Suppose the egg has a diameter of 200μm . What fractional change in internal Na^+ concentration

step 1 Let's suppose that the egg is perfectly spherical. So its volume is given by v is equal to 4 by

Suppose the egg has a diameter of 200μm . What fractional...

Suppose the egg has a diameter of 200$\mu \mathrm{m} .$ What fractional change in internal $\mathrm{Na}^{+}$ concentration results from the fertilization-induced change in $V_{m} ?$ Assume that the $\mathrm{Na}^{+}$ ions are distributed throughout the cell volume. A. Increases by 1 part in $10^{4}$ B. Increases by 1 part in $10^{5}$ C. Increases by 1 part in $10^{6}$ D. Increases by 1 part in $10^{7}$

Suppose the egg has a diameter of 200$\mu \mathrm{m} .$ What fractional change in internal $\mathrm{Na}^{+}$ concentration results from the fertilization-induced change in $V_{m} ?$ Assume that the $\mathrm{Na}^{+}$ ions are distributed throughout the cell volume.

A. Increases by 1 part in $10^{4}$
B. Increases by 1 part in $10^{5}$
C. Increases by 1 part in $10^{6}$
D. Increases by 1 part in $10^{7}$

Key Concepts

Order-of-Magnitude Estimation

Often used in biological contexts to quickly assess the scale of a phenomenon, this approach helps determine that a small change in stored charge (as a result of a membrane potential change) leads to an extremely small fractional change in the overall ion concentration. It emphasizes the importance of comparing the number of ions added to the vast total number already present in the cell.

Uniform Ion Distribution

This key concept assumes that ions, once they enter the cell, are evenly distributed throughout the cytoplasm. This uniform distribution implies that any added number of ions (such as Na+ during fertilization) will not remain localized but rather be spread out across the entire volume, thereby reducing the impact on local concentration metrics.

Membrane Capacitance

This concept relates to the ability of the cell membrane to store electrical charge. The membrane acts similarly to a capacitor, where a small amount of charge accumulation can lead to a measurable change in the membrane potential. This relationship is key in understanding how ion movement, such as Na+ influx during fertilization, alters the electrical characteristics of the cell.

Surface-to-Volume Ratio

In spherical cells, the surface area, where the electrical charge is stored, is divided by the cell volume, which contains the distributed ions. Because many eggs are relatively large, the ratio is small, meaning that even if surface charge changes significantly, the resulting change in ion concentration throughout the volume is very diluted.

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