Kim “Avrama” Blackwell George Mason University

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

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

3. Mechanisms underlying LTP : NMDAR Channel Detects Coincidence Hyperpolarized Depolarized Ca++ AMPAR NMDAR AMPAR NMDAR Mg++ Mg++ Na+ Na+ Ca++

4. 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

5. 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

6. Multiple Calcium Actions in LTP and LTD • Which molecules bind more calcium? • Winner of competition determines synaptic plasticity direction? Figure provided by Ted Abel

7. Other Kinases Involved in LTP > 2 hours <= 2 hours translation Figure provided by Ted Abel

8. G protein coupled (metabotropic) receptors involved in LTP • Neuromodulators activate GPCRs • Direct action • G subunit directly gates channel • Indirect action • G protein binds to enzyme • Enzyme produces intracellular second messenger • E.g., Stimulatory G protein activates adenylyl cyclase, which produces cAMP that activates PKA • Dopamine Receptor in Striatum • Beta-Adrenergic receptor in Hippocampus, Cortex

9. Ionotropic vs Metabotropic Receptors • Metabotropic receptors are not channels • Receptor bound to neurotransmitter is enzyme that activates G protein • G protein activates downstream second messengers Direct transmitter action L L Ionotropic receptor channel Indirect transmitter action L L Metabotropic receptor Second Messenger Ion channel

10. Activation of GTP Binding Protein • Three subunits (Heterotrimeric) • Alpha: Binds to guanosine nucleotides, many different subtypes • GDP is inactive, GTP is active • Beta and Gamma • Binds to alpha subunit, prevents it from interacting with effector

11. Direct Modulation of Channel via Active G Protein Subunits • G subunit directly gates channel • Limited spatial extent • Usually G

12. Indirect action • G protein binds to enzyme • Enzyme produces intracellular second messenger • Wide spatial extent due to diffusible second messenger

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

14. 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 • Cascade of biochemical reactions

15. What are the Equations Describing Signaling Pathways? • Interactions between molecules are biochemical reactions, e.g. • Transition from closed channel to open channel is 1st order biochemical reaction mc ↔ mo • Dynamics controlled by forward and backward rate constants • What types of reactions are there?

16. 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

17. 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

18. Kf Kb Bimolecular Reactions • First order reaction: substrate product • At equilibrium: •Kb/Kf also known as dissociation constant, KD •Rate constants give frequency of transitions (identical to alpha and beta in ion channels)

19. 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

20. Kf Kb Bimolecular Reactions • Second order reaction: subs1 + subs2 product • 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)

21. Kf Kb Bimolecular Reactions • Third order reaction: subs1 + 2  subs2 product • 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)

22. Kf Kb Enzymatic Reactions • Special type of two step reaction • Enzyme is regenerated in the second step • Backward reaction rate for second step is ~0 • Each enzyme molecule can make multiple product molecules! Enz + Subs ES Enz + Product Kcat

23. Kf Kb Enzymatic Reactions • Enzyme reaction is a sequence of reactions • Equation for ES includes all paths to/from ES • One equation required for each unknown Enz + Subs ES Enz + Product Kcat

24. Michaelis-Menten Dynamics • Under Michaelis-Menten conditions, equations can be simplified • ES rapidly reaches equilibrium • Substrate is in excess (enzyme quantity is rate limiting) Total enzyme is constant: Enz = Etot - ES Equilibrium:

25. Michaelis-Menten Dynamics Solve equation for ES: Use ES in equation for product KM is affinity. No need to know Kb and Kf

26. Example using cerebellar LTD • 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

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

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

29. 1 1 (unless inject) 2 2 (unless MM) 3 3 4 Conserve Eq. Diff. Eq.

30. 4 5 4 6 We are not tracking degraded IP3 or Gq, but may include decay in Eqn. Conserve Eq. Diff. Eq.

31. General rules LHS molecule molecule • One differential equation for each molecule in the system of biochemical reactions • Conservation equations can replace some differential equations • One term on the right hand side of a differential equation for each arrow • must be in two different differential equations • Michaelis Menten approximation reduces number of equations and rate constants • But often is incorrect with transient stimuli

32. Equations Describing Reactions Molecule 1 Eqn: In some simulations we will be stimulating with Glu.mGluR Molecule 3 Eqn (using MM enzyme and degradation): No consumption of Glu.mGluR (Eqn1) when using MM No equation for G.Glu.mGluR when using MM Eqn 3 includes terms from next binding reaction

33. Equations Describing Reactions Molecule 4 Eqn: PLC.Gqα terms are of opposite sign then in Eqn 3. Molecule 5 Eqn (non-MM enzyme): Molecule 6 Eqn (production and degradation):

34. 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 • For information on reactions in Neuron, see: http://www.neuron.yale.edu/neuron/static/docs/rxd/index.html

35. 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

36. Compartment-Like Objects • Keep track of molecule quantities and concentrations • Similar to compartment or segment 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 • Rxnpool, pool, conservepool

37. Compartment-Like Objects Showobject rxnpool (Chemesis) • dC/dt =  A -  B C • A = change in quantity independent of present quantity • B = rate of change (decay) • 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)

38. Compartment-Like Objects • Keep track of molecule quantities and concentrations • conservepool (Chemesis) • C = Ctot - Ci • 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 - Ci(if flag is set to conserve) • Can also implement stochastic reactions

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

40. 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

41. 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

42. Basic Genesis Commands Create object elementname Setfield elementname field value (field value) Showfield elementname * Addmsg source dest MESSAGE sourcefield Showmsg elementname Le (list elements, like ls), Ce (change element, like cd) Reset, step (run simulation) Setclock (control dt of simulation)

43. Chemesis Example • Metabotropic receptor to PLC to IP3 • 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

44. Moose New “version” of Genesis Fantastic python interface http://moose.sourceforge.net/pymoose/moose_quickstart.html Genesis le => moose.le() Genesis showmsg element => moose.showmsg(element) Genesis showfield element * => moose.showfield(element) Genesis create object element => moose.object(element), or shortname=moose.object(element) Genesis setfield => shortname.fieldname=value