Protein binding: the impact of unbound drug

I’ve provided two charts that summarize. This first one summarizes dose and volume changes. Now I don’t I don’t expect you to memorize what’s in these charts by any means. These are meant to illustrate the relationships between all the variables we’ve been discussing and you should be able to go through this chart and understand why certain combinations result in an increase or a decrease. What I’d like to point out is the no change. Now we know that C average steady state is not affected by volume whether the volume increases or decreases there’s no impact on C average steady state because that depends on dose over tau divided by clearance.

Likewise, area under the curve is not affected by changes in volume either increasing or decreasing when we consider C Max minus C min if the dose and volume both change proportionally that they cancel each other out there will be no change on the in the value of C Max minus C min.

This chart compares the impact of both the dosing interval and the clearance through a series of variables and we can see that as the dosing interval changes or k or also clearance changes we can see increases in decreases in e to the minus K tau C maxi C min C average steady state increases in tau or k have no impact whatsoever on C max minus C min the only two variables that impact see max minus C min are dose and volume Area under the curve has not changed in any way by changing the dosing interval because it’s the area under the curve between those two doses and that depends only on the dose divided by the clearance so area of the curve does not change in response to a dosing interval change and if the tau and the K both change inversely, essentially they they cancel each other out with only one exception and that is area under the curve.

If we change both tau and K inversely only the the K affects a change in area under the curve so however the the K changes you would expect a corresponding change in area under the curve but again you don’t need to memorize this chart that would be self-defeating. What’s important about this chart is you can read any cell within the chart that consider the variables represented within that cell and make sure you understand why the variable would increase or decrease or stay the same. Now let’s consider the impact of protein binding on serum concentrations.

If we increase the fraction unbound from point one to point two what we see is an increase in the unbound concentration from point zero two five milligrams per liter to zero point zero five milligrams per liter Now what I represented here graphically the blue and the yellow combined in the rectangle represents the total serum concentration of two milligrams per liter.

So instantaneously when the fraction unbound increases from point one to point two the total concentration doesn’t change but because the fraction unbound double the concentration unbound would double However because the fraction the increase in fraction unbound increases the clearance of the drug then when steady state is reestablished under this new higher clearance the total concentration is only going to be half as much the total concentration would drop from two milligrams per liter down to one milligrams per liter and the fact that the fraction unbound is now twenty percent rather than ten percent the unbound concentration is actually going to be going to be the same as it was initially 0.025 milligrams per liter.

We can represent this graphically as shown The concentration unbound is the line on the bottom and the total concentration is the line on the top Now in the beginning situation we see that the fraction unbound is 10% concentration is 0.025 unbound and the total concentration is 2 milligrams per liter The point at which the fraction unbound doubles from point one to point two We see that the concentration unbound doubled because of the change in fraction unbound but initially the total serum concentration did not change at indication number two When steady state is reestablished in number three we still have the doubling of the fraction unbound that hasn’t changed What we see now is because the clearance doubled at point two the concentration of both the total concentration and the unbound concentrate from that point would be cut in halfㄡ The difference is that we started at the actual total concentration so the doubling of clearance would cause the total concentration to drop down to half of what it was from two milligrams per liter to one milligram per liter.

But since the unbound concentration initially doubled then the doubling of the clearance would cause that concentration to fall on half which actually takes it back to what it was originally at 0.025 milligrams per liter. Now let’s consider what happens in terms of the pharmacologic effects during this process At 0.1 the the original total concentration and the original unbound concentration at point two we have the doubling of the fraction unbound and we can see the concentration of the unbound drug doubling the concentration of the total drug has not yet begun to change at point two. So we have at point two is a temporary increase in the pharmacologic effect of the drug because the unbound concentration has doubled.

However at point 3 when steady state has reestablished the unbound concentration because of the increased clearance has now returned to what it was initially. So in this situation when we have a highly protein bound drug then that demonstrates an increase in the fraction unbound what will happen is the therapeutic effect the pharmacologic effect of the drug will initially increase but it’s only temporary until steady state conditions are re-established because at that point the unbound concentration which is what determines the pharmacologic effect of the drug will have returned to what it was initially. Let’s consider another exercise.

The patient is being treated with a highly protein bound drug if the fraction unbound doubles then at that instant before steady state is reestablished what has changed?