Kim “Avrama” Blackwell George Mason University

1. Modeling Signaling Pathways underlying Synaptic Plasticity Kim “Avrama” BlackwellGeorge Mason University

2. Importance of Signaling Pathways • Neuromodulators, e.g. Dopamine and Norepinphrine, modulate channel behaviour via intracellular signaling pathways • Synaptic plasticity, cell excitability, gene regulation and memory are controlled by intracellular signaling pathways • Intracellular signaling pathways are modelled as biochemical reactions

3. Mammalian Synaptic Plasticity • Long Term Synaptic Plasticity • Long lasting, activity dependent change in synaptic strength • Duration is one hour or more • Potentiation - increase in synaptic strength • Depression – decrease in synaptic strength • Persistence and activity dependence of change makes this an attractive mechanism for memory storage

4. Hippocampal LTP 5 ms 1 mV • Hippocampus involved in memory storage • Damage produces amnesia

5. Long-term potentiation of Schaffer collateral-CA1 synapses • High frequency stimulation of CA1 afferents enhances synaptic transmission • Repetitions of 1 sec of 100 hz • Pathway 1 receives high frequency stimulation • Stimulus 2 is unstimulated • High frequency stimulation required for firing of post-synaptic neuron (Hebb’s postulate)

6. Long-term potentiation of Schaffer collateral-CA1 synapses • Synaptic Pathway Specificity • Only stimulated pathway enhanced • Strengthening persists for hours Field Recordings Nguyen, Abel and Kandel. 1994. Science

7. Frequency requirement of LTP Low frequency stimulation produces long term depression Heynen et al. Neuron 2000 Dudek and Bear, J Neurosci 1993

8. Properties of long-term potentiation of CA1 synapses Cooperativity Magnitude of induction increases with number of stimulated afferents Associativity Weak stimulation of pathway 2 during strong stimulation of pathway 1 potentiates pathway 2 Cooperativity

9. Mechanisms Underlying LTP Depolarization of post-synaptic neuron (Hebb’s postulate) explains many properties of LTP Cooperativity: multiple fibers required for sufficient depolarization of post-synaptic neuron Frequency dependence – high frequency required for depolarization to accumulate Associativity – high frequency of strong pathway produces depolarization for weak pathway Pre-synaptic activation of weak pathway required for glutamate release NMDA receptor channel explains depolarization requirement

10. NMDAR Channel Detects Coincidence, Permeable to Calcium Hyperpolarized Depolarized Ca++ AMPAR NMDAR AMPAR NMDAR Mg++ Mg++ Na+ Na+ Ca++

11. NMDA Receptors and Calcium NMDA type glutamate receptors are calcium permeable Calcium required for LTP Intracellular calcium buffers block LTP, without disrupting the non-patched neurons Malenka et al. Science 1988

12. Calcium and Plasticity • Type of plasticity, i.e. depression versus potentiation depends on NMDA receptor activation, which controls calcium influx • Low activity = small calcium elevation = LTD • High activity = large calcium elevation = LTP Replotted from Johnston et al. (2003) Philos Trans R Soc Lond B

13. Role of Calcium in LTP Calcium (influx through NMDA receptor) binds to Calmodulin Calmodulin activates calcium calmodulin dependent kinase type II (CaMKII) Inhibition of CaMKII blocks LTP Replotted from Otmakhov et al., J Neurosci 1997

14. Multiple Calcium Actions in LTP

15. LTP and Memory Late phase of LTP (L-LTP) shares more characteristics with memory storage than early phase Produced by 4 bursts of tetanic stimulation Persists for more than two hours Requires transcription and translation

16. PKA and Late-phase LTP > 2 hours <= 2 hours translation

17. STDP • Spike Timing Dependent Plasticity • Recent experiments show that relative timing of action potentials plays a critical role in determining sign and amplitude of changes in synaptic efficacy • These experiments typically involve paired intracellular recordings • AP induced in pre-synaptic neuron • Release of Glutamate • AP induced in post-synaptic neuron • Requires AP to propagate backward into the dendritic tree

18. Spike Timing Dependent Plasticity • Pre-synaptic AP before post → LTP • Pre-synaptic AP may have contributed to post-synaptic activity • Pre-synaptic AP after post → LTD • pre-synaptic AP could NOT have contributed • Relationship between calcium elevation and sign of plasticity ? Pawlak and Kerr J Neurosci 2008

19. Can Calcium Explain STDP? In neocortical pyramidal neurons, magnitude of peak calcium does not predict direction of plasticity Nevian and Sakmann J Neurosci 2006 • Calcium and CaMKII does not explain everything! • LTD also requires endocanabinoids • Produced post-synaptically, • Diffuse to pre-synaptic receptors

20. How to Model Signaling Pathways • Identify and describe biochemical reactions comprising the signaling pathway • Metabotropic Receptors • G proteins • Membrane bound enzyme • Diffusible second messenger • Kinase or phosphatase activation

21. How to Model Signaling pathways • Metabotropic Receptors • Protein does not form channel • Protein is linked to GTP binding protein (G protein) • Effect mediated by • Activated G protein subunits • Downstream second messengers • Receptor bound to neurotransmitter is an enzyme which activates G protein

22. Ionotropic vs Metabotropic Direct transmitter action L L Ionotropic receptor Indirect transmitter action L L Second Messenger Metabotropic receptor Ion channel

23. Heterotrimeric GTP Binding Proteins • Binds to GTP or GDP • GDP bound form is inactive • GTP bound form is active • Three subunits • Alpha • Binds to guanosine nucleotides: GDP or GTP • Many different subtypes • Beta and Gamma • Binds to alpha subunit, prevents it from interacting with effector • Stabilizes G protein in membrane • Can be effectors

24. Activation of GTP Binding Protein

25. Direct and Indirect Action of G Proteins • Direct action • G subunit directly gates channel • Limited spatial extent • Usually Gbg • Indirect action • G protein binds to enzyme • Enzyme produces intracellular second messenger • Wide spatial extent due to diffusible second messenger

26. Direct Modulation of Channel via Active G Protein Subunits

27. Indirect action

28. Enzymes Activated by G proteins • Adenylyl Cyclase • Also activated by calcium-calmodulin • Produces cAMP • Activates protein kinase A • Activates cyclic nucleotide gated channels (IH) • Phospholipase C • Produces diacylgylcerol and Inositol triphosphate • DAG activates protein kinase C • IP3 causes calcium release from the ER

30. Biochemical Reactions • Bimolecular Reactions • Stoichiometric interactions between substrate molecules to form product molecule • Formation of bond between the substrate molecules • Stoichiometric implies that the reaction specifies the number of each molecule required for reaction • Molecules are consumed in order to make product

31. Biochemical Reactions • Bimolecular Reactions • Reaction order is the number of simultaneously interacting molecules • First order reaction: single substrate becomes product • Rate constants: rate (units: per sec) at which substrate becomes product • Ratio of rate constants gives concentration of substrates and products at equilibrium

32. Bimolecular Reactions • First order reaction: • At equilibrium:

33. Bimolecular Reactions Differential equations express rate of change of molecule quantity with respect to time Rate constants give frequency of transitions Equations describe behavior of large numbers of molecules (mass action kinetics) In closed system, mass is conserved, thus: Substrate = initial value - produce

34. Bimolecular Reactions • Second order reaction: • Each molecule of product requires 1 molecule of subs1 and 1 molecule of subs2 • Conservation of mass applies to both substrates • Subs1(t) = subs1(t=0) - product(t) • Subs2(t) = subs1(t=0) - product(t)

35. Bimolecular Reactions • Third order reaction: • Order of reaction is number of molecules needed for product • Substrate 2 is consumed twice as fast as substrate 1 • Subs1(t) = subs1(t=0) - product(t) • Subs2(t) = subs1(t=0) - 2  product(t)

42. LTD in the Cerebellum Purkinje cells are projection neurons of the cerebellum Many parallel fiber inputs from granule cells synapse on spines • A single climbing fiber from inferior olivary nucleus synapses massively onto dendrites From Neuromorpho.org, NMO_00892

43. Associative LTD in the Cerebellum LTD requires concurrent stimulation of parallel fibers (glutamate) and climbing fibers (depolarization) PF CF 30 s 8 pulses 100 Hz 3 pulses 20 Hz • Long term decrease in parallel fiber EPSP Before After Schreurs et al. J Neurophys 1996

44. LTD Mechanism in the Cerebellum Calcium influx through VDCC Release of calcium from the ER Activation of protein kinase C • Glutamate binds to metabotropic glutamate receptor • Production of DAG and IP3

47. General rules • One differential equation for each molecule in the system of biochemical reactions • Two terms on the right hand side of a differential equation for each set of arrows • Both terms must be in two different differential equations • Conservation equations can replace some differential equations • Michaelis Menten approximation reduces number of equations

50. XPPAUT example General purpose ODE solver commonly used in neuroscience http://www.math.pitt.edu/~bard/xpp/xpp.html Xppaut mglu-ip3.ode Evaluate role of aG decay Evaluate role of IP3 decay