Calculating Tau and Lambda Flashcards
What is the equation to calculate the length constant (original and simplified)
I = square root|(Rm/[Ri+Ro])
I = Square root| (Rm/ Ri)
Define Length constant (Lambda λ)
Distance at which the Vm decays to 37% of its original value
How are Rm and Ri related
They are related to diameter of the cell or axon
Rm is inversely related to what
and inversely proportional to what
membrane surface area
inversely proportional to the radius
what is geometry of a cylinder
As= 2prh
Ri is inversely related to what
and inversely proportional to what
The volume of the cytoplasm
inversely proportional to the square of the radius
Geometry of a circle
Ax= pr2
an increase in diameter will decrease what, Which will decrease faster
What will an increase of diameter increase
decrease both Rm & Ri, Ri will decrease faster
Increase in diameter increases lambda λ
(ie. the distance of electronic spread)
More channels = more what
= more depolarization
relatively small changes in diameter results in a fairly large change in what
large changes in the length constant
Tau and Lambda result from…
Also called what?
passive electrical potentials
Also called cable properties
what 3 are inherent features of membrane
resistance (Rm and Ri)
Capacitance
geometry
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.
EPSP
IPSP
Excitatory post-synaptic potential
Inhibitory post-synaptic potential
EPSPs move Vm towards the threshold voltage; if threshold is reached…
an AP is generated at the axon hillock
IPSPs move Vm away from threshold, makes it harder to…
Harder to generate an AP
AP results from change in Rm
changing resistance through membranes, by opening channels
What are the 5 main characteristics of an AP?
- Exhibits a threshold voltage (all or nothing)
- Displays a rapid change in Rm
- Has sequential opening and closing of voltage-gated channels (depolarization, repolarization)
- Once generated, is actively propagated (unchanged & in one direction) along axonal membrane
- is a discrete signal; transient with quick return to RMP
Three types of Vm in a neuron
- Resting membrane potential (RMP) - all areas of membrane ie. K+ leak channels
- graded (electrotonic) potential (GP) - used in dendrites and axons ie. no channels (electrotonic)
- Action potentials (AP) - used in axon & terminals ie. voltage-regulated Na+ and K+ channels
Describe a dendrite
short axons, therefore small resistance and small diameter,
Electrical properties of a cell membrane are either…
Passive- do not change over time or
active - change over time (voltage-gated channels
what are the two passive electrical properties of cell membrane are…
resistance (R)
capacitance (C)
Passive membrane properties determine:
- 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)
biomembranes act as…
where is potential stored?
capacitors (nonconductors that store charge
- opposite charges line-up along membrane surfaces
- potential is stored along the membrane surfaces
bioelectricity would not be possible without…
capacitance
because of capacitance, only a few….
few ions are needed to generate a transmembrane potential (Vm)
Rm is lowered due to…
K+ leak channels
Cm holds charges where
at membrane surfaces
RMP is the result of?
Resting membrane potential is a result of the passive electrical properties interacting with a transmembrane I(k)
measuring Vm over time
RMP stays unchanged over time just as long as nothing disturbs the equilibrium established by the I(k) through its leak channels
what is the change in Vm due to a surface current called?
electrotonic potential - flow of current along surface
where are electrotonic potentials used
used in dendrites and along axons of neurons & in t-tubules of skeletal muscles:
- to propagate an electrical signal along membrane surfaces
How do passive properties influence currents along membrane surface?
over time - measured as a time constant Tau
over distance - measured as length constant lambda
what do tau and lambda affect?
the electrical propagation in neurons and muscles
time constant tau:
time required for Vm to reach 63% of its maximum
the longer the tau the longer it takes to reach polarization
what is the equation for Tau
tau = RmCm
where is there more tau in, neurons or muscle?
less in neurons more in muscle
Which variable (Rm or Cm) could easily change to decrease tau (ie. to reach maximum Vm faster)?
Resistance is the easiest to change - by adding or increasing or opening channels
- having a shorter tau makes a faster capacitance
measuring the length constant lambda…
injected current flows along surface due to opposites attract, like repel
- but size of Vm due to injected current decays over distance
Injected current “escapes” along..
the path of least resistance
what are the two paths for current to follow…
through the membrane Rm and the Cytoplasm Ri
which is bigger Rm or Ri
Rm
which is the only group of animals without specific neurons or muscle cells?
sponges
from the top down list what is in an axon nerve
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)
Neurons use electrical potential to…
communicate with other cells
what is a nerve
a collection of axons from several neurons
Neurons are signalling cells with four functional regions:
- Reception & integration of signals - dendrites, cell body - receives signals from environment (pressure, temp, sight, sound etc)
- Generation of signal - axon hillock
- Conduction of signal - axon
- Transmission of signal - terminals, synapses
membrane potentials in a neuron are due to…
- passive electrical properties (RMP & GP)
- active electrical properties (AP ) - results from changes in RMP - channels open or close
In RMP what establishes the ion gradient
Na+ K+ ATPase
Na out
K in
Neurons and muscle cells have K+ leak channels
- the Rm to K+ is very low
- allows a large outward K+ current I(k)
- I(k) establishes a large equilibrium potential
lambda is easily adjusted by changes in what
diameter
dendrites - small diameter means what type of tau or lambda?
a smaller diameter means a short lambda
a longer axon =
bigger diameter = higher Rm
How do we know the RMP is due to the outward I(k)
by comparing the actual and theoretical potentials
example for nernst equation:
K+ out = 20
K+ in = 400
Ek = ?
Ek = RT/zF ln [Ko]/[Ki] = 58 mV log10 (20mM/400mM) = -76mV
At rest (in a non-excited state), a neuron/muscle cell:
- is electrically polarized
- remains in a steady-state (equilibrium) as long as cell has ATP
Depolarized
Hyperpolarized
Repolarized
Depolarized - Vm moves towards zero
Hyperpolarized - Vm is larger than the RMP - further from zero
Repolarized - Vm moves back towards the RMP
What two ways can membrane polarity be moved away from RMP?
- 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*
Where do GP commonly occur?
- commonly occur along membrane of dendrites/cell body
- Dendrites receive input from other neurons via SYNAPSES
few ion channels in dendrites are opened by…
neurotransmitters from other neurons
channel opens > ions _____ > moves_______
channel opens > ions move in > moves along membrane (electrotonically)
RMP conditions in a dendrite:
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
the change in Vm decreases in size as ….
is a type of graded potential called…
it spreads along membrane
synaptic potential
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 ________
- hyperpolarize
- Depolarize
- Hyperpolarize (repolarize?)
why does decay of Vm happen?
it happens over distance due to leakage through cytoplasm/K+ leak channels
