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Permeance-Weighted Voltage Formula
The Goldman-Hodgkin-Katz equation is used to calculate the membrane potential given the permeability and concentration of certain ions.
Over the course of an action potential, the change in the concentration of ions inside and outside a cell will be small compared to the change in
the relative permeability of each ion. The blue line on the graph to the right represents the reversal potential
of Na+ at rest, and the orange line represents the reversal potential of K+ at rest. The membrane potential gets more positive with
the increase in relative Na+ permeability as voltage-gated Na+ channels open, reaching its peak close to the reversal potential
of Na+.
At rest, Na+ is even less permeable compared to K+, and so the resting potential is close to the reversal potential of K+.
Since Vm is not equal to Eion, Vm - Eion will be greater or lesser than 0. We call Vm - Eion the driving force. The driving force is multiplied by the conductance for that ion to calculate the ion's net current. A negative driving force, in the case of an anion, will produce a net inward current, while a negative driving force in the case of a cation represents a net outward current. Likewise, a positive driving force suggests an outward current for an anion or an inward current for a cation.
\[ V_m = \frac{RT}{F} \ln \left( \frac{P_{K^{+}}[K^{+}]_{out} + P_{Na^{+}}[Na^{+}]_{out}P_{Cl^-}+ [Cl^-]_{in}}{P_{K^{+}}[K^{+}]_{in} + P_{Na^{+}}[Na^{+}]_{in} + P_{Cl^-}[Cl^-]_{out}} \right) \]
At rest, Na+ is even less permeable compared to K+, and so the resting potential is close to the reversal potential of K+.
Since Vm is not equal to Eion, Vm - Eion will be greater or lesser than 0. We call Vm - Eion the driving force. The driving force is multiplied by the conductance for that ion to calculate the ion's net current. A negative driving force, in the case of an anion, will produce a net inward current, while a negative driving force in the case of a cation represents a net outward current. Likewise, a positive driving force suggests an outward current for an anion or an inward current for a cation.
\[ V_m = \frac{RT}{F} \ln \left( \frac{P_{K^{+}}[K^{+}]_{out} + P_{Na^{+}}[Na^{+}]_{out}P_{Cl^-}+ [Cl^-]_{in}}{P_{K^{+}}[K^{+}]_{in} + P_{Na^{+}}[Na^{+}]_{in} + P_{Cl^-}[Cl^-]_{out}} \right) \]
Na+/K+ ATPase Pump
Requires ATP to move 3 Na+ ions out of the cell per
every 2 K+ moved into the cell. This relatively slow process is constant.
Simple diffusion passively moves K+ ions from areas of high concentration (inside the cell) to areas of low concentration (outside the cell). Na+ passively moves from areas of high concentration (outside the cell) to areas of low concentration (inside the cell). This pump moves K+ and Na+ in the opposite direction of their concentration gradient. For every 2 K+ ions that the pump moves into the cell, 3 Na+ ions are moved out. This helps the cell maintain the unequal concentration gradients at rest and contributes to negative membrane potential as fewer cations are pumped in than pumped out.
Simple diffusion passively moves K+ ions from areas of high concentration (inside the cell) to areas of low concentration (outside the cell). Na+ passively moves from areas of high concentration (outside the cell) to areas of low concentration (inside the cell). This pump moves K+ and Na+ in the opposite direction of their concentration gradient. For every 2 K+ ions that the pump moves into the cell, 3 Na+ ions are moved out. This helps the cell maintain the unequal concentration gradients at rest and contributes to negative membrane potential as fewer cations are pumped in than pumped out.
K+ Leak Channels
K+ leak channels are K+-selective leak channels play an important role in maintaining the cell's resting membrane potential as they passively allow the positively charged K+
leave the cell to the less concentrated extracellular space.
Voltage-Gated Na+ Channels
Feature an inactivated, open, and closed state.
Channels in this family typically open when the membrane potential has depolarized (become more positive) to the action potential threshold — usually around -55mV. Once the peak of the action potential has been reached, the channel is quickly blocked by an inactivation gate. This state of inactivation leads to rapidhyperpolarization (the voltage becoming more negative) as the membrane is no longer as
relatively permeable to sodium ions. This also contributes to refractory periods: periods in which it can be harder
(relative refractory periods) or nearly impossible (absolute refractory periods) to generate another action potential.
Channels in this family typically open when the membrane potential has depolarized (become more positive) to the action potential threshold — usually around -55mV. Once the peak of the action potential has been reached, the channel is quickly blocked by an inactivation gate. This state of inactivation leads to rapid
Voltage-Gated K+ Channels
Ion channels in this family often open around the time sodium channels inactivate, and they play an important role in the falling phase and afterhyperpolarization phase of an action potential as the cell becomes more relatively permeable to potassium and repolarizes. It also takes longer for these passive channels to stop conducting ions than it does for voltage-gated sodium channels, resulting in a period in which potassium is even more permeable than at rest and the membrane potential. This makes the membrane potential more negative than at rest. This period is known as afterhyperpolarization, and this stage contributes to the relative refractory periods as it takes more excitation to trigger an action potential.
Ion channels in this family often open around the time sodium channels inactivate, and they play an important role in the falling phase and afterhyperpolarization phase of an action potential as the cell becomes more relatively permeable to potassium and repolarizes. It also takes longer for these passive channels to stop conducting ions than it does for voltage-gated sodium channels, resulting in a period in which potassium is even more permeable than at rest and the membrane potential. This makes the membrane potential more negative than at rest. This period is known as afterhyperpolarization, and this stage contributes to the relative refractory periods as it takes more excitation to trigger an action potential.
EPSPs and IPSPs
Neurons receive inputs from multiple sources via various receptors, each producing excitatory or inhibitory postsynaptic potentials (EPSPs or IPSPs). Summation refers to the additive effects of multiple EPSPs and IPSPs occurring close together in time or space. Temporal summation involves repeated stimuli over a short period of time, while spatial summation involves simultaneous stimuli from different locations on the neuron. If the combined effects of these potentials reach the threshold level, an action potential is triggered.
Neurons receive inputs from multiple sources via various receptors, each producing excitatory or inhibitory postsynaptic potentials (EPSPs or IPSPs). Summation refers to the additive effects of multiple EPSPs and IPSPs occurring close together in time or space. Temporal summation involves repeated stimuli over a short period of time, while spatial summation involves simultaneous stimuli from different locations on the neuron. If the combined effects of these potentials reach the threshold level, an action potential is triggered.
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