Nerves and muscles: study guide

Key ideas

Nerve cells carry signals as changes in membrane potential, and muscle cells shorten when thin and thick filaments slide. The questions mix ion equilibrium, conduction times and the phases of the action potential.

• The equilibrium potential of an ion at 37 °C is E = (61.5 mV ÷ z) × log₁₀([outside] ÷ [inside]). For K⁺ it is strongly negative, which sets the resting potential near −70 mV.
• An action potential fires if the membrane reaches threshold. Na⁺ channels open (depolarization), then K⁺ channels open (repolarization), and a short undershoot follows.
• Conduction velocity is distance ÷ time. Myelin and a wider axon raise it. Several small EPSPs must sum to reach threshold.
• Muscle contracts by thin filaments sliding over thick ones, which shortens the sarcomere while the filaments keep their length.

Key equations

• E = (61.5 mV ÷ z) × log₁₀([out] ÷ [in])
• velocity = distance ÷ time
• EPSPs needed = (threshold − rest) ÷ size
• length after = rest length × (1 − fraction shortened)

Worked example

For K⁺ with 5 mM outside and 140 mM inside, E = 61.5 × log₁₀(5 ÷ 140) = 61.5 × (−1.45) = −89 mV. A neuron at −70 mV with a threshold of −55 mV, and EPSPs of 5 mV each, needs (−55 − (−70)) ÷ 5 = 3 EPSPs. An impulse that travels 120 mm in 4 ms has a velocity of 30 m/s.

Common mistakes

• Putting the inside concentration over the outside in the Nernst equation, which flips the sign.
• Saying the action potential gets bigger with a stronger stimulus. It is all-or-nothing; only the frequency changes.
• Thinking the filaments shorten during contraction. They slide; the sarcomere shortens.

Practice

Test yourself with practice questions on this topic: Nerves and muscles