Effects of Dopamine and Glutamate on Synaptic Plasticity: A Computational Modeling Approach for Drug Abuse as Comorbidity in Mood Disorders

Abstract

Major depressive disorder (MDD) affects about 16% of the general population and is a leading cause of death in the United States and around the world. Aggravating the situation is the fact that “drug use disorders” are highly comorbid in MDD patients, and vice versa. Drug use and MDD share a common component, the dopamine system, which is critical in many motivation and reward processes, as well as in the regulation of stress responses in MDD. A potentiating mechanism in drug use disorders appears to be synaptic plasticity, which is regulated by dopamine transmission. In this article, we describe a computational model of the synaptic plasticity of GABAergic medium spiny neurons in the nucleus accumbens, which is critical in the reward system. The model accounts for effects of both dopamine and glutamate transmission. Model simulations show that GABAergic medium spiny neurons tend to respond to dopamine stimuli with synaptic potentiation and to glutamate signals with synaptic depression. Concurrent dopamine and glutamate signals cause various types of synaptic plasticity, depending on input scenarios. Interestingly, the model shows that a single 0.5 mg/kg dose of amphetamine can cause synaptic potentiation for over 2 h, a phenomenon that makes synaptic plasticity of medium spiny neurons behave quasi as a bistable system. The model also identifies mechanisms that could potentially be critical to correcting modifications of synaptic plasticity caused by drugs in MDD patients. An example is the feedback loop between protein kinase A, phosphodiesterase, and the second messenger cAMP in the postsynapse. Since reward mechanisms activated by psychostimulants could be crucial in establishing addiction comorbidity in patients with MDD, this model might become an aid for identifying and targeting specific modules within the reward system and lead to a better understanding and potential treatment of comorbid drug use disorders in MDD.

References

• 1 APA .Diagnostic and Statistical Manual of Mental Disorders (DSM-IV-TR Fourth Edition; Text Revision).. Washington, DC: Americal Psychiatric Association; 2000
• 2 Barbano PE, Spivak M, Flajolet M. et al . A mathematical tool for exploring the dynamics of biological networks.  Proc Natl Acad Sci USA. 2007;  104 19169-19174
• 3 Bewernick BH, Hurlemann R, Matusch A. et al . Nucleus accumbens deep brain stimulation decreases ratings of depression and anxiety in treatment-resistant depression.  Biol Psychiatry. 2010;  67 110-116
• 4 Bhalla US, Iyengar R. Emergent properties of networks of biological signaling pathways.  Science. 1999;  283 381-387
• 5 Bibb JA, Snyder GL, Nishi A. et al . Phosphorylation of DARPP-32 by Cdk5 modulates dopamine signalling in neurons.  Nature. 1999;  402 669-671
• 6 Calabresi P, Centonze D, Gubellini P. et al . Glutamate-triggered events inducing corticostriatal long-term depression.  J Neurosci. 1999;  19 6102-6110
• 7 Calabresi P, Pisani A, Mercuri NB. et al . Long-term Potentiation in the Striatum is Unmasked by Removing the Voltage-dependent Magnesium Block of NMDA Receptor Channels.  Eur J Neurosci. 1992;  4 929-935
• 8 Castellani GC, Bazzani A, Cooper LN. Toward a microscopic model of bidirectional synaptic plasticity.  Proc Natl Acad Sci USA. 2009;  106 14091-14095
• 9 Conner KR, Pinquart M, Holbrook AP. Meta-analysis of depression and substance use and impairment among cocaine users.  Drug Alcohol Depend. 2008;  98 13-23
• 10 Dackis CA, Gold MS, Sweeney DR. The physiology of cocaine craving and ‘crashing’.  Arch Gen Psychiatry. 1987;  44 298-300
• 11 Desdouits F, Cheetham JJ, Huang HB. et al . Mechanism of inhibition of protein phosphatase 1 by DARPP-32: studies with recombinant DARPP-32 and synthetic peptides.  Biochem Biophys Res Commun. 1995;  206 652-658
• 12 Di Chiara G, Imperato A. Drugs abused by humans preferentially increase synaptic dopamine concentrations in the mesolimbic system of freely moving rats.  Proc Natl Acad Sci USA. 1988;  85 5274-5278
• 13 Drevets WC, Price JL, Furey ML. Brain structural and functional abnormalities in mood disorders: implications for neurocircuitry models of depression.  Brain Struct Funct. 2008;  213 93-118
• 14 Fernandez É, Schiappa R, Girault JA. et al . DARPP-32 is a robust integrator of dopamine and glutamate signals.  PLoS Comput Biol. 2006;  2 e176
• 15 Gaiarsa JL, Caillard O, Ben-Ari Y. Long-term plasticity at GABAergic and glycinergic synapses: mechanisms and functional significance.  Trends Neurosci. 2002;  25 564-570
• 16 Gawin FH, Kleber HD. Abstinence symptomatology and psychiatric diagnosis in cocaine abusers. Clinical observations.  Arch Gen Psychiatry. 1986;  43 107-113
• 17 Girault JA, Hemmings Jr HC, Williams KR. et al . Phosphorylation of DARPP-32, a dopamine- and cAMP-regulated phosphoprotein, by casein kinase II.  J Biol Chem. 1989;  264 21748-21759
• 18 Hayer A, Bhalla US. Molecular switches at the synapse emerge from receptor and kinase traffic.  PLoS Comput Biol. 2005;  1 137-154
• 19 Hemmings Jr HC, Greengard P. DARPP-32, a dopamine- and adenosine 3′:5′-monophosphate-regulated phosphoprotein: regional, tissue, and phylogenetic distribution.  J Neurosci. 1986;  6 1469-1481
• 20 Hemmings Jr HC, Nairn AC, Greengard P. DARPP-32, a dopamine- and adenosine 3′:5′-monophosphate-regulated neuronal phosphoprotein. II. Comparison of the kinetics of phosphorylation of DARPP-32 and phosphatase inhibitor 1.  J Biol Chem. 1984;  259 14491-14497
• 21 Hofmann F, Bechtel PJ, Krebs EG. Concentrations of cyclic AMP-dependent protein kinase subunits in various tissues.  J Biol Chem. 1977;  252 1441-1447
• 22 Hyman SE, Malenka RC. Addiction and the brain: the neurobiology of compulsion and its persistence.  Nat Rev Neurosci. 2001;  2 695-703
• 23 Hyman SE, Malenka RC, Nestler EJ. Neural mechanisms of addiction: the role of reward-related learning and memory.  Annu Rev Neurosci. 2006;  29 565-598
• 24 Janowsky DS, Overstreet DH. The role of acetylcholine mechanisms in mood disorders.. In:, Bloom FE,, Kupfer DJ, eds, Psychopharmacology: The fourth generation of progress. New York: Raven Press, Ltd; 1995. xlii+2002
• 25 Kauer JA. Learning mechanisms in addiction: synaptic plasticity in the ventral tegmental area as a result of exposure to drugs of abuse.  Annu Rev Physiol. 2004;  66 447-475
• 26 Kessler RC, Berglund P, Demler O. et al . The epidemiology of major depressive disorder: results from the National Comorbidity Survey Replication (NCS-R).  Jama. 2003;  289 3095-3105
• 27 Khantzian EJ. The self-medication hypothesis of addictive disorders: focus on heroin and cocaine dependence.  Am J Psychiatry. 1985;  142 1259-1264
• 28 Kim M, Huang T, Abel T. et al . Temporal sensitivity of protein kinase a activation in late-phase long term potentiation.  PLoS Comput Biol. 2010;  6 e1000691
• 29 Koob GF, Kenneth Lloyd G, Mason BJ. Development of pharmacotherapies for drug addiction: a Rosetta stone approach.  Nat Rev Drug Discov. 2009;  8 500-515
• 30 Krystal JH. N-methyl-D-aspartate glutamate receptor antagonists and the promise of rapid-acting antidepressants.  Arch Gen Psychiatry. 2010;  67 1110-1111
• 31 Lindskog M, Kim M, Wikstrom MA. et al . Transient calcium and dopamine increase PKA activity and DARPP-32 phosphorylation.  PLoS Comput Biol. 2006;  2 e119
• 32 Luscher B, Shen Q, Sahir N. The GABAergic deficit hypothesis of major depressive disorder.  Mol Psychiatry. 2010; 
• 33 Maletic V, Robinson M, Oakes T. et al . Neurobiology of depression: an integrated view of key findings.  International journal of clinical practice. 2007;  61 2030-2040
• 34 Markou A, Kosten TR, Koob GF. Neurobiological similarities in depression and drug dependence: a self-medication hypothesis.  Neuropsychopharmacology. 1998;  18 135-174
• 35 Mayberg HS. Limbic-cortical dysregulation: a proposed model of depression.  J Neuropsychiatry Clin Neurosci. 1997;  9 471-481
• 36 Mayberg HS. Defining the neural circuitry of depression: Strategies toward treatment selection based on neuroimaging phenotypes.  Psychiatric Annals. 2006;  36 259-268
• 37 Mayberg HS. Targeted electrode-based modulation of neural circuits for depression.  J Clin Invest. 2009;  119 717-725
• 38 Monk CS, Klein RG, Telzer EH. et al . Amygdala and nucleus accumbens activation to emotional facial expressions in children and adolescents at risk for major depression.  Am J Psychiatry. 2008;  165 90-98
• 39 Murray CJ, Lopez AD. Global mortality, disability, and the contribution of risk factors: Global Burden of Disease Study.  Lancet. 1997;  349 1436-1442
• 40 Nagase T, Murakami T, Nozaki H. et al . Tissue and subcellular distributions, and characterization of rat brain protein phosphatase 2A containing a 72-kDa delta/B” subunit.  J Biochem. 1997;  122 178-187
• 41 Nakano T, Doi T, Yoshimoto J. et al . A kinetic model of dopamine- and calcium-dependent striatal synaptic plasticity.  PLoS Comput Biol. 2010;  6 e1000670
• 42 Nestler EJ, Carlezon Jr WA. The mesolimbic dopamine reward circuit in depression.  Biol Psychiatry. 2006;  59 1151-1159
• 43 Nishi A, Bibb JA, Snyder GL. et al . Amplification of dopaminergic signaling by a positive feedback loop.  Proc Natl Acad Sci USA. 2000;  97 12840-12845
• 44 Ouimet CC, da Cruz e Silva EF, Greengard P. The alpha and gamma 1 isoforms of protein phosphatase 1 are highly and specifically concentrated in dendritic spines.  Proc Natl Acad Sci USA. 1995;  92 3396-3400
• 45 Patel S, Morris SA, Adkins CE. et al . Ca2+-independent inhibition of inositol trisphosphate receptors by calmodulin: redistribution of calmodulin as a possible means of regulating Ca2+ mobilization.  Proc Natl Acad Sci USA. 1997;  94 11627-11632
• 46 Pelizza L, Ferrari A. Anhedonia in schizophrenia and major depression: state or trait?.  Ann Gen Psychiatry. 2009;  8 22
• 47 Price JL, Drevets WC. Neurocircuitry of mood disorders.  Neuropsychopharmacology. 2010;  35 192-216
• 48 Qi Z, Miller GW, Voit EO. Computational systems analysis of dopamine metabolism.  PLoS One. 2008;  3 e2444
• 49 Qi Z, Miller GW, Voit EO. A mathematical model of presynaptic dopamine homeostasis: implications for schizophrenia.  Pharmacopsychiatry. 2008;  41 (Suppl. 1) S89-S98
• 50 Qi Z, Miller GW, Voit EO. The internal state of medium spiny neurons varies in response to different input signals.  BMC Syst Biol. 2010;  4 26
• 51 Raison CL, Capuron L, Miller AH. Cytokines sing the blues: inflammation and the pathogenesis of depression.  Trends Immunol. 2006;  27 24-31
• 52 Rakhilin SV, Olson PA, Nishi A. et al . A network of control mediated by regulator of calcium/calmodulin-dependent signaling.  Science. 2004;  306 698-701
• 53 Rao U, Hammen CL, Poland RE. Mechanisms underlying the comorbidity between depressive and addictive disorders in adolescents: interactions between stress and HPA activity.  The American journal of psychiatry. 2009;  166 361-369
• 54 Rayport SG, Kandel ER. Development of plastic mechanisms related to learning at identified chemical synaptic connections in Aplysia.  Neuroscience. 1986;  17 283-294
• 55 Reynolds JN, Hyland BI, Wickens JR. A cellular mechanism of reward-related learning.  Nature. 2001;  413 67-70
• 56 Reynolds JN, Wickens JR. Substantia nigra dopamine regulates synaptic plasticity and membrane potential fluctuations in the rat neostriatum, in vivo.  Neuroscience. 2000;  99 199-203
• 57 Reynolds JN, Wickens JR. Dopamine-dependent plasticity of corticostriatal synapses.  Neural Netw. 2002;  15 507-521
• 58 Ross HE, Glaser FB, Germanson T. The prevalence of psychiatric disorders in patients with alcohol and other drug problems.  Arch Gen Psychiatry. 1988;  45 1023-1031
• 59 Ross HE, Glasser FB, Stiasny S. Sex differences in the prevalence of psychiatric disorders in patients with alcohol and drug problems.  Br J Addict. 1988;  83 1179-1192
• 60 Sanacora G, Mason GF, Rothman DL. et al . Reduced cortical gamma-aminobutyric acid levels in depressed patients determined by proton magnetic resonance spectroscopy.  Arch Gen Psychiatry. 1999;  56 1043-1047
• 61 Sanderson WC, Beck AT, Beck J. Syndrome comorbidity in patients with major depression or dysthymia: prevalence and temporal relationships.  Am J Psychiatry. 1990;  147 1025-1028
• 62 Shi SH, Hayashi Y, Petralia RS. et al . Rapid spine delivery and redistribution of AMPA receptors after synaptic NMDA receptor activation.  Science. 1999;  284 1811-1816
• 63 Sim AT, Ratcliffe E, Mumby MC. et al . Differential activities of protein phosphatase types 1 and 2A in cytosolic and particulate fractions from rat forebrain.  J Neurochem. 1994;  62 1552-1559
• 64 Snyder GL, Allen PB, Fienberg AA. et al . Regulation of phosphorylation of the GluR1 AMPA receptor in the neostriatum by dopamine and psychostimulants in vivo.  J Neurosci. 2000;  20 4480-4488
• 65 Stahl SM. Stahl's Essential Psychopharmacology: Neuroscientific Basis and Practical Applications.. 3rdedition ed: Cambridge University Press; 2008: 1132
• 66 Sulzer D, Sonders MS, Poulsen NW. et al . Mechanisms of neurotransmitter release by amphetamines: a review.  Prog Neurobiol. 2005;  75 406-433
• 67 Takahashi S, Ohshima T, Cho A. et al . Increased activity of cyclin-dependent kinase 5 leads to attenuation of cocaine-mediated dopamine signaling.  Proc Natl Acad Sci USA. 2005;  102 1737-1742
• 68 Tang K, Low MJ, Grandy DK. et al . Dopamine-dependent synaptic plasticity in striatum during in vivo development.  Proc Natl Acad Sci USA. 2001;  98 1255-1260
• 69 Tisch S, Silberstein P, Limousin-Dowsey P. et al . The basal ganglia: anatomy, physiology, and pharmacology.  Psychiatr Clin North Am. 2004;  27 757-799
• 70 Usui H, Inoue R, Tanabe O. et al . Activation of protein phosphatase 2A by cAMP-dependent protein kinase-catalyzed phosphorylation of the 74-kDa B” (delta) regulatory subunit in vitro and identification of the phosphorylation sites.  FEBS Lett. 1998;  430 312-316
• 71 Voit EO. Computational analysis of biochemical systems: a practical guide for biochemists and molecular biologists.. Cambridge, UK: Cambridge University Press; 2000. xii, 531 p.
• 72 Voit EO, Qi Z, Miller GW. Steps of modeling complex biological systems.  Pharmacopsychiatry. 2008;  41 (Suppl. 1) S78-S84
• 73 Weiss RD, Mirin SM, Griffin ML. Methodological considerations in the diagnosis of coexisting psychiatric disorders in substance abusers.  Br J Addict. 1992;  87 179-187
• 74 Wickens JR, Begg AJ, Arbuthnott GW. Dopamine reverses the depression of rat corticostriatal synapses which normally follows high-frequency stimulation of cortex in vitro.  Neuroscience. 1996;  70 1-5
• 75 Willner P. Dopamine and depression: a review of recent evidence. I. Empirical studies.  Brain Res. 1983;  287 211-224
• 76 Willner P. Dopamine and depression: a review of recent evidence. II. Theoretical approaches.  Brain Res. 1983;  287 225-236
• 77 Willner P. Dopamine and depression: a review of recent evidence. III. The effects of antidepressant treatments.  Brain Res. 1983;  287 237-246
• 78 Zetterstrom T, Sharp T, Ungerstedt U. Further evaluation of the mechanism by which amphetamine reduces striatal dopamine metabolism: a brain dialysis study.  Eur J Pharmacol. 1986;  132 1-9

Appendix

Reactions, kinetics, and initial conditions in the mathematical model of signal transduction and trafficking of AMPA receptors

All reactions are represented in the form of an enzymatic reaction or a simple binding reaction, with K_f denoting the rate constant for the forward process, K_b denoting the rate constant for the backward process, and K_c denoting the rate constant for the catalytic step in a Michaelis-Menten kinetics.

Table 1 Reactions and rate constants of signal transduction for DARPP-32 phosphorylation in dendrites of medium spiny neurons in the striatum (see legend of [Fig.2c] for abbreviations).

Reaction	Kf (nM−1.s−1)#	Kb (s−1)	Kc (s−1)	Ref.
D1+DA ↔ D1_DA	1.1E−3	10.0		[31]
D1_DA+Gαβγ ↔ D1_DA_Gαβγ	6.0E−4	1.0E−3		[31]
D1+Gαβγ ↔ D1_Gαβγ	6.0E−5	3.0E−4		[31]
D1_Gαβγ+DA ↔ D1_DA_Gαβγ	3.3E−3	10.0		[31]
D1_DA_Gαβγ → D1_DA+GαGTP+Gβγ	20.0a			[31]
GαGTP → GαGDP	10.0a			[31]
GαGDP+Gβγ → Gαβγ	100.0			[31]
GαGTP+AC5 ↔ GαGTP_AC5	3.9E−2	50.0		[31]
GαGTP_AC5+ATP ↔ GαGTP_AC5_ATP	1.3E−4	2.6E−1		[31]
GαGTP_AC5_ATP ↔ GαGTP_AC5+cAMP	28.5a	2.6E−4b		[31]
PKA+2 cAMP ↔ PKA_cAMP2	3.5E−8c	6.0E−2		[41]
PKA_cAMP2+2 cAMP ↔ PKA_cAMP4	2.7E−5c	0.28		[41]
PKA_cAMP4 ↔ 2 PKAc+PKAr	0.05a	8.5E−8c		[41]
PDE1+cAMP ↔ PDE1_cAMP → PDE1+AMP	2.0E−3	72.0	18.0	[31]
PDE4+cAMP ↔ PDE4_cAMP → PDE4+AMP	2.0E−3	72.0	18.0	[31]
PKAc+PDE1 ↔ PKAc_PDE1 → PKAc+PDE1p	6.0E−3	36.0	9.0	[4]
PDE1p → PDE1	1.0E−1a			[4]
PKAc+PDE4 ↔ PKAc_PDE4 → PKAc+PDE4p	6.0E−3	36.0	9.0	[4]
PDE4p → PDE4	1.0E−1a			[4]
→ Ca2+	1.0E+2e			[4]
Ca2+ →	2.0a			[4]
2 Ca2++PP2Bi ↔ PP2Bi_Ca2	6.0E−3	0.91		[4]
2 Ca2++PP2Bi_Ca2 ↔ PP2B	0.1	10.0		[4]
AC5+Ca2+ ↔ AC5_Ca	1.0E−3	0.9		[31]
GαGTP+AC5_Ca ↔ GαGTP_AC5_Ca	1.9E−2	25.0		[31]
GαGTP_AC5_Ca+ATP ↔ GαGTP_AC5_Ca_ATP	6.0E−5	1.3E−1		[31]
GαGTP_AC5_Ca_ATP ↔ GαGTP_AC5_Ca+cAMP	14.2a	1.3E−4b		[31]
PP2A+4 Ca2+ ↔ PP2Ac	7.7E−12d	1.0E−2		[31]
PP2A+PKAc ↔ PP2A_PKAc → PP2Ap+PKAc	2.5E−3	0.3	0.1	[70]
PP2Ap → PP2A	4.0E−3a			[31]
CK1 → CK1p	1.0a			[14]
PP2B+CK1p ↔ PP2B_CK1p → PP2B+CK1	3.0E−2	24.0	6.0	[14]
CDK5+Ca2+ ↔ CDK5c	3.0E−3	1.0
PDE1p+cAMP ↔ PDE1p_cAMP → PDE1p+AMP	5.0E−3	80.0	20.0
PDE4p+cAMP ↔ PDE4p_cAMP → PDE4p+AMP	5.0E−3	80.0	20.0
a: Unit in s−1 ; b: Unit in nM−1.s−1 ; c: Unit in nM−2.s−1 ; d: Unit in nM−4.s−1; e: Unit in nM.s−1
#: For a chemical reaction, Kf is the rate constant for the forward process, Kb is the rate constant for the backward process, while Kc is the rate constant for the catalytic step in a Michaelis-Menten kinetics

Table 2 Reactions and rate constants of DARPP-32 phosphorylation in dendrites of medium spiny neurons in the striatum (see legend of [Fig. 2c] for abbreviations).

Reaction	Kf (nM−1.s−1)#	Kb (s−1)	Kc (s−1)	Ref.
D+PKAc ↔ D_PKAc → D34+PKAc	2.7E−3	8.0	2.0	[31]
D34+PP2B ↔ D34_PP2B → D+PP2B	1.0E−2	2.0	0.5	[31]
D+CDK5 ↔ D_CDK5 → D75+CDK5	4.5E−4	2.0	0.5	[31]
D75+PP2Ap ↔ D75_PP2Ap → D+PP2Ap	4.0E−4	12.0	3.0	[31]
D75+PP2Ac ↔ D75_PP2Ac → D+PP2Ac	4.0E−4	12.0	3.0	[31]
D+CK2 ↔ D_CK2 → D102+CK2	4.0E−4	6.4	1.6	[17]
D102 → D	1.6a
D+CK1 ↔ D_CK1 → D137+CK1	4.4E−3	12.0	3.0	[67]
D137+PP2C ↔ D137_PP2C → D+PP2C	7.5E−3	12.0	3.0	[14]
D34+PP1 ↔ D34_PP1	1.0E−2	1.0		[14]
D34_PP1+PP2B ↔ D34_PP1_PP2B → D+PP1+PP2B	1.0E−3	2.0	0.5	[14]
D75+PKAc ↔ D75_PKAc	4.6E−3	2.4		[5]
D+CDK5c ↔ D_CDK5c → D75+CDK5c	1.8E−3	4.0	1.0
2 Ca2++CaM ↔ Ca2CaM	6.0E−3b	9.1		[31]
2 Ca2++Ca2CaM ↔ Ca4CaM	0.1b	1.0E+3		[31]
CaMKII+Ca4CaM ↔ CaMKII_Ca4CaM	0.01	0.8		[31]
CaMKII_Ca4CaM → CaMKIIp+Ca4CaM	5.0E−3a			[31]
CaMKIIp+PP1 ↔ CaMKIIp_PP1 → CaMKII+PP1	1.0E−4	1.4	0.35	[28] [31]
PKAc+I1 ↔ PKAc_I1 → PKAc+I1p	1.4E−3	5.6	1.4	[28] [31]
PP1+I1p ↔ PP1_I1p	1.0E−3	5.0E−3
PP2B+I1p ↔ PP2B_I1p → PP2B+I1	3.8E−3	12.0	3.0
a: Unit in s−1 ; b: Unit in nM−1.s−1 ; c: Unit in nM−2.s−1 ; d: Unit in nM−4.s−1; e: Unit in nM.s−1
#: For a chemical reaction, Kf is the rate constant for the forward process, Kb is the rate constant for the backward process, while Kc is the rate constant for the catalytic step in a Michaelis-Menten kinetics

Table 3 Reactions and rate constants of AMPAR trafficking, AMPAR phosphorylation, and AMPAR dephosphorylation in the postsynapse of striatal projection neurons (see legend of [Fig. 2c] for abbreviations).

Reaction	Kf (nM−1.s−1)	Kb (s−1)	Kc (s−1)	Ref.
cAMPAR+PKAc ↔ cAMPAR_PKAc → cAMPAR_Ser845p+PKAc	2.5E−3	4.0	1.0	[41]
cAMPAR_Ser845p+PP1 ↔ cAMPAR_Ser845p_PP1 → cAMPAR+PP1	5.0E−4	12.0	3.0	[64]
cAMPAR_Ser845p+PP2Ap ↔ cAMPAR_Ser845p_PP2Ap → cAMPAR+PP2Ap	1.7E−4	12.0	3.0	[64]
cAMPAR_Ser845p+PP2Ac ↔ cAMPAR_Ser845p_PP2Ac → cAMPAR+PP2Ac	1.7E−4	12.0	3.0	[64]
cAMPAR_Ser845p+CaMKIIp ↔ cAMPAR_Ser845p_CaMKIIp → cAMPAR_Ser845p_Ser831p+CaMKIIp	1.0E−4	2.0	0.5	[41]
cAMPAR_Ser845p_Ser831p+PP1 ↔ cAMPAR_Ser845p_Ser831p_PP1 → cAMPAR_Ser845p+PP1	5.0E−4	4.0	1.0	[64]
cAMPAR_Ser845p_Ser831p+PP2Ap ↔ cAMPAR_Ser845p_Ser831p_PP2Ap → cAMPAR_Ser845p+PP2Ap	1.7E−4	4.0	1.0	[64]
cAMPAR_Ser845p_Ser831p+PP2Ac ↔ cAMPAR_Ser845p_Ser831p_PP2Ac → cAMPAR_Ser845p+PP2Ac	1.7E−4	4.0	1.0	[64]
mAMPAR+PKAc ↔ mAMPAR_PKAc → mAMPAR_Ser845p+PKAc	2.5E−3	4.0	1.0	[41]
mAMPAR_Ser845p+PP1 ↔ mAMPAR_Ser845p_PP1 → mAMPAR+PP1	5.0E−4	0.8	0.2	[64]
mAMPAR_Ser845p+CaMKIIp ↔ mAMPAR_Ser845p_CaMKIIp → mAMPAR_Ser845p_Ser831p+CaMKIIp	1.0E−4	2.0	0.5	[41]
mAMPAR_Ser845p_Ser831p+PP1 ↔ mAMPAR_Ser845p_Ser831p_PP1 → mAMPAR_Ser845p+PP1	5.0E−4	4.0	1.0	[64]
mAMPAR → cAMPAR+Anchor	0.8E−3a			[18]
cAMPAR_Ser845p_Ser831p+Anchor ↔ mAMPAR_Ser845p_Ser831p	1.0E−5	0.1		[18]
cAMPAR ↔ Bulk_cAMPAR	1a	1.8E−2		[18]
cAMPAR_Ser845p → Bulk_cAMPAR	2.0E−5a			[18]
cAMPAR_Ser845p_Ser831p → Bulk_cAMPAR	2.0E−5a			[18]
a: Unit in s−1
#: For a chemical reaction, Kf is the rate constant for the forward process, Kb is the rate constant for the backward process, while Kc is the rate constant for the catalytic step in a Michaelis-Menten kinetics

Table 4 Initial values for the DARPP-32 phosphorylation system in dendrites of medium spiny neurons in the striatum (see legend of [Fig. 2c] for abbreviations).

Molecule	Concentration (nM)	Reference
DA	10.0	[31]
D1	5.0E+2	[31]
Gαβγ	3.0E+3	[31]
AC5	2.5E+3	[31]
ATP	2.0E+6	[31]
PDE1	5.0E+2	[31]
PDE4	5.0E+2	[31]
DARPP-32	3.0E+4	[19]
PKA	6.6E+3	[21]
PP2Bi	4.0E+3	[31]
CDK5	1.2E+3	[31]
PP2A	8.0E+2	[40] [63]
CK1	2.0E+3
PP2C	2.0E+3
PP1	2.3E+3	[11] [44]
CK2	2.0E+3
Anchor	11.56E+3	[41]
Bulk_cAMPAR	6.0E+3	[41]
CaM	1.0E+4	[45] [52]
CaMKII	2.0E+4	[31]
I1	1.0E+3

Correspondence