In Silico Analysis of Interactions Between NFkB and HSF Pathways

Jaroslaw Smieja

, Malgorzata Kardynska

, Anna Naumowicz

, Patryk Janus

1,2

Piotr Widlak

and Marek Kimmel

1,3

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Maria Sklodowska-Curie Memorial Cancer Center and Institute of Oncology, Gliwice 44–100, Poland

Department of Statistics, Rice University, Houston, TX 77005, U.S.A.

Keywords: Signalling Pathways, NFkB, HSF, HSP, Heat Shock.

Abstract: Motivation: Inhibition of NFkB pathway is known to promote apoptosis and therefore may constitute one of

the goals in anticancer therapies. Experimental results show that heat shock induces such inhibition in

cancer cells. However, the mechanisms of interactions between heat shock and NFkB pathways are not fully

understood yet. Development of a combined mathematical model of these pathways and its subsequent

computational analysis should help to uncover these mechanisms and determine the time window in which

heat shock treatment preceding chemotherapy would be the most efficient.

Results: An original mathematical model has been developed, allowing for computational testing of various

hypotheses concerning main sources of interplay between HSF and NFkB pathways. Computational

analysis strongly suggests that the competition for IKK, known from literature, cannot be the only

mechanism. Two plausible hypotheses are that either a kinase activating IKK can misfold due to heat shock

or that heat shock affects TNF receptors, blocking activation of NFkB pathway at the cell membrane.

1 INTRODUCTION

NFkB transcription factor regulates expression of

various genes, including those important for cell

survival. Therefore it has been the subject of

research for many years now, and its role in

promoting or blocking apoptotic pathways has been

investigated as one of the key molecular players

determining fate of cancer cells after radio- or

chemotherapy. In particular, various ways of

inhibition of NFkB pathway have been the focus of

attention in many cancer studies (e.g. Yamamoto

and Gaynor, 2001, Amman et al., 2009, Domingo-

Domènech et al., 2008, Zanotto-Filho et al., 2011).

On the other hand, hyperthermia was suggested

to have a potential of improving the efficacy of

chemo- or radiotherapy by many authors (e.g.

Neznanov et al., 2011) and be a promising treatment

in itself (Lee Titsworth et al., 2014). Bringing cells

under a heat stress initiates many biochemical

processes, including, among others, an apparent

inhibition of the NFkB pathway (Janus et al., 2011).

While the precise mechanism of this inhibition is not

clear, it has been observed that this inhibition

remains in place for some time after the source of

heat shock have been removed. Moreover, it is

known that HSF1 is the primary transcription factor

activated under stress conditions that is responsible

for induction of genes encoding heat shock proteins

(Fujimoto and Nakai, 2010, Morimoto 2011,

Westerheide et al., 2012), hence the HSF1 pathway

is a natural candidate for investigation. Uncovering

the mechanisms behind this inhibition should yield

two direct benefits: (i) finding the best (in terms of

maximum reduction of cancer cell population) time

lag between short thermal shock and subsequent

irradiation or chemotherapeutic agent delivery, (ii)

expanding knowledge about other possible

molecular interactions that could be utilized to

increase treatment efficacy even further.

Of the two components that are combined in this

work, the NFkB pathway has been studied much

more extensively and many models have been

developed so far. It appears that one of the most

often cited models is the one published in (Lipniacki

et al., 2004), whose structure was later modified to

some extent in later works (e.g., Wang et al., 2011,

Wang et al., 2012, Zambrano et al., 2014). Much

less attention was devoted to the HSF pathway,

though one can find several papers dealing with

201

Smieja J., Kardynska M., Naumowicz A., Janus P., Widlak P. and Kimmel M..

In Silico Analysis of Interactions Between NFkB and HSF Pathways.

DOI: 10.5220/0005256602010206

In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2015), pages 201-206

ISBN: 978-989-758-070-3

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

mathematical modeling of the intracellular processes

that are initiated by heat shock (Rieger et al., 2005,

Szymanska and Zylicz, 2009, Petre et al., 2011,

Rybinski et al., 2013). To our knowledge, there has

been no published attempt to combine models of

both pathways into a single one, which could bring

some important conclusions about possible

inhibition of NFkB pathway by heat shock, and its

implications for clinical applications. While recently

some work has been done on analysis of NFkB

pathway dynamics under heat shock conditions, it

was done only through manipulating the parameters

of NFkB model (Sheppard et al., 2014). While such

approach might be welcome as it does not

necessitate increasing the complexity of the model,

it is not useful if the question posed concerns the

nature of interactions between the pathways, their

dynamics and possible crosstalk with other

pathways. In this work, we aim at building a model

that might help answering these questions.

2 METHODS

The model presented in this work is clearly

deterministic. While it has been proven that

stochasticity plays a crucial role in intracellular

processes described by signaling pathways models,

deterministic approach is much more convenient

when the initial model is developed. Stochastic

modeling should inevitably follow, in particular

when the analysis would be focused on determining

the ultimate fate of cells. That, however, is beyond

the scope of this paper.

Taking into account that the separate models of

each of the two pathways under consideration have

already been published, we decided to arbitrarily

chose their representatives and introduce the

necessary modifications concerning both the

proposed crosstalk mechanisms and parameter

values that would compensate the crosstalk in

control (i.e. not excited) cells. Additionally, the HSF

pathway has been further modified, to take into

account both assumptions needed to apply the law of

mass action that is behind the most part of the

deterministic modeling and the implications of

experimental results that are available.

The detailed description of canonical NFkB and

HSF pathways can be found in many papers,

including those cited in the Introduction section.

Here they will be only briefly summarized in the

following two paragraphs.

In unstimulated cells, NFkB forms a cytoplasmic

complex with its inhibitor IκB proteins. The

pathway can be activated, among others, by Tumor

Necrosis Factor (TNF) stimulation. Then, the kinase

IKK is activated and it subsequently phosphorylates

the inhibitors, targeting them for degradation. Freed

NFkB is imported into the nucleus, where it serves

as a transcription factor for many genes. These genes

include, among others, the genes coding IκB

inhibitors. Thus a negative feedback is formed.

Another feedback loop involves the A20 protein,

whose gene is also activated in the pathway.

In the heat shock activated pathway, in turn, the

main players are HSP and HSF proteins. Under

normal conditions, they mostly reside in complexes

with each other. Following heat shock, some of the

proteins in a cell denature and become misfolded.

These denaturated proteins cause HSP|HSF complex

to dissociate, following HSP binding to the

misfolded proteins. Free HSF molecules undergo

phosphorylation and subsequently form trimers,

which are transported into nucleus. Once there, the

trimers serve as transcription factors of heat-shock

inducible genes, including the family of HSP

proteins. Newly produced HSP proteins can bind

HSF, thus creating a negative feedback loop.

In all simulations aimed at checking the possible

inhibition of the NFkB pathway, the excitation

protocol comprised of a short, 30 minute heat shock

of 42 degrees, followed by TNF stimulation. The

time lag between the end of heat shock and

beginning of TNF treatment was varied, to check

when the NFkB pathway regains its functionality.

Cytoplasmic IKK and nuclear NFkB proteins were

chosen to represent the pathway response. In order

to check if the pathway was inhibited, the results

were compared to the ones obtained when only TNF

was used (see Figure 1).

It was assumed that the model should satisfy the

following assumptions, indicated by experimental

data (Ciocca and Calderwood 2005; Daugaard et al.,

2007, Morimoto, 2011, Janus et al., 2011 and our

own, unpublished results):

 there are two types of HSP: constitutive, present

at high levels all the time, and inducible; though

they are represented by separate variables in the

model, they perform the same actions; therefore

the model should be applicable both in the case

when they are the same and when they are

different species of HSP.

 Most of the constitutive HSP is located in the

cytoplasm in a normal physiological state.

 Following the beginning of a heat shock, most of

the HSP is transported to the nucleus so that in

less than 1 hour most of it appears in the nucleus.

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202

 3 to 4 hours after the heat shock begun, inducible

HSP is observed in cytoplasm.

 Of all possible complexes formed by HSF1 taken

into account in the model, only the trimer can

shuttle between nucleus and cytoplasm.

 If the TNF is given earlier than 6 hours after heat

shock has ended, a partial inhibition of the NFkB

pathway is observed. If this time lag is greater

than 6 hours, inhibition does not take place.

Figure 1: The reference plots for not inhibited NFkB

pathway.

3 THE MATHEMATICAL MODEL

One of the most frequently mentioned mechanisms

of possible crosstalk between the two pathways

under consideration is the competition for IKK

proteins through creation of IKK|HSP complexes

(e.g. Ran et al., 2004). Therefore, this process has

been incorporated into our model and it involves

both constitutive and inducible HSPs (Figure 2a).

Another possible mechanism might involve a kinase

responsible for IKK activation. Heat shock causes,

among others, misfolding of some proteins. If that

kinase was misfolded (Figure 2b), it would be

unable to activate IKK (however, this could be

repaired by the constitutive HSP). Yet another

possibility is the effect of heat shock on the TNF

receptor. Receptor-dependent sensitivity of NF-κB

pathway has already been reported in another

context (Yang and Zhou, 2013). If TNF receptors

are inactivated by heat shock, then obviously the

NFkB pathway would be inhibited. In that case, one

could always choose model parameters to adjust the

time of inactivation and since the results of such

simulation are obvious, they are not presented in the

paper.

As indicated in the preceding section, the model

proposed in this work is built on the previously

published ones, which described either NFkB or

HSF1 pathways separately. Of these, the NFkB

model comes from (Lipniacki et al., 2004) and was

changed only in the parts that are responsible for the

crosstalk between the pathways, shown in the Figure

2 and summarized in the Table 1.

Figure 2: Possible crosstalk mechanisms between HSF and

NFkB pathways: (a) creation of IKK|HSP complexes, (b)

misfolding of kinase activating IKK.

The existing HSF1 pathway model (Szymanska

and Zylicz, 2009) had to be modified to a much

greater extent and these changes are summarized

below:

 First, both this and other models (e.g. Rieger et

al., 2005, Petri et al., 2011) treat the cell as a

single compartment. Here, in order to satisfy the

assumptions presented in the preceding section,

it was necessary to distinguish cytoplasmic and

nuclear levels of proteins and complexes.

 Constitutive and inducible HSPs are described by

separate variables.

 The complexes of the HSF1 trimer and its

corresponding Heat Shock Element (HSE) in the

promoter region of the HSP gene are not

modeled explicitly. It seems that here law of

mass action is not applicable due to a small

number of HSEs and to take into account these

complexes properly one should use a stochastic

approach. Instead, transcription rate of the HSP

gene is assumed to be proportional to the nuclear

level of the trimer.

 The function describing temperature-dependent

protein degradation rate has been modified from

its original version (Peper et al., 1997) which

was subsequently used in (Rybinski et al., 2013)

to be zero for the temperature of 37 degrees.

 In addition to forming complexes with HSF1 and

misfolded proteins, HSP can also form

complexes with IKK.

While the introduction of nuclear and

cytoplasmic compartments, as well as constitutive

and inducible forms of HSP have not changed the

main reasoning behind the previously published

HSF pathway models, the number of changes might

be confusing without a proper presentation.

Therefore, the list of reactions in the model is

presented in the Table 1.

InSilicoAnalysisofInteractionsBetweenNFkBandHSFPathways

203

Table 1: Reaction list for the HSF pathway.

Reactions both in cytoplasm and nucleus:

Prot → mfProt

mfProt + HSP

cons

→ HSP

cons

:mfProt

mfProt + HSP

ind

→ HSP

ind

:Prot

HSP

cons

:mfProt → HSP

cons

+ Prot

HSP

ind

:Prot → HSP

ind

+ Prot

HSP

cons

+ HSF → HSP

cons

:HSF

HSP

ind

+ HSF ↔ HSP

ind

:HSF

HSP

cons

:HSF + mfProt → HSP

cons

:mfProt + HSF

HSP

ind

:HSF + mfProt → HSP

ind

:mfProt + HSF

3HSF → HSF

HSF3 + HSP

ind

→ HSP

ind

:HSF + 2 HSF

HSP

ind

→

mRNA →

Reactions taking place only in the nucleus:

HSF

→ HSF

+ mRNA

Reactions taking place only in cytoplasm:

mRNA → mRNA + HSPF

ind

HSF

cons

+ IKKa → HSP

cons

:IKK

HSF

ind

+ IKKa → HSP

ind

:IKK

HSP

cons

:IKK → HSP

cons

+ IKKn

HSP

:IKK → HSP

+ IKKn

Transport:

HSP

cons,cyt

↔ HSP

cons,nuc

HSP

ind,cyt

↔ HSP

ind,nuc

HSF

3 c

↔ HSF

3 nuc

Additional reactions in the model B

IKKn

,







IKKa



→ mfX

mfX + HSP

kons

→ HSP

kons

:mfX

mfX + HSP

ind

→ HSP

ind

:mfX

HSP

kons

:mfX → HSP

kons

+ X

HSP

:mfX → HSP

+ X

In all, three models have been tested. The first

one took into account IKK|HSP formation as the

only mechanism behind the inhibition of NFkB

pathway. Since it has yield no positive results, its

simulations are not included in the subsequent

section. The second model (Model A) additionally

incorporated nuclear import of HSP proteins as a

temperature-dependent process to reflect nuclear

accumulation of constitutive HSP following the heat

shock. In the third model (Model B), concentration

of a kinase activating IKK is explicitly modeled,

with the kinase being prone to misfolding in a

temperature-dependent manner.

4 RESULTS AND DISCUSSION

Due to abundance of constitutive HSP, despite

formation of HSP|IKK complexes the NFkB

pathway does not affect dynamics of the HSF1

pathway. Therefore, only exemplary results,

showing the main molecules in the HSF1 pathway

are shown in Figure 3. The remaining plots

concentrate on possible inhibition of the NFkB

pathway.

Figure 3: HSF and HSP levels following 30-minute heat

shock.

The initial assumption that the IKK|HSP

complexes formation alone might be responsible for

the NFkB pathway inhibition have failed. Although

one might choose the kinetic parameters to

completely block all IKK in the complexes, this

would subsequently result in a prolonged inhibition,

not observed experimentally. Therefore, in addition

to this process, other mechanisms had to be

proposed.

First, the temperature-dpendent mechanism of

nuclear import had to be introduced. Without it, one

could not capture nuclear accumulation of

constitutive HSP, when in a normal state most of it

should be located in cytoplasm. Since the precise

mechanism behind this transport is not known,

instead of introducing new, unknown molecules that

might mediate this ttansport, we decided to describe

it in the simplest way, introducing the temperature-

dependent transport ration into the equations:









∙







∙



∙

∙

,∙

(1)









∙



∙







∙



∙

∙



∙

,∙

(2)

where k

imp

and k

exp

are nuclear import and nuclear

export rates in normal conditions, k

is the ratio of

nuclear and cytoplasmic volumes. Both constitutive

and inducible HSP is assumed to follow that kind of

transport, though the normal rates might differ

between them.

Other than in the model developed by

Szymanska and Zylicz (2009) we wanted to

distinguish between two different outcomes of HSP

acting on the misfolded proteins: through creation of

complexes with them, HSP can either repair them or

target for degradation. Therefore we have created a

pool of generic proteins, both in the nucleus and in

cytoplasm, that are negatively affected by the

temperature and transformed into misfolded

proteins:

BIOINFORMATICS2015-InternationalConferenceonBioinformaticsModels,MethodsandAlgorithms

204









∙



∙







∙



∙

(3)

∙







:



∙



∙



:









∙



∙











∙

(4)

∙









∙



∙









∙

where α represents the efficacy of the repair process

and 



is a function dependent on the temperature

as in (Petre et al., 2011):





1

0,4





∙1,4



∙1,45∙

(5)

∙10



8,7∙10









with the last term introduced by us to have





0

(6)

Figure 4 illustrates partial inhibition of the NFkB

pathway in the Model A (Figure 4a) which ceases to

exist if the period between the end of heat shock and

NFkB activation with TNF is too long (Figure 4b).

Despite these promising results, if the TNF

stimulation follows directly heat shock, no such

inhibition is observed (Figure 5a). This is a direct

result of the changes introduced to obtain nuclear

accumulation of constitutive HSP following heat

shock. Since HSP proteins, following their release

from the complexes with HSF1 are transported to

nucleus, too little of them remain in cytoplasm to

effectively bind IKK. Only after inducible form of

HSP is produced as a result of HSF1 pathway, these

newly translated proteins are in place to block NFkB

pathway through IKK inhibition.

As a result, the inhibition of the NFkB pathway

stimulated shortly after the heat shock must be

mediated otherwise than through IKK|HSP

complexes formation. It seems that the inhibition

should be located upstream of IKK activation. One

of the possible explanations is temperature-

dependent misfolding of a kinase activating IKK,

which renders it incapable of such activation. This

assumption is behind the modification introduced in

the model B. Then, inhibition of the NFkB pathway

is visible also in the case when TNF stimulations

follows directly the heat shock (Figure 5b). It is

worth noticing that the frequency of oscillations,

regarded as a specific feature of the NFkB pathway,

remains unchanged even when models of both

pathways are coupled.

a) b)

Figure 4: NFkB pathway responses for two different time

lags between heat shock and TNF stimulation.

a) b)

Figure 5: NFkB pathway response for (a) Model A and (b)

Model B.

5 CONCLUSIONS

This paper presents results of a computational

analysis of a combined HSF1-NFkB pathway. The

model that has been developed captures the

phenomenon of NFkB pathway inhibition through a

heat shock that can last several hours after the heat

shock has ended. The mechanisms behind this

inhibition that have been proposed, i.e. (a) IKK|HSP

complexes creation; (b) temperature-dependent

nuclear import of HSP proteins; (c) temperature-

dependent activation of IKK proteins do not involve

purely theoretical new proteins and it seems that

they are biologically viable. Nevertheless, another

possible explanation could be that the inhibition

takes place at the cell membrane and involves

inactivation of the TNF receptor - a hypothesis that

is currently the subject of experimental

investigation.

InSilicoAnalysisofInteractionsBetweenNFkBandHSFPathways

205

ACKNOWLEDGEMENTS

This work was supported by grants DEC-

2012/05/B/NZ2/01618 (JS, AN, PJ, PW, MKimmel)

and BKM/524/RAU1/2014/t.5 (MKardynska).

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