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| | and release of GABA. </B> | | and release of GABA. </B> |
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| − | In biological systems, signal transmission occurs primarily through two mechanisms: (i) | + | In biological syste |
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| − | mass-action laws governing protein synthesis, degradation and interactions; and (ii)
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| − | standard Michaelis-Menten formulation for reactions catalyzed by enzymes [3].
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| − | <br><br>
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| − | Broadly, mathematical models of biochemical reactions can be divided into two
| + | |
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| − | categories: deterministic systems and stochastic systems [3]. In deterministic models,
| + | |
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| − | the change in time of the components’ concentrations is completely determined by
| + | |
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| − | specifying the initial and boundary conditions; by contrast, the changes in
| + | |
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| − | concentrations of components with respect to time cannot be fully predicted in
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| − | stochastic models [3]. In the previous two modules, we modeled the delivery device and
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| − | RNA interference using deterministic models.
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| − | <br><br>
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| − |
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| − | <h3> 3.2.1 Modeling the activation of MOR </h3>
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| − | MOR belongs to the class A (Rhodopsin) family of heterotrimeric Gi/o protein-coupled
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| − | 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
| + | |
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| − | first step of signal transmission, the degree of activation of MOR in response to
| + | |
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| − | opioid has a direct and far-reaching influence on the behavior of mice.
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| − | <br><br>
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| − | Deterministic models were applied to describe the biochemical reactions occurring in
| + | |
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| − | 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].
| + | |
| − | | + | |
| − | <br><br>
| + | |
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| − | <!-- 插入第九张图> <img src="https://static.igem.org/mediawiki/2015/e/e3/NJU-China-
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| − | Model_Figure9.jpg" style="width:600px" > <br><br>
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| − | Figure 9. Reaction schemes for the activation of MOR in the simulation. Reversible
| + | |
| − | | + | |
| − | reactions are represented as bidirectional arrows; irreversible reactions, as
| + | |
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| − | unidirectional arrows. This figure is adapted from the literature [5]. <br><br>
| + | |
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| − | <h3> 3.2.2 Modeling adenylate cyclase inhibtion </h3>
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| − | | + | |
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| − | The concentration of second messenger is a significant indicator of excitability of
| + | |
| − | | + | |
| − | GABAergic neurons. Thus, we chose to simulate cAMP levels and adenylate cyclase (AC)
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| − | | + | |
| − | activity to determine the effect of downregulating MOR protein levels on morphine
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| − | | + | |
| − | reward signaling networks.
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| − | <br><br>
| + | |
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| − | | + | |
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| − | AC1/8 is a type of adenylate cyclases involved in the signaling of the acute morphine
| + | |
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| − | reward pathway [6]. When MOR is activated, the disassociated Gα subunit reacts with
| + | |
| − | | + | |
| − | AC1/8 and subsequently inhibits its activity, leading to a decrease in cellular cAMP
| + | |
| − | | + | |
| − | levels. The parameters of this model were primarily derived from the literature [5]
| + | |
| − | | + | |
| − | with slight modifications to fit to the data presented in the literature [7].
| + | |
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| − | <br><br>
| + | |
| − | | + | |
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| − | <!-- 插入第十张图 --> <img src="https://static.igem.org/mediawiki/2015/7/78/NJU-China-
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| − | Model_Figure10.jpg" style="width:400px" > <br><br>
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| − | 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.
| + | |
| − | <br><br>
| + | |
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| − | <h3> 3.2.3 Modeling GABA vesicle releases </h3>
| + | |
| − | | + | |
| − | | + | |
| − | A stochastic model was applied to describe the random behavior of neurotransmitter
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| − | | + | |
| − | 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].
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | <!-- 插入第十一张图 --> <img src="https://static.igem.org/mediawiki/2015/1/16/NJU-China-
| + | |
| − | | + | |
| − | Model_Figure11.jpg" style="width:600px" > <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | Figure 11. Schematic representation of GABA release in which four steps are modeled
| + | |
| − | | + | |
| − | using mass action law and the stochastic method. <br><br>
| + | |
| − | | + | |
| − | <h3> 3.2.4 Gillespie’s algorithm </h3>
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| − | | + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <h2> 3.3 Results </h3>
| + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <B> Thus, the concentration of MOR protein was set at half of the level in the case
| + | |
| − | | + | |
| − | study. </B>
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <B> 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. </B>
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <!-- 插入第十二张图 --> <img src="https://static.igem.org/mediawiki/2015/b/b3/NJU-China-
| + | |
| − | | + | |
| − | Model_Figure12.jpg" > <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | <!-- 插入第十三张图 --> <img src="https://static.igem.org/mediawiki/2015/d/d4/NJU-China-
| + | |
| − | | + | |
| − | Model_Figure13.jpg" > <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | <B> 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].
| + | |
| − | </B>
| + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <!-- 插入第十四张图 --> <img src="https://static.igem.org/mediawiki/2015/5/51/NJU-China-
| + | |
| − | | + | |
| − | Model_Figure14.jpg" style="width:600px" > <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <h2> 3.4 Conclusion and remarks </h4>
| + | |
| − | <B>
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | </B>
| + | |
| − | | + | |
| − | <h2> 3.5 Model equations, variables and parameters </h5>
| + | |
| − | | + | |
| − | | + | |
| − | 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | These parameters, as well as initial conditions, can be accessed in our uploaded files
| + | |
| − | | + | |
| − | and we selectively list part of them below.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | <h3> 3.5.1 Activation of MOR </h3>
| + | |
| − | | + | |
| − | Model Parameters
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <img src="https://static.igem.org/mediawiki/2015/d/de/NJU-China-model-sig-1.jpg" >
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | ???: 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.
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | Model Equations
| + | |
| − | | + | |
| − | <!-- 插入第一张公式 --> <img src="https://static.igem.org/mediawiki/2015/b/ba/NJU-China-
| + | |
| − | | + | |
| − | Equation_Sig_1.jpg" style="width:300px"> <br><br>
| + | |
| − | | + | |
| − | <!-- 插入第二张公式 --> <img src="https://static.igem.org/mediawiki/2015/0/0b/NJU-China-
| + | |
| − | | + | |
| − | Equation_Sig_2.jpg" style="width:300px" > <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | <h3> 3.5.2 Activation of MOR </h3>
| + | |
| − | | + | |
| − | Model Parameters
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <img src = "https://static.igem.org/mediawiki/2015/f/f2/NJU-China-model-sig-2.jpg" >
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | ???: 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].
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | Model Equations
| + | |
| − | | + | |
| − | <img src="https://static.igem.org/mediawiki/2015/a/a7/NJU-China-
| + | |
| − | | + | |
| − | Equation_Sig_3.jpg"> <br><br>
| + | |
| − | | + | |
| − | | + | |
| − | <h3> 3.5.3 GABA release </h3>
| + | |
| − | | + | |
| − | Model Parameters
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | <img src = "https://static.igem.org/mediawiki/2015/1/19/NJU-China-model-sig-3.jpg" >
| + | |
| − | | + | |
| − | <br><br>
| + | |
| − | | + | |
| − | References: <br>
| + | |
| − | 1.Fields, H.L. and Margolis, E.B. (2015) Understanding opioid reward. Trends in
| + | |
| − | | + | |
| − | neurosciences, 38, 217-225. <br>
| + | |
| − | 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. <br>
| + | |
| − | 3.Eungdamrong, N.J. and Iyengar, R. (2004) Computational approaches for modeling
| + | |
| − | | + | |
| − | regulatory cellular networks. Trends in cell biology, 14, 661-669. <br>
| + | |
| − | 4.Waldhoer, M., Bartlett, S.E. and Whistler, J.L. (2004) Opioid receptors. Annual
| + | |
| − | | + | |
| − | Review of Biochemistry, 73, 953-990. <br>
| + | |
| − | 5.Bhalla, U.S. and Iyengar, R. (1999) Emergent properties of networks of biological
| + | |
| − | | + | |
| − | signaling pathways. Science, 283, 381-387. <br>
| + | |
| − | 6.Nestler, E.J. and Aghajanian, G.K. (1997) Molecular and cellular basis of addiction.
| + | |
| − | | + | |
| − | Science, 278, 58-63. <br>
| + | |
| − | 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. <br>
| + | |
| − | 8.Ribrault, C., Sekimoto, K. and Triller, A. (2011) From the stochasticity of molecular
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| − | | + | |
| − | processes to the variability of synaptic transmission. Nature reviews. Neuroscience,
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| − | | + | |
| − | 12, 375-387. <br>
| + | |
| − | 9.Stephens, G.J. (2009) G-protein-coupled-receptor-mediated presynaptic inhibition in
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| − | | + | |
| − | the cerebellum. Trends Pharmacol Sci, 30, 421-430. <br>
| + | |
| − | 10.Gillespie, D.T. (1977) Exact stochastic simulation of coupled chemical reactions.
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| − | The Journal of Physical Chemistry, 81, 2340-2361. <br>
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