Formal modeling of the key determinants of Hepatitis C Virus … · 2018-01-23 · Formal modeling...

Formal modeling of the key determinants of Hepatitis C Virus

(HCV) induced adaptive immune response network: An

integrative approach to map the cellular and cytokine-

mediated host immune regulations

Ayesha Obaid 1 , Anam Naz 1 , Shifa Tariq Ashraf 1 , Faryal Mehwish Awan 1 , Aqsa Ikram 1 , Muhammad Tariq

Saeed 2 , Abida Raza 3 , Jamil Ahmad 2 , Amjad Ali Corresp. 1

1 Atta-ur-Rahman School of Applied Bio-science(ASAB), National University of Sciences and Technology (NUST), Islamabad, Pakistan

2 Research Center for Modeling and Simulation (RCMS), National University of Science and Technology, Islamabad, Pakistan

3 National Institute of Lasers and Optronics (NILOP), Islamabad, Pakistan

Corresponding Author: Amjad Ali

Email address: [email protected]

Background. Hepatitis C Virus (HCV) is a major causative agent of liver infection leading to critical liver

damage. In response to HCV, the improper regulation of host immune system leads to chronic infection.

The host immune system employs multiple cell types, diverse variety of cytokine mediators and

interacting signaling networks to neutralize the HCV infection. To understand the complexity of the

interactions within the immune signaling networks, systems biology provides an efficient alternative

approach. Integrating such approaches with immunology and virology helps to study highly complex

immune regulatory networks within the host and presents a concise view of the whole system.

Methods. Initially, a logic-based diagram is generated based on multiple reported interactions between

immune cells and cytokines during host immune response to HCV. Furthermore, an abstracted sub-

network is modeled qualitatively which consists of both the key cellular and cytokine components of the

HCV induced immune system. Rene’ Thomas formalism is applied in the study to generate a qualitative

model which requires only the qualitative thresholds and associated logical parameters generated via

SMBioNet software in accordance with biological observations. Furthermore, the continuous dynamics of

the model have been studied via Petri nets based analysis.

Results. In the presence of NS5A protein of HCV, the behaviors of the Natural Killer (NK) and T

regulatory (Tregs) cells along with cytokines such as IFN-γ, IL-10, IL-12 are predicted. The model also

attempts to consider the viral strategies to circumvent immune response mediated by viral proteins. The

state graph analysis enabled the prediction of paths leading to disease state. The most probable cycle is

predicted based on maximum betweenness centrality. Furthermore, to study the continuous dynamics of

the modeled network, a Petri net (PN) model was generated. The predictive ability of the model

implicates the critical role of IL-12 over-expression in pathogenesis. This observation speculates that IL-

12 has a dual role under varying circumstances and leads to varying disease outcomes.

Conclusion. This model attempts to reduce the noisy biological data and captures a holistic view of the

regulations amongst the key determinants of HCV induced adaptive immune responses. The observations

warrant for further studies to elucidate the role of IL-12 under varying external and internal stimuli. Also,

introducing diversion by therapeutic perturbation may divert the system from diseased paths to recovery

by stabilizing the activation of IFN-γ producing NK cells. The modeling approach employed in this study

can be extended to include real-time experimental data to propose new therapeutic interventions.

PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018

1 Formal modeling of the key determinants of Hepatitis C Virus

2 (HCV) induced adaptive immune response network: An integrative

3 approach to map the cellular and cytokine-mediated host immune

4 regulations

5

6 Ayesha Obaid1, Anam Naz1, Shifa Tariq Ashraf 1, Faryal Mehwish Awan1, Aqsa Ikram1,

7 Muhammad Tariq Saeed2, Abida Raza3, Jamil Ahmad2, Amjad Ali1*

8

9 1Atta-ur-Rahman School of Applied Biosciences (ASAB), National University of Sciences and Technology

10 (NUST), Islamabad, 44,000 Pakistan

11 2Research Center for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST),

12 Islamabad, Pakistan

13 3National Institute of Lasers and Optronics (NILOP), Islamabad, Pakistan

14

15 Email Addresses:

16 Ayesha Obaid: [email protected]

17 Anam Naz: [email protected]

18 Shifa Tariq Ashraf: [email protected]

19 Aqsa Ikram: [email protected]

20 Faryal Mehwish Awan: [email protected]

21 Muhammad Tariq Saeed: [email protected]

22 Abida Raza: [email protected]

23 Jamil Ahmad: [email protected]

24 * Correspondence:

25 * Corresponding author

26 Amjad Ali

27 E-mail: [email protected], [email protected],

28

29 Abstract


mailto:[email protected]









30 Background. Hepatitis C Virus (HCV) is a major causative agent of liver infection leading to

31 critical liver damage. In response to HCV, the improper regulation of host immune system leads

32 to chronic infection. The host immune system employs multiple cell types, diverse variety of

33 cytokine mediators and interacting signaling networks to neutralize the HCV infection. To

34 understand the complexity of the interactions within the immune signaling networks, systems

35 biology provides an efficient alternative approach. Integrating such approaches with

36 immunology and virology helps to study highly complex immune regulatory networks within the

37 host and presents a concise view of the whole system.

38

39 Methods. Initially, a logic-based diagram is generated based on multiple reported interactions

40 between immune cells and cytokines during host immune response to HCV. Furthermore, an

41 abstracted sub-network is modeled qualitatively which consists of both the key cellular and

42 cytokine components of the HCV induced immune system. Rene’ Thomas formalism is applied

43 in the study to generate a qualitative model which requires only the qualitative thresholds and

44 associated logical parameters generated via SMBioNet software in accordance with biological

45 observations. Furthermore, the continuous dynamics of the model have been studied via Petri

46 nets based analysis.

47 Results. In the presence of NS5A protein of HCV, the behaviors of the Natural Killer (NK) and

48 T regulatory (Tregs) cells along with cytokines such as IFN-γ, IL-10, IL-12 are predicted. The

49 model also attempts to consider the viral strategies to circumvent immune response mediated by

50 viral proteins. The state graph analysis enabled the prediction of paths leading to disease state.

51 The most probable cycle is predicted based on maximum betweenness centrality. Furthermore, to

52 study the continuous dynamics of the modeled network, a Petri net (PN) model was generated.

53 The predictive ability of the model implicates the critical role of IL-12 over-expression in

54 pathogenesis. This observation speculates that IL-12 has a dual role under varying circumstances

55 and leads to varying disease outcomes.

56


57 Conclusion. This model attempts to reduce the noisy biological data and captures a holistic view

58 of the regulations amongst the key determinants of HCV induced adaptive immune responses.

59 The observations warrant for further studies to elucidate the role of IL-12 under varying external

60 and internal stimuli. Also, introducing diversion by therapeutic perturbation may divert the

61 system from diseased paths to recovery by stabilizing the activation of IFN-γ producing NK

62 cells. The modeling approach employed in this study can be extended to include real-time

63 experimental data to propose new therapeutic interventions.

64 Keywords:

65 Hepatitis C Virus, computational biology, HCV modeling, Systems biology, HCV immune

66 response

67 1 Introduction

68 Hepatitis C Virus (HCV) is the major cause of hepatitis C disease that is characterized by

69 inflamed liver leading to fibrosis, cirrhosis and hepatocellular carcinoma (HCC)(Choo et al.

70 1989; Lindenbach & Rice 2005). Approximately 0.17 billion people are infected with HCV

71 around the globe, and it is believed that amongst them 20%–30% recover naturally, and others

72 mostly develop chronic infection often leading to HCC (Gower et al. 2014). Moreover, 0.35

73 million deaths ensue every year because of HCV infection related diseases and HCC (Ott et al.

74 2012). Studies have confirmed that existing treatment by PEGylated interferon-alpha and

75 ribavirin (PegIFN-α/RBV) deliver inadequate efficacy in clearance of viremia and are poorly

76 tolerated by patients (Manns et al. 2006). The side effects associated with HCV treatment

77 sometimes require a decrease in dose and premature termination of treatment, thus increasing the

78 risk of treatment failure (Cacoub et al. 2012; Chopra et al. 2013; Fried 2002). Development of an

79 effective prophylactic vaccine has met little success so far due to high mutation frequency of

80 HCV also the presence of quasispecies (Dunlop et al. 2015; Lechmann et al. 2001).

81 Direct acting antivirals (DAAs) have proved effective in certain cases to improve the

82 SVR rates (Cento et al. 2015). However, it is met with the issue of drug resistance, drug-drug

83 interactions and varying drug regimens with genotype and sub-populations making it

84 complicated (Cento et al. 2015). Treatment of significant percentage of patients with drug


85 resistance and therapeutic failure still pose a challenge to biologists and increases the pressure

86 for developing new, effective and tolerable therapies. A well-defined antiviral and

87 immunomodulatory therapy is need of the hour to restore HCV-specific immune response in

88 order to clear the virus effectively from the host (Chatel-Chaix et al. 2010). In this regard, it is

89 necessary to analyze all the aspects of immune regulation during infection, so that the critical

90 factors of effective host immune response can be determined and exploited for therapeutic

91 interventions.

92 The complex interconnected signaling and regulatory pathways are difficult to analyze as

93 a single system via conventional mathematical approaches such as ordinary differential equations

94 (ODEs). ODEs require details of the kinetics of each reaction which are difficult to obtain. Thus,

95 the analysis of abstracted biological regulatory sub-networks within the complex pathway and

96 formerly studying them via Biological Regulatory Network (BRN) modeling and analysis

97 approaches pose a better alternative. A well-known mathematical formalism of René Thomas

98 (Bernot et al. 2004) was applied to formulate the HCV BRN which uses graph theory to explore

99 the evolution of states/genes within the modeled system. Furthermore, the several properties of

100 the modeled BRN are depicted by the state space (state graph which is representative of the

101 states and associated directed paths) in which imperative behaviors can easily be examined as

102 either a cyclic path or diverging routes leading towards disease/pathogenic state. The state graph

103 represents the activation profile of the included entities in the BRN at any given state during the

104 infection course. It represents a state space as a discrete abstraction which makes it easy for

105 inspecting various behaviors along the paths of pathogenesis. Qualitative modeling such as BRN

106 analysis is suitable enough for performing model checking based reasoning to estimate and then

107 apply unknown parameters of the entities in the BRN (Ahmad et al. 2012). In this study, we have

108 developed a qualitative model of HCV induced immune signaling with a special focus on IL-10

109 and IL-12 mediated immune modulation and control of viremia along with the activation of the

110 Natural killer (NK) and T-regulatory (Tregs) cells.

111 The HCV induced immune signaling pathway is activated through the HCV particle

112 entering the hepatocytes and releasing its RNA (Rehermann 2009a). Figure 1 represents the

113 illustration of the pathways involved in immune clearance of the infection.

114


115 The linear genomic RNA molecule of HCV contains a single open reading frame (ORF),

116 which encodes for a precursor polyprotein of ~3k amino acid residues (Lohmann et al. 1999;

117 Moradpour et al. 2007). The virus replicates by cleaving the polyprotein of HCV in three

118 structural proteins (core, E1, E2), also seven non-structural proteins (p7, NS2, NS3, NS4A,

119 NS4B, NS5A, NS5B). It is achieved by the action of viral and the host enzymes (Figure 1)

120 (Lohmann et al. 1999). HCV structural proteins constitute critical constituents of HCV virions,

121 while HCV non-structural proteins are involved in the RNA replication and virion

122 morphogenesis (Moradpour et al. 2007). Amongst non-structural proteins, NS5A (56–58 kDa) is

123 a phosphorylated, zinc-metalloprotein which has a significant role during virus replication and

124 cellular pathways regulation (Egger et al. 2002; Elazar et al. 2004; Gosert et al. 2003).

125 In response to viral infection, host machinery acts to eradicate the infection by activating

126 immune response (Figure 1). Dendritic Cells (DCs) and NK cells residing in the liver are

127 triggered for the release of pro-inflammatory cytokines including but not limited to IFN-γ and

128 IL-12 which play a critical role in eliminating the virus either directly or by indirect activation of

129 supporter immune function (Fan et al. 2007; Takahashi et al. 2010). Thus, NK cells start an early

130 host defense against viral pathogens (Nellore & Fishman 2011; Vivier et al. 2011). They are a

131 major source of interferon gamma (IFN-γ ) which inhibits viral replication without destroying

132 liver cells (Rehermann 2015). As a result, CD4+ and CD8+ T-cells are activated which act by

133 destroying cells catalytically and non-catalytically (Rosen 2013a) by the secretion of antiviral

134 cytokines IFN-γ and TNF-α (Bowen & Walker 2005; Gorham 2007; Heim & Thimme 2014;

135 Neumann-Haefelin & Thimme 2013; Rehermann 2009a; Thimme et al. 2012; Vivier et al. 2011).

136 Diverse kinds of Tregs cells are known to be involved in HCV immunology (Zhao et al. 2012).

137 Tregs are involved in the inhibition of HCV-specific T-cells during acute infection, which

138 contributes in T-cell failure and leads to chronic infection, also it protects from related tissue

139 injury during HCV chronic infection (Rosen 2013a).

140 On the other hand, several mechanisms in relation to HCV-specific defects in immunity

141 have been proposed in previous studies (Neumann-Haefelin & Thimme 2013; Rehermann 2009a;

142 Thimme et al. 2012). HCV proteins directly or indirectly inhibit host cellular responses via

143 various signaling pathways. Amongst them, failure to sustain rigorous and effective immune

144 response include i) lack of CD4+ T-cell help, ii) constant antigen triggering, iii) Tregs action iv)


145 reduced potential of cytotoxic T-cells, v) reduced secretion of Th1-type cytokines v) a reduced

146 proliferative capacity in response to ex vivo antigenic stimulation (Thimme et al. 2012).

147 The study was focused on the main antagonist cytokine players involved in the cellular

148 immune response i.e. IL-10 and IL-12. These cytokines are responsible to mediate the signaling

149 and functional activity of Tregs and NK cells (Rehermann 2009b). IL-10 has been implicated as

150 a cytokine responsible for the failure of immune response to clear infection (Moore et al. 2001).

151 HCV, in turn also augments IL-10, and inhibits NK cells and IL-12 which results in the

152 activation of Tregs (Aste-Amezaga et al. 1998; Blackburn & Wherry 2007; Fiorentino et al.

153 1991; Hu et al. 2006; Sene et al. 2010). IL-10 is considered to be an anti-inflammatory as well

154 as an immunomodulatory cytokine (Blackburn & Wherry 2007). Once infection occurs, IL-10

155 inhibits NK cells, Th1 cells, macrophages and the activity of pro-inflammatory cytokines

156 (including IL-12 and TNF-α) (Moore et al. 2001). As a result, IL-10 can hinder pathogen

157 clearance as well as limit the damage caused by immunopathology. In essence, a critical balance

158 between both pro-inflammatory and anti-inflammatory response determines the outcome of

159 infection. Also, it is worth mentioning that, it is not necessary that maximum pathogen control or

160 clearance will ensure disease recovery because a higher inflammatory response may lead to

161 greater tissue damage. It is known that the side effects and complications during infection are the

162 consequence of superfluous immune activation leading to tissue injury (Napoli et al. 1996;

163 Schuppan et al. 2003; Spengler & Nattermann 2007). IL-12, on the other hand, is known to be a

164 pro-inflammatory cytokine which activates CD4+ and CD8+ T cells, promoting infection

165 clearance. It also stimulates the cytotoxic function of NK cells and T-cells by stimulating the

166 release of IFN-γ (Aste-Amezaga et al. 1998; Barth et al. 2003; Sun et al. 2015; Zhao et al. 2012).

167 IL-12 restricts the function of Tregs thus inducing viral clearance (Zhao et al. 2012).

168 In order to characterize the behaviors of NK cells and Tregs under the influence of IL-10

169 and IL-12 during the presence of HCV infection, a BRN was constructed and analyzed. It was

170 then further examined to see the deadlock behavior leading to a pathophysiological state or

171 homeostasis conditions. Furthermore, the BRN was transported into a Petri net (PN), which

172 allowed the study of the continuous dynamic behavior of the entities.

173 2 Methods:


174 The lack of kinetic data for each reaction for complex disease networks such as cancers,

175 hepatitis, and other microbial diseases is a challenge for a biologist. Also, the holistic analysis of

176 such large networks is difficult through conventional approaches of wet-lab experimentation.

177 Furthermore, the biological systems are multifaceted and non-linear in nature and thus are quite

178 difficult to model mathematically as well. Thus, the existing graph-based modelling methods

179 mainly utilize linear approaches to nearly estimate various behaviors shown by the biological

180 networks/systems. The methodology followed for the construction of BRN and analysis has been

181 represented in Figure 2.

182 2.1 Abstraction of the prior knowledge based interaction network:

183 The presented signaling pathway of HCV and the associated immune response is a highly

184 connected, complex network of receptors, enzymes and signaling molecules such as cytokines.

185 To understand the complexity in interactions within the immune signaling networks, a prior

186 knowledge based logical diagram is generated (Figure 1) based on multiple reported interactions

187 between immune cells and cytokines to estimate the outcome of immune stimulation in response

188 to viral components. To characterize the cytokines mediated HCV clearance and the role of NK

189 cells in the viral clearance, the prior knowledge based logical diagram is reduced to form a BRN.

190 A BRN consists of a set of interactions (activation or inhibition) amongst biological entities (e.g.,

191 proteins, genes in a biological signaling network) which can exhibit the behaviors of the entities

192 in holistic manner represented by a state graph, exhibiting cyclic behaviors, deadlock (disease)

193 state (s) and the paths in between. However, constructing a BRN for a large set of entities, with

194 an increased number of nodes, renders a very large state graph and suffers from state space

195 explosion. Also, one of the limitations of BRN formalism is that once the number of entities

196 increases roughly from seven, it becomes challenging to assign parameters and hence the

197 interpretation of state graph (Richard et al. 2012). Thus, the complex signaling network from

198 literature (Figure 1) was abstracted based on the fact that if an entity (enzymes, cytokines, etc.)

199 activates/deactivates a downstream process via several intermediate entities, the network can be

200 reduced by omitting intermediate entities to show the final effect of the activation or inhibition

201 on that particular entity being studied. This method allows us to model the complex biological

202 networks using BRN analysis tools while preserving the core functions of signaling network.


203 This kind of abstraction has been explained in in detail by Naldi et al. 2009 and Saadatpour et al.

204 2013 (Naldi et al. 2009; Saadatpour et al. 2013).

205 2.2 Qualitative framework for modeling the Hepatitis C Virus (HCV) induced immune

206 regulations and construction of Network

207 In order to simplify the analysis of biological behaviors and construction of the BRN

208 models, the Rene’ Thomas formalism is best alternative as it does not require quantitative data

209 such as the exact concentrations and kinetic reaction rates, (Samaga & Klamt 2013). Qualitative

210 model assembly involves only the qualitative thresholds and associated logical parameters

211 (Ahmad et al. 2012; Bernot et al. 2004; Motta & Pappalardo 2013; Naldi et al. 2009). The

212 qualitative thresholds are adjusted per the literature findings and the logical parameters are

213 computed by computational tree logic (CTL) using SMBioNet tool (Khalis et al. 2009) and

214 discussed below under section “Parameters Interpretation using Model Checking”. The detailed

215 semantics of the kinetic logic formalism (Samaga & Klamt 2013) have already been discussed in

216 the studies of Ahmad et al., (2012) and Saeed et al., (2016) (Ahmad et al. 2012; Saeed et al.

217 2016). However, some of the important definitions and the terms quite necessary to comprehend

218 the semantics employed in this study have been stated below.

219 2.2.1 Directed Graph:

220 A directed graph D (V, E) is a 2-tuple where:

221 V represents the set of nodes and

222 E is used to represent an ordered set of arcs or edges.⊆ V × V

223 In D (V, E), an edge is always directed from one node to another node (entity). 𝐷 ‒ (𝑥) 𝑎𝑛𝑑 𝐷 +

224 and in a directed graph symbolize the antecedent and descendant nodes of a specific node(𝑥)

225 , respectively. (𝑥 ∈ 𝑉)

226 2.2.2 Biological Regulatory Network:

227 It is a labeled form of directed graph , where V represents the set of biological 𝑫(𝑽, 𝑬)

228 entities (nodes) and represents all possible interaction amongst entities (edges).𝑬 ⊆ 𝑽 × 𝑽


229 Each edge of a BRN can be characterized with a pair where is the level of (𝜎,𝜓) 𝜎230 qualitative threshold (positive integer) and represents the sign of interaction (“+” or “–” 𝜓231 signs i.e., “activation” or “inhibition”, respectively).

232 Threshold level of each individual node has a certain limit that is equal to the number (𝑙𝑎)

233 of outgoing edges (out-degree). This is represented by and ∀𝑏 ∈ 𝐷 + (𝑎) 𝜎𝑎𝑏 ∈ {1,2,3,….,𝑟𝑎}

234 , where shows the threshold levels of an entity, which can be from “1” to its 𝑟𝑎 ≦ 𝑙𝑎

235 “outdegree”, and as it has only 1 outgoing edge, so the threshold level can only be “1”.

236 Qualitative expressions of each entity in a BRN, (say entity a) are given in the set 𝑍𝑎 =

237 .{0,1,2,….,𝑟𝑎}

238 2.2.3 States:

239 In BRN, a state is a tuple , where is: , 𝒔 ∈ 𝑴 𝑴 𝑴 = ∏𝒂 ∈ 𝑽 𝒁𝒂240 The qualitative states of a BRN are characterized by , where shows the level (𝑀𝑣)∀𝑎 ∈ 𝑉 𝑣241 of expression of an entity (e.g., “a”). “M” represents the Cartesian product of abstract

242 expressions of all entities.

243 2.2.4 Resources:

244 Resources is a set a of variable where, 𝑹𝒗𝒂 𝒂 ∈ 𝑽245 V defined as.𝑹𝒗𝒂 = {𝒃 ∈ 𝑫 ‒

(𝒂)|(𝒗𝒃 ≥ 𝝈𝒃𝒂 𝒂𝒏𝒅 𝝍𝒃𝒂 = + ) 𝒐𝒓 (𝒗𝒃 < 𝝈𝒃𝒂 𝒂𝒏𝒅 𝝍𝒃𝒂 = ‒ )}

246 The set of logical parameters, defining the dynamic behavior of BRN, is represented as 𝑲(𝑫) =247 {𝑲𝒂 (𝑹𝒗𝒂) ∈ 𝒁𝒂∀ 𝒂 ∈ 𝑽}

248

249 2.2.5 State Graph:

250 Let D (V, E) be a BRN and is expression level of in a state . Then the state graph G = 𝐬𝐯𝐱 𝐯𝐱 𝐬 ∈ 𝐌251 (M, T) is a directed graph, where M represents set of states, and is a relation between 𝐓 ⊆ 𝐌 × 𝐌252 states, also called the transition relation, such that iff:𝐌→𝐌' ∈ 𝐓253

254 a unique such that , and ∃ vx εV svx

≠ s'

vx and s

'v

x= sv

x↱Kx(Rv

x)


255 ∀vy εV ∖ {x}s'

vy

= svy

256 2.3 Parameters Interpretation using Model Checking:

257 Model parameters are calculated utilizing known experimental observations via formal

258 verification method, known as model checking. The generated parameters are then used to

259 interpret the BRN into a qualitative model. The analysis of the model further highlights

260 significant states as paths, including stable states/deadlock state, and various cycles in the form

261 of a state graph. In CTL, experimental observations from the literature are programmed in the

262 form of formulas by means of a set of quantifiers that describe conditions to discover various

263 states or paths initiating from a starting state. The detailed semantics of the quantifiers can be

264 found in (Ahmad et al. 2012). The parameter estimation of the biological network was done

265 using SMBioNet tool (Khalis et al. 2009; McAdams & Shapiro 1995). It calculates all of the

266 possible parameters which are compatible with the biological observations and have been

267 encoded in the form of CTL formula. Subsequently, all of the generated models that satisfy

268 encoded CTL properties have been shortlisted and used to develop the final BRN model. Logical

269 parameters have been described by using the relation

270 . Where, resources are the entities connected with 𝑲𝒕𝒂𝒓𝒈𝒆𝒕 𝒆𝒏𝒕𝒊𝒕𝒚 ({𝒓𝒆𝒔𝒐𝒖𝒓𝒄𝒆𝒔}) = 𝒏 𝒘𝒉𝒆𝒓𝒆 𝒏 ∈ {𝟎, 𝟏, 𝟐 ,….}.

271 any evolving or target entity of the BRN. Thus, these resources may either be inhibitors or

272 activators during a particular state, which depends primarily on their absence or presence.

273 2.4 Hepatitis C Virus (HCV) induced BRN construction and analysis:

274 The BRN of the abstracted biological pathway is constructed using GINsim and

275 GENOTECH tools (Ahmad et al. 2006; Gonzalez et al. 2006). BRN consists of nodes,

276 representatives of the biological entities, while the directed arcs amongst them show the

277 interactions amongst them. There are two types of interactions/connections. Activating

278 connection is represented by a solid line and +1 integer, while the negative connection is

279 represented by -1 integer. Each of the entity in the modeled BRN is allocated a set of logical

280 parameters (generated via SMBioNet) which generates a state graph (the qualitative model)

281 depicting the likely steady state and cyclic behaviors of the BRN. The state graph is generated

282 via GENOTECH and GINsim tools (Gonzalez et al. 2006) (Ahmad et al. 2006) to identify

283 various paths leading to the diseased/deadlock state or the homeostatic state. The imperative


284 paths involved in disease progression and the recovery are identified by the analysis of the

285 network and related state graph. The diseased state/deadlock state is identified form which no

286 other state is further possible. Also, the cyclic paths leading the system to homeostasis were also

287 analyzed by using maximum betweenness centrality.

288 2.5 Petri net model of the Hepatitis C Virus (HCV)-induced regulatory network:

289 The biological pathways are continuous in nature, thus, in order to study the network

290 dynamics, generated BRN is converted to a PN. It allows the study various biological behaviors

291 in a continuous manner. GINsim (Gonzalez et al. 2006) lets the export of BRN into a PN format

292 to be studied via SNOOPY tool (Heiner et al. 2012). A PN is a directed bipartite graph in which

293 places (represented by circles) and transitions (represented by squares) represent entities of a

294 pathway and the processes in between them respectively. Furthermore, the places and transition

295 are connected via directed arcs to allow the flow of tokens in the modeled pathway. The

296 transition firings can influence the number of tokens assigned to the target place through the

297 source, referred to as the token-count. This kind of modeling enables the flow of signals via

298 directed protein interactions in a cellular pathway. The “simulation run” property of PN allows

299 the study of continuous dynamics of the proteins/genes involved in the signaling pathway.

300 3 Results & Discussion:

301 3.1 Abstraction of the prior knowledge based interaction network and then analysis of

302 the abstracted model

303 The lifecycle of HCV begins with the transfer of viral RNA into the human hepatocytes.

304 The role of various cellular responses mediated by cytokines in the resolution of HCV infection

305 is evident from the studies on chimpanzees, describing that a self-clearing progression of acute

306 hepatitis C is characterized by strong NK cells response along with CD4+ and CD8+ T cell

307 responses, which can target multiple HCV proteins. It is also associated with intrahepatic

308 induction of IFN-γ and other related cytokines (Bowen & Walker 2005; Heim & Thimme 2014;

309 Jenne & Kubes 2013). Clearance of acute HCV infection is connected to T cell recovery and the

310 ability to produce IFN-γ (Bowen & Walker 2005; Heim & Thimme 2014; Jenne & Kubes 2013).

311 Literature was searched to identify critical pathways necessary to activate HCV induced immune


312 responses that are directly or indirectly affected by NK cells, Tregs and IL-10, IL-12 cytokines.

313 The prior knowledge based immune response pathway (Figure 1) was reduced such that the

314 interactions amongst the targeted proteins, cytokines, and immune cells highlight the ultimate

315 effect on each other in the form a network. The reduced BRN is shown in Figure 3, while it is

316 abridged to allow for easy interpretation and study of the state graph, however, the essence of the

317 interactions and their functions are preserved in the reduced pathway network.

318 The reduced network was then employed to model the BRN. There are six nodes

319 representing T-regulatory cells (Tregs), IL-10, NS5A (HCV non-structural protein 5 A), IL-12,

320 IFN-γ, NK cells. The integers -1 and +1 are used with the directed arcs to show activation (+1

321 with a straight line) and inhibition (-1with dashed line) mediated by the viral and host cellular

322 components. NS5A is a multifunctional protein which is a part of HCV replication complex. It

323 also exerts its effect on host cellular pathways via protein-protein interactions and effects host

324 immune response. That is why it is a highly important protein for HCV replication and also

325 poses a very important therapeutic target.

326 3.2 Hepatitis C Virus (HCV) regulatory network constructed with estimated parameters

327 based on biological observation

328 The parameters for the construction of a regulatory network are estimated such that they

329 can ensure the interactions amongst the BRN entities according to the experimental observations.

330 It maintains the interdependencies of contributing entities on each other (activation or

331 deactivation). To estimate all the plausible combination of parameters which satisfies the CTL

332 formula based on the biological observations, SMBioNet (Khalis et al. 2009) is used (explained

333 in the Methods section). Table 1 represents the encoded CTL formula and the related biological

334 observations from the literature.

335 In the CTL formula, “A” characterizes all probable pathways which start from the present

336 state. “F” signifies at least one state included in either future or successors states. “G” denotes all

337 the set of states included in either future or successor states. The CTL formula is based on the

338 fact that NS5A inhibits NK cells function via inducing imbalance in inflammatory cytokines. NK

339 cells are known produce IFN-γ which in turn inhibits HCV production. Furthermore, Tregs

340 modulates the immune system by decreasing immune intensity thus indirectly augmenting HCV


341 production. IL-12 inhibits Tregs function indirectly while IL-10 inhibits NK function. Similarly,

342 HCV augments the activation of IL-10 so that it can dampen the anti-inflammatory response

343 against HCV. Thus, the encoded CTL depicts these observations during inhibition of HCV

344 infection i.e. NS5A=0, during which the host poses an effective inflammatory response. The

345 expression of Tregs is also downregulated (Treg=0) during effective clearance of infection by

346 increasing the inflammatory response. IFNγ=1, depicting the ample expression of IFNγ by NK

347 cells and IL-10=0. This CTL was used by SMBioNet and on the basis of which it generated six

348 sets of parameters (supplementary file 1), each set representing a specific model. Each of the

349 generated parameters set was then further subjected to analysis in the GENOTECH tool (Ahmad

350 et al. 2006) so that a state graph can be generated. Each of the state graphs was intensely studied

351 for cycles, diseased state, and recovery/ homeostatic conditions. Out of six, one model was

352 selected whose state graph correctly represented and conformed to the biological observations

353 from literature. The selected parameters are presented in Table 2. The BRN generated using the

354 selected set of parameters in GENOTECH as well as GINsim tool was used (Gonzalez et al.

355 2006) to check for any ambiguity, and a state graph was generated for further analysis.

356 3.3 Analysis of the state graph for identification of pathophysiological paths, cycles, and

357 homeostasis:

358 The state graph is presented in Figure 4, having 64 nodes and 192 edges. The state graph

359 signifies all probable transitions from one state to another, and each state displays the relative

360 expression of each entity at a specific point in time. The sequence of entities in any given state is

361 “Tregs, IL-10, NS5A, IL10, IFN-γ, NK cells”. “1” represents the upregulation of an entity and

362 “0” represents the downregulation of an entity in the same sequence stated above. As all states in

363 a state graph progress asynchronously, thus, in every successor state, level of only one entity can

364 change its level at a time. The state graph was analyzed for those states showing important

365 biological behaviors, in terms of either disease progression or recovery. The state “001010”

366 marks the initiation of HCV infection. Thus “Tregs= 0, IL-10 = 0, NS5A= 1, IL-12=0, IFN-γ =1,

367 NK cells =0” constitutes an initial state of the disease progression in the system. It depicts that as

368 soon as HCV infects the cells it immediately starts the production of its proteins (NS5A) via

369 efficient translation of its viral genome at the endoplasmic reticulum (Bartenschlager et al.

370 2013). Further analysis revealed that system can lead to either a diseased state “111100”


371 (represented by red color in the graph) or a reset state “000000”. The disease or stable state is an

372 irreversible state and also called a deadlock. In the state graph, it is presented by “Tregs=1, IL-

373 10=1, NS5A=1, IL-12=1, IFN-γ=0, NK cells=0”. The chronic activation of Tregs, IL-10, NS5A

374 (HCV), and IL-12 and downregulation/deactivation of NK cells and IFN-γ will lead to chronic

375 infection from which reversal is only possible through intervention by various kinds of

376 treatments to block the intermediate paths prior to reaching this state (Aste-Amezaga et al. 1998;

377 Bartenschlager et al. 2013; Belkaid & Rouse 2005; Brady et al. 2003). On the other hand, such

378 state is also identified in the graph “000000” also known as reset or recovery state exhibited by

379 “Tregs=0, IL-10=0, NS5A=0, IL-12=0, IFN-γ=0, NK cells=0” which is characterized by low

380 titers of HCV proteins in the system and is part of homeostasis cycle. The state graph with the

381 presence of two types of behaviors (Homeostasis/ deadlock) in the same state graph shows that

382 the host immune system can either work efficiently to stabilize the biological system or move

383 towards such a pathogenic state from which no further state is possible.

384 3.4 Prediction of cycles based on maximum betweenness centrality leading to homeostasis

385 The host immune systems’ main players such as IFN-γ and NK cells move the system

386 towards maintaining immune homeostasis. We are interested in that particular cycle which

387 follows a well-ordered, efficient pattern/path and keeps the system in homeostatic condition.

388 Since the model shows cycles of varying lengths, therefore, it is important to identify the most

389 plausible biological cycle(s). Hence, we employed “betweenness centrality” computed by

390 Cytoscape tool (Shannon et al. 2003) that is able to sort all of the states in the graph on the basis

391 of their maximum betweenness centralities. Betweenness centrality has wide application in the

392 graph theory based analysis as it highlights those nodes which are central to the state

393 graph/diagram. It calculates those nodes that lie in the shortest paths maximum number of times.

394 The most probable cycle has been singled out in Figure 5.

395 The cycle “000000, 000001, 100001, 110001, 111001, 111011, 111111, 111110, 110110,

396 010110, 010100, 010000, 000000” shows the sequence of events occurring in the cyclic path.

397 The host immune system works competently to protect it from going into a pathogenic state, as a

398 result, the system remains in a cyclic behavior. As this cycle has maximum betweenness

399 centrality it represents that all other paths must pass through this cycle serving as a bridge for all

400 other nodes in the state space. The intrahepatic activation of NK cells via immune-related


401 cytokines occurs through dendritic cells (Cook et al. 2014). NK cells lie at the junction of innate

402 and adaptive immunity and exert its function by releasing IFN-γ in the hepatocytes. IFN-γ act as

403 a main mediator of the host adaptive immunity by activating CD4+ and CD8 + cellular responses

404 (Lanford et al. 2003). IFN-γ also acts to nullify the effects of IL-10 (Hu et al. 2006). The IL-10

405 cytokine is an immune modulatory cytokine, which dampens the inflammatory responses to

406 protect host tissue, as a result, helping HCV infection and virus proliferation (Blackburn &

407 Wherry 2007). IL-12 helps to tip the balance of immune response towards clearance of infection

408 by inhibiting the effects of Tregs (Aste-Amezaga et al. 1998; Zhao et al. 2012). Tregs also act as

409 immunomodulators thus it is necessary to attenuate their function to overcome the infection

410 (HCV). Enhanced IFN-γ activation is the indicator of robust immune response along with the

411 downregulation of IL-10.

412 3.5 Identification and analysis of the pathophysiological state and various associated

413 paths

414 In addition to cyclic behavior, various branching states also exist in the state graph (Figure

415 6) which can lead the system to the diseased state. The diseased state or the deadlock state is also

416 called as a stable state, which behaves like a basin towards which many paths converge which

417 does not allow the system to evolve to any other state. Also, it has lowest betweenness centrality

418 depicting that the system is moving towards a deadlock. The analysis of the state graph revealed

419 the most probable and biologically plausible paths which lead towards a stable state (111100)

420 and shown in red (Figure 6). The state “111100”, represents the continuing activation of Tregs,

421 IL-10, NS5A (HCV), and IL-12 and deactivation or absence of NK cells and IFN-γ. It highlights

422 the role of NK cells in the immune clearance of HCV. Also, the global effect of IFN-γ in

423 reducing the disease burden is emphasized. The shortest but biologically correct diseased path

424 from the initial state “001001” comes out to be, “001001, 001000, 001010, 101010, 101000,

425 111000, 1111000”. While several other downstream bifurcation paths also arise and shown in

426 Figure 6 which leads to a stable state. It is worth noting that majority of the states in the disease

427 pathway are having an activated NS5A and deactivated NK cells in high proportions. This

428 demonstrates that either the system remains in the cycle by overcoming the infection or moves

429 towards diseased state when the host immune system is overwhelmed by viral proteins. One very

430 interesting observation pertains to the expression of IL-12 and its role in the pathogenesis.


431 The upregulation of IL-12 in a diseased state is an interesting prediction of the model.

432 Classically, IL-12 is known to be an activator of CD4+ and CD8+ T cells, NK cells, and

433 macrophages and negative regulator of Tregs(Wang et al. 2000). It has been shown that IL-12

434 leads the system towards clearance of infection by promoting the differentiation of naïve T-cells

435 (Eckels et al. 2000; Wang et al. 2000). However, the prediction of upregulated IL-12 in

436 pathogenesis by our model implicates that IL-12 is differentially regulated in chronic infection. It

437 conforms to the earlier observation by Pockros et al., 2003 and other groups have shown in a

438 small pilot study that despite the pro-cytolytic function of IL-12, IL-12 monotherapy is not

439 useful against chronic HCV (Barth et al. 2003; Pockros et al. 2003). It follows the same pattern

440 in our model as well depicting strong induction in the disease state. It warrants for further studies

441 to decipher the exact mechanism by which IL-12 may lead the system towards the pathogenic

442 state. The exact mechanism and the circumstances involved also needs to be studied further to

443 study whether it can be a therapeutic target for HCV.

444 3.6 Petri net (PN) model for continuous dynamic analysis of the Hepatitis C Virus (HCV)

445 induced immune regulation

446 The BRN in GINsim was exported to PN format for the dynamic analysis of properties and

447 holistic behavior of proteins of the model. As biological systems behavior is continuous in

448 nature, the generated discrete PN was further exported into a continuous PN format using

449 SNOOPY tool shown in Figure 7.

450 PN modeling allows the use of simulations to critically observe the relative changes in the

451 expression levels of biological entities such as proteins/enzymes with time. The converted PN

452 consists of two types of places for each entity of the network. One prime place (representing

453 activated state) and another complementary state (representing deactivated state). Similarly, their

454 associated transitions have been labeled “p” and “n” to differentiate among activating signal and

455 deactivating signal. The biological proteins have different activation status during the course of

456 an infection. Therefore, it is necessary to include the deactivated places for the proteins to cater

457 for the intracellular inhibiting signals being received. Also, the transitions created by GINsim

458 represent each SMBioNet generated parameter exclusively which helps in the analysis of the

459 dynamics of the modeled BRN. It has been discussed previously that the network connectivity is


460 a single most determinant factor for signal propagation in the signaling pathway (Polak et al.

461 2017; Ruths et al. 2008). The specific kinetic parameters for each reaction is difficult to obtain

462 thus we rely on the structure of PN only. The reason behind such assumption is that the

463 biological signaling pathways have evolved to such an extent that the connectivity of the network

464 has a stabilizing effect on the proteins and other related interactions of the system. Thus, the

465 graph theory based PN analysis makes it easy to interpret the simulations based results to predict

466 the behaviors under varying external or internal stimuli. The generated PN is simulated with

467 Mass action kinetics (1) for all the transitions and the markings in the places represent the

468 presence of tokens.

469 3.7 The analysis of the network model and its continuous evolution:

470 The simulation property of the PN was used to study the evolution of proteins and their relative

471 changes with time. The simulation results are shown in Figure 8A truthfully represents the stable

472 state “111100” of the state graph in which the levels of NK cells and IFN-γ are downregulated as

473 compared to Tregs, IL-10, NS5A, and IL-12. On the other hand, Figure 8B shows the recovery

474 of the NK cells and IFN-γ leading to downregulation of HCV NS5A and associated factors. It

475 emphasizes the role of NK cells in clearance of infection.

476 NK cells exert a pressure on the immune system to clear the virus via its direct cytotoxic

477 actions and ample production of IFN-γ. Another function of NK cells includes the regulation of

478 adaptive and innate immune responses via direct or indirect reciprocal activation of DCs,

479 macrophages and T cells (Nellore & Fishman 2011). The relative overexpression of IL-12 in

480 Figure 8A during pathogenic state is an interesting prediction by our model. The proposed

481 implication of IL-12 in autoimmune pathogenesis is evidenced in several studies (Sun et al.

482 2015). A study by Orange et al., 1994 on LCMV reported that IL-12 can affect the infection both

483 ways. Either it works towards eliminating the viral infection or detrimental to the host

484 depending primarily on the induced environment ant and intracellular stimuli it receives. On the

485 other hand, IL-10 is known to be an immunomodulatory cytokine which is primarily considered

486 to reduce the cytotoxic potential of T cells as well as NK cells (Blackburn & Wherry 2007).

487 However, IL-10 being a strong immunomodulatory agent is essential for regulating inflammatory

488 responses and helps to reduce several immune-related inflammatory injuries to the tissue


489 (Fiorentino et al. 1991). The high levels of IL-10 during pathogenesis stresses the need for such

490 immunomodulatory therapy which inhibits Tregs or IL-10 so that NK cells functionality is

491 recovered. One such therapy option is using anti IL-10 antibody in conjunction with IFN-a/RBV

492 therapy. IFN-a/RBV increases the effectiveness of IFN-γ and are also known to recover NK cells

493 via immunomodulation of anti-inflammatory cytokines (Caetano et al. 2008; Kamal et al. 2002;

494 Lanford et al. 2003; Nakamura et al. 2015; Stevenson et al. 2011; Testoni et al. 2013; Werner et

495 al. 2014).

496 4 Conclusion:

497 The robust computational and mathematical approaches offer a promising platform for unifying a

498 large number of independent observations to get a precise view of the cellular signaling

499 networks. These approaches have the potential to showcase inert yet a holistic view of the small

500 regulatory sub-networks as a component of the whole complex network, along with the

501 discovery of alternative pathways, junctions and crosstalk, and hubs. The ability to identify the

502 probable target-specific events and pathways leading to pathogenic/homeostatic state makes it

503 suitable for studying complex disease systems such as Hepatitis C. Various computational and

504 mathematical approaches are in practice, helping in finding new potential targets for therapeutic

505 intervention which are expensive to explore otherwise. BRN construction represents an efficient

506 alternative to model biological networks as compared to conventional mathematical approaches

507 such as models based on ODEs. The developed BRN model of immune regulation and the role of

508 HCV NS5A in antagonizing the effects of host immune control has been studied exclusively.

509 Particular focus has been put on the IL-10 and IL-12 cytokines mediated regulation from the

510 initial state to terminal state. It can be concluded that the global immunomodulatory effects of

511 IL-10 help in the viral control of host machinery. The effects of IL-10 are more profound as

512 compared to IL-12, which results in a pathogenic state. Also, it is observed that the IL-12

513 overexpression benefits the pathogenic state more as compared to its anti-viral effects. The host

514 immune system does work to recover the system but it is overwhelmed by the efficient HCV

515 immune evasion process. Any diversion from the diseased paths either via host immune recovery

516 or therapeutic intervention to stabilize the levels of IFN-γ producing NK cells will lead the

517 system towards recovery.


518 5 Authors Contributions:

519 AA and AO designed the study. AO contributed to model generation, analysis, interpretation of

520 data and draft composition. AN, STA, MTS, FMA, and AI helped in designing formal models and

521 analysis. AA, AN, AI, FMA, JA, and AR critically analyzed the draft and helped AO in organizing

522 the final version.

523 6 Conflict of Interest Statement:

524 The authors declare that the research was conducted in the absence of any commercial or financial

525 relationships that could be construed as a potential conflict of interest.

526 7 Acknowledgement:

527 This research is supported by Higher Education Commission (HEC) of Pakistan, NRPU grant

528 no.4362.

529


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Table 1(on next page)

Related biological observations and the corresponding CTL Formula.

The experimental observations are converted into temporal logic formulas. The CTL formula

is constructed using state quantifiers (X, F, G), path quantifiers (E, A) and implication (→). The

first part of implication shows a sufficient condition or a cause of the second part on the right

side (effect). The formula further contains temporal operator F and G representing the Future

and Global (all the time). Moreover, CTL operator A represents all the possible behaviors

(dynamics or trajectories). Now the CTL formula represents that in the future of all behaviors,

a state always exists where NS5A, Tregs, and IL10 are expressed (at qualitative level 1) and

NK cells and IFN-γ are not expressed (at qualitative level 0). Furthermore, this state is caused

by the qualitative state (NS5A=0&Treg=0&IFNy=1&NKCells=1&IL10=0)


Biological

Observations

References CTL Formula

01 NS5A inhibits NK

cells function via

inducing imbalance

in inflammatory

cytokines

(Tseng and

Klimpel,

2002;Sene

et al.,

2010;Kim et

al., 2014)

(NS5A=0&Treg=0&IFNy=1&NKCells=1&IL10=

0)

→AF(AG(NS5A=1&Treg=1&IL10=1&NKCells=

0&IFNy=0))

02 NK cells produce

IFN-γ

which in turn

inhibits HCV

production

(Frese et al.,

2002;Li et

al.,

2004;Gatton

i et al.,

2006)

03 Tregs modulates the

immune system by

decreasing it

intensity thus

indirectly

augmenting HCV

production

(Belkaid

and Rouse,

2005;Rushb

rook et al.,

2005;Sturm

et al., 2010)

05 HCV augments the

activation of IL-10

(Brady et

al., 2003)

06 IL-10 inhibits IL-12 (Aste-

Amezaga et

al.,

1998;Waggo

ner et al.,

2007)


Table 2(on next page)

Selection of logical parameters generated via SMBioNet.


Parameter Resources Range of Values Selected Parameters

KTreg { } 0 0

KTreg {NS5A} 0, 1 1

KTreg {IL-12, NS5A} 0, 1 1

KIL10 { } 0 0

KIL10 {NS5A} 0, 1 1

KIL10 {Treg} 0, 1 1

KIL10 {NS5A, Treg} 0, 1 1

KNS5A { } 0 0

KNS5A {IFNy} 1 1

KIL12 { } 0 0

KIL12 {NS5A} 1 1

KIFNy { } 0 0

KIFNy {NK Cells} 1 1

KNK Cells { } 0 0

KNK Cells {IL-12} 0, 1 1

KNK Cells {IL-10} 0, 1 0

KNK Cells {IL-12, IL-10} 0, 1 0


Figure 1(on next page)

Prior knowledge-based logical interaction network of HCV induced immune response.

Figure 1: Prior knowledge-based logical interaction network of Hepatitis C Virus

(HCV) induced immune response: HCV RNA is recognized by host cells triggering an

antiviral state (Rehermann 2009a; Takahashi et al. 2010). Dendritic cells (mDC) activate

natural killer (NK) cells, CD8+ cells, and CD4+ cells by releasing cytokines IL-12, IL-4 and IL-

15 (Takahashi et al. 2010) NK cells produce interferon-γ (IFN-γ) to mediate antiviral effects.

CD8+ cells and CD4 + cells control the T-helper cells (Th1 & Th2) which in turn regulate the

function of macrophages, induce cytolytic T-cells and T-regulatory cells (Tregs) (Rosen

2013b) HCV protein binds the NK CD81 receptor, decreasing release of IFN-γ and cytotoxic

granules by NK cells (Amadei et al. 2010) HCV protein increases major histocompatibility

complex class I expression on infected hepatocytes, decreasing Natural Killer (NK) cell

activity against infected cells (Herzer et al. 2003). HCV also increases the regulatory T cell

(Tregs) population in the liver (Belkaid & Rouse 2005). Regulatory T cells secrete

transforming growth factor–β (TGF -β) and IL-10 to decrease NK cell function (Belkaid &

Rouse 2005).


HCV

ActivationInhibition

Core

E1

E2

P7

NS2

NS3

NS4A

NS4B

NS5A

NS5B

HCVProteins

5’ 3’HCVRNA

CD 8+

Cells

CD 4+

CellsNK Cells

DCs

T reg Th1 Th2 CTL mT CellIFN-y

IL-12

Macrophages

NS5A

IL-12, IL-15, IL_6

IL-21

IL-10

NS5A

IFN-y

Core

IL-10

IL-10



Workflow of the methodology adopted to study the Biological Regulatory Network of

Hepatitis C Virus (HCV) induced immune response.


Continuous

Model Simulations

BRN Construction

Qualitative Modelling

Model Analysis

Literature

Review

Qualittaive cycles/

Disease Paths

HCV Immune

pathway

Abstracted Pathway

Model

Temporal Logic

Formulas

BRN of

HCVPathway

Qualitative Model

Network

Analysis

Parameter

Inference

Conversion

into Petri netSimulations

HCV therapeuticsPeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018


Biological Regulatory Network (BRN) depicting Hepatitis C Virus (HCV) mediated

immune regulation.

There are six nodes representing T-regulatory cells (Tregs), IL-10, NS5A (HCV non-structural

protein 5 A), IL-12, IFN-γ, NK cells. The integers -1 and +1 are used with the directed arcs to

show activation (+1 with a straight line) and inhibition (-1 with dashed line) mediated by the

viral and host cellular components.


NS5A

T-Regs IL-12

IL-10 NK Cells

IFN-y

Activation

Inhibition

KEY:

+ 1 + 1

+ 1

+ 1

+ 1 - 1

+1

- 1

+ 1

- 1

+1

- 1



State transition graph of the HCV immune network associated BRN.

The state space is represented by various interconnected nodes via directed arcs showing

the evolution of the entities in the state graph. stable state 111100 (red) also known as

deadlock/disease state is highlighted.


010011

100010

110001

010001

000010

000011

101001

001001

011100011000110000

100000

001101

010000

111100

101000

101101

000000

010100

000110

000100

010110

001010

111000

001011

001100

110110

101100

001000

110100

111110

001110

011110

111010010010110011110010

101010000001

100011 011010100111100001

100101

100110

011001

100100

110101010101

011101

111011

011011

011111

111111

000101

010111

110111

111001

111101

001111

101011

000111

101110

101111

111100 Deadlock state

Order of Entities in States:

T regulatory Cells (Tregs), IL-10, NS5A, IL-12, IFN-y, Natural Killer (NK) Cells



State graph of HCV mediated immune response based on betweenness centrality.

The state graph was analyzed on the basis of betweenness centrality. The most probable

recovery cycle has been singled out for analysis which had maximum betweenness

centrality. The size and color of the nodes have been scaled according to betweenness

centrality using Cytoscape tool (Shannon et al. 2003).


001000

101010

001001

001111

001011

001010

010110

000111010100

001101

110010

100111

110011

010000

010011

100011

111010

000000

011100111100

011000111000

110000 110111 111101

111110

101000

100110

110110

100101

100100110100

100010

100000

110101 101100

101111

101110

101011101001

111111

101101

010001111001

010101

110001

000101

011001

000100

011101

000010

000110

000011

001100111011

011011

011010

001110

011111

011110

100001010010

010111

000001

High Low Low High

Order of Entities in States: Tregulatory Cells

(Tregs), IL-10, NS5A, IL-12, IFN-y, Natural Killer (NK) Cells



The disease paths leading to a pathogenic deadlock state singled out from the state

space.

The main diseased paths including the shortest route to a stable state from the initial state

has been isolated and represented in pink color leading to a stable state in red color. The

alternate trajectories have also been highlighted which shows that there are multiple routes

to a diseased state.


010001

010110

110110

110001

100110

000011

100111000111

011011010011

001111

011101

010111

111101101101 110111

001000

001011

001010101010

100101 111111

101111

001101

110101

010101

111100

111000

110000

101011

110011

100011

110010

111011

011100

101100

001100

010100

110100

011110

111110

000101

111001

101110

011001

001110

000010100010

010010011010100001

000001

000110

100100

011111

100000

010000

011000

000100

000000

001001

111100 Deadlock State

KEY:

111010

Intermediate States

Order of Entities in States:

T regulatory Cells (Tregs), IL-10, NS5A, IL-12, IFN-y, Natural Killer (NK) Cells

101000



Illustration of the continuous Petri net (PN).

A place is depicted by a circle representing cellular enzymes, receptor complexes, and various proteins. A

continuous transition is shown by a square box which is the representative of all cellular processes. A

directed arc (arrow) connects a place with a transition and vice versa. Weights of the arcs are equal to 1

unless mentioned otherwise. “_” represents deactivated state of an entity. “P” presents positive regulation,

“n” represents negative regulation. The number of transitions represents the number and type of

regulations provided in the BRN.


I FNy

I L10

I L12

NKcel l s

NS5ATr egs

1

_I FNy

1 _I L10

1_I L12

1

_NKcel l s

1

_NS5A

1

_Tr egs

t _I FNy_0n

t _I FNy_1p

t _I L10_0p

t _I L10_2p

t _I L12_0n

t _I L12_1p

t _NKcel l s_0p

t _NKcel l s_1n

t _NS5A_0n

t _NS5A_1p

t _NS5A_2n

t _Tr egs_0p

t _Tr egs_1n

t _Tr egs_2

t _I L10_0n



Petri net (PN) analysis through simulation run.

x-axis shows time units while the y-axis represents relative activity change of the entities in

the PN. Figure 8A shows the diseased state where NK cells (Pink line) and IFN-γ (black line)

are downregulated. Figure 8B represents the recovery state where HCV NS5A (green line) is

downregulated by the activation of NK cells (pink line) and IFN-γ (black line).


0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e ex

pres

sion

Time

_IFNy

_IL10_IL12

_NKcells

_NS5A

_Tregs

_IFNy

_IL10_IL12

_NKcells

_NS5A

_Tregs

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e ex

pres

sion

Time

A

B


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