A very short half-life for passage across a biological membrane

Question

BlackTom AI · Accepted Answer

A very short membrane passage half-life means the substance crosses the barrier rapidly because the transfer rate constant is large.

1) Relevant concepts
- For first-order translocation kinetics, half-life (t1/2) and the rate constant (k) are related by t1/2 = ln2 / k (ln2 ≈ 0.693).  
- A small t1/2 therefore corresponds to a large k — i.e., rapid translocation.  
- Mechanistic information (passive diffusion vs carrier-mediated) requires additional evidence such as saturation kinetics, temperature dependence, or specificity.

2) Step-by-step reasoning
- Start from the quantitative relationship t1/2 = 0.693/k.  
- If t1/2 is "very short", t1/2 is small. Rearranging gives k = 0.693 / t1/2, so k becomes large. A large k means the flux across the membrane is high and the compound equilibrates quickly between compartments.

3) Calculations / intermediate steps (illustrative)
- Example: if t1/2 = 1 min, k = 0.693 / 1 min = 0.693 min^-1.  
- If t1/2 = 10 min, k = 0.693 / 10 min = 0.0693 min^-1.  
- Thus a tenfold shorter half-life corresponds to a tenfold larger rate constant and therefore tenfold faster translocation.

4) Why the correct answer is correct
- Because half-life is inversely proportional to the rate constant, a very short half-life directly suggests fast translocation across the membrane (answer a).

5) Why the other options are incorrect
- b (indicates carrier-mediated): Carrier mediation implies saturability and selectivity; a short half-life alone does not distinguish carrier from high-permeability passive diffusion.  
- c (readily recognized by molecular target): Recognition by a target refers to pharmacodynamics (binding), not the kinetics of membrane passage.  
- d (even distribution/shallow gradient): A shallow concentration gradient reduces net flux and would lengthen, not shorten, the apparent half-life.

6) Conclusion
- Therefore, the correct choice is a. suggests fast translocation, which matches the provided answer.

A very short half-life for passage across a biological membrane单项选择题

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