Transcript 생리현상에 대한 공학적해석

생리현상에 대한 공학적해석
5: Dendrite Summation
Neuron and Dendrite
 3 parts of Neuron
: dendrite(input)
: body(processor)
: axon (output)
 Hillock
그림 569
: initial section of axon
: lowest threshold; 8mV
: AP is generated
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Dendrite Tree
 Input architecture of neuron
: branch collects about 100,000 messages
: coming from preceding neurons
: via synaptic & electrical gap junction
 Dendrite branches
: nonregenerating & unmyelinated
: rapid attenuation of signal
 dendrite potential
그림 569
 Inhibitory inputs
: relatively weak & close to neuron body
: raise firing threshold of neuron
 Output resulting from combination of input signals
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Dendrite Potential
 Propagates toward neuron body
: increase in time width, decrease in voltage
: neuron body is excited by simultaneous APs
: less attenuation for closer junctions
 fewer stimulating neuron
 Generation of Action Potential
: when net summation exceeds threshold
 Graded potential generating neuron
: proportional potential to net summation of DPs
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Four targets for the messages
1. To skeletal muscle
: result in contraction
2. To cardiac, smooth muscle & visceral organs
: Action Potential & Graded Potential(Sometimes)
: release of chemical transmitter  stimulated target tissue
 Heart muscle
- sympathetic nerve stimulation  adrenaline
 increase contraction of heart muscle
- parasympathetic nerve stimulation acetylcholine
 decrease contraction
 Pancreas
- parasympathetic nerve stimulation acetylcholine
 increase production of digestive enzyme
- sympathetic nerve stimulation(during stress)
 adrenaline  inhibit production of digestive enzyme
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
4 Targets for the messages
3. To neurosecretory cells
: release of neurohormones
 Hypothalamus neuron
: send axon to nearby posterior pituitary
 secretion of substance
 stimulate or inhibit the secretion of hormones of pituitary
4. On the dendrites of other neurons
: transmission of message
: processing of message
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Spatial Summation of Dendrite
cf) Temporal summation
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Dendrite
 Treelike structure
: dendritic tree
: gather messages
: fewer to 100,000
: via synaptic junction
: via electrical gap junction
: single AP at the periphery
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그림 5-1
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Synaptic Junction
 Dimension
- diameter; 1m(10,000Å)
- synaptic gap; 200Å
 Transmission
: Action Potential arrival
 excitatory transmitter
(acetylcholine)
 diffuse across the junction
 stimulate carrier protein
 transport Na+ into dendrite
 events similar to Action Potential
 Postsynaptic Potential(PSP)
: Calcium plays a vital role
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그림570
서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Post Synaptic Potential
 Waveform of PSP
: 0.6ms delay for gap transmission
: acetylcholine molecules
- not march in unison
- straggle across, spread out in space & time
: 2ms delay for peak appearance
: Pre Synaptic Potential(2ms)  Post Synaptic Potential(4ms)
: 100mV high, 4ms wide
 200Å junction gap
: provides access for different chemical messengers(hormone,--)
: modify the excitability of the dendritic terminal gap
: mediation by alcohol or drug
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Chemical Inhibition
 Chemical messengers decreasing the excitability
: inhibition
: gamma aminobutylic acid(GABA)
- stimulate potassium carrying protein
- blocking sodium carrying
: negative charges inside the axon
 negative spike  PSP is negative
: relatively weak; 10mV of PSP( instead of 100mV)
 GP generating junction gap
: as in retina (distances between cells are small)
: junction filled with chemical transmitters
: chemical messengers carry GP across the gap
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Electrical Gap Junction

Electrical gap junction
: 2ms time delay is intolerable
: no need of alternation of excitability
: no need of 200 Å
: replaced by tight or electrical gap junction
- axon terminal and dendrite are tightly interwined
- finite but negligibly small gap
- electrical signal gets across to the dendrite
: transmit APs, GPs, but no inhibition
 Population of Synaptic Junctions
: axon to dendrite & axon to soma junctions
 axon to axon junction & dendrite to dendrite junction
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Dendrite
Tree Model
 Tree model
: levels 4,3,2,1,0
: level 4 (periphery of the tree)
: level 0 (neuron body, soma)
: signals from left to right
(to a lower level)
: funnel & modify messages
: a single output axon
 collateral branches
(upto 1000s)
: can generate APs or GPs
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그림 5-1
서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Attenuation in Dendrite
 Information flood?
: PSP is 4ms wide  250 PSPs can flood the neuron
: flood  steady & meaningless stream
: for 10,000 junctions
250PSPs/s/dendrite = 0.025 spikes/s/junction (40s)
: spontaneous activity of 50 spikes/s
 five of these input can saturate neuron ?!
 Attenuation of PSP
: dendrite tree
- nonregenerating
- unmyelinated
: shunt leakage conductance G
- long nonregenerative fiber
- excessive error without G
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Figure 5-2
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
RCG Dendrite Cable Model
dV
= - I•R
dx
Figure 5-2
dI(s)
= - (G+sC)V(s)
dx
R : series axoplasm resistance
C : shunt membrane capacitance
G : shunt leakage conductance
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d2V(s)
= R(G+sC)V(s)
dx2
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Attenuation through RC Cable
d2V(s)
= R(G+sC)V(s)
dx2
V(s) = c1e-xR(G+sC)+ c2e x R(G+sC)
: c2= 0 (V  0 as x   )
: c1= Vin(V=Vin at x=0)
V(s)= Vin (s) e-x R(G+sC)
: Vin(s)= A0 (Vin impluse of A0 V•s)
Ax
V = 03/2
2t
=
A0x
2t3/2


RC
x2RC Gt
exp()

4t
C
Gt
RC
x2RC
exp()•exp(- )

4t
C
RC Model
Solution
G effect
V(s)= A0 e-x R(G+sC)
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Waveform of PSP
 Length Constant
: associated with DC response
 C=O
: V(s)= A0 e-x R(G+sC) = A0 e-x RG
 0 = 1/  RG
 Normalized distance
: z = x/ 0 = x RG
: x = z/ RG
 Membrane time constant
: RC= C/G =4(ms)
 C=4G(ms)
 A0=3054mV•ms
A0x
RC
x2RC Gt
V = 3/2 
exp()
2t

4t
C
A0z
z2 t
V = 3/2 exp(- - )
t
4
 t
V=
1723z
z2 t
exp(- )
t3/2
t 4
Peak at tp=  9+4z2 -3
PSP of 4ms wide 100mV high at z=2
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Waveform Parameters
1723z
z2 t
V = 3/2 exp(- - )
t
t 4
 Peak of PSP
: at tp=  9+4z2 -3
: tp =2ms for z = 2
: Vp =100mV at tp =2ms
 Area of PSP waveform
: exponentially decay
: due to shunt leakage
: Area = A0exp(-z)
 Equivalent wave width
: tw = Area/Vp
 PSP at z=2
: 4ms wide
: 100mV peak
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branch length = 0 /2
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Modeled Post Synaptic Potential
Level z
tp
Vp
Area
tw
(ms) (mV) (mVms) (ms)
413
V(z,t) (mV, ms unit)
4 t
4.13 V(2,t) = 3446
exp(- )
t3/2
t 4
4
2.0
2.00
100
3
2.5
2.83
49.0 251
2
3.0
3.71
9 t
25.3 152 6.01 V(3,t) = 5169
exp(- )
t3/2
t 4
1
3.5
4.62
13.5
0
4.0
5.54 7.4
92
56
4307.5
6.25 t
5.12 V(2.5,t) = 3/2
exp(- )
t
t
4
12.25 t
6.83 V(3.5,t) = 6030.5
exp(- )
t3/2
t
4
7.59
V(4,t) =
6892
16 t
exp(- )
t3/2
t 4
When 16 Aps are arrived simultaneously at t=0, at the periphery terminal junctions
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Dependence on Diameter
 Resistance
l=125[cm]
R= l ll /Ac
R= 159.2/d2 [/cm]
 Leakage Conductance
m=5.647109 [ cm]
G= As/m lm
G= 7.41810-4d [1/cm]
 Characteristic Resistance  Length Constant
R0= (R/G)1/2
R0 = 463.2/d3/2 [, cm unit]
d  (R0)-2/3
R0 = 14.65M when d=10um
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0 = 1/(RG)1/2
0= 2.910 d [cm unit]
0  (R0)-1/3
0=0.46mm when d=10um
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Rall's Assumption
 Constant characteristic resistance R0
: independent of number of branches
 Calculation Assumption
: values for entire branches rather than /cm
: 10um in level 0( z=3.5~ 4)
: each branch length = half of length constant
: constant ensemble characteristic resistance R0
 One level to next higher level
: increase of characteristic resistance : doubles
: diameter decrease: 22/3
: length decrease: 21/3
: surface area: halved (2-1)
: total surface area of each row: 28,900um2(constant)
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Calculated Dendrite Model Parameters
d
0
R0
Area
R
C
Branches (um) (mm) (M) (um2) (M) (pF)
Number of
G
(nS)
Level
z
4
2 to 2.5
16
2.50
0.230 117.2 1807 58.58 17.06 4.266
3
2.5 to 3
8
3.97
0.290 58.59 3614 29.29 34.13 8.533
2
3 to 3.5
4
6.30
0.365 29.30 7227 14.65 68.26 17.07
1
3.5 to 4
2
10.0
0.460 14.65 14455 7.323 136.5 34.13
0
soma
1
15.9
Ratio
2
21
2-2/3
-
7.324
-
-
-
-
2-1/3
2
2-1
2
2-1
2-1
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Number of Synaptic Junctions
 On a single Dendrite Tree
: total surface area ; 116,000um2
: junction diameter :1um
 junction area 1um2
 100,000 junctions on a dendrite tree
 signals from 10,000 different neurons is possible
(10% use)
 Many junctions on soma directly
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Position is everything in life?
 Importance of Position in dendrite junction
: tree is democratic
: important neuron should terminate closer to soma
- impossible for genetic coding of junction location
(10,000 junctions/neuron: beyond capabilities of DNA)
: location dominance; gradually modifies with aging
 Learning and Memory
: learning  growth and/or movements of junctions
: memory  location and strength of junctions
(more than one junction on same dendrite)
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Human Memory
 1 hour from short term memory to long term memory
: accident victim; severe blow, electroconvulsive shock
- partial or full erase of memories during last one hour
- no effect on events experienced, synaptic junctions
: plenty of room for new junctions(100,000 junctions)
- anatomical evidence is lacking, difficult in vivo (theory)
 Forgetting: Junction migration(no evidence; theory)
: new junction  move of old junction to higher level
- if not, tree will be saturated with junctions
: forget as much as learn
: person who cannot learn recent event, remarkably recall distant events
: old dog; cannot teach new trick, don't forget old ones
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Message sequences
 Complicated function
: dendritic location
: time of occurrence
: complicated responses
: computer simulation
for arbitrary set of inputs
Fig. 5-3
z
Node or Time PSP peak
value branch# in ms in mV
2
06
0.0 100
2
06
7.5 100
2
06
15.0 100
2
06
22.5 100
2
06
30.0 100
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Message sequences
 Solid Line
z
Node or
value branch#
2 01~16
2.5 01~08
3 01~04
3.5 01~02
Time PSP peak
in ms in mV
0.0 100
0.0 100
0.0 100
0.0 100
Fig. 5-4
 Dotted Line
z
value
2
2.5
3
3.5
26
Node or
branch#
01~16
01~08
01~04
01~02
Time PSP peak
in ms in mV
0.0 100
1.0 100
2.5 100
4.0 100
서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Sequence with Inhibitory Inputs
 Solid Line
z
value
2
2.5
3
3.5
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Node or
branch#
01~16
01~08
01~04
01~02
Time
in ms
0.0
0.0
0.0
0.0
PSP peak
in mV
100
100
100
-92
Fig. 5-6
서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Effects of Inhibitory PSP
 without inhibition
: threshold; -82mV
: -80mV; 10Hz AP
: -61mV; 50Hz AP
Fig. 3.2
 with inhibition
: threshold; -72mV
: -80mV; no AP
: -61mV; 16.6Hz
Fig.5.6
Inhibition  No AP or reduced rates of APs
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서울대학교 대학원 의용생체공학 협동과정
5: Dendrite Summation
생리현상에 대한 공학적해석
Of what use is inhibition?
 Muscle contraction
: muscles come in pairs(flexor,extensor)
: doesn't stimulate at the same time
: wired to function antagonistically
: flexor(excitation)  extensor(inhibition)
extensor(excitation)  flexor(inhibition)
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서울대학교 대학원 의용생체공학 협동과정
생리현상에 대한 공학적해석
5: Dendrite Summation
Pattern of Inhibitory Inputs
 Weaker than excitatory PSP: 1/10 level
: to be effective  close to body, on the body
: on the body  not raise to 10mV
( because of large volume of body)
: simultaneous inhibition  block or reduce rate of APs
 Effective Inhibition
: inhibitory PSP arrives first
: sustained inhibition
 continuous barrage of inhibitory inputs
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서울대학교 대학원 의용생체공학 협동과정