BME 502 / handout #1
BME 502 -- Handout #1
IONIC BASIS OF MEMBRANE POTENTIAL
Cell Membrane
cell soma size ranges from 5-100 μm, though most mammalian CNS 10-40 μm
demarcated by a plasma membrane, surrounding a volume of cytoplasm
cytoplasm: salt solution of Na+, K+, Cl-, Ca2+, and Anions, i.e., large, negatively charged
proteins that cannot pass through membrane
molecular structure
membrane composed of proteins (60%), lipids (38%), and carbohydrates (1-2%)
two types of lipids--neutral lipids (cholesterol) and phospholipids
phospholipids: glycerol backbone, alpha and beta hydroxyls are esterified into two long
fatty acid chains. All phospholipids consist of two portions:
one which is nonpolar--the two long fatty acid chains,
second which is polar and contains charged phosphate groups
in water or salt solution, phospholipids orient in a unique fashion with the polar group being
hydrophilic and the fatty acid chains being hydrophobic. Water molecules are polar and so
generate a particular orientation of phospholipids in water
 there is a particular structure of the membrane: a lipid bilayer
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membrane function
primary signal for communication between nerve cells is electrical,
involves the flow of current, in this case, flow of ions
for current to flow, must be a voltage difference (V = I R),
therefore, must be a mechanism for maintaining voltage difference,
or a mechanism for separating charges
transmembrane potential, Vm : evidence of separation of charge
magnitude of potential difference, Vm = Vin - Vout
primary ionic constituents: K+, Na+, Ca2+, Cl, and anions
for "resting membrane potential":
membrane largely permeable to K+
slightly permeable to Climpermeable to Na+ and Ca2+
concentration differences:
K+: 100 mM inside 5 mM outside; 20x
Na+: 10 mM inside 150 mM outside; 15x
Cl-: 5 mM inside 110 mM outside; 22x
Ca2+: 10-4 mM inside 5 mM outside; 50,000x
basis of membrane potential: selective permeability of the membrane
because ions are the charged particles carrying the transmembrane current, and
because ions are in solution (intracellular and extracellular fluids), no transmembrane
current can flow without overcoming waters of hydration
i.e., there is a strong electrostatic force of attraction between, e.g., a K + ion, and its
associated water molecule; for an ion to pass through the membrane, there must be a
mechanism which provides an attractive force greater than that offered by a water
molecule so that there will be a transfer of ions from the water molecule to the
membrane
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phospholipid bilayer
hydophilic / hydrophobic components
resists movement of ions through membrane
molecular structure of channels: hydrophilic (lined with polar amino acid groups)
energy barrier provided by the electrostatic charge that must be overcome for an ion to
(i) approach the pore opening (see figure below), (ii) dehydrate, and as a result, transfer
to the polar amino acid components of the channel wall, (iii) transfer to different
subregions of the channel wall, (iv) rehydrate at the opposite end of the channel, and (v)
overcome the force of attraction of the opposite end of the channel
because the membrane can be treated as a capacitor, the energy barrier that obstructs
the movement of ions through the channel can be conceptualized as the work required
to overcome the dialectric properties of the membrane (WE) and the work required to
overcome the chemical reactions (Wchem) of hydration and rehydration:
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distribution of ions against their concentration gradients, i.e., mechanisms that maintain the
resting membrane potential
dimensions for evaluating pumps, exchanges, transporters:
species of ions involved
specificity of pump, exchange, transporter
energy consuming or driven by concentration gradient
electrogenic or non-electronic
Na+-K+ pump
3 Na+ ions out for every 2 K+ ions in
thus, electrogenic, because of net transfer of charge
(as shown on p.84 of Nicolls), if cell under voltage-clamp, and inject Na+, there will be an
activation of the pump, and thus a net outflow of Na +, leading to a hyperpolarization
note slow time course, i.e., peak current flux not reached for 2-3 minutes
if no extracellular K+, then will be no hyperpolarization of the membrane even when Na +
injected
energy for pump derived from hydroylsis of ATP
very specific requirement for Na+, i.e., must be Na+ to be pumped out
is the only cation not accepted to be pumped in
(so lithium, cesium, etc, can substitute for K + in the extracellular fluid, but if no good
substitute exists, will be no transport even if Na + is injected into the cell)
pumped is blocked by ouabain
Na+-Ca2+ exchange
3 Na+ ions in for every 1 Ca2+ ion out
because Na+ is driven down its concentration gradient, the gradient itself provides the
energy for the pump (not ATP-derived); thus, Na+-Ca2+ exchange depends in part on Na+-K+
pump
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Ca2+ pump
ATP-driven pump located in both the plasma membrane and membrane of endoplasmic
reticulum
keeps cytosolic Ca2+ concentration low
Cl--Na+-K+ cotransporter
driven by Na+ influx
transports Na+ in, K+ in, and Cl- in with a ratio of 1:1:2
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CHANNELS: MECHANISMS FOR TRANSMEMBRANE CURRENT
for transmembrane potential to change, there must be a transmembrane current, i.e., a flow of
ions across the membrane
the molecular composition of the basic structure of the membrane renders it impermeable to
most ions
therefore, there must be a modification in the structure of the membrane that facilitates
overcoming the electrostatic charge between ions and water molecules, and thus allows
transmembrane ion movement, i.e., current
the structural unit within the membrane which provides this function is the channel:
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three important properties w/re to their facilitation of transmembrane current:
structure: protein-lined pore that can overcome waters of hydration
selectivity: most channels allow only one or two classes of ions to pass
gating mechanisms: most channels incorporate mechanisms through which the protein
structure of the channel changes conformation i.e., undergo the transition from closed to
open, in response to particular stimulus events
some channels are non-selective and non-gated -- contribute to leakage current
mechanisms of selectivity:
polarity
size ( = 10-10 m)
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mechanisms of gating:
ligand, voltage
second-messenger
ion sensitive
examples of voltage-gated mechanisms
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forces controlling current flow through channels:
concentration gradient
K+: 100 mM inside 5 mM outside; 20x
Na+: 10 mM inside 150 mM outside; 15x
Cl-: 5 mM inside 110 mM outside; 22x
Ca2+: 10-4 mM inside 5 mM outside; 50,000x
electrical gradient
relative balance between the concentration and electrical gradients:
Nernst equation: expresses the equilibrium potential, or that potential which would result if
the membrane were permeable to only one ion species, and all of the channels for that ion
were to open simultaneously and remain open
also termed the reversal potential, because it is the potential around which the direction of
current carried by that species of ion changes sign
Install Equation Editor and doubleclick here to view equation.
where R is the thermodynamic gas constant, T is the absolute temperature, z is the valence
of the ion, F is the Faraday constant (# of coulombs of electric charge in one mole of
monovalent ion). The expression RT/zF has the dimensions of volts is = approx 25mV at
room temperature (20-25C; specific value at 25C is 25.69 mV). If use the log to the base
10 rather than natural log, RT/zF is approximately 2.3x the value determined using ln {58mV
at 25C). If core temperature of mammalian system is assumed (37C), this value
increases to approx 60mV.
Install Equation Editor and doubleclick here to view equation.
Install Equation Editor and doubleclick here to view equation.
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thus,
but because Vm  E for a given ion, net driving force
Install Equation Editor and doubleclick here to view equation.
if assume a resting membrane potential of -70 mV,
K+
Na+
etc.
(-70mV) - (-75mV) = +5mV (net outward)
(-70mV) - (+60mV) = -130mV (net inward)
Goldman-Hodgkin-Katz equation
used to determine Vm as a function of permeability and relative concentration
of each ion; assumes that Vm is not changing
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CONDUCTANCE and PERMEABILITY
a significant transmembrane current cannot be generated without a change in the
permeability of the membrane
the structural unit within the membrane that allows for such a change in permeability is the
channel, and specifically:
channel structure, i.e., protein-lined pore that can overcome waters of hydration
channel mechanisms that allow it to change conformation i.e., undergo the transition
from closed to open, in response to particular stimulus events
conductance
conductance is defined as the inverse of resistance of the channel, the magnitude of ionic
current that flows through a single channel:
Install Equation Editor and doubleclick here to view equation.
where g' is the conductance in units of Siemens (S), S=1/Ω, and S is measured in terms of
transmembrane current as a function of voltage; typically, membrane potential in mV, current
in picoamps, so g in picosiemens, e.g., if +20 mV leads to 2.2pA, then 2.2/20 = 110 pS
(Nicolls, pp. 38-39)
channel opening and closing is a probabilistic process
experimental observations show that opening and closing of channels is an all-or-nothing
event, i.e., a probabilistic event
stimuli that change the permeability of the cell membrane do so by changing the probability
of channel opening, i.e., channels do not remain open for duration of stimulus, but
continually open and close with a probability that changes in presence of stimulus
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transmembrane current represents the behavior of a population of channels
conductance of a population of channels of the same species (i.e., "macro-scopic"
conductance)
is
determined by the number of
open channels
given that g' is the membrane conductance for one ion, then total membrane conductance
Install Equation Editor and doubleclick here to view equation.
is equivalent to channel conductance x number of channels
equivalent circuit for a channel
g', conductance for the ion passing through the channel
E, equilibrium potential for that ion
using a modified form of Ohm's Law, ionic conductance for a given ion, e.g., K+
Install Equation Editor and doubleclick here to view equation.
Install Equation Editor and doubleclick here to view equation.
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 conductance = the amount of current per unit driving force
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distinction between permeability and conductance:
permeability depends on the state of channel, e.g., is it open or closed
conductance depends on membrane permeability and driving force, e.g., if all channels
through which K+ can pass are open, permeability of the membrane is said to be high, but if
Vm is near -75 mV, conductance will be near-zero given the low driving force
I-V relationship defines channel properties
recall that there are several different classes of channels based on the gating mechanism that
determines the probability of channel opening:
non-gated
ligand-gated
voltage-gated
second messenger-gated
ion-sensitive
given definition of conductance, it follows that different classes of channels may be
identified on the basis of their current-voltage relationship (I, y-axis; V, x-axis)
assume a ligand-gated channel
membranes with 1,2,3 channels in them, represented by I-V
curves with increasing slopes of 1,2,3
because all I-V curves pass through the origin, indicates
that primary force driving ionic current is electrical potential
and not equilibrium potential, i.e., equilibrium potential for
ion is 0 mV; or that channel is non-selective, i.e., becomes
permeable to all monovalent cations
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assume a ligand-gated channel with a non-zero equilibrium potential, i.e., a chemical
gradient
a non-zero equilibrium potential will shift the IV curve
along the x-axis
with
x-intercept indicating Vm where I=0
y-intercept indicating inward (-) or outward (+) current
E1 appropriate for a K+ current, i.e., net efflux of positive
ions
E2 appropriate for a Na+ current, i.e., net influx of
positive ions
assume a voltage-gated channel: conductance varies in a nonlinear manner with
transmembrane voltage:
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given above example, can see that:
E1 appropriate for a voltage-dependent K+ current, i.e., net efflux of positive ions for a
channel that is closed at resting membrane potential (assume rest near E1)
E2 appropriate for a voltage-dependent Na+ current, i.e., net influx of positive ions for a
channel that is closed at resting membrane potential (assume rest near E1)
assume a voltage-gated channel with a discontinuous I-V relationship:
multiple conductance "states"
step function change in I-V relationship
different I-V slope for each part of function
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