Neuron and Dendrite
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Neuron and Dendrite.  3 parts of Neuron : dendrite(input) : body(processor) : axon (output)  Hillock : initial section of axon : lowest threshold; 8mV : AP is generated. 그림 569. Dendrite Tree.  Input architecture of neuron : branch collects about 100,000 messages

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Neuron and Dendrite

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Neuron and dendrite

Neuron and Dendrite

3 parts of Neuron

: dendrite(input)

: body(processor)

: axon (output)

Hillock

: initial section of axon

: lowest threshold; 8mV

: AP is generated

그림 569


Neuron and dendrite

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

Inhibitory inputs

: relatively weak & close to neuron body

: raise firing threshold of neuron

Output resulting from combination of input signals

그림 569


Neuron and dendrite

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 ofAction Potential

: when net summation exceeds threshold

Graded potential generating neuron

: proportional potential to net summation of DPs


Neuron and dendrite

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


Neuron and dendrite

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


Spatial summation of dendrite

cf) Temporal summation

Spatial Summation of Dendrite


Neuron and dendrite

Dendrite

 Treelike structure

: dendritic tree

: gather messages

: fewer to 100,000

: via synaptic junction

: via electrical gap junction

: single AP at the periphery

그림 5-1


Neuron and dendrite

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

그림570


Neuron and dendrite

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


Neuron and dendrite

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


Neuron and dendrite

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


Neuron and dendrite

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

그림 5-1


Neuron and dendrite

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

Figure 5-2


Neuron and dendrite

RCG Dendrite Cable Model

dV

dx

= - I•R

Figure 5-2

dI(s)

dx

= - (G+sC)V(s)

d2V(s)

dx2

= R(G+sC)V(s)

R : series axoplasm resistance

C : shunt membrane capacitance

G : shunt leakage conductance


Neuron and dendrite

Attenuation through RC Cable

d2V(s)

dx2

A0x RC x2RC Gt

2t3/2 4t C

= R(G+sC)V(s)

V = exp(- - )

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)

V(s)= A0e-x R(G+sC)

Gt

C

A0x RC x2RC

2t3/2 4t

= exp(- )•exp(- )

RC Model Solution

G effect


Neuron and dendrite

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

2t3/2 4t C

V = exp(- - )

A0z z2 t

t3/2 t 4

V = exp(- - )

1723z z2 t

t3/2 t 4

V = exp(- - )

Peak at tp=  9+4z2 -3

PSP of 4ms wide 100mV high at z=2


Neuron and dendrite

Waveform Parameters

1723z z2 t

t3/2 t 4

Area of PSP waveform

: exponentially decay

: due to shunt leakage

: Area = A0exp(-z)

 Equivalent wave width

: tw = Area/Vp

V = exp(- - )

Peak of PSP

: at tp=  9+4z2 -3

: tp =2ms for z = 2

: Vp =100mV at tp =2ms

 PSP at z=2

: 4ms wide

: 100mV peak

branch length = 0 /2


Neuron and dendrite

Modeled Post Synaptic Potential

tpVp Area tw

Level z (ms) (mV) (mVms) (ms) V(z,t) (mV, ms unit)

4 2.0 2.00 100 413 4.13

3 2.5 2.83 49.0 251 5.12

2 3.0 3.71 25.3 152 6.01

1 3.5 4.62 13.5 92 6.83

0 4.0 5.547.4 56 7.59

3446 4 t

t3/2 t 4

V(2,t) = exp(- - )

4307.5 6.25 t

t3/2 t 4

V(2.5,t) = exp(- - )

5169 9 t

t3/2 t 4

V(3,t) = exp(- - )

6030.5 12.25 t

t3/2 t 4

V(3.5,t) = exp(- - )

6892 16 t

t3/2 t 4

V(4,t) = exp(- - )

When 16 Aps are arrived simultaneously at t=0, at the periphery terminal junctions


Neuron and dendrite

Dependence on Diameter

 Resistance

l=125[cm]

R= lll/Ac

R= 159.2/d2 [/cm]

 Leakage Conductance

m=5.647109 [cm]

G= As/mlm

G= 7.41810-4d [1/cm]

 Characteristic Resistance

R0= (R/G)1/2

R0 = 463.2/d3/2 [, cm unit]

d  (R0)-2/3

R0 = 14.65M when d=10um

 Length Constant

0 = 1/(RG)1/2

0= 2.910 d [cm unit]

0  (R0)-1/3

0=0.46mm when d=10um


Neuron and dendrite

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)


Neuron and dendrite

Calculated Dendrite Model Parameters

Number of d 0 R0 Area R C G

z Branches(um) (mm) (M) (um2) (M) (pF) (nS)

2 to 2.5 16 2.500.230117.2180758.5817.064.266

2.5 to 3 83.970.29058.59361429.2934.138.533

3 to 3.5 46.300.36529.30722714.6568.2617.07

3.5 to 4 210.00.46014.65144557.323136.534.13

soma 115.9 - 7.324 - - - -

Ratio2 2-2/3 2-1/3 22-122-1 2-1

Level

4

3

2

1

0


Neuron and dendrite

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


Neuron and dendrite

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)


Neuron and dendrite

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


Neuron and dendrite

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

206 0.0100

206 7.5100

20615.0100

20622.5100

20630.0100


Neuron and dendrite

Message sequences

 Solid Line

z Node or Time PSP peak

value branch# in ms in mV

2 01~16 0.0100

2.5 01~08 0.0 100

3 01~04 0.0 100

3.5 01~02 0.0 100

Fig. 5-4

 Dotted Line

z Node or Time PSP peak

value branch# in ms in mV

201~16 0.0100

2.5 01~08 1.0 100

301~04 2.5 100

3.5 01~02 4.0 100


Neuron and dendrite

Sequence with Inhibitory Inputs

 Solid Line

z Node or Time PSP peak

value branch# in ms in mV

201~16 0.0100

2.5 01~08 0.0 100

301~04 0.0 100

3.5 01~02 0.0 -92

Fig. 5-6


Neuron and dendrite

Effects of Inhibitory PSP

 without inhibition with inhibition

: threshold; -82mV : threshold; -72mV

: -80mV; 10Hz AP: -80mV; no AP

: -61mV; 50Hz AP : -61mV; 16.6Hz

Fig. 3.2 Fig.5.6

Inhibition  No AP or reduced rates of APs


Neuron and dendrite

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)


Neuron and dendrite

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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