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Biology 317 > Calculating Tau and Lambda > Flashcards

Calculating Tau and Lambda Flashcards

1
Q

What is the equation to calculate the length constant (original and simplified)

A

I = square root|(Rm/[Ri+Ro])

I = Square root| (Rm/ Ri)

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2
Q

Define Length constant (Lambda λ)

A

Distance at which the Vm decays to 37% of its original value

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3
Q

How are Rm and Ri related

A

They are related to diameter of the cell or axon

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4
Q

Rm is inversely related to what
and inversely proportional to what

A

membrane surface area
inversely proportional to the radius

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5
Q

what is geometry of a cylinder

A

As= 2prh

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6
Q

Ri is inversely related to what
and inversely proportional to what

A

The volume of the cytoplasm
inversely proportional to the square of the radius

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7
Q

Geometry of a circle

A

Ax= pr2

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8
Q

an increase in diameter will decrease what, Which will decrease faster

What will an increase of diameter increase

A

decrease both Rm & Ri, Ri will decrease faster

Increase in diameter increases lambda λ
(ie. the distance of electronic spread)

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9
Q

More channels = more what

A

= more depolarization

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10
Q

relatively small changes in diameter results in a fairly large change in what

A

large changes in the length constant

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11
Q

Tau and Lambda result from…
Also called what?

A

passive electrical potentials

Also called cable properties

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12
Q

what 3 are inherent features of membrane

A

resistance (Rm and Ri)
Capacitance
geometry

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13
Q

Example: If you have an extension cord and you try to plug your car in in the winter, so you take a couple extension cords and put them together to make one long extension cord, then it seems your car didn’t get enough juice from the extension cord. You should get a thicker cord because the diameter of the cord doesn’t allow for the flow of the charge to reach your car.

A
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14
Q

EPSP
IPSP

A

Excitatory post-synaptic potential
Inhibitory post-synaptic potential

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15
Q

EPSPs move Vm towards the threshold voltage; if threshold is reached…

A

an AP is generated at the axon hillock

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16
Q

IPSPs move Vm away from threshold, makes it harder to…

A

Harder to generate an AP

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17
Q

AP results from change in Rm

A

changing resistance through membranes, by opening channels

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18
Q

What are the 5 main characteristics of an AP?

A
  1. Exhibits a threshold voltage (all or nothing)
  2. Displays a rapid change in Rm
  3. Has sequential opening and closing of voltage-gated channels (depolarization, repolarization)
  4. Once generated, is actively propagated (unchanged & in one direction) along axonal membrane
  5. is a discrete signal; transient with quick return to RMP
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19
Q

Three types of Vm in a neuron

A
  1. Resting membrane potential (RMP) - all areas of membrane ie. K+ leak channels
  2. graded (electrotonic) potential (GP) - used in dendrites and axons ie. no channels (electrotonic)
  3. Action potentials (AP) - used in axon & terminals ie. voltage-regulated Na+ and K+ channels
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20
Q

Describe a dendrite

A

short axons, therefore small resistance and small diameter,

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21
Q

Electrical properties of a cell membrane are either…

A

Passive- do not change over time or
active - change over time (voltage-gated channels

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22
Q

what are the two passive electrical properties of cell membrane are…

A

resistance (R)
capacitance (C)

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23
Q

Passive membrane properties determine:

A
  • magnitude of electrical current travelling on membrane surface
  • time course (shape) of any Vm change
  • Distance an electrical current will travel on membrane surface
  • speed of action potential propagation along axon (conduction velocity)
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24
Q

biomembranes act as…
where is potential stored?

A

capacitors (nonconductors that store charge
- opposite charges line-up along membrane surfaces

  • potential is stored along the membrane surfaces
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25
Q

bioelectricity would not be possible without…

A

capacitance

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26
Q

because of capacitance, only a few….

A

few ions are needed to generate a transmembrane potential (Vm)

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27
Q

Rm is lowered due to…

A

K+ leak channels

28
Q

Cm holds charges where

A

at membrane surfaces

29
Q

RMP is the result of?

A

Resting membrane potential is a result of the passive electrical properties interacting with a transmembrane I(k)

30
Q

measuring Vm over time

A

RMP stays unchanged over time just as long as nothing disturbs the equilibrium established by the I(k) through its leak channels

31
Q

what is the change in Vm due to a surface current called?

A

electrotonic potential - flow of current along surface

32
Q

where are electrotonic potentials used

A

used in dendrites and along axons of neurons & in t-tubules of skeletal muscles:
- to propagate an electrical signal along membrane surfaces

33
Q

How do passive properties influence currents along membrane surface?

A

over time - measured as a time constant Tau
over distance - measured as length constant lambda

34
Q

what do tau and lambda affect?

A

the electrical propagation in neurons and muscles

35
Q

time constant tau:

A

time required for Vm to reach 63% of its maximum
the longer the tau the longer it takes to reach polarization

36
Q

what is the equation for Tau

A

tau = RmCm

37
Q

where is there more tau in, neurons or muscle?

A

less in neurons more in muscle

38
Q

Which variable (Rm or Cm) could easily change to decrease tau (ie. to reach maximum Vm faster)?

A

Resistance is the easiest to change - by adding or increasing or opening channels
- having a shorter tau makes a faster capacitance

39
Q

measuring the length constant lambda…

A

injected current flows along surface due to opposites attract, like repel
- but size of Vm due to injected current decays over distance

40
Q

Injected current “escapes” along..

A

the path of least resistance

41
Q

what are the two paths for current to follow…

A

through the membrane Rm and the Cytoplasm Ri

42
Q

which is bigger Rm or Ri

A

Rm

43
Q

which is the only group of animals without specific neurons or muscle cells?

A

sponges

44
Q

from the top down list what is in an axon nerve

A

dendrites (short branches)
|
Nucleus
|
Soma
|
Axon hillock
|
Axon initial segment
|
Axon
|
Schwann cells & myelin sheath
|
Terminal branches
|
Presynaptic terminal branches (release chemical signal from pre to post)

45
Q

Neurons use electrical potential to…

A

communicate with other cells

46
Q

what is a nerve

A

a collection of axons from several neurons

47
Q

Neurons are signalling cells with four functional regions:

A
  1. Reception & integration of signals - dendrites, cell body - receives signals from environment (pressure, temp, sight, sound etc)
  2. Generation of signal - axon hillock
  3. Conduction of signal - axon
  4. Transmission of signal - terminals, synapses
48
Q

membrane potentials in a neuron are due to…

A
  • passive electrical properties (RMP & GP)
  • active electrical properties (AP ) - results from changes in RMP - channels open or close
49
Q

In RMP what establishes the ion gradient

A

Na+ K+ ATPase
Na out
K in

50
Q

Neurons and muscle cells have K+ leak channels

A
  • the Rm to K+ is very low
  • allows a large outward K+ current I(k)
  • I(k) establishes a large equilibrium potential
51
Q

lambda is easily adjusted by changes in what

A

diameter

52
Q

dendrites - small diameter means what type of tau or lambda?

A

a smaller diameter means a short lambda

53
Q

a longer axon =

A

bigger diameter = higher Rm

54
Q

How do we know the RMP is due to the outward I(k)

A

by comparing the actual and theoretical potentials

55
Q

example for nernst equation:
K+ out = 20
K+ in = 400
Ek = ?

A

Ek = RT/zF ln [Ko]/[Ki] = 58 mV log10 (20mM/400mM) = -76mV

56
Q

At rest (in a non-excited state), a neuron/muscle cell:

A
  • is electrically polarized
  • remains in a steady-state (equilibrium) as long as cell has ATP
57
Q

Depolarized
Hyperpolarized
Repolarized

A

Depolarized - Vm moves towards zero
Hyperpolarized - Vm is larger than the RMP - further from zero
Repolarized - Vm moves back towards the RMP

58
Q

What two ways can membrane polarity be moved away from RMP?

A
  • by graded (electrotonic) potentials (GP) [due to passive electrotonic spread]
    and
  • by an action potential (AP) [due to an electrical property that changes and interacts with the passive electrical properties]
  • changing the polarity of neurons*
59
Q

Where do GP commonly occur?

A
  • commonly occur along membrane of dendrites/cell body
  • Dendrites receive input from other neurons via SYNAPSES
60
Q

few ion channels in dendrites are opened by…

A

neurotransmitters from other neurons

61
Q

channel opens > ions _____ > moves_______

A

channel opens > ions move in > moves along membrane (electrotonically)

62
Q

RMP conditions in a dendrite:

A

Axon terminal from presynaptic neuron with neurotransmitter (nt)
membrane capacitor is holding charge
- neurotransmitter released into synapse
- neurotransmitter causes channel to open
- cation flows through open channel
- opposites attract, like repel - change in transmembrane potential
- channel closes, is a small depolarization in Vm adjacent to channel
- depolarization spreads away from channels
- distance travelled by electrotonic spread depends on lambda

63
Q

the change in Vm decreases in size as ….
is a type of graded potential called…

A

it spreads along membrane
synaptic potential

64
Q

answer depolarize or hyperpolarize
Opening a K+ channel in the synapse will ____
Opening a Na+ channel in the synapse will ______
Opening a Cl- channel in the synapse will ________

A
  1. hyperpolarize
  2. Depolarize
  3. Hyperpolarize (repolarize?)
65
Q

why does decay of Vm happen?

A

it happens over distance due to leakage through cytoplasm/K+ leak channels

Biology 317 (6 decks)

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