS

d t k lps ;1 LPS 1 LPS k lps ;2 LPS 144

3. Modeling the dual negative regulation LPS recognitionmechanism

3.1. Putative structure of the regulation network

LPS is recognized by its transmembrane signaling receptor,TLR4, and the accessory protein MD-2. The binding of LPS andTLR4 results in the formation of a complex, LPSR, and the recruit-ment of the adaptor molecules MyD88 [42] and TIRAP [43] . Thiswill further result in recruiting and activating IRAK [44]subsequently activating TRAF6 [45] . Further intracellular events

ultimately result in the activation of the IKK complex, involvingphosphorylation and degradation of I j Ba , enabling the nuclear

translocation of NF- j B [17] resulting in the expression of inam-mation related genes. The inammatory dynamics are the manifes-tation of the complex interaction between activating andinhibitory interactions in order to constantly strike a balance be-tween activation and inhibition and to drive the immune systemback to homeostasis [46] . Numerous cytokines are responsiblefor amplifying the inammatory reaction, through the critical IKKnode [47] , while negative proteins inhibit IRAK which will nallysuppress the release of inammatory mediators [18] . We will focusspecically on four putative modes of regulation:

(i) IRAK-M is one of the most important negative regulators of IRAK and has been shown to prevent dissociation of IRAKfrom MyD88 and the formation of the IRAK-TRAF6 complex

[21] . Though other proteins, such as MyD88 and TRAF6,which play critical role in the recruitment and activationof downstream enzymes in the TLR4 signaling pathway arealso tightly regulated by their specic negative regulators,MyD88s (the short form of MyD88) and A20 respectively[18] , we consider a simplied feedback loop consisting onlyof IRAK and IRAK-M, since the redundancy of negative regu-lation of IRAK by several controllers, including IRAK-M,SOCS-1, and TOLLIP, implies the signicance of this node[48] .

(ii) A critical pathway in the inhibition of TLR4 signaling is thePI3K/Akt kinase signaling pathway which is triggered byLPS stimulation [31] . Recently, the interaction of PI3K and

ligand receptor interactions

dRd t k syn ;mRNA;R mRNA; R k 2 LPSR k 1 LPSR k syn RdLPSR

d t k 1 LPSR k 3 LPSR k 2 LPSR dmRNA;R

d t k in ;mRNA;R 1 k mRNA;R;P P k out ;mRNA;R R

8>>>:

2

NFj B signaling dynamics

dIKKd t k 3 IKK=1 IkBa k 4 IKK P

IKK2

1 IKK2

dNFj Bnd t kNFj B;1 IKK1NFj Bn1 IkBa k NFj B;2 NFj Bn IkBadmRNA IkBa

d t k in ;IkBa 1 k IkBa;1 NFj Bn k out ;IkBa mRNA; IkBadIkBa

d t k I;1 mRNA; IkBa k I;2 1 IKK 1 NFj Bn IkBa k I;1

8>>>>>>>>>>>:

3

Intrinsic transcriptional responses

dP d t k in ;P 1 k P ;NFj Bn NFj Bn 1 k P ;E E = A k out ;P P d Ad t k in ; A 1 k A;cAMP cAMP 1 k A;E E 1 k A;FRN FR N

k out ; A AdE d t k in ;E 1 k E ;P P = A k out ;E E

8>>>>>>>:

4

neuro-endocrine immune system interactions

dF d t w F ex Rin ;F k in ;F 1 k F ;P P k out ;F F dRm

d t k syn Rm 1 FR N

IC50 Rm FR N k deg Rm

dRFd t k syn R Rm r f k re FR N k on F RF k dgr R RF

dFR d t k on F RF k T FR

dFR Nd t k T FR k re FR N

dEPId t w EPI;ex Rin ;EPI k in ;EPI 1 k EPI;P P k out ;EPI EPI

dREPId t k

0REPI

k 1;REPI 1 k REPI EPI k 2;REPI REPIdEPIR

d t k 1;REPI 1 k REPI EPI REPI k 3;EPIR EPIR dcAMP

d t 1s EPIR

n cAMP

wF ex 1; exogenous hormone0; elsewhere

w EPIex 1; exogenous hormone0; otherwise

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

5

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MyD88 in response to LPS was reported. Ojaniemis study onLPS-induced PI3K activation [49] demonstrated thatactivation of TLR4 results in the formation of the PI3K-MyD88 complex, implying that one mode of activation of the PI3K/Akt pathway following exposure to LPS is via LPS-TLR4-MyD88 approach. It was also shown that inhibitionof PI3K/Akt pathway enhances LPS-induced TNF- a geneexpression via increased activation of NF- j B [31] . Thus, thePI3K/Akt pathway imposes a braking mechanism limitingthe expression of TNF- a in LPS-stimulated monocytes andensures transient expression of these inammatorymediators.

(iii) Recent data demonstrate that the expression of IRAK-M

depends on the activation of the PI3K/Akt signaling pathway.Zacharioudaki et al. [50] demonstrated that administration

27of PI3K inhibitors abolished IRAK-M induction by LPS sug-27gesting that LPS mediates its signal via PI3K/Akt pathway27to promote IRAK-M gene expression.28(iv) Finally, the work [51] demonstrated that LPS precondition-28ing resulted in lowered levels of proinammatory cytokines28(indicative of tolerance) accompanied with increased levels28of IRAK-M mRNA expression. Therefore, it is hypothesized28that pro-inammatory cytokines exert an inhibitory effect28on the expression of mRNA IRAKM .28

28Thus, we hypothesize that the LPS-induced activation of TLR 28signaling pathway is tightly regulated by different mechanisms28at multiple levels. Routes (i), (iii) and (iv) eventually control the

29activity of IRAK whereas route (ii) affects signaling through 29NF- j B. Thus we hypothesize the existence of a minimal dual

Fig. 1. Basic topological interactions composing the multi-level model of endotoxin induced human inammation with dual negative regulation.



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regulation of LPS recognition signaling. All the aforementionedqualitative relations are depicted in the form of a network inFig. 1 . Here, we just focus on MyD88-dependent pathway. In fact,LPS-induced activation of TLR4 signaling have been divided intoMyD88-dependent and MyD88-independent (TRIF-dependent)pathways [52] . The study [53] on induction of cross-tolerance tomultiple TLR ligands by in vivo LPS exposure of human blood leu-kocytes proposes a strong support that LPS tolerance in MyD88-dependent pathway is mediated by IRAK-M which has alreadybeen observed in many previous experiments [54,55] . However,the factor which induces the tolerance in MyD88-independentpathway is still unknown [53] . Moreover, the MyD88-dependentpathway has been shown to mediate the expressionof the majorityof pro-inammatory cytokines, while to date the MyD88-indepen-dent pathway is associated only with the induction of Type 1 inter-feron [56] . Since we focus on the LPS-induced inammatorymediators expression, the indicator of endotoxin tolerance, in thisstudy, we just consider the MyD88-dependent pathway as LPS-activated TLR4 signaling pathway.

3.2. Quantifying the dual negative regulation model

The hypotheses earlier described are quantied in the followingway:

Negative feedback regulation of IRAK by IRAK-M: We proposed tomodel IRAK as a transient signal as described in Eq. (6) . The cellularsurface complex LPSR induces theactivation of kinase activity IRAKwith a rate k 3, while being eliminated with a rate kout,IRAK . More-over, its increase is suppressed by the presence of its primaryinhibitor IRAK-M which adversely affects the transmission of thesignal to the downstream. The dynamics of the gene transcript of IRAK-M, mRNA IRAKM , are characterized by a zero order productionrate kin,mRNA,IRAKM which is stimulated by Akt (per mechanism iii,see above) while inhibited by P (per mechanism iv, see above)and a rst order degradation rate kout,mRNA,IRAKM , Eq. (7) . Thedynamics of IRAK-M, the inhibitor of IRAK, is based on the transla-tion of its corresponding transcript, mRNA IRAKM , with synthesisrate kin,IRAKM and a rst order degradation rate kout,IRAKM , Eq. (8) .

Negative feedback regulation of TLR4 signaling pathway by PI3K/ Akt pathway: The inhibition of NF- j B by PI3K/Akt is modeled viathe indirect stimulation of the production of I j Ba with rate kIk-Ba,Akt . The degradation of the I j Ba is described as in the earliermodel [38] , Eq. (9) .

Activation of kinase PI3K/Akt via LPSR: PI3K, the kinase which isconstitutively expressed in immune cells, is activated by LPSR indi-rectly with activation rate kin,PI3K and eliminated with a rate kout,-

6 PI3K , (per mechanism ii, see above) Eq. (10) . The activation of thekinase Akt by PI3K is modeled using a transit compartment model[57] with transit time s , Eq. (11)

9dIRAK

d t k 3LPSR

1 IRAKM k out ;IRAKIRAK 611

2dmRNA IRAKM

d t k in ;mRNA;IRAKM

1 k mRNA;IRAKM;AktAkt1 k mRNA;IRAKM;P P

k out ;mRNA;IRAKMmRNAIRKAM 7445

dIRAKMd t

k in ;IRAKMmRNA; IRAKM k out ;IRAKMIRAKM k in ;IRAKM

8778

dIkBad t

k I;1 mRNAIkBa1 k IkBa;AktAkt

k I;2 1 IKK1 NFj BIkBa kI;1 900

dPI3Kd t

k in ;PI3KLPSR k out ;PI3KPI3K 10

dAktd t

1s

PI3K-Akt 11

Of note, induction of IRAK-M mRNA and IRAK-M in macro-phages, following 10 ng/ml LPS stimulation and measured using

Northern and Western blot respectively, in the study by Kobayashiet al. [3] were found to be correlated and dependent on LPS thusIRAK-M is not constitutively expressed. Therefore, in our model,equation (7) describes the expression of IRAK-M whereas equation(8) describes the dynamics of protein synthesis which is assumedto correlate with the activated kinase. The constitutive expressionof IRAK was demonstrated in the Kobayashi study, whereas bothPI3K [4] and Akt [5] are also constitutively expressed in most cells.Thus gene expression and protein activities are not expected to becorrelated; therefore, in our work we model the dynamics of theactivated kinase (see model Eqs. (6), (10) and (11) for IRAK, PI3Kand Akt, respectively).

4. Results and discussion

4.1. Estimation of relevant model parameter

The dual negative regulation model components as described inEqs. (6)(11) introduce 10 new parameters. In order to robustlyestimate their appropriate values a variant of bootstrap in conjunc-tion with least squares is explored [60] . Estimates of the parametervalues and associated condence interval are evaluated. The boot-strap sampling with replacement is basedon the 4 replicates of onerepresentative gene in each essential motif as well as the corre-sponding measurements of mRNA R , mRNA IkBa , mRNA IRAKM . Thethree responses P , A, E following LPS stimulation are obtained byusing the slingshot clustering method which include 343, 502and 2919 coexpressed probe sets, respectively [61] . In previous

[61] and current study, we select the transcriptional signature of specic genes representative of each essential response in orderto reproduce the experimental data. IL-1 b is selected to serve asthe representative biomarker of P , the pro-inammatory re-sponse. The gene transcript of IL10RB is considered to be indicativeof the immune-regulatory signal of A, the anti-inammatoryresponse. Finally, a subunit of NADH ubiquinone dehydrogenasecomplex (mitochondrial component) NDUFC2 is considered asthe proxy for the energetic component. Of note, the purpose forus to use the P component in our modeling methodology is to

Table 1

Values of the parameters involved in the propagation of LPS signaling on the

transcriptional response level neuro-endocrine immune axis.Parameter Value Parameter Value Parameter Value

kLPS,1 4.500 K I,1 1.400 k3,REPI 2.500kLPS,2 6.790 kI,2 0.870 K out,EPI 7.286ksyn 0.020 K in,P 0.030 kR,EPI 0.649K 1 3.000 K out,P 0.330 kin,Fen 0.842K 2 0.040 K in,A 0.461 k A,FRN 0.401K 3 5.000 K out,A 0.809 kFen, P 0.256K 4 2.240 K in,E 0.080 kout, F 1.058K in,mRNA, R 0.090 K out,E 0.280 kA,FRN 0.401K out,mRNA, R 0.250 K mRNA,P,R 1.740 kin,EPI 5.921kNFj B,1 16.290 kP,NF j Bn 29.75 k0REPI 6.594

K NFj B,2 1.180 kP,2 9.050 Rin, F (W Fex = 1 ) 2.922K in,IKBa 0.460 kA,E 0.534 Rin, F (W Fex = 0) 0K out,IkBa 0.4634 kA,cAMP 0.145 k2,REPI 2.213kIkBa,1 13.270 k1,REPI 2.657 T s 0.723

n s 1.185



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explore the broader concept of pro-inammatory mediator activa-tion. Therefore, the use of the IL-1 b data was used only for quanti-cation purposes. This is also valid for A and E . For eachbootstrap sample a vector of model parameters is estimated usinga least squares method. The mean of the multiple bootstrap esti-mates (2000 runs in our case) is reported as the most likely param-

eter value [62] ,^

b Pni1

b in , where i denotes bootstrap iteration.

Parameters associated with the prior model, which are consideredxed, are presented in Table 1 , while the estimated parameter val-ues associate with the dual-regulation model are depicted in Table2 . The performance of themodel in reproducing theself-limited re-sponses is shown in Fig. 2 .

The estimated condence intervals for each parameter are de-noted by

^

b la ;^

b ua , where subscript l and u respectively denotethe lower and the upper limits of the vector of model parameters band percentiles are estimated using the a central condence inter-

41val. The 100( a /2) and 100 (1 a /2) percentile values of the boot-41strap distribution are used as the upper and lower condence41limits for a parameter. The value of a (0 < a < 1) indicates a41100 a% condence that b 2 [b l(a ), bu(a )]. In this study, a is chosen41as 0.05, then 95% condence limits for b based on 2000 bootstrap41replications are given by b l 50th and b u 1950th largest esti-41mates of b [62] . The condence intervals for parameter are also41shown in Table 2 . Typical histograms of 2000 bootstraps are shown41in Fig. 3 . A dashed line drawn at theparameter estimate and dotted41lines drawn at the two condence limits are included with each42histogram. All histograms are roughly Gaussian in shape, suggest-42ing that the condence interval evaluation based on bootstrap per-42centile is reasonable. All the simulation and perditions in this study42are done by using Matlab.

424.2. Timing of the secondary stimulus

42It is believed that the timing of the secondary stimulus, i.e. LPS42administration, plays a vital role in affecting the outcome be it42either potentiation or tolerance [3] . The model allows us to explore42the alternative effects by varying the injection time of the second-42ary LPS stimulus. We assume that two equal, non-lethal doses are43administered the rst at time t = 0 and the second x times units la-43ter, i.e., LPS(0) = LPS( x) = 1. In order to evaluate the implication of 43the time delay between the two injections we evaluate the ratio43of P 2 to P c, where P 2 is the peak value of the pro-inammatory re-43sponse P following the second injection where P c is the corre-43sponding peak in the pro-inammatory response following a43single injection of LPS, namely:43

P ratio P 2P c

; P 2 f P 2;max ; LPS0 1; LPS x 1g;

P c f P c;max ; LPS0 0; LPS x 1g 4343

Table 2

Estimated value of parameters involved in the dual negative regulation of TLR4signaling.

Parameter Average Min Max 5% Quantile 95% Quantile

K IkBa, Akt 0.4030 0.0001 2.149 0.0001 1.22175K out,IRAK 3.1568 1.3031 6.4827 1.8426 4.2462K in,mRNA,IRAKM 0.9010 0.5248 1.6999 0.69529 1.1375K out,mRNA,IRAKM 0.7089

kmRNA,IRAKM,P 0.2709 0.0459 1.2129 0.1018 0.5261kmRNA,IRAKM,Akt 27.9706 10.2058 46.0046 22.4290 31.4328K in,IRAKM 1.1571 0.7179 1.8030 0.8311 1.4910K out,IRAKM 0.0499 0.0467 0.0559 0.0483 0.0515K in,PI3K 16.8220 9.2529 40.0392 12.787 21.3832K out,PI3K 0.6506 0.5361 1.4178 0.6233 0.6769s 0.6475 0.5096 1.0464 0.6181 0.6671

Fig. 2. Model building results: dynamic proles of the elements that constitute the mechanistic model of endotoxin-induced inammation. Experimentally [33] measurednormalized mRNA transcript levels are denoted by symbols ( ), solid lines () are the model predictions.



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0 The denitionsof P 2 and P c are graphically depicted in Fig. 4 (toppa-nel). The in silico experiments depicted in Fig. 4 (bottompanel) indi-cate that signicant potentiation of the inammatory response isobserved when the interval between the two successive injections

4 is within a critical time window. It should also be noted that ob-served potentiation is not a simple additive effect by two successiveinjection of LPS since levels of P 2 are much larger than the maxi-mum value of the peak of P following a single injection of LPS withdose equal to 2. The robustness of the inammatory response isdiminished as the interval x between the two successive injection

0 increases until a maximum tolerance, quantied as a relative sup-pression of the pro-inammatory response, occurs when the inter-val between the injections is reached. Fromthat point on, the extentof tolerance diminishes and eventually the effects of precondition-

4 ing slowly dissipate and the memory effects completely disappear(bottom panel of Fig. 4 ).

The predicted trends related to the effect of timing of the sec-ondary stimulation are qualitatively consistent with the result invant Veers studies [54] , in which the release of TNF- a per mono-cytes in whole blood was drastically diminished in the period 38 h after LPS injection. TNF- a measurement [54] is considered asa prototypical inammatory response, which corresponds to P inour model. Furthermore, it has been documented that the endo-toxin tolerance is preserved over long periods of time as in severalstudies of the induction of endotoxin tolerance in animals, normalresponsiveness resumes after 8 days of tolerance [2] .

4.3. Lethal potentiation

When the time between successive administrations is short, ourmodel predicts potentiation of the response consistent with

experimental evidence [4] . Part of the internal system dynamics,and the associated dysregulation of the responses, are depicted

in Fig. 5 . This phenomenon is feasible since the preconditioninghas already changed the state in which the system lies when thesecond stimulus is given. The main stimulus 0.5 h following pre-conditioning will further activate the NF-

jB which has already

been stimulated and cause it to be persistently active which leadsto the signicantly increased and lasting pro-inammatory andanti-inammatory responses. Thus, an extra abrupt stimulus mightdysregulate the dynamics of the host response to infection whichmay, in turn, have a lethal effect in the physiological state of thesystem.

4.4. Endotoxin tolerance

As the interval between the successive administrations is in-creased rather than a persistent production of proinammatorycytokines, a much less vigorous inammatory response is ob-served. Our model predicts this kind of response when the system

is pre-exposed to a non-lethal stimulus 24 h prior to the secondendotoxin injection and system dynamics are depicted in Fig. 6 .In Fig. 6 , a deduced activation of IRAK, NF- j B could be observedwhich will nally lead to the suppressed P , the pro-inammatoryresponse. Our results are in agreement with experiment observa-tions that some components in the signaling pathways are down-regulated such as IRAK [16] , NF- j B [63] . And studies of ET inducedin vivo [8] have shown a decrease in the production of several cyto-kines by macrophages including IL-1 b , TNF- a , and IL-6 which arebiomarkers of proinammatory response. It is worth noting thatthe concentration of IRAK-M induced by preconditioning is rela-tively high when the main stimulus is given at the 24th hour inFig. 6 . In our model, the presence of IRAK-M is the key in inductionof ET and to inhibit the signaling pathways required for the inam-

matory process. The stimulation of IRAK-M transcripts expressionwas reected at the protein level, and signicant quantities of this

Fig. 3. Histograms of 2000 bootstrap estimates of four parameters. The bars represent frequency. The average bootstrap estimator values of parameters^

b are indicated by adashed line and its lower and upper condence limits b l (0.05), b u (0.05) are represented by dotted lines respectively.



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kinase were detected 24 h after incubation with LPS [51] . Thebuild-up of the IRAK-Mat 24 h, induced by preconditioning, results

in a reductionof the inammatory response through strong inhibi-tion of IRAK activation.

However, recent experiments reveal that not all kinases in theTLR4 signaling pathway will be suppressed when the endotoxintolerance occurs. When pretreated cells were again stimulatedwith LPS 24 after rst stimulus, the levels of IRAK-M mRNA andproteins were twofold greater than the maximal levels producedby the rst induction [51] . This observation indicates that endo-toxin tolerance is no longer to be considered as a global downreg-ulation of the immune response as before [16] . An increasedproduction of IRAK-M is predicted by our model in Fig. 6 . Theaugmentation of IRAK-M is due to the signicantly decreased inhi-bition of mRNA IRAKM by P . Therefore, the most important featureof current model is that it offers the opportunity to explore the

leukocyte reprogramming which referrers to the alterations insignaling pathways and chromatin remodeling with the induction

52of LPS tolerance [64] . This hypothesis implies that the endotoxin52tolerance is not simultaneous suppression of all the immune re-

52sponse in the immune cells but an expression of a simultaneous52upregulation of some components and downregulation of other52components in the pathway. In other words, ET may not be52generated from global kinases activity suppression in signaling52pathways which nally leads to reduced production of proinam-52matory cytokines. The variety of responses to LPS after precondi-52tioning implies extremely sophisticated mechanisms to support52the proper magnitude of the immune response and to protect the53host from its harmful edge in multiple levels and various phases53[32] .

534.5. Protective tolerance

53The extreme case of endotoxin tolerance as initially described

53was that animals survived a lethal dose challenge if they had been 53previously treated with a sublethal stimulus [4] . The pre-exposure

Fig. 4. The effect of the timing of the secondary pro-inammatory stimulus on the tolerance. The doses for two injections are equal and nonlethal to the subjects with theinitial condition LPS(0) = LPS( x) = 1 where x, the time point at which the secondary stimulus is introduced, varies from 0 h to 192 h. The outcome is monitored by the ratio of P 2 to P c, where P 2 is the peak value of the P of the second response. P c, the control, is the P , proinammatory response under only one stimulus with the initial conditionLPS(0)= 0, LPS( x) = 1 . P 2 and P c are intuitively depicted in top panel as well as the result in bottom panel.



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to a lower nonlethal dose of LPS could modulate its intracellulardynamics by reversing the lethal outcome of the main much higherone which is responsible for an overwhelming inammatory re-sponse in Fig. 7 . The physiological signicance of LPS tolerancecan be best demonstrated through the protection by a nonlethal

LPS against the lethal outcomes of a secondary high-dose LPS inanimals [65] . In this experiment it was shown that wild type miceprimed with a sublethal dose of LPS and then challenged with alethal dose of LPS remained healthy. It is important to note thatsuch a rescue is possible because the preconditioning has already

Fig. 5. Lethal potentiation: successive administration of small doses of endotoxin can lead to an unresolved inammatory response. Solid line: LPS ( t = 0 h)= 1 and LPS(t = 0.5 h) = 1. Dashed line: LPS ( t = 0 h)= 0 and LPS ( t =0.5 h) = 1.

Fig. 6. Tolerance: pre-exposure the system with a smaller inammatory insult results in a reduction in the cell capacity to produce pro-inammatory cytokines which ischaracterized as an attenuation scenario. Solid line: LPS ( t = 0)= 1 and LPS ( t = 24) = 1. Dashed line: LPS ( t = 0 h)= 0 and LPS ( t = 2 4 h ) = 1 .



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changed the state in which the system lies when the lethal dose isencountered. Specically, the active IRAK-M rises enough to inhibitthe activation of IRAK so that when the previously lethal endotoxinstimulus is given, the system will be driven back to the healthystate, rather than that of the unhealthy state. We conclude thatby preconditioning the system with a low dose of LPS, one can re-duce the response obtained with a larger dose of LPS.

Interestingly, the induction of LPS tolerance during clinical con-ditions may in the short term be benecial by preventing excessiveinammation, but in the longer term be deleterious by hamperingan adequate defense response to opportunistic infections [53] . Thismay be demonstrated by the recent clinical observation that thesevere immunosppressionQ2 demonstrated by signicant endotoxintolerance in sepsis patients have high correlation with mortality[55] . The signicant decrease of IRAK and elevation IRAK-M mRNAexpression in mononuclear cells are the notable characters of thesesevere sepsis patients. Thus, endotoxin tolerance is just like adouble-edged sword. The transient induction of IRAK-M in healthy

56animals after preconditioning will protect the host from overacti-56vation of another wave of proinammation following the second-56ary exposure to LPS. However, the long lasting high level IRAK-M56expression in sepsis patient is an indicator of poor outcome and56mortality [55] .

564.6. The effect of IRAK-M on Tolerance

57As discussed in previous section, the suppression of IRAK by57IRAK-M may play a role in the endotoxin tolerance. However,57whether IRAK-M is the factor which actually induces ET is still57not claried. Thus, we are interested in exploring the effect of 57IRAK-M by knocking out this gene to check if it is required for tol-57erance. Our model allows us to test the effect of the knockout of 57IRAK-M gene on LPS tolerance in the system which is pre-exposed57to a stimulus forabout 24 h before themain endotoxin challenge. It57is not surprising to nd that the disruption of the gene encoding57the negative regulator IRAK-M for the signaling pathway results

Fig. 7. Protective tolerance: pre-existing infection might cause a profound hypo-responsiveness in systems response to a lethal LPS challenge. Solid line: LPS ( t = 0 h ) = 1 a n dLPS (t = 24 h) = 4. Dashed line: LPS ( t = 0 h)= 0 and LPS ( t = 2 4 h ) = 4 .

Fig. 8. The lack of tolerance in in silico experiment with IRAK-M knockout animal . Knocking out of mRNA leads to the lack of endotoxin tolerance. Left plot: solid line: LPS

(t = 0)= 1 and LPS ( t = 24) =1, IRAK-M knockout animal; Dashed line: LPS ( t = 0)= 1 and LPS ( t = 24) = 1, wild animal. Right plot: solid line: LPS ( t = 0)= 1 and LPS ( t =24) = 4,IRAK-M knockout animal. Dashed line: LPS ( t = 0)= 1 and LPS ( t = 24) = 4, wild animal.



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in the lack of the endotoxin tolerance as seen in left plot in Fig. 8 .This result is consistent with Kobayashis other experiment in thesame publication [21] . It is reported IRAK-M / macrophagesshowed a loss of endotoxin tolerance demonstrated by the cyto-kine levels produced upon LPS restimulation. Moreover, comparedwith the scenario in Fig. 7 , under the same condition, it is furtherexpected that the preconditioning of smaller dose lost protectiveeffect for a subsequent lethal dose injection when

IRAK-M gene is

knocked out as seen in the right plot in Fig. 8 . The model predictedthat the inhibition of stimulation of IRAK and the subsequent geneexpression is lost due to disappearance of IRAK-M. Therefore, wecan conclude that IRAK-M may be a key component of this impor-tant control system since the development of tolerance upon re-peated stimulation with LPS is dampened without IRAK-M.

4.7. Increased cytokine production through IRAK-M gene knock-out or administration of a PI3K inhibitor

Both IRAK-M and PI3K are negative regulators of TLR4 signalingpathway, so, it is expected that an enhanced proinammatory re-sponse will be observed in the absence of these regulators. As illus-

trated in the upper plots in Fig. 9 , we perform both an IRAK-M knock-out experiment and an administration of a PI3K inhibitorexperiment respectively. The model is manipulated so that thereis no de novo transcriptional synthesis of IRAK-M which is respon-sible for negative regulation of IRAK. After the disruption of IRAK-M gene, no expression of mRNA IRAKM and protein IRAK-Mis observed.The knockout causes an increased expression for P, pro-inamma-tion which is in agreement with the Kobayashis report that IRAK-M/ macrophages revealed increased production of TNF a , IL-6and IL-12 when compared to wild-type macrophages at 6 hr afterstimulation [21] . Similarly, in the lower plots in Fig. 9 , administra-tion of Wortmannin, the PI3K inhibitor, shows enhanced TLR4 sig-naling and enhanced production of TNF- a [31] . The neutralizationof active PI3K is mimicked by increasing the degradation rate of

PI3K by ve times. The increased production of the prototypicalinammatory response P in our current model is reected in theenhanced production of TNF- a [31] after in silico administrationof Wortmannin. Thus, both IRAK-M and PI3K negatively regulateTLR4 signaling pathway though theyfunction in different timeper-iod. The PI3K will be activated immediately in response to stimulusand lose its activity within 9 h which only inhibits the activation of NF-

jB transiently. However, the IRAK-M will be stimulated a little

bit latter but last for much longer time period. It appears that thedifferent time periods directly decide their individual functionsin controlling the TLR4 signaling pathway which will be addressedin detail in the discussion of crosstalk between these twoproteins.

4.8. The crosstalk between PI3K and IRAKM

Its interesting to nd a relationship between two negative reg-ulators, the induction of IRAK-M is induced by the other kinasePI3K. Thus, we expect there will be protein level change of IRAK-M by pretreatment of the cells with specic inhibitor of PI3K. Weexamine the inuence of administrating Wortmannin against

PI3K to the response by increasing the degradation rate of PI3K,kout,PI3K by 10 times which mimics the neutralization of activePI3K by its inhibitor. We discussed the role PI3K played by usingpre-administration of its inhibitor Wortmannin. The roles it playsin both single LPS stimulation as well as preconditioningare shownin Fig. 10 . As seen in Fig. 10 , 024 h shows the pre administrationof Wortmannin leads to the abolished expression of IRAK-M aswell as enhanced production of pro-inammatory cytokinesfollowing single LPS stimulus. The result is in agreement withrecent observation that LPS-derived immune cells pretreated withthe PI3K inhibitor expressed signicantly abolished expression of IRAK-M [7] . The 2448 h responses show the effect of second LPSstimuli, we could see that the signicantly decreased productionof IRAK-M following the rst stimulus fails to inhibit the activation

Fig. 9. The increased proinammatory response in in silico experiment with IRAK-M knockout animal or pretreatment with PI3K inhibitor. Upper plots: solid line: LPS

(t = 0 h) = 1.5 with an IRAKM / animal; dashed line: LPS ( t = 0 h) = 1.5 with wild type animal. Lower plots: Solid line: LPS ( t = 0 h) = 1.5 pretreated with PI3K inhibitor;dashed line: LPS ( t = 0 h) = 1.5, pretreated with saline.



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of IRAK and NFkB following the second LPS insult. This nally leadsto the strongly enhanced productionof pro-inammatory responsecompared to the control. Thus, inhibiting the activation of the PI3Kwith enough inhibitor will also lead to the loss of tolerance. This issupported by the observation that ablation of Akt which blocks theactivation of IRAK-M by PI3K/Akt pathway inhibits the induction of endotoxin tolerance [8] .

Model behavior implies that the presence of dual regulationmechanisms leads to dual pattern of negative feedback, wherePI3K/Akt is an early negativeswitch that attenuates the initial sig-nal propagation, whereas IRAK-M represents the memory compo-nent of the system responsible for the tolerance behavior.However, the question arises as to if IRAK-M alone can accomplishthe general response of induction of ET, or what additional roledoes the PI3K/Akt pathway have? Actually, there is a crosstalk be-tween the two negative regulators; the induction of IRAK-M is dueto activation of PI3K/Akt signaling pathway which implies thatPI3K may function as a transient alarming signal to the systemwhichwill further activate and intensify the magnitude of negativeregulation of TLR4 by activating other proteins in a long lastingtime interval for a sustained suppression. It is implied that IRAK-M is a direct regulator for induction of ET, while PI3K/Akt playthe role behind the curtain. Thus, ablation of Akt which blocksthe activation of IRAK-M by PI3K/Akt pathway inhibits the induc-tion of endotoxin tolerance [66] .

5. Uncited references

[41,58,59] .Q3

Acknowledgements

Q.Y. and I.P.A. acknowledge support from NIHGM082974. S.E.C.

and S.F.L. are supported, in part, from NIGMS Grant GM34695. Thedata used are part of the Inammation and the Host Response to

67Injury Glue Grant program which is supported by the National67Institute of General Medical Sciences.

67References

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27 May 2011
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