How long would it take 100 molecules of valinomycin to...

How long would it take 100 molecules of valinomycin to transport enough $\mathrm{K}^{+}$ to change the concentration inside an erythrocyte of volume $100 \mu \mathrm{m}^{3}$ by $10 \mathrm{mM} ?$ (Assume that the valinomycin does not also transport any $\mathrm{K}^{+}$ out of the cell, which it really does, and that the valinomycin molecules outside the cell are always saturated with $\mathrm{K}^{+}$.)

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Key Concepts

Concentration and Mole Conversion

This involves converting concentration changes, given in millimolar units, and cell volume, often specified in microscopic units, into actual numbers of ions using stoichiometric relationships. By applying Avogadro’s number, one can relate changes in molarity within a defined volume to the total number of ions transported.

Assumptions in Modeling Transport Dynamics

Simplifying assumptions, such as unidirectional transport and external saturation, are often made to facilitate calculations. Recognizing these assumptions is crucial for understanding the limitations of the estimated time required for ion transport under idealized conditions.

Membrane Ion Transport

This concept involves the movement of ions across cell membranes using specific transporter proteins. It is central to understanding how molecules like valinomycin facilitate the selective movement of potassium ions, altering the internal ionic concentration of cells, such as erythrocytes.

Carrier Protein Kinetics

Carrier proteins, including ionophores, exhibit a turnover rate that dictates how many ions can be transported per unit time. Understanding these kinetics is essential for calculating the overall rate of ion transport when only a small number of transporter molecules are involved.

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