# Modeling the Dynamics of Acute Phase Protein Expression in Human Hepatoma Cells Stimulated by IL-6

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## Abstract

**:**

## 1. Introduction

## 2. Model Development for the Kinetics of Acute Phase Proteins in IL-6 Stimulated Hepatocytes

#### 2.1. IL-6 Signal Transduction Model

**x**is a vector of the state variables of the model,

**p**is a vector of the parameters, and u is the input to the system. The model consists of 68 ordinary differential equations representing the mass balances of the individual proteins and protein complexes, 117 parameters describing reaction constants, and one input given by the extracellular IL-6 concentration.

_{2}complex. This phosphorylated dimer serves as the starting point for both the JAK-STAT and the MAPK pathways. In the JAK-STAT signaling, the phosphorylated dimer recruits the transcription factor STAT3, which is also tyrosine phosphorylated. The phosphorylated STAT3 dissociates from the receptor complex (IL6-gp80-gp130-JAK)

_{2}and undergoes dimerization. The dimerized STAT3 complex translocates to the nucleus and functions as a transcription factor for the expression of SOCS3, which in turn binds to the receptor gp130 and blocks the activation of JAK, thus inhibiting both STAT3 activation and MAPK activation. In the MAPK signaling, phosphorylated gp130 recruits SHP2 which subsequently undergoes phosphorylation. The phosphorylated SHP2 interacts with Grb2 and SOS. The binding of Grb2 and SOS to the receptor complex leads to the activation of RAS, which further leads to the activation of the MAPK cascade up to transcription factor C/EBPβ.

**Figure 1.**Implemented reaction network for Interleukin-6 (IL-6) induced signal transduction in hepatocytes. Adapted with permission from [10]. Copyright 2011, IET.

#### 2.2. Extended Model of Acute Phase Protein Expression Dynamics

**Figure 2.**Extension of an existing Interleukin-6 (IL-6) signal transduction model [10] to include reactions describing the expression dynamics of haptoglobin, fibrinogen, and albumin. The two dashed lines represent the JAK-STAT and MAPK-C/EBPβ pathways (see Figure 1). Adapted with permission from [10]. Copyright 2011, IET.

#### 2.3. Estimation of Unknown Parameters in the Extended Model

**Y**is a vector of the outputs calculated by the model at corresponding time points, i.e., $\left[\begin{array}{cccc}y({t}_{1})& y({t}_{2})& \cdots & y({t}_{n})\end{array}\right]$. The norm is the Euclidean (ℓ

_{2}) norm. The values of Err for the secretion rates of haptoglobin, fibrinogen, and albumin were found to be 14.41%, 12.16%, and 7.17%, respectively. All of relative errors were below 15%, which indicates that the prediction was reasonably good in comparison to the magnitude of the error bars in the experimental data.

**Figure 3.**Comparison of model-predicted secretion rates of haptoglobin, fibrinogen, and albumin to experimental data obtained from the HepG2 cultures stimulated daily by 2 nM Interleukin-6 (IL-6): (

**A**) the secretion rate of haptoglobin; (

**B**) the secretion rate of fibrinogen; (

**C**) the secretion rate of albumin.

#### 2.4. Validation of the Developed Model

#### 2.4.1. Relaxation Kinetics of Albumin, Fibrinogen, and Haptoglobin in HepG2 Cultures under a Pulse-Chase Stimulation of IL-6

**Figure 4.**Comparison of model prediction to experimental secretion rates of haptoglobin, fibrinogen, and albumin for HepG2 cells under a pulse-chase stimulation of 2 nM Interleukin-6 (IL-6): (

**A**) secretion rate of haptoglobin; (

**B**) secretion rate of fibrinogen; (

**C**) secretion rate of albumin.

#### 2.4.2. Steady State Values of Dose-Dependent Secretion Rates of Fibrinogen and Albumin in IL-6 Stimulated HepG2 Cultures

_{50}value for the fibrinogen dose-dependence profile (ED

_{50}= 0.74 nM) was approximately double the corresponding value for the albumin dose response curve (ED

_{50}= 0.32 nM). This result was consistent with the relationship between the ED

_{50}values that was observed by [1] for fibrinogen and albumin secretion. Given that measurements by [1] represent an independent data set that was not used for parameter estimation, the agreement between model predictions and the published dose response curves provided additional validation of the model.

**Figure 5.**Predicted steady state values of secretion rates of fibrinogen, albumin, and haptoglobin under various stimulation doses of Interleukin-6 (IL-6): (

**A**) Steady state values of secretion rates of fibrinogen; (

**B**) Steady state values of secretion rates of albumin; (

**C**) Steady state values of secretion rates of haptoglobin.

## 3. Investigation of Influence from the Reactions in IL-6 Signaling on the Expression Dynamics of Haptoglobin, Fibrinogen, and Albumin

_{i,j}, was then quantified by Equation (11), in which the partial derivative of the output y

_{j}with respect to parameter p

_{i}(i.e., a reaction rate constant) was normalized by the nominal values of p

_{i}and y

_{j}(i.e., ${p}_{i}^{0}$ and ${y}_{j}^{0}$ respectively);

**P**

_{0}is a vector of nominal values of all parameters in the model. In this work, the output of the system, i.e., y

_{j}in Equation (11), was set to the seven-day mean value of the secretion rate of haptoglobin, fibrinogen, and albumin, respectively for j equal to 1, 2, and 3.

_{i,j}was ranked in a decreasing order (listed in Table 1, only the top 20 parameters are listed).

Rank, i | Impact on the Secretion Rate of Haptoglobin (j = 1) | Impact on the Secretion Rate of Fibrinogen (j = 2) | Impact on the Secretion Rate of Albumin (j = 3) | |||
---|---|---|---|---|---|---|

Parameter, p_{i} | Sensitivity, |s_{i,j}| | Parameter, p_{i} | Sensitivity, |s_{i,j}| | Parameter, p_{i} | Sensitivity, |s_{i,j}| | |

1 | V_{m_h} | 7.8168 | V_{m_f} | 7.0475 | V_{m_a} | 3.7746 |

2 | k_{t-h} | 4.0417 | K_{m-f} | 3.7901 | k_{i_a} | 1.0222 |

3 | K_{m_h} | 3.0482 | k_{f}_{7} | 2.0167 | K_{m_a} | 1.0222 |

4 | k_{f51} | 0.5061 | V_{m_}_{24} | 1.8237 | k_{d_a} | 1.0221 |

5 | k_{f55} | 0.3774 | k_{26} | 1.8237 | k_{t_a} | 0.5915 |

6 | k_{58} | 0.3091 | k_{d}_{31} | 1.8100 | k_{f51} | 0.1788 |

7 | k_{f71} | 0.0075 | k_{f}_{27} | 1.8055 | k_{f55} | 0.1070 |

8 | k_{r71} | 0.0075 | k_{d}_{30} | 1.8046 | k_{58} | 0.0764 |

9 | K_{m69} | 0.0045 | K_{m_}_{24} | 1.7836 | k_{r71} | 0.0114 |

10 | V_{m69} | 0.0044 | k_{t-f} | 1.7688 | k_{f71} | 0.0114 |

11 | k_{70} | 0.0043 | k_{r}_{27} | 1.7573 | K_{m69} | 0.0068 |

12 | k_{f}_{1} | 0.0019 | k_{8} | 0.9580 | V_{m69} | 0.0068 |

13 | k_{54} | 0.0011 | k_{r}_{7} | 0.9403 | k_{70} | 0.0066 |

14 | k_{f}_{46} | 0.0011 | k_{6} | 0.8621 | k_{f}_{1} | 0.0015 |

15 | k_{6} | 0.0010 | k_{f}_{28} | 0.7990 | k_{54} | 0.0011 |

16 | k_{f}_{3} | 0.0008 | k_{f}_{1} | 0.7675 | k_{f}_{66} | 0.0010 |

17 | k_{r}_{1} | 0.0008 | k_{f}_{3} | 0.7628 | k_{f}_{46} | 0.0009 |

18 | k_{r}_{3} | 0.0007 | k_{r}_{1} | 0.7621 | k_{r}_{1} | 0.0009 |

19 | k_{r5} | 0.0006 | k_{r}_{3} | 0.7619 | k_{r}_{3} | 0.0009 |

20 | k_{f}_{5} | 0.0006 | k_{21} | 0.7480 | k_{f}_{63} | 0.0008 |

^{*}, the activation of MEK, ERK-PP, and nuclear C/EBPβ were important to the expression of both haptoglobin and albumin.

_{i}). Components gp80, JAK, gp130 were selected as they construct the receptor complex ${(\text{IL}6-\text{gp}80-\text{gp}130-\text{JAK})}_{2}^{*}$ which was involved in several important reactions. The other four drug targets were either directly involved or phosphorylated in those important reactions. These seven drug targets were further evaluated in Section 4 based upon the efficacy of the interaction with their drug counterparts on regulating the dynamics of acute phase proteins.

**Figure 6.**Identification of the reactions from the Interleukin-6 (IL-6) signal transduction pathway that have the largest impact on acute phase protein expression, based on results of sensitivity analysis (Table 1). The figure is adapted from [10], and the numerical labels correspond to the reaction numbering used in the model by [10]. Adapted with permission from [10]. Copyright 2011, IET.

## 4. Virtual Screening of Drug Targets and Drugs for Acute Phase Response

#### 4.1. A Model-Based Platform to Study the Influence from the Drug (Imidazo-Pyrrolopyridine) on Acute Phase Protein Secretion

_{i}was the equilibrium constant, k

_{f}was the forward rate constant, and k

_{f}/K

_{i}was the backward rate constant. The value of K

_{i}for a drug-target pair can be obtained from experiment or computational interpretation [24]. In order to quantify the influence from the drug on the signaling pathway and thus the system output, differential equations for the drug and the drug-target complex were added into the ODE model. The differential equation for the receptor was modified accordingly. Among the seven drug targets identified from Section 3, JAK had been extensively studied for its interaction with existing drugs. Therefore, JAK and its drug counterpart imidazo-pyrrolopyridine were used as the example to illustrate our approach in this section. The corresponding value of K

_{i}was determined to be 2.5 nM

^{−1}from experiment [18]. Since no information was found for k

_{f}in the literature, a value of 0.01 nM

^{−1}·s

^{−1}was assigned to k

_{f}to study the dynamics of the three acute phase proteins upon the treatment with various doses of imidazo-pyrrolopyridine in Figure 7. The value of 0.01 nM

^{−1}·s

^{−M}was selected for k

_{f}here because a larger value didn’t further change the expression dynamics of the three acute phase proteins in the simulation.

_{f}reflected the speed of the drug binding reaction. Figure 8 showed the kinetics of fibrinogen expression for four values of k

_{f}, as no experimental data were found for the k

_{f}value. Since imidazo-pyrrolopyridine had a large influence on the secretion of fibrinogen, only the result for fibrinogen was shown here to save space. It seems that a small increase in k

_{f}value from zero was able to suppress the secretion of fibrinogen significantly. When k

_{f}increased to 0.01 nM

^{−1}·s

^{−1}, the binding of imidazo-pyrrolopyridine to JAK reached its saturated speed.

**Figure 7.**Dose effect of imidazo-pyrrolopyridine targeting at JAK on the production of three acute phase proteins: (

**A**) haptoglobin; (

**B**) fibrinogen; (

**C**) albumin.

#### 4.2. Ranking Drug Targets Based upon the Influence from Their Interaction with the Drug on the Dynamics of Acute Phase Proteins

_{i}value shown in Section 4.1). However, no binding kinetic data were found for the other six drug targets identified in Section 3, although data might exist in commercial database from pharmaceutical companies (which was not accessible by public). Since the value of K

_{i}for the other six drug targets was not available in literature, it was assumed in this section that these targets were bound by the drug with the same kinetics as the one for imidazo-pyrrolopyridine and JAK. Based upon this, simulations were performed to evaluate the effectiveness of each drug-target pair on regulating the secretion rates of the three acute phase proteins. The effectiveness was quantified by the maximum percentage change in the secretion rate of each acute phase protein upon the binding of the drug to each target (Figure 9). The values of K

_{i}and k

_{f}were kept the same as those used in Section 4.1. The drug dose was set to 60 nM because the simulation result in Figure 7 implies that was a high enough concentration to suppress the fibrinogen secretion. The binding of the drug to each of gp80, JAK, and gp130 reduced the secretion rates of fibrinogen (by 74.4%, 71.0%, and 71.8%) and haptoglobin (by 44.5%, 4.2%, and 5.3%) but enhanced the production rate of albumin (by 22.9%, 1.7%, and 2.2%). The interaction from these drug-target pairs generally inhibited the acute phase response, especially in suppressing the secretion of fibrinogen. This can be explained by the fact that these three receptors played an important role in initiating both JAK-STAT and MAPK-C/EBPβ pathways. The binding of a drug to STATC inhibited the expression of fibrinogen (by 2.6%), slightly enhanced the section of haptoglobin (by 0.01%), and barely reduced the expression of albumin (by 0.006%). This made sense, as inhibition of STAT3C prevented the activation of nuclear STAT3 dimer and thus down-regulated the expression of fibrinogen. The deactivation of JAK-STAT pathway released some ${(\text{IL}6-\text{gp}80-\text{gp}130-\text{JAK})}_{2}^{*}$ complex to MAPK-C/EBPβ pathway for enhancing the production of haptoglobin. Therefore, the drug-STAT3C interaction only partially suppressed the acute phase response. The binding of the drug to Raf and C/EBPβ

_{i}enhanced the secretion rate of albumin (by 0.08% and 54.2%), but reduced the secretion rate of haptoglobin (by 0.5% and 72.6%). Since Raf and C/EBPβ

_{i}were the upstream components for the activation of nuclear C/EBPβ, inhibition of these two components by drugs down-regulated haptoglobin expression and restored albumin activation. The drugs binding to either Raf or C/EBPβ

_{i}only partially inhibited the acute phase response, as the secretion of fibrinogen was enhanced by 0.2% and 0.001% upon the drug binding. The drug-MEK pair showed similar effect on acute phase response as the drug-Raf or drug-C/EBPβ

_{i}pair, however, the effect from the drug-MEK pair was very limited (less than 0.001%). One potential reason for this was that the initial concentration of MEK (i.e., 41,667 nM) overwhelmed the drug dose (i.e., 60 nM) in this simulation.

_{i}was used for all the drugs in this study for screening drug targets, this assumption can be relaxed if kinetic data are available in the future.

**Figure 9.**Maximum change of the secretion rates of the three acute phase proteins upon the binding of a drug with the concentration of 60 nM to each of the selected seven drug targets.

#### 4.3. Influence of Multiple Drug Treatment on Acute Phase Protein Secretion

**Figure 10.**The accumulation rates of fibrinogen in the cell with only one of gp80, JAK, and gp130 bound by a single drug (10 nM) and in the cell with all gp80, JAK, gp130 bound by their drugs (each drug is of a 10 nM dose).

## 5. Discussion

## 6. Conclusions

_{i}. Imidazo-pyrrolopyridine targeted at JAK was used as an example drug to illustrate an approach in which the drug-target interaction is integrated with kinetic models to study the drug dose response. The simulation result showed that imidazo-pyrrolopyridine inhibited the acute phase response, especially the secretion of fibrinogen. The developed approach was used to further rank seven drug targets, with the assumption that each of them was targeted by a drug with similar binding kinetics. This assumption can be removed in the future when drug binding kinetic data are available for all drug targets. Upon binding to the drug, the targets gp80, JAK, and gp130 were found to have the largest effect on regulating the secretion of fibrinogen and on attenuating acute phase response. The developed platform was then applied to investigate the effectiveness of the drugs that bind to these three most effective targets on the regulation of fibrinogen. The simulation results show that the multiple-drug treatment approach can reduce the drug dosage to obtain the same treatment effectiveness when compared to single drug treatment approaches.

## Acknowledgments

## Author Contributions

## Appendix

_{h0}, r

_{f0}, and r

_{a0}are the initial secretion rates of haptoglobin, fibrinogen, and albumin, respectively. Their values are determined to be 0.0027, 0.0341, and 0.4463 nM/s, from the experimental data for non-stimulated HepG2 cells. These reactions are integrated into the IL-6 signaling model presented in Moya et al. [10], to predict the expression dynamics of haptoglobin, fibrinogen, and albumin. The values of parameters from Equations (A1) to (A7) are listed in the following table.

Name | Value | Unit |
---|---|---|

V_{m_h} | 0.06457 | nM/s |

K_{m_h} | 99.7421 | nM |

k_{t_h} | 2.5389 × 10^{−5} | 1/s |

V_{m_f} | 1.1841 | nM/s |

K_{m_f} | 58.1310 | nM |

k_{t_f} | 7.8158 × 10^{−6} | 1/s |

k_{i_a} | 1.0861 × 10^{−3} | 1/s |

k_{d_a} | 0.06866 | 1/s |

V_{m_a} | 0.1470 | nM/s |

K_{m_a} | 0.5118 | nM |

k_{t_a} | 4.2195 × 10^{−6} | 1/s |

## Conflicts of Interest

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**MDPI and ACS Style**

Xu, Z.; Karlsson, J.O.M.; Huang, Z.
Modeling the Dynamics of Acute Phase Protein Expression in Human Hepatoma Cells Stimulated by IL-6. *Processes* **2015**, *3*, 50-70.
https://doi.org/10.3390/pr3010050

**AMA Style**

Xu Z, Karlsson JOM, Huang Z.
Modeling the Dynamics of Acute Phase Protein Expression in Human Hepatoma Cells Stimulated by IL-6. *Processes*. 2015; 3(1):50-70.
https://doi.org/10.3390/pr3010050

**Chicago/Turabian Style**

Xu, Zhaobin, Jens O. M. Karlsson, and Zuyi Huang.
2015. "Modeling the Dynamics of Acute Phase Protein Expression in Human Hepatoma Cells Stimulated by IL-6" *Processes* 3, no. 1: 50-70.
https://doi.org/10.3390/pr3010050