Revision as of 08:17, 18 September 2015

model

3 Signaling module

3.1 Introduction

In our laboratory work, we performed CPP tests to explore the impact of downregulating MOR protein on mouse behavior after morphine administration, which is the ultimate goal of our project. In this module, computational and systems biology approaches were applied to examine the root of behavior changes quantitatively at the molecular level. The most important brain reward circuit involves dopamine-containing neurons in the VTA of the midbrain. Morphine can cause indirect excitation of VTA dopamine neurons by reducing inhibitory synaptic transmission mediated by GABAergic neurons [1,2].

We modeled the signaling network to investigate the emergent properties of the reward pathway. By comparing the activation degree of the reward pathway before and after downregulating MOR protein levels, we could have a better mechanistic understanding of drug effects. Although we did not perform any experiment to support this modeling module, the methods and parameters we chose are grounded in literature reports.

Figure 8. Reward pathway of acute morphine administration. We focused on activation of MOR, inhibition of AC and release of GABA vesicles in this module. The reference pathway and figure are adapted from Kyoto Encyclopedia of Genes and Genomes database (KEGG).

3.2 Model methods

We used both deterministic and stochastic models to describe the activation of GPCR and release of GABA. In biological systems, signal transmission occurs primarily through two mechanisms: (i) mass-action laws governing protein synthesis, degradation and interactions; and (ii) standard Michaelis-Menten formulation for reactions catalyzed by enzymes [3].

Broadly, mathematical models of biochemical reactions can be divided into two categories: deterministic systems and stochastic systems [3]. In deterministic models, the change in time of the components’ concentrations is completely determined by specifying the initial and boundary conditions; by contrast, the changes in concentrations of components with respect to time cannot be fully predicted in stochastic models [3]. In the previous two modules, we modeled the delivery device and RNA interference using deterministic models.

3.2.1 Modeling the activation of MOR

MOR belongs to the class A (Rhodopsin) family of heterotrimeric Gi/o protein-coupled receptors [4]. The binding of opioids to MOR activates the G protein, upon which both G-protein α and βγ subunits interact with multiple cellular effector systems. As the first step of signal transmission, the degree of activation of MOR in response to opioid has a direct and far-reaching influence on the behavior of mice.

Deterministic models were applied to describe the biochemical reactions occurring in the diagram below. We used the Matlab Simbiology package to draw the diagram and to design the equation, the details of which are accessible on the uploaded files. This model was created on the basis of work by Bhalla and Iyengar on the activation of glutamate receptor [5].

Figure 10. Reaction schemes for inhibition of AC in simulation. Reversible reactions are represented as bidirectional arrows, and enzyme reactions are drawn as an arrow with two bends. AC: adenylate cyclase; PDE: phosphodiesterase.

3.2.3 Modeling GABA vesicle releases

A stochastic model was applied to describe the random behavior of neurotransmitter vesicles release [8]. GABA is an important inhibitory neurotransmitter, the level of which directly determines the firing rate of dopamine neurons and other physiological and behavioral statuses. The GABA synaptic vesicle cycle consists of three discrete processes: synthesis of GABA vesicles, docking of GABA vesicles at the inner membrane of presynapses and release of GABA vesicles reacting to a certain signal. The release of GABA vesicles is strictly regulated by cellular signaling networks. When Gi/o is activated and the cellular cAMP level drops, the release of GABA is inhibited. Many complicated mechanisms are involved in the inhibition of GABA release due to activation of Gi/o. Here, we simply studied the action potential-independent pathway of GABA release, through which the release of GABA is directly inhibited by activated Gβγ subunits [9].

Figure 11. Schematic representation of GABA release in which four steps are modeled using mass action law and the stochastic method.

3.2.4 Gillespie’s algorithm

When spatially restricted reactions, such as the release of neurotransmitter vesicles, are studied, the traditional deterministic model is no longer effective for ignoring the discrete nature of the problem [3]. Stochastic models convert reaction rates to probability, which allows users to explore the noise and randomness of signaling networks. A standard algorithm dealing with stochastic model is Gillespie’s algorithm. This algorithm starts with the initial condition for each molecule type in the reaction network. Then, Monte Carlo simulation is applied to generate some random variables and to calculate the smallest time interval in which the reaction will occur [3,10]. Finally, the number of molecules in the reaction network is updated, and the process is repeated.

3.3 Results

The simulation results revealed the kinetics of MOR activation in case and control studies. In the CPP test, the Western blot result demonstrated that the relative level of MOR protein after MOR-siRNA injection was 0.5. Thus, the concentration of MOR protein was set at half of the level in the case study.

The results indicated that almost all the MOR protein is activated in response to morphine. The quantity and action of Gα and βγ subunits highly correlates with the quantity of MOR protein. By downregulating the MOR protein to half of its initial level, we also inhibit approximately half of activated Gα and βγ subunits.

Figure 12. Concentration-time curves for the activation of MOR in response to morphine. A: Control study with the concentration of MOR set at 1 mM. B: Case study with the concentration of MOR set at 0.5 mM due to downregulation by MOR-siRNA. Ga_GTP and Gbg represents activated Gα and βγ subunit, respectively.

The primary effector of activated Gα subunit is AC. The activation degree of AC influences its product cAMP—an important second messenger that indicates the excitability of GABAergic neurons. We now theoretically predicted and compared the inhibition of Gα subunit on AC and the subsequent decrease in cellular cAMP levels in control (wild type) and case (MOR-siRNA injected) studies.

Figure 13. Effect of downregulating MOR protein on AC activity (A) and cellular cAMP levels (B) in response to morphine. The input level of MOR protein is based on the result shown in Figure 10.

Activation of wild type MOR protein inhibited over 25% of AC, and relative cellular cAMP levels dropped below 70%, which is consistent with findings in the literature[7]. The injection of MOR-siRNA reduces the activation quantity of MOR and significantly attenuates the inhibition of AC and decrease in cAMP levels. Maintaining the cellular cAMP level induced by the drug plays a crucial role in blocking reward pathways.

Finally, we explored the relationship between MOR activation and GABA release. The wild type study revealed significant inhibition of GABA vesicles due to activated G βγ subunits. MOR-siRNA counteracted this trend by downregulating MOR protein and activated G βγ subunit levels as depicted in the case study. Maintaining GABA release reduces the excitability and firing rate of dopamine neurons, which is consistent with the expected drug effect on blockage of the reward pathway and explain the behavioral changes observed in the CPP tests.

Figure 14. Stochastic modeling of GABA release. A: Control study with the establishment of mass balance between synthesized, docked and released GABA vesicles. B: Case study with MOR-siRNA injected to attenuate the inhibition of GABA release. C: Wild type study with a normal level of MOR protein activation resulting in inhibition of GABA release. D: Summary of numbers of released and inhibited GABA vesicles in different treatments. The results are presented as the mean±S.D.

3.4 Conclusion and remarks

In this module, we used deterministic and stochastic methods to model the cell signaling network and to predict the blockage of the reward pathway by injecting MOR- siRNA. The simulation results could somewhat explain the behavioral changes observed in the CPP tests (function tests) mechanistically.

3.5 Model equations, variables and parameters

The modeling details of the activation of MOR protein and inhibition of AC are truncated here because we use software to help us design the model and there are too many parameters and equations. We have uploaded relevant source code and files for those individuals interested in exploring the models. However, we want to emphasize that our parameters are all derived from the literature. The modeling of GABA release is inspired by the literature [8] and the parameters were estimated from literature [2]. These parameters, as well as initial conditions, can be accessed in our uploaded files and we selectively list part of them below.

These parameters, as well as initial conditions, can be accessed in our uploaded files and we selectively list part of them below.

3.5.1 Activation of MOR

Model Parameters

*********************这里插第一幅表格************************************

???: Although activation of MOR has not been modeled yet, we use activation of Glutamate receptor, which has been modeled in the literature as an approximation.

Model Equations

3.5.2 Activation of MOR

Model Parameters

*********************这里插第二幅表格************************************

???: No literature has directly reported binding and disassociation constant of Gi to AC. Therefore, we use the binding and disassociation constant of Gs to AC as an approximation derived from literature[5].

Model Equations

3.5.3 GABA release

Model Parameters

*********************这里插第三幅表格************************************

References:
1.Fields, H.L. and Margolis, E.B. (2015) Understanding opioid reward. Trends in neurosciences, 38, 217-225.
2.Sotomayor, R., Forray, M.I. and Gysling, K. (2005) Acute morphine administration increases extracellular DA levels in the rat lateral septum by decreasing the GABAergic inhibitory tone in the ventral tegmental area. Journal of neuroscience research, 81, 132-139.
3.Eungdamrong, N.J. and Iyengar, R. (2004) Computational approaches for modeling regulatory cellular networks. Trends in cell biology, 14, 661-669.
4.Waldhoer, M., Bartlett, S.E. and Whistler, J.L. (2004) Opioid receptors. Annual Review of Biochemistry, 73, 953-990.
5.Bhalla, U.S. and Iyengar, R. (1999) Emergent properties of networks of biological signaling pathways. Science, 283, 381-387.
6.Nestler, E.J. and Aghajanian, G.K. (1997) Molecular and cellular basis of addiction. Science, 278, 58-63.
7.Charalampous, K.D. and Askew, W.E. (1977) Cerebellar cAMP levels following acute and chronic morphine administration. Can J Physiol Pharmacol, 55, 117-120.
8.Ribrault, C., Sekimoto, K. and Triller, A. (2011) From the stochasticity of molecular processes to the variability of synaptic transmission. Nature reviews. Neuroscience, 12, 375-387.
9.Stephens, G.J. (2009) G-protein-coupled-receptor-mediated presynaptic inhibition in the cerebellum. Trends Pharmacol Sci, 30, 421-430.
10.Gillespie, D.T. (1977) Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81, 2340-2361.

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