Neurophysiology III: Membrane Models and Action Potentials - Prof. Thomas M. Talavage, Study notes of Biology

Download Neurophysiology III: Membrane Models and Action Potentials - Prof. Thomas M. Talavage and more Study notes Biology in PDF only on Docsity! 2/2/2009 1 BME 528 / ECE 528 Measurement and Stimulation of the Nervous System Neurophysiology III: Membrane Models and Action Potentials Neurophysiology III • Membrane Models • Action Potentials BME/ECE 528 2 2/2/2009 2 Cell Types • Small Cells – Exhibit equipotentials throughout the cell such that , Vm is independent of position. • Large Cells BME/ECE 528 3 – Vm varies as a function of position; typically physically larger cells Small Cell Membrane Model Small signal model:DC+ac Model: RC Circuits! BME/ECE 528 4 ( ) ( ) ( )      +×= tvg dt tdvcAreati mmmmm 2/2/2009 5 Large Cell Small Signal Analysis • Substitution yields: ( ) ( ) ( ) ( )tzkrtzvcrrtzvgrrtzv mm ,)()(, 2 ∂ +++ ∂ • This resembles a classic cable equation: i h i d tz eomoimmoi ,,2 −∂ = ∂ ( ) ( ) ( ) ( )t,zkr t t,zvt,zv z t,zv eo 2 c m Mm2 m 2 2 c λτλ −∂ ∂ += ∂ ∂ BME/ECE 528 9 w t t me constant an space constant m m m m m m M G C ag2 ac2 g c === π πτ mio c grr )( 1 + =λ Neurophysiology III • Membrane Models • Action Potentials BME/ECE 528 10 2/2/2009 6 The Action Potential BME/ECE 528 11 Unmyelinated Axon BME/ECE 528 12 2/2/2009 7 Ion Channel Behavior: Na+ BME/ECE 528 13 Ion Channel Behavior in AP Na+ K+ BME/ECE 528 14 2/2/2009 10 Ion Channel Distribution Concentrated at Nodes of Ranvier BME/ECE 528 19 Saltatory Conduction • Consider two axons: radius = h Axon 1 Axon 2 radius = 2h BME/ECE 528 20 Recall: d Areacm × = ε Myelin thickness ↑ = Capacitance ↓ 2/2/2009 11 Saltatory Conduction • So, more myelin yields lower capacitance • Consider behavior of C: Continuity equation: CVq = qV BME/ECE 528 21 • Lower C → less q required to achieve same V C = Saltatory Conduction • Fewer ions (q) required to produce an AP • Greater spatial constant – Fewer channels under myelin – Lower gm → Higher λc mio c grr )( 1 + =λ BME/ECE 528 22 • Depolarization propagates more quickly Faster conduction!