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
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018
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
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018
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
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018
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
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018
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)
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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:
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018
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.
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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
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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)
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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
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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
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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
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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”
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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
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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.
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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
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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
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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.
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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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PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.26456v1 | CC BY 4.0 Open Access | rec: 23 Jan 2018, publ: 23 Jan 2018
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)
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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)
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Table 2(on next page)
Selection of logical parameters generated via SMBioNet.
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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
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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).
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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
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Figure 2(on next page)
Workflow of the methodology adopted to study the Biological Regulatory Network of
Hepatitis C Virus (HCV) induced immune response.
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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
Figure 3(on next page)
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.
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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
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Figure 4(on next page)
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.
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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
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Figure 5(on next page)
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).
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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
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Figure 6(on next page)
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.
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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
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Figure 7(on next page)
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.
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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
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Figure 8(on next page)
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).
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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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