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

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 AMPARNMDAR Mg ++ Na + AMPARNMDAR Mg ++ Na + Hyperpolarized Depolarized 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 E.g., Stimulatory G protein activates adenylyl cyclase, which produces cAMP that activates PKA Dopamine Receptor in Striatum Beta-Adrenergic receptor in Hippocampus, Cortex Neuromodulators activate GPCRs Direct action  G subunit directly gates channel Indirect action  G protein binds to enzyme  Enzyme produces intracellular second messenger

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

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 (I H ) Phospholipase C (Gq)  Produces diacylgylcerol and Inositol triphosphate  DAG activates protein kinase C  IP 3 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 1 st order biochemical reaction m c ↔ m o 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. First order reaction: substrate product At equilibrium: Bimolecular Reactions K b /K f also known as dissociation constant, K D Rate constants give frequency of transitions (identical to alpha and beta in ion channels) KfKf KbKb

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. 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) Bimolecular Reactions KfKf KbKb

21. 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) Bimolecular Reactions KfKf KbKb

22. 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 KfKf KbKb Enzymatic Reactions K cat

23. 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 KfKf KbKb K cat

24. 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 Michaelis-Menten Dynamics Equilibrium:

25. Michaelis-Menten Dynamics Solve equation for ES: Use ES in equation for product K M is affinity. No need to know K b and K f

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. 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

28. LTD Mechanism in the Cerebellum Calcium influx through VDCC  Release of calcium from ER Activation of protein kinase C Glutamate binds to metabotropic glutamate receptor  Production of DAG and IP 3

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

30. 45 6 4 Conserve Eq. Diff. Eq. We are not tracking degraded IP 3 or Gq, but may include decay in Eqn.

31. General rules 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 molecule LHS molecule

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/ind ex.html http://www.neuron.yale.edu/neuron/static/docs/rxd/ind ex.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 -  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

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 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

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 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

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