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

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. 5 ms 1 mV Hippocampal LTP 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 2000Dudek 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 AMPARNMDAR Mg ++ Na + AMPARNMDAR Mg ++ Na + Hyperpolarized Depolarized 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 Calcium and CaMKII does not explain everything! –LTD also requires endocanabinoids Produced post-synaptically, Diffuse to pre-synaptic receptors Nevian and Sakmann J Neurosci 2006

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

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 G  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 (I H ) Phospholipase C – Produces diacylgylcerol and Inositol triphosphate – DAG activates protein kinase C – IP 3 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. First order reaction: At equilibrium: Bimolecular Reactions

33. 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. 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) Bimolecular Reactions

35. 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) Bimolecular Reactions

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 8 pulses 100 Hz 3 pulses 20 Hz 30 s – Long term decrease in parallel fiber EPSP Schreurs et al. J Neurophys 1996 Before After

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 IP 3

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

51. Three Types of Objects in Chemesis/Kinetikit Pools of molecules – Keep track of concentration Uni- and Bi-molecular Reactions – Transformation of one or more molecules into equal number of another molecule Enzyme reactions – One enzyme molecule can transform multiple copies of substrate into equal number of product

52. Compartment-Like Objects Keep track of molecule quantities and concentrations Similar to compartment calculating voltage Requires geometry/morphology values length Radius Takes messages from reaction objects, enzyme objects, calcium release objects and current influx Integrates all increases and decreases Divides quantity by volume to calculate concentration

53. Compartment-Like Objects Rxnpool (chemesis) Morphology fields: Len (length) Radius Surface area and volume (vol) calculated from shape (cylinder or shell) area of outer surface area of inner surface (can be zero) area of side surface UNITS fields!!! units: 1 for SI, 1e-3 for mmole, etc Dunits (length): 1 for SI, 1e-3 for mmeter, etc Iunits: 1e-12 to convert from nA, msec to A, sec

54. Compartment-Like Objects – rxnpool (Chemesis) dC/dt =  A -  B C A = change in quantity independent of present quantity B = rate of change Receives messages with quantities A and/or B from other objects (enzymes, reactions, also calcium influx) RXN0 (A), RXN1 (B), RXN2 (A and B) For concentration inputs RXN0MOLES (A), RXN2MOLES (A and B) For quantity inputs CURRENT (valence current)

55. Compartment-Like Objects Keep track of molecule quantities and concentrations – conservepool (Chemesis) C = Ctot -  C i  Quantity is remainder after all other forms of molecule accounted for Also has volume and units fields – pool (Kinetikit) dC/dt =  A -  B C Or C = Ctot -  C i  (if flag is set to conserve) Can also implement stochastic reactions

56. Concentration Pools chemesis genesis #1 > showobject rxnpool genesis #2 > showobject conservepool genesis #3 > showobject pool

57. Enzyme and Reaction objects Calculate changes due to reactions – mmenz (Chemesis) Use if MM assumptions are met Fields: Km and Vmax Inputs: enzyme, substrate concentration Calculates V max times [Enzyme] times [substrate] divided by ([substrate] + Km) Send messages RXN0 or RXN0moles to rxnpool Empirical feedback modification of enzyme activity can be added

58. Enzyme and Reaction objects Calculate changes due to enzyme reactions Stores ES substrate concentration Has fields for volume Fields: Kcat, Kf, Kb – Enzyme (Chemesis) Fields: units, surface areas (as rxnpool) Inputs: enzyme, substrate quantity Calculates change in product, enzyme, substrate – Enz (kinetikit) Inputs: enzyme, substrate quantity Can implement stochastic reactions

59. Enzyme and Reaction objects Calculate changes due to reactions – reaction (Chemesis) or reac (kinetikit) Fields: kf, kb Inputs (messages): substrates and products Calculates: – forward rate constant times substrate molecules – backward rate constant times product molecules send messages RXN0 - RXN2 to rxnpool

60. Enzyme and Reaction objects Genesis #4> showobject mmenz Genesis #5> showobject enzyme – Compartment dimensions allows membrane bound enzyme to have different volume than substrate and products Genesis #5> showobject enz Genesis #6> showobject reaction Genesis #7> showobject reac

61. Creating Chemesis Simulation Create rxnpool pool1 Create conservepool pool2 Setfield pool1 Cinit initvalue... Addmsg pool1 pool2 CONC Conc

62. Creating Chemesis Simulation Create reaction rxn1 Setfield rxn1 kf kfvalue kb kbvalue Addmsg pool1 rxn1 SUBSTRATE Conc Addmsg pool2 rxn1 SUBSTRATE Conc Addmsg pool3 rxn1 PRODUCT Conc Addmsg rxn1 pool1 RXN2 kbprod kfsubs – To substrate – kbprod is first Addmsg rxn1 pool3 RXN2 kfsubs kbprod – To product – kfsubs is first

63. Chemesis Example Metabotropic receptor to PLC to IP 3 – mglu-ip3-chemesis.g for complete example – Setclock – to determine the time step – Include param.g – set of parameters used – Create several instances of rxnpool, conservepool, reaction, enzyme and mmenz – Include graphs.g to plot some output – Step - to run simulation