Revision as of 17:48, 17 September 2015

model

2. RNAi module

2.1 Introduction

RNA interference (RNAi) is a major tool for transiently suppressing the expression of genes. Many mathematical models have been constructed to elucidate the mechanism of RNA interference and provide accurate predictions. Nevertheless, most of the current models focus merely on RNAi and fail to consider the delivery process. We modeled the delivery process and the input variant in this module should be the output result of the delivery module.

A challenge for the successful clinical application of RNAi-based drugs is determining the dosing schedule required for efficacy. Patients may ask the following questions: How soon will RNAi-based drugs take to exert efficacy after injection? How long will the efficacy last? What is the dose I need to take, and will it be too costly? How soon will the level of Mu opioid receptor (MOR) protein recover? Is RNAi therapy safe enough? Mathematical modeling using simple kinetic equations for each step in the RNAi process can shed light on many of these questions.

2.2 Model methods

This model is inspired by the paper written by Bartlett and Davis [1]. The system uses the presence of the RISC complex, which is formed in exosomes and escaped from endosome, as a stable source to provide silencing power. Then, the RISC units are targeted to mRNA having the same sequence as the siRNA that triggers this process, binding with mRNA to form an activated RISC-mRNA complex. Once bound to complementary mRNA, activated RISC may induce the degradation of mRNA and further silence protein expression.

Figure 5. Schematic diagram of RNA interference pathway. Degradation of the RISC complex, siRNA, mRNA and protein is not shown here for clear illustration. However, these processes are included in the model equations.

Applying the usual mass action to the reaction network, we can easily obtain the following model equations:

The RISC complex, derived from endosomal escape, may disassociate into free RISC and siRNA, form an activated mRNA-RISC complex or be degraded, as represented by kdisRISC, kformRISCm and kdegRISC, respectively. The free RISC and siRNA may again form a RISC complex, which is represented by kformRISC. The amount of free RISC proteins available for the formation of activated complex is rtot (free RISC protein) – R – C – kdisRISC*R (disassociated RISC protein derived from endosomes). Thus, the total numbers of siRNA- RISC complexes can be modeled using the equations below.

The number of free siRNA in the cytosol is governed by the equation below.

Activated RISC complex bound to mRNA induces the cleavage of target mRNA (kcleavage). Additionally, activated RISC complex may undergo degradation (kdegRISC) or disassociation (kdisRISCm).

The balance of formation (kformmRNA) and degradation (kdegmRNA) of mRNA and protein (kformprot kdegprot) is interrupted by RISC-induced cleavage of mRNA.

The variables and parameters of this model can be accessed here. All the parameters we used in this module are reported in the literature [1].

2.3 Results

The simulation results demonstrate the effect of siRNA on MOR knockdown in vivo.

Figure 6. Effect of siRNA on MOR mRNA (B) and protein (A) knockdown in vivo. The quantity of total exosomes injected is 300 μg which contains 3 nmol siRNA.

As depicted in the figure, the expression level of MOR protein exhibits a rapid exponential decay and reaches lowest level 12 hours after exosome injection, following a similar pattern observed with the relative level of MOR mRNA.

Figure 7. Effect of dose on MOR mRNA (A) and protein (B) knockdown in vivo. The initial quantity of total exosome injected was set at 50 μg, 100 μg, 200 μg, 400μg and 600 μg, containing 0.5 nmol, 1 nmol, 2 nmol, 4 nmol and 6 nmol siRNA, respectively.

To explore the dose effect on MOR knockdown, we set different initial conditions and ran simulations. The result shows that the concentrations of exosomes and siRNA have significant impact on knockdown efficiency and recovery time. A high dosing schedule leads to more complete knockdown of MOR protein and takes longer for MOR protein levels to recover.

To optimize the dosing schedule, the lasting times for efficiency and recovery needs to be considered. Elongating the lasting time of drug efficiency while shortening the recovery time seems paradoxical based on the simulation data. The literature has reported that 3 nmol of siRNA is adequate for repressing reward effects after 7 days of injection with the relative level of MOR protein reaching approxiamately 80%. If we assume that the threshold of relative level of MOR protein below which opioid reward effects are repressed, is 80% [2], then injecting 400 μg exosome (4 nmol siRNA) might be the best choice. The efficacy of the drug could last for about one week, and another week would be required for MOR protein levels to absolutely recover. Increasing the frequency of dosing may also help to lengthen the drug efficacy time.

2.4 Model Variables

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

2.5 Model Parameters

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

References:
1.Bartlett, D.W. and Davis, M.E. (2006) Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging. Nucleic Acids Res, 34, 322-333.
2.Zhang, Y., Landthaler, M., Schlussman, S.D., Yuferov, V., Ho, A., Tuschl, T. and Kreek, M.J. (2009) Mu opioid receptor knockdown in the substantia nigra/ventral tegmental area by synthetic small interfering RNA blocks the rewarding and locomotor effects of heroin. Neuroscience, 158, 474-483.

@@ Line 269: / Line 269: @@
 	</TD>
      <TD width="73%" bgColor=#FFFFFF style="vertical-align:top;padding-left:80px;padding-right:80px;padding-top:50px;padding-bottom:50px;word-wrap:break-word;">
-		<h1> 3 Signaling module </h1>
+			<h1> 2. RNAi module </h1>
+	<h2> 2.1 Introduction </h2>
-	<h2> 3.1 Introduction </h2>
 &nbsp;&nbsp;&nbsp;
-In our laboratory work, we performed CPP tests to explore the impact of downregulating
+RNA interference (RNAi) is a major tool for transiently suppressing the expression of
-MOR protein on mouse behavior after morphine administration, which is the ultimate goal
+genes. Many mathematical models have been constructed to elucidate the mechanism of RNA
-of our project. In this module, computational and systems biology approaches were
+interference and provide accurate predictions. Nevertheless, most of the current models
-applied to examine the root of behavior changes quantitatively at the molecular level.
+focus merely on RNAi and fail to consider the delivery process.
-The most important brain reward circuit involves dopamine-containing neurons in the VTA
+<B>
+We modeled the delivery process and the input variant in this module should be the
-of the midbrain. Morphine can cause indirect excitation of VTA dopamine neurons by
+output result of the delivery module. </B>
-reducing inhibitory synaptic transmission mediated by GABAergic neurons [1,2].
 <br><br>
@@ Line 294: / Line 292: @@
 &nbsp;&nbsp;&nbsp;
-<B>
+A challenge for the successful clinical application of RNAi-based drugs is determining
-We modeled the signaling network to investigate the emergent properties of the reward
+the dosing schedule required for efficacy. Patients may ask the following questions:
-pathway. By comparing the activation degree of the reward pathway before and after
+How soon will RNAi-based drugs take to exert efficacy after injection? How long will
-downregulating MOR protein levels, we could have a better mechanistic understanding of
+the efficacy last? What is the dose I need to take, and will it be too costly? How soon
-drug effects. Although we did not perform any experiment to support this modeling
+will the level of Mu opioid receptor (MOR) protein recover? Is RNAi therapy safe
-module, the methods and parameters we chose are grounded in literature reports.
+enough? <B> Mathematical modeling using simple kinetic equations for each step in the
-</B>
+RNAi process can shed light on many of these questions. </B>
 <br><br>
-<!--插入第八张图--> <img src="https://static.igem.org/mediawiki/2015/e/ec/NJU-China-
+	<h2> 2.2 Model methods </h2>
-Model_Figure8.jpg"> <br><br>
+&nbsp;&nbsp;&nbsp;
-Figure 8. Reward pathway of acute morphine administration. We focused on activation of
+This model is inspired by the paper written by Bartlett and Davis [1]. The system uses
-MOR, inhibition of AC and release of GABA vesicles in this module. The reference
+the presence of the RISC complex, which is formed in exosomes and escaped from
-pathway and figure are adapted from Kyoto Encyclopedia of Genes and Genomes database
+endosome, as a stable source to provide silencing power. Then, the RISC units are
-(KEGG).<br><br>
+targeted to mRNA having the same sequence as the siRNA that triggers this process,
+binding with mRNA to form an activated RISC-mRNA complex. Once bound to complementary
+mRNA, activated RISC may induce the degradation of mRNA and further silence protein
+expression.
-	<h2> 3.2 Model methods </h2>
+<br><br>
+<!-- 插入第五张图 --> <img src="https://static.igem.org/mediawiki/2015/5/55/NJU-China-
+Model_Figure5.jpg"> <br><br>
+Figure 5. Schematic diagram of RNA interference pathway. Degradation of the RISC
-&nbsp;&nbsp;&nbsp;
+complex, siRNA, mRNA and protein is not shown here for clear illustration. However,
-<B> We used both deterministic and stochastic models to describe the activation of GPCR
+these processes are included in the model equations.
-and release of GABA. </B>
-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].
 <br><br>
 &nbsp;&nbsp;&nbsp;
+Applying the usual mass action to the reaction network, we can easily obtain the
-Broadly, mathematical models of biochemical reactions can be divided into two
+following model equations:
-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.
 <br><br>
-	<h3> 3.2.1 Modeling the activation of MOR </h3>
 &nbsp;&nbsp;&nbsp;
-MOR belongs to the class A (Rhodopsin) family of heterotrimeric Gi/o protein-coupled
+The RISC complex, derived from endosomal escape, may disassociate into free RISC and
-receptors [4]. The binding of opioids to MOR activates the G protein, upon which both
+siRNA, form an activated mRNA-RISC complex or be degraded, as represented by
-G-protein α and βγ subunits interact with multiple cellular effector systems. As the
+<I>kdisRISC</I>, <I>kformRISCm</I> and <I>kdegRISC</I>, respectively. The free RISC and
-first step of signal transmission, the degree of activation of MOR in response to
+siRNA may again form a RISC complex, which is represented by <I>kformRISC</I>. The
-opioid has a direct and far-reaching influence on the behavior of mice.
-<br><br>
-&nbsp;&nbsp;&nbsp;
-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
+amount of free RISC proteins available for the formation of activated complex is
-design the equation, the details of which are accessible on the uploaded files. This
+<I>rtot</I> (free RISC protein) – <I>R</I> – <I>C</I> – <I>kdisRISC</I>*<I>R</I>
-model was created on the basis of work by Bhalla and Iyengar on the activation of
+(disassociated RISC protein derived from endosomes). Thus, the total numbers of siRNA-
-glutamate receptor [5].
+RISC complexes can be modeled using the equations below.
 <br><br>
+<!-- 插入第一张公式 --> <img src="https://static.igem.org/mediawiki/2015/7/7a/NJU-China-
-<!-- 插入第九张图>   <img src="https://static.igem.org/mediawiki/2015/e/e3/NJU-China-
+Equation_RNAi_1.jpg"> <br><br>
-Model_Figure9.jpg"> <br><br>
-Figure 9. Reaction schemes for the activation of MOR in the simulation. Reversible
-reactions are represented as bidirectional arrows; irreversible reactions, as
-unidirectional arrows. This figure is adapted from the literature [5]. <br><br>
-	<h3> 3.2.2 Modeling adenylate cyclase inhibtion </h3>
 &nbsp;&nbsp;&nbsp;
-The concentration of second messenger is a significant indicator of excitability of
+The number of free siRNA in the cytosol is governed by the equation below.
-GABAergic neurons. Thus, we chose to simulate cAMP levels and adenylate cyclase (AC)
+<br><br>
-activity to determine the effect of downregulating MOR protein levels on morphine
-reward signaling networks.
+<!-- 插入第二张公式 --> <img src="https://static.igem.org/mediawiki/2015/d/da/NJU-China-
-<br><br>
+Equation_RNAi_2.jpg"> <br><br>
 &nbsp;&nbsp;&nbsp;
-AC1/8 is a type of adenylate cyclases involved in the signaling of the acute morphine
+Activated RISC complex bound to mRNA induces the cleavage of target mRNA
-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]
+(<I>kcleavage</I>). Additionally, activated RISC complex may undergo degradation
-with slight modifications to fit to the data presented in the literature [7].
+(<I>kdegRISC</I>) or disassociation (<I>kdisRISCm</I>).
 <br><br>
+<!-- 插入第三张公式 --> <img src="https://static.igem.org/mediawiki/2015/a/a4/NJU-China-
-<!-- 插入第十张图 --> <img src="https://static.igem.org/mediawiki/2015/7/78/NJU-China-
+Equation_RNAi_3.jpg"> <br><br>
-Model_Figure10.jpg"> <br><br>
 &nbsp;&nbsp;&nbsp;
-Figure 10. Reaction schemes for inhibition of AC in simulation. Reversible reactions
+The balance of formation (<I>kformmRNA</I>) and degradation (<I>kdegmRNA</I>) of mRNA
-are represented as bidirectional arrows, and enzyme reactions are drawn as an arrow
+and protein (<I>kformprot</I> <I>kdegprot</I>) is interrupted by RISC-induced cleavage
-with two bends. AC: adenylate cyclase; PDE: phosphodiesterase.
+of mRNA.
-<br><br>
-	<h3> 3.2.3 Modeling GABA vesicle releases </h3>
-&nbsp;&nbsp;&nbsp;
-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].
 <br><br>
+<!-- 插入第四张公式 --> <img src="https://static.igem.org/mediawiki/2015/1/1f/NJU-China-
-<!-- 插入第十一张图 --> <img src="https://static.igem.org/mediawiki/2015/1/16/NJU-China-
+Equation_RNAi_4.jpg"> <br><br>
-Model_Figure11.jpg"> <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>
 &nbsp;&nbsp;&nbsp;
-When spatially restricted reactions, such as the release of neurotransmitter vesicles,
+The variables and parameters of this model can be accessed here. All the parameters we
-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.
+used in this module are reported in the literature [1].
 <br><br>
-	<h2> 3.3 Results </h3>
+	<h2> 2.3 Results </h2>
 &nbsp;&nbsp;&nbsp;
-The simulation results revealed the kinetics of MOR activation in case and control
+The simulation results demonstrate the effect of siRNA on MOR knockdown in vivo.
-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
+<!-- 插入第六张图 --> <img src="https://static.igem.org/mediawiki/2015/2/26/NJU-China-
-morphine. The quantity and action of Gα and βγ subunits highly correlates with the
+Model_Figure6.jpg"> <br><br>
-quantity of MOR protein. By downregulating the MOR protein to half of its initial
+Figure 6. Effect of siRNA on MOR mRNA (B) and protein (A) knockdown in vivo. The
-level, we also inhibit approximately half of activated Gα and βγ subunits. </B>
+quantity of total exosomes injected is 300 μg which contains 3 nmol siRNA.
-<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>
@@ Line 557: / Line 439: @@
 &nbsp;&nbsp;&nbsp;
-The primary effector of activated Gα subunit is AC. The activation degree of AC
+As depicted in the figure, the expression level of MOR protein exhibits a rapid
-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
+exponential decay and reaches lowest level 12 hours after exosome injection, following
-control (wild type) and case (MOR-siRNA injected) studies.
+a similar pattern observed with the relative level of MOR mRNA.
 <br><br>
+<!-- 插入第七张图 --> <img src="https://static.igem.org/mediawiki/2015/e/e9/NJU-China-
-<!-- 插入第十三张图 --> <img src="https://static.igem.org/mediawiki/2015/d/d4/NJU-China-
+Model_Figure7.jpg"> <br><br>
-Model_Figure13.jpg"> <br><br>
+Figure 7. Effect of dose on MOR mRNA (A) and protein (B) knockdown in vivo. The initial
+quantity of total exosome injected was set at 50 μg, 100 μg, 200 μg, 400μg and 600
-Figure 13. Effect of downregulating MOR protein on AC activity (A) and cellular cAMP
+μg, containing 0.5 nmol, 1 nmol, 2 nmol, 4 nmol and 6 nmol siRNA, respectively.
-levels (B) in response to morphine. The input level of MOR protein is based on the
-result shown in Figure 10.
 <br><br>
@@ Line 585: / Line 461: @@
 &nbsp;&nbsp;&nbsp;
-<B> Activation of wild type MOR protein inhibited over 25% of AC, and relative cellular
+To explore the dose effect on MOR knockdown, we set different initial conditions and
-cAMP levels dropped below 70%, which is consistent with findings in the literature[7].
+ran simulations. The result shows that the concentrations of exosomes and siRNA have
-</B>
-The injection of MOR-siRNA reduces the activation quantity of MOR and significantly
+significant impact on knockdown efficiency and recovery time. A high dosing schedule
-attenuates the inhibition of AC and decrease in cAMP levels. Maintaining the cellular
+leads to more complete knockdown of MOR protein and takes longer for MOR protein levels
-cAMP level induced by the drug plays a crucial role in blocking reward pathways.
+to recover.
 <br><br>
@@ Line 600: / Line 475: @@
 &nbsp;&nbsp;&nbsp;
-Finally, we explored the relationship between MOR activation and GABA release. The wild
+To optimize the dosing schedule, the lasting times for efficiency and recovery needs to
-type study revealed significant inhibition of GABA vesicles due to activated G βγ
+be considered. Elongating the lasting time of drug efficiency while shortening the
-subunits. MOR-siRNA counteracted this trend by downregulating MOR protein and activated
+recovery time seems paradoxical based on the simulation data. The literature has
-G βγ subunit levels as depicted in the case study. Maintaining GABA release reduces
+reported that 3 nmol of siRNA is adequate for repressing reward effects after 7 days of
-the excitability and firing rate of dopamine neurons, which is consistent with the
+injection with the relative level of MOR protein reaching approxiamately 80%.
-expected drug effect on blockage of the reward pathway and explain the behavioral
+<B>
+If we assume that the threshold of relative level of MOR protein below which opioid
-changes observed in the CPP tests.
+reward effects are repressed, is 80% [2], then injecting 400 μg exosome (4 nmol siRNA)
-<br><br>
+might be the best choice.
+</B>
-<!-- 插入第十四张图 --> <img src="https://static.igem.org/mediawiki/2015/5/51/NJU-China-
+The efficacy of the drug could last for about one week, and another week would be
-Model_Figure14.jpg"> <br><br>
+required for MOR protein levels to absolutely recover. Increasing the frequency of
+dosing may also help to lengthen the drug efficacy time.
-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>
-&nbsp;&nbsp;&nbsp
+	<h2> 2.4 Model Variables </h2>
-In this module, we used deterministic and stochastic methods to model the cell
+*********************这里插第一幅表格*********************************************
-signaling network and to predict the blockage of the reward pathway by injecting MOR-
+	<h2> 2.5 Model Parameters </h2>
-siRNA. The simulation results could somewhat explain the behavioral changes observed in
+*********************这里插第二幅表格*********************************************
-the CPP tests (function tests) mechanistically.
-<br><br>
-</B>
-	<h2> 3.5 Model equations, variables and parameters </h5>
-&nbsp;&nbsp;&nbsp
-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>
-&nbsp;&nbsp;&nbsp
-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>
-*********************这里插第一幅表格************************************ <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"> <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"> <br><br>
-	<h3> 3.5.2 Activation of MOR </h3>
-Model Parameters
-<br><br>
-*********************这里插第二幅表格************************************
-<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
-<!-- 插入第三张公式 --> <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>
-*********************这里插第三幅表格************************************
 <br><br>
 References: <br>
-.	Fields, H.L. and Margolis, E.B. (2015) Understanding opioid reward. Trends in
+.Bartlett, D.W. and Davis, M.E. (2006) Insights into the kinetics of siRNA-mediated
-neurosciences, 38, 217-225. <br>
-.	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>
-.	Eungdamrong, N.J. and Iyengar, R. (2004) Computational approaches for modeling
-regulatory cellular networks. Trends in cell biology, 14, 661-669. <br>
-.	Waldhoer, M., Bartlett, S.E. and Whistler, J.L. (2004) Opioid receptors. Annual
-Review of Biochemistry, 73, 953-990. <br>
+gene silencing from live-cell and live-animal bioluminescent imaging. Nucleic Acids
-.	Bhalla, U.S. and Iyengar, R. (1999) Emergent properties of networks of
-biological signaling pathways. Science, 283, 381-387. <br>
+Res, 34, 322-333. <br>
-.	Nestler, E.J. and Aghajanian, G.K. (1997) Molecular and cellular basis of
+.Zhang, Y., Landthaler, M., Schlussman, S.D., Yuferov, V., Ho, A., Tuschl, T. and
-addiction. Science, 278, 58-63. <br>
+Kreek, M.J. (2009) Mu opioid receptor knockdown in the substantia nigra/ventral
-.	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>
+tegmental area by synthetic small interfering RNA blocks the rewarding and locomotor
-.	Ribrault, C., Sekimoto, K. and Triller, A. (2011) From the stochasticity of
-molecular processes to the variability of synaptic transmission. Nature reviews.
+effects of heroin. Neuroscience, 158, 474-483. <br>
-Neuroscience, 12, 375-387. <br>
-.	Stephens, G.J. (2009) G-protein-coupled-receptor-mediated presynaptic
-inhibition in the cerebellum. Trends Pharmacol Sci, 30, 421-430. <br>
-.	Gillespie, D.T. (1977) Exact stochastic simulation of coupled chemical
-reactions. The Journal of Physical Chemistry, 81, 2340-2361. <br>