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How long would it take 100 molecules of valinomycin to transport enough K+ to change the concentration inside an erythrocyte of volume 100 µm3 by 10 mM? (Assume that the valinomycin does not also transport any K+ out of the cell, which it really does, and that the valinomycin molecules outside the cell are always saturated withK+.)

Short Answer

Expert verified

The time taken by 100 molecules of Valinomycin to transport enough K+ ions to change the concentration inside an erythrocyte is 10 mins.

Step by step solution

01

Valinomycin

Valinomycin is a well-studied ionophore that binds specifically to a K+ion. It's a cyclic ionophore with ester linkage, peptide bonds, and D and L-amino acids. The channel-forming ionophore valinomycin generates transmembrane channels or pores through which chosen ions can flow.

02

Calculating the number of ions transported

The volume of erythrocyte is100μm3

The change in concentration inside the cell is10mM

The number of ions is6.023×1023ionsmol-1100μm310mM

On calculating,

=0.010molL-110-13L6.02×1023ionsmol-1=6.02×108ions

03

Calculating the time required

There are 100 ionophores and therefore each transport 6.02x106ions.

The time needed for the transport is,

Time=6.02×106ions1s104ionsTime=602secTime=10min

Hence, 100 molecules of Valinomycin take 10 minutes to transfer enough ions to alter the concentration inside one erythrocyte.

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