Free drug and protein binding
Open a PK/PD paper and you will often see a little f in front of the target: fT>MIC, fAUC/MIC. That letter is easy to skim past. It is also where many simulations go wrong.
Most antibacterial targets are written for free (unbound) drug. Many concentration models are fitted to total plasma levels. If you compare total curves to free targets, the regimen looks stronger than the rule you claimed to test.
Unit hygiene for exposure-effect work. Not a dosing calculator.
What free means in plain language
In plasma, some drug molecules stick to proteins such as albumin. The usual modeling story says the unbound molecules are the ones available to act. The MIC assay is generally interpreted on that unbound-compatible scale. So the simulator should put free concentration versus time next to MIC.
A simple linear correction is:
[ C_{}(t)=f_uC_{}(t) ]
where (f_u) is the unbound fraction. This is a starting point, not a religion. Binding can change with albumin, pregnancy, burns, or critical illness. For a highly bound drug, a small error in (f_u) becomes a large error in free exposure.
A numbers intuition
If fu = 0.2, only one fifth of the total concentration counts toward a free-drug target. Using the total curve unchanged is like pretending there is five times more active drug than your target definition allows.The free curve is the one that should meet a free-drug MIC rule.
Where people get hurt in practice
- Target says free, plotted series is total.
- fu comes from healthy volunteers, applied unchanged to hypoalbuminemic ICU patients.
- The infection is not in plasma (ELF, CSF, tissue), but the model never leaves the plasma compartment.
- Combination regimens use one fu for both components without checking.
Model outputs total concentration, multiplies by a cited fu, then tests 100% fT>MIC. The methods line states free/total conversion and the fu source.
Model outputs total concentration and directly counts time above MIC using a free-drug target wording. PTA looks great. The claim is overstated by roughly the binding factor.
A short checklist before you run PTA
- Label every series: free or total.
- Cite fu and whether it is fixed, sampled, or covariate-dependent.
- Re-run with lower and higher fu as a one-way sensitivity check.
- For BL/BLI pairs, bind each component on its own terms.
- If the effect site is not plasma, say so and move to the effect-site lesson with honest humility.
Walk through one messy case
You fit a model to total plasma concentrations. The target you want is 100% fT>MIC. Literature fu is 0.25 in healthy volunteers, but your population is critically ill and often hypoalbuminemic. A first run uses fu = 0.25. A second run uses fu = 0.40 as a what-if for lower binding. A third run keeps total concentrations and “forgets” the f, which wrongly inflates attainment.
Only the first two runs belong in a serious report, and both should be shown if binding is uncertain. The third run is a unit error dressed as optimism.
When you present results, say the free/total conversion out loud before you show the PTA plot. If listeners cannot tell whether the curve is free or total, the figure is not ready.
Takeaway
Binding is not cosmetic formatting. It decides which curve is allowed to talk to the MIC. Align the binding state of the PK output with the binding state of the PD target before you interpret attainment.
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