One thousand $\mathrm{Ca}^{2+}$ channels open in the plasma membrane of a cell that is $1000 \mu \mathrm{m}^{3}$ in size and has a cytosolic $\mathrm{Ca}^{2+}$ concentration of $100 \mathrm{nM}$. For how long would the channels need to stay open in order for the cytosolic $\mathrm{Ca}^{2+}$ concentration to rise to $5 \mu$ M? There is virtually unlimited $\mathrm{Ca}^{2+}$ available in the outside medium (the extracellular $\mathrm{Ca}^{2+}$ concentration in which most animal cells live is a few millimolar), and each channel passes $10^{6} \mathrm{Ca}^{2+}$ ions per second.
Added by Antonio S.
Step 1
First, we need to find the total number of $\mathrm{Ca}^{2+}$ ions needed to raise the cytosolic concentration from $100 \mathrm{nM}$ to $5 \mu \mathrm{M}$. Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 81 other Biology educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Cytosolic Ca2+ concentrations typically rise about 50-fold when Ca2+ channels open in the plasma membrane. Assume that 1000 Ca2+ channels open in a cell with a volume of 1000 mm3 and an internal Ca2+ concentration of 100 nM. Each Ca2+ channel passes 106 Ca2+ ions per second. For how long would the channels need to stay open in order to raise the cytosolic Ca2+ concentration 50-fold to 5 mM?
Sri K.
Using the Nernst equation and the ion concentrations given in Table $12-1$ (p. 391 ), calculate the equilibrium membrane potential of $\mathrm{K}^{+}$ and $\mathrm{Na}^{+}-$ that is, the membrane potential where there would be no net movement of the ion across the plasma membrane (assume that the concentration of intracellular $\mathrm{Na}^{+}$ is $10 \mathrm{mM}$ ). What membrane potential would you predict in a resting animal cell? Explain your answer. What would happen if a large number of $\mathrm{Na}^{+}$ channels suddenly opened, making the membrane much more permeable to $\mathrm{Na}^{+}$ than to $\mathrm{K}^{+}$ ? (Note that because few ions need to move across the membrane to change drastically the charge distribution across that membrane, you can safely assume that the ion concentrations on either side of the membrane do not change significantly.) What would you predict would happen next if the $\mathrm{Na}^{+}$ channels closed again?
Recommended Textbooks
Biology for AP Courses
Objective Biology for NEET
Introduction to General, Organic and Biochemistry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD