Membrane potentials and electrochemical gradients
1. Two neurons have identical resting membrane potentials of −70 mV. However, Neuron A has an equilibrium potential for K⁺ of −90 mV, while Neuron B has an equilibrium potential for K⁺ of −50 mV. A researcher opens the same number of identical K⁺ channels in both neurons. Predict how the membrane potential changes in each neuron and explain the difference.
1. Neuron A will hyperpolarize as K⁺ exits the cell, while Neuron B will depolarize as K⁺ enters, because opening K⁺ channels drives Vm toward each neuron's respective K⁺ equilibrium potential.
1. Two neurons receive identical depolarizing stimuli at the same distance from their axon hillocks. Neuron A has twice as many open leak channels as Neuron B, but both have identical cytoplasmic resistance. Predict which neuron will experience a greater depolarization at the axon hillock and explain why.
1. Neuron B will experience greater depolarization at the axon hillock because fewer open leak channels result in higher membrane resistance, allowing less current to escape during passive propagation.
1. Two neurons have identical resting membrane potentials and voltage-gated Na⁺ channels. However, Neuron A has voltage-gated K⁺ channels that activate almost immediately upon depolarization, while Neuron B has K⁺ channels that activate after a delay. Both neurons receive the same suprathreshold stimulus. Predict how their action potential graphs would differ and explain the physiological mechanism responsible.
1. Neuron A will likely have a smaller, shorter action potential, while Neuron B will have a larger, longer action potential because earlier K⁺ channel activation opposes Na⁺-driven depolarization sooner.
1. A researcher modifies a neuron so that its voltage-gated K⁺ channels close much faster than normal following an action potential, while its voltage-gated Na⁺ channels remain unchanged. Predict how this modification affects the relative refractory period and explain why.
1. Faster closure of voltage-gated K⁺ channels will generally shorten the relative refractory period because reduced K⁺ conductance decreases after-hyperpolarization and makes the neuron easier to excite again.
2. A neuron has a resting membrane potential of −70 mV, an equilibrium potential for Na⁺ of +60 mV, and an equilibrium potential for K⁺ of −90 mV. A researcher increases Na⁺ permeability while simultaneously decreasing K⁺ permeability. Predict the direction of the change in membrane potential and explain how both modifications contribute to the result.
2. The neuron will depolarize because increasing Na⁺ permeability drives Vm toward +60 mV, while decreasing K⁺ permeability reduces the influence of Eₖ (−90 mV).
2. A researcher applies a depolarizing stimulus to a dendrite, but the resulting graded potential becomes too small to trigger an action potential by the time it reaches the axon hillock. The researcher then increases the diameter of the dendrite without changing its membrane permeability or the original stimulus. Predict how this modification affects the likelihood of generating an action potential and explain the underlying mechanism.
2. Increasing dendrite diameter increases the likelihood of generating an action potential because it decreases internal resistance, allowing electrotonic current to spread farther with less attenuation.
2. A researcher stimulates the middle of a resting axon with an electrode strong enough to generate an action potential. Unlike normal stimulation at the axon hillock, the action potential begins in the middle of the axon. Predict how the action potential will propagate and explain why this differs from normal propagation in a neuron.
2. Increasing voltage-gated Na⁺ channel density lowers the threshold for action potential generation because greater Na⁺ influx allows regenerative depolarization to occur with a smaller initial stimulus.
2. A researcher stimulates the middle of a resting axon with an electrode strong enough to generate an action potential. Unlike normal stimulation at the axon hillock, the action potential begins in the middle of the axon. Predict how the action potential will propagate and explain why this differs from normal propagation in a neuron.
2. The action potential will propagate in both directions from the middle of the resting axon because neither side is refractory, unlike normal propagation where recently activated membrane behind the action potential prevents backward propagation.
3. A neuron has a resting membrane potential of −70 mV and an equilibrium potential for K⁺ of −90 mV. A researcher increases the extracellular concentration of K⁺ without changing its intracellular concentration or the membrane's permeability. Predict how the equilibrium potential for K⁺ and the resting membrane potential will change, explaining the relationship between the two.
3. Increasing extracellular K⁺ makes Eₖ less negative, causing the resting membrane potential to become less negative (depolarize) because Vm is strongly influenced by K⁺ permeability.
3. A neuron receives a strong depolarizing stimulus at the end of a long dendrite and a weaker depolarizing stimulus much closer to the axon hillock in separate trials. Explain how the weaker stimulus could trigger an action potential while the stronger stimulus fails to do so.
3. The weaker stimulus can trigger an action potential because graded potentials decrease in amplitude with distance, allowing a nearby stimulus to produce greater depolarization at the axon hillock than a stronger, distant stimulus.
3. A neuron normally produces an action potential with a rapid rising phase, a rapid falling phase, and an after-hyperpolarization. A researcher blocks most voltage-gated K⁺ channels immediately before stimulating the neuron. Predict how the resulting action potential graph would change and explain the physiological mechanism.
3. Blocking voltage-gated K⁺ channels will slow repolarization, broaden the action potential, and reduce after-hyperpolarization because less outward K⁺ current is available to return Vm toward resting potential.
3. Two axons have identical diameters, ion channels, and resting membrane potentials. However, Axon A is heavily myelinated, while Axon B has no myelin. A researcher then increases the diameter of Axon B without changing any other properties. Explain how increasing the diameter could compensate for the absence of myelin and whether this necessarily means Axon B will conduct action potentials faster than Axon A.
3. Increasing Axon B's diameter decreases internal resistance and increases conduction speed, partially compensating for the absence of myelin, but it does not guarantee faster conduction than myelinated Axon A.