Passive properties of membranes & synaptic integration

Dauphin Island Sea Lab 2014 Passive propertiesof membranes & synaptic integration

Overview • electrical signaling in neurons • dendritic synaptic inputs • membrane time constant • transfer to the soma • membrane length constant • cable theory - filtering • generate Aps (initial segment) • axonal propagation • insulation & diameter

How does electricity flow? • Wire contains charged metal ions • wire thickness • Electrons move • Positive charge moves in opposite direction • H20 flows down the path of least resistance • Waterfalls…. • Buckets & plumbing • Pipe diameter (Ri) • Leaky pipe (Rm)

What does the membrane do? • separate and maintain (pumps) gradients of solutions with different concentrations of charged ions • selectively allow certain ionic species to cross the membrane

But, the membrane is a capacitor • membrane is a very thin insulator between two conducting solutions • (membrane bilayer ≈ 4 nm) • separates and stores charge • V = q/Cm • Cm ≈ 1 F/cm2

Think about how the membrane potential arises… • Initial [X+] difference • Diffusion down [X+] gradient • Leave X- charges behind…

And, the membrane potential is… • due to the charge separation across the membrane capacitance • and the only way to change the membrane potential is to change the amount of stored charge • only a small fraction of ions are required to flux

Changing the membrane potential.. • Change the charge on the capacitor, which takes time… • Capacitance (Cm) ~ speed of change • Resistance (Rm) ~ amplitude of change • Filling a “leaky” and “stretchy” bucket

voltage must be the same across a parallel R and C • membrane time constant: m = Rm.Cm

EPSPs are rise and fall slower? • EPSC reflects direct opening / closing of ion channels • the EPSP is affected by passive membrane properties • Synaptic summation? fast slow

 and synaptic summation… • membrane capacitance is “fixed” • changing resistance (leak) can permit hi-fidelity synaptic transmission….

How electrical signals propagate • passive decay • length constant • AC/DC filtering

Cable theory (filtering) • with distance current leaks out across rm • amplitude is smaller: • less current to change voltage (V = i. rm) • rise time is slower • less current to change charge (V / t = i / C ) • leaky pipe

Synaptic Scaling [Magee & Cook, 2003] (see V-D conductances)

(DS Weiss) excitatory input excitatory input inhibitory input EPSP EPSP IPSP inhibitory input threshold action potential no action potential Combining excitation and inhibition

(DS Weiss) Shunting inhibition Hyperpolarizing IPSP EEPSP Threshold Ohm’s Law Vm EIPSP Change in Vm Depolarizing IPSP EEPSP Threshold EIPSP Vm

AP propagation • APs are conducted along excitable cell membranes away from their point of origin • e.g. down the axon from cell soma to terminal

the inward current carried by Na ions during the AP depolarizes adjacent portions of the membrane beyond threshold and the regenerative AP travels (in both directions) along the membrane depolarization of the membrane during the AP is not restricted to a single spot Local circuits

Myelination • local circuit propagation is slow (< 2 m/s) • In motorneurons propagation is fast 100 m/s • Schwann cell • envelop axons • layer of insulation • increase resistance • decrease capacitance • nodes of Ranvier • discontinuity in myelin sheath (every few 200+ m)

APs are only generated at Nodes of Ranvier high density of Na / K channels current flows rapidly between nodes AP “jumps” down fiber as successive nodal membrane capacitances are discharged little or no inter-nodal capacitance to discharge high inter-nodal rm most current flows thru ri Saltatory conduction

Passive properties of membranes & synaptic integration