In silico stochastic simulation of Ca 2+ triggered synaptic release - PowerPoint PPT Presentation

In silico stochastic simulation of Ca 2+ triggered synaptic release Andrea Bracciali Enrico Cataldo Pierpaolo Degano Marcello Brunelli Dipartimento di Informatica Dipartimento di Biologia Universit` a di Pisa Universit` a di Pisa { braccia,degano } @di.unipi.it { ecataldo,mbrunelli } @biologia.unipi.it NETTAB 2007 – Pisa, – June 12-15, 2007 – p.1/23

Models of the neural function The functional capabilities of the nervous system arise from the complex organization of the neural network Models are needed to understand the ways in which neural circuits generate behavior, the ways in which experience alters the functional properties of circuits and therefore their behaviour (plasticity/memory), ... (and many other issues). (some) Key elements are the intrinsic biophysical/biochemical properties of the individual neurons the pattern of the synaptic connections amongst neurons the physiological properties of synaptic connections NETTAB 2007 – Pisa, – June 12-15, 2007 – p.2/23

Models of the neural function Focus: 1. A model of a pre-synaptic calcium triggered release Synapses: points of functional contact between neurons Chemical synapses: presynaptic action potentials cause chemical intermediary (neurotransmitters) to influence postsynaptic terminal Chemical synapses are plastic: modified by prior activity NETTAB 2007 – Pisa, – June 12-15, 2007 – p.3/23

Models of the neural function Focus: 1. A model of a pre-synaptic calcium triggered release Synapses: points of functional contact between neurons Chemical synapses: presynaptic action potentials cause chemical intermediary (neurotransmitters) to influence postsynaptic terminal Chemical synapses are plastic: modified by prior activity 2. A (first) stochastic model NETTAB 2007 – Pisa, – June 12-15, 2007 – p.4/23

Models of the neural function Focus: 1. A model of a pre-synaptic calcium triggered release Synapses: points of functional contact between neurons Chemical synapses: presynaptic action potentials cause chemical intermediary (neurotransmitters) to influence postsynaptic terminal Chemical synapses are plastic: modified by prior activity 2. A (first) stochastic model 3. A computational (process-algebra based) approach formal executable compositional NETTAB 2007 – Pisa, – June 12-15, 2007 – p.5/23

Presynaptic calcium triggered release 1. Calcium gradient 2. Vescicle activation (exocitosis) 3. Neuro-transimitter release 4. Calcium extrusion 5. Vescicle recharging 6. . . . 7. Neuro-transmitter reception 8. . . . From: Sudhof TC. The synaptic vesicle cycle. Annu Rev Neurosci. 27:509-47, 2004. NETTAB 2007 – Pisa, – June 12-15, 2007 – p.6/23

Presynaptic calcium concentration profile - Microdomains of Calcium concentrations near open channels - trigger the exocytosis of synaptic vescicles. - Calcium concentration during release is not homogeneous - unless subsequently in not effective concentrations. - Uncaging: An experimental method capable to induce spatially homo- geneous Calcium elevation in the From: Zucker RS, Kullmann DM, Schwartz TL. Release of Neurotransmitters. In: From presynaptic terminal. Applied to the molecules to networks - An introduction to cellu- lar and molecular neuroscience. Elsevier pp 197- synapse Calyx of Held . 244 2004. NETTAB 2007 – Pisa, – June 12-15, 2007 – p.7/23

Calyx of Held: deterministic model From: www.cs.stir.ac.uk/ bpg/research/syntran.html By means of the uncaging method, a 5-step model of release has been defi ned based on concentrations, [SN00N]: 5 k on k on − − − → − − → γ Ca 2+ + Ca 2+ + Ca 2+ + V V Ca 2+ . . . V 4 Ca 2+ V 5 Ca 2+ → T − i i i ← − − − − ← − − − − − i i i k off b 0 5 k off b 4 where k on = 9 × 10 7 M − 1 s − 1 , k off = 9500 s − 1 , γ = 6000 s − 1 and b = 0 . 25 have been defi ned by experimental fitting (complex). NETTAB 2007 – Pisa, – June 12-15, 2007 – p.8/23

Calyx of Held: stochastic model of calcium uncaging Deterministic model: unsuitable for small concentrations and volumes, e.g. if [ Ca 2+ ] = 10 µM , in a volume of 60 nm 3 there is a single free ion; the assumption that binding of Ca 2+ to vescicle does not affect the [ Ca 2+ ] concentration not adequate (with vescicle diameter ∼ 17 − 22 nm , V = 60 nm 3 few Ca 2+ ions). NETTAB 2007 – Pisa, – June 12-15, 2007 – p.9/23

Calyx of Held: stochastic model of calcium uncaging Deterministic model: unsuitable for small concentrations and volumes, e.g. if [ Ca 2+ ] = 10 µM , in a volume of 60 nm 3 there is a single free ion; the assumption that binding of Ca 2+ to vescicle does not affect the [ Ca 2+ ] concentration not adequate (with vescicle diameter ∼ 17 − 22 nm , V = 60 nm 3 few Ca 2+ ions). Stochastic model: actual quantities and stochastic rate constants: c = k 1st order c = k/ ( NA × V ) 2nd order NETTAB 2007 – Pisa, – June 12-15, 2007 – p.9/23

Calyx of Held: stochastic model of calcium uncaging Deterministic model: unsuitable for small concentrations and volumes, e.g. if [ Ca 2+ ] = 10 µM , in a volume of 60 nm 3 there is a single free ion; the assumption that binding of Ca 2+ to vescicle does not affect the [ Ca 2+ ] concentration not adequate (with vescicle diameter ∼ 17 − 22 nm , V = 60 nm 3 few Ca 2+ ions). Stochastic model: actual quantities and stochastic rate constants: c = k 1st order c = k/ ( NA × V ) 2nd order Calyx [SF06CTR]: clustered in groups of about 10 in a volume with a diameter of a vast “parallel” arrangement of almost 1 µ m. active zones (3-700) action potential activates all the each one with up to 10 vescicles active zones. NETTAB 2007 – Pisa, – June 12-15, 2007 – p.9/23

Calyx of Held: stochastic model of calcium uncaging Deterministic model: unsuitable for small concentrations and volumes, e.g. if [ Ca 2+ ] = 10 µM , in a volume of 60 nm 3 there is a single free ion; the assumption that binding of Ca 2+ to vescicle does not affect the [ Ca 2+ ] concentration not adequate (with vescicle diameter ∼ 17 − 22 nm , V = 60 nm 3 few Ca 2+ ions). Stochastic model: actual quantities and stochastic rate constants: c = k 1st order c = k/ ( NA × V ) 2nd order Calyx [SF06CTR]: clustered in groups of about 10 in a volume with a diameter of a vast “parallel” arrangement of almost 1 µ m. active zones (3-700) action potential activates all the each one with up to 10 vescicles active zones. A cluster of 10 active zone each one with 10 vescicles in V = 0 . 5 10 − 15 liter NETTAB 2007 – Pisa, – June 12-15, 2007 – p.9/23

Calyx of Held: stochastic model of calcium uncaging The obtained stochastic model: c on = 9 × 10 7 / (6 . 02 × 10 23 × 0 . 5 × 10 − 15 ) s − 1 = 0 . 3 s − 1 , c off = 9500 s − 1 , γ = 6000 s − 1 b = 0 . 25 . Ca 2+ ions: 300, 3000 and 6000, corresponding to molar concentrations [ Ca 2+ ] of 1, 10 and 20 µ M. c on 5 c on − − → − − − → γ Ca 2+ + Ca 2+ + Ca 2+ + V V Ca 2+ . . . V 4 Ca 2+ V 5 Ca 2+ → T − i i i ← − − − − − ← − − − − i i i 5 c off b 4 c off b 0 NETTAB 2007 – Pisa, – June 12-15, 2007 – p.10/23

Results 7000 10000 100 V V Vstar Ca2 T Ca2 V1Ca V1Ca 90 V2Ca V2Ca 6000 V3Ca V3Ca V4Ca V4Ca 80 Vstar Vstar T T 1000 P 5000 70 60 4000 100 50 3000 40 30 2000 10 20 1000 10 1 0 0 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 Step-like calcium uncaging, V = 100 , Ca 2+ = 6000 . Results are coherent with literature, [SN00N], e.g. High sensitivity of vescicles to Ca 2+ concentration Calyx of Held triggers vescicle release with concentrations lower than 100 µM (usual values for other synapses are 100 − 300 µM ). In the fi gure 6000 Ca 2+ correspond to 20 µM . NETTAB 2007 – Pisa, – June 12-15, 2007 – p.11/23

Results 7000 10000 100 V V Vstar Ca2 T Ca2 V1Ca V1Ca 90 V2Ca V2Ca 6000 V3Ca V3Ca V4Ca V4Ca 80 Vstar Vstar T T 1000 P 5000 70 60 4000 100 50 3000 40 30 2000 10 20 1000 10 1 0 0 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 7000 10000 80 V V Vstar Ca2 T Ca2 V1Ca V1Ca V2Ca V2Ca 70 6000 V3Ca V3Ca V4Ca V4Ca Vstar Vstar T T 1000 60 5000 50 4000 100 40 3000 30 2000 10 20 1000 10 1 0 0 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 Variation of b = 0 . 4 (was b = 0 . 25 ): lower and more uniform release rate con 5 con − − − → − − − − → Ca 2+ + Ca 2+ + Ca 2+ + V V . . . V . . . Ca 2+ 4 Ca 2+ ← − − − − − − − i ← − − − − − − i i 5 coff b 4 coff b 0 i i NETTAB 2007 – Pisa, – June 12-15, 2007 – p.12/23