Excitable Cells: Graded Potentials and Action Potentials

Excitable Cells

Overview of Electrical Potentials in Cells

Excitable cells, such as neurons and muscle cells, generate and respond to electrical signals. These signals are essential for communication, movement, and many physiological processes. The study of electrical potentials includes understanding resting membrane potential, graded potentials, and action potentials.

• Resting Membrane Potential (Vm): The baseline electrical charge across the cell membrane when the cell is not actively sending a signal.

• Graded Potentials: Small, variable changes in membrane potential that can lead to action potentials if they reach a certain threshold.

• Action Potentials: Large, rapid changes in membrane potential that propagate along excitable cells, enabling signal transmission.

Graded Potentials

Terminology & Properties Review

Graded potentials are transient changes in membrane potential that occur in response to stimuli. Unlike action potentials, they are not all-or-none events and can vary in amplitude and duration.

• Definition: Graded potentials are local changes in membrane potential that vary in size, depending on the strength of the stimulus.

• Location: Typically occur in the dendrites and cell body of neurons.

• Characteristics:

  • Not all-or-none: Amplitude depends on stimulus strength.

  • Can be depolarizing (more positive) or hyperpolarizing (more negative).

  • May "sum" spatially or temporally to reach threshold for action potential.

  • Decay with distance from the site of origin (passive decay).

• Depolarization: Membrane potential becomes less negative (moves toward zero or positive values).

• Hyperpolarization: Membrane potential becomes more negative.

Example: A neurotransmitter binding to a receptor may open Na+ channels, causing a depolarizing graded potential.

Graphical Representation

The following graph illustrates how membrane potential changes during depolarization and repolarization:

• Depolarization: Upward deflection (more positive).

• Repolarization: Return toward resting potential (more negative).

Synaptic Potentials: EPSPs and IPSPs

Excitatory and Inhibitory Postsynaptic Potentials

Graded potentials at synapses are classified as either excitatory (EPSPs) or inhibitory (IPSPs), depending on the type of ion channel opened by neurotransmitter binding.

• EPSP (Excitatory Postsynaptic Potential): Depolarizes the postsynaptic membrane, increasing the likelihood of action potential generation.

• IPSP (Inhibitory Postsynaptic Potential): Hyperpolarizes the postsynaptic membrane, decreasing the likelihood of action potential generation.

• Mechanism:

  • EPSPs often result from opening Na+ or Ca2+ channels.

  • IPSPs often result from opening K+ or Cl- channels.

Example: Glutamate binding to its receptor typically produces an EPSP, while GABA binding produces an IPSP.

Summation of Graded Potentials

Temporal and Spatial Summation

Graded potentials can combine to influence whether a neuron reaches the threshold for action potential initiation.

• Temporal Summation: Multiple graded potentials from the same location occur in rapid succession, adding together.

• Spatial Summation: Graded potentials from different locations on the neuron add together.

• Threshold: The membrane potential at which an action potential is triggered, typically around -55 mV in neurons.

Example: Two EPSPs arriving close together in time or space can sum to reach threshold and trigger an action potential.

Comparison: Graded Potentials vs. Action Potentials

Key Differences

Graded potentials and action potentials differ in their properties, mechanisms, and physiological roles.

Feature	Graded Potentials	Action Potentials
Location	Dendrites & cell body	Axon (trigger zone)
Amplitude	Variable, depends on stimulus	All-or-none, fixed amplitude
Summation	Can be summed (spatial/temporal)	Cannot be summed
Decay	Decreases with distance	No decay; propagates without loss
Threshold	No threshold; amplitude varies	Requires threshold stimulus
Refractory Period	None	Has refractory period

Equations: Nernst and Goldman-Hodgkin-Katz (GHK)

Calculating Membrane Potentials

The Nernst and GHK equations are used to calculate equilibrium and resting membrane potentials based on ion concentrations and permeabilities.

• Nernst Equation: Calculates the equilibrium potential for a single ion.

$E_{ion} = \frac{RT}{zF} \ln \left( \frac{[ion]_{out}}{[ion]_{in}} \right)$

• Goldman-Hodgkin-Katz (GHK) Equation: Calculates the resting membrane potential considering multiple ions and their permeabilities.

$V_m = \frac{RT}{F} \ln \left( \frac{P_{K^+}[K^+]_{out} + P_{Na^+}[Na^+]_{out} + P_{Cl^-}[Cl^-]_{in}}{P_{K^+}[K^+]_{in} + P_{Na^+}[Na^+]_{in} + P_{Cl^-}[Cl^-]_{out}} \right)$

Example: If Na+ permeability increases, the membrane potential moves closer to the Na+ equilibrium potential.

Passive Decay of Graded Potentials

Distance and Strength

Graded potentials decrease in strength as they spread from their point of origin due to passive decay.

• Passive Decay: The reduction in amplitude of a graded potential as it moves away from the site of initiation.

• Length Constant (λ): The distance over which the potential decreases to 37% of its original value.

Example: An EPSP generated at a dendrite may be much weaker by the time it reaches the axon hillock.

Summary

Graded potentials are essential for integrating synaptic inputs and determining whether a neuron will fire an action potential. Their properties—variable amplitude, ability to sum, and passive decay—contrast with the all-or-none nature of action potentials. Understanding these concepts is fundamental for studying neural signaling and physiology.