COGS107B/201A
Systems Neuroscience
Instructor: Flavia Filimon
Lecture 2
1
today
• electrotonic potentials; equivalent electrical
circuits
• NMDA and LTP/ learning continued
2
Electrotonic Potentials/ graded
potentials
• passively spreading electric
current
• (as opposed to actively propagated
action potentials)
• usually from dendritic inputs; or
current injection via electrode
3
4
Quantifying passive spread
• cable theory; cable analogy with submarine
telegraph cable on the floor of the Atlantic
Ocean 1850s
5
Rm and Cm
membrane has
resistance (Rm)
membrane has
capacitance (Cm)
6
RL
• axons/dendrites have internal/axial/longitudinal
resistance (R )
• NOTE: outside resistance negligible (zero)
L
7
Basic concepts
• R = resistance (difficulty of spreading; e.g. Library Walk)
• I = current (amount of flow) (I = Q/t)
• V = voltage (e.g. “water pressure”)
• C = capacitance (how much charge you can
hold); C
area/distance betw. plates (e.g. 5 nm)
• g = conductance = 1/R
• Q = charge = C*V
8
Symbols
• resistor
• capacitor
• battery
• Nernst potential across channel
9
Laws
• Ohm’s Law: V=I*R
• Current in series is equal
• Voltage in parallel is equal
10
Laws cont’d
• Uncharged capacitor = zero resistance
• charged capacitor = infinite resistance
• it takes time to charge a capacitor
• current follows the path of least resistance
11
Adding resistances in parallel or in series
•
resistances in series add: the longer the dendrite, the more
resistance current encounters
•
resistances in parallel add as reciprocals: the smaller Rm, the
leakier the membrane; e.g. R1= 3, R2 = 3, R3 = 3; Rtot =1
12
Circuit in Series vs. in Parallel
13
Current flow and Voltage change in Series
Circuit
IR = current through resistor IC =
current through capacitor; VR =
voltage across resistor;VC =
voltage across capacitor
14
Current flow and Voltage change in Parallel
Circuit
15
Equivalent Electrical Model of
Dendrite
In membrane, Cm and Rm are
in parallel; RL are in series
16
patch of membrane with
Nernst potential across
channel - battery
What happens if we inject
current into dendrite?
Current will start
to flow everywhere,
following the path of
least resistance
current electrode
17
Steady-state current: with and
without capacitance
V or I
V or I
no capacitance
with capacitance
18
Transient impulse: with and
without capacitance
V or I
V or I
with capacitance
no capacitance
19
• spread of
electrotonic
potentials is
delayed and of
smaller amplitude
the farther away
from injection site
20
Length constant
• characteristic length (membrane space
constant) λ (lambda) - depends on Rm and
RL (also on diameter of process - big
diameter, low RL)
• the length of dendrite over which the
electrotonic potential decays to a value of
0.37 of value at injection site
21
high Rm and low RL
increase λ
big diameter
increases λ
22
Time constant τ
• membrane time constant τ (tau) depends on
Cm
• the time required for voltage change across
membrane to reach 0.37 of its final value
(i.e. of maximally charged capacitor)
• the greater the capacitance, the greater τ is
23
Myelin decreases capacitance
* Myelin separates the plates of the capacitor - current
won’t get wasted charging up the capacitor
* (myelin also INcreases Rm - less leakage)
24
Increasing diameter of axon
volume = π r2 * h
surf. area = 2 π r * h
25
→ volume goes up faster than membrane
surface area with increased diameter
→ decrease in longitudinal resistance greater
than increase in Cm or decrease in Rm
26
low impedance vs. high
impedance
• high conductance load/ low impedance
(from small to large diameter: voltage
change due to current is reduced due to low
resistance). Current sucked up by capacitor.
• high impedance (from large to small
diameter): greater voltage change (V= IR)
27
• in order to spread electrotonic potentials as
far as possible, we want:
• high membrane resistance (myelin)
• low membrane capacitance (myelin)
• low internal resistance (large diameter)
NMDA channels act as AND
gates
NMDA requires both depolarization AND
glutamate
29
LTP
• long term potentiation
30
Inducing and measuring LTP
If EPSP2 > EPSP1, LTP has occurred
31
Timing of pre-synaptic stimulation and
post-synaptic response matters
32
Spike-timing dependent
plasticity (STDP)
33
Synaptic strength change
• if pre spikes within 50 ms before post: LTP
• if post spikes within 50 ms before pre: LTD
• if pre and post spike > 50 ms apart: no
change
34
Possible LTP mechansims
35