More shallow the gradient, the better the resolution?

[pipettemonkey]

I'm working separating peptides on reverse phase HPLC. In general, it seems a more shallow gradient of CH3CN, the better the resolution.

Is this always the case? If not, is it the case more often than not?

[Uwe Neue]

As an overview for the separation of many analytes, it is correct that shallower gradients give better overall resolution. However, for any individual pairs of analytes, a shallower gradient may be better or may be worse.

[tom jupille]

A shallower gradient is the equivalent to a weaker isocratic solvent. As Uwe pointed out, overall, this improves resolution (but suffers from "diminishing returns"). "Overall" may or may not apply in specific cases.

[lmh]

You have to think about what, physically, is happening on the column. This is a hand-wavy version, so someone who knows more about it can shoot it down in flames:

If you imagine a theoretical zero-length column with beautiful analytes that "come off" at a particular percentage, then all peaks will have zero-width, and a shallow gradient will put them further apart.

Now consider analytes that behave a bit more realistically, so that at 50% acetonitrile they begin to come off the column, partitioning between the column and the eluent. The peak will now have a width, as material on the column comes off gradually to maintain the correct partitioning ratio.

In a real gradient, the percentage is increasing, so the peak will come off faster and faster. Once nearly all the peak is "off", the amount remaining on the collumn is shrinking, so even though partitioning is now strongly in favour of the solvent, material will be leaving the column more slowly again.

(irrelevant to this discussion, but on top of this, material will diffuse, and wash in and out of any dead volumes in the system, so even if a narrow peak leaves the column, a Gaussian-style broader peak will arrive at the detector.)

So in a real system, if you make the gradient too steep, peak A will take a certain volume of solvent to elute, and the steep gradient means that peak B might begin to encounter eluting conditions before all of A is gone. This creates bad resolution.

Also, if you make your gradient too steep, with a column of measurable volume, it's hard to know exactly what percentage different parts of the column are really seeing.

But if the gradient becomes unnecessarily slow, peak A will begin to come off, but do so very slowly; it will take longer to get enough volume of the (low percentage) solvent through to elute the first bit of peak A, before the precentage climbs enough for the elution to "really get going". This makes very slow broad peaks.

So the general situation is that if you're eluting using roughly the flow rate described by the manufacturers, and your gradient has the same steepness as the manufactuer's gradient, then the chances are it is already near optimal (manufacturers can't afford to show unoptimal gradients in their brochures). If you reduce the steepness, you will probably find that increased peak-width wipes out any benefit from greater difference in retention time.

[Uwe Neue]

I like to work with equations, and to show something in equations is often much simpler that a million words.

The peak capacity P** is the number of the peaks that can be stuffed between the first peak to elute and the last peak, which have the retention factors k1 and kf before the gradient starts (kf can be very large, k1 can be about 10). This number can be calcuated from the following equation:

P** = sqrt(N) /(G+1) * ln(kf/k1)

N is the true isocratic plate count, which is assumed to be about the same for all peaks. If we don't change the solvent composition at the beginning of the gradient, the ratio kf/k1 remains the same.

The parameter G is the gradient slope. For a step gradient, it is infinite, and the peak capacity becomes 0. For a very flat gradient G approaches 0, and the peak capacity becomes nearly constant: with other words, you can still make the gradient flatter (= gradient run time longer), but you gain very little.

This factor G is defined as:

G = S * delta C *to/tg

to is the column dead time, tg is the gradient run time. delta C is the difference in solvent composition between the beginning and the end of the gradient, expressed as volume fraction. S is around 10 for most small molecules. If we run a gradient over 50% organic and the analytes are small molecules, then S * delta C ~ 5. A reasonable ratio of gradient run time to column dead time is around 20, which means that for common conditions G is about 0.25. If I make the gradient 10 times longer, then G+1 changes from 1.25 to 1.025, and you can see that I have only gained 25% in peak capacity for waiting 10 times longer.

For those interested, I suggest to play a bit more with this equation.

[adam]

Now you've got the hard core theory. But some things can also be approached very simplistically.

Here's the simplest possible answer: "The main purpose of a gradient is to reduce resolution. That is to say excess resolution"

Any resolution beyond 1.5 does not offer any added value. In most cases where a gradient is used we would otherwise have huge gaping spaces between peaks, that you could drive a truck through. These spaces contribute nothing positive, they simply result in a long run time, more mobile phase consumption, and more waste generation...oh and worse sensitivity too".

[pipettemonkey]

Thanks for the replies.

One thing to keep in mind is that I am working with 3-4,000 MW peptides, not small molecules.

It is my understanding that proteins do not experience this dynamic adsorption/desorption like small molecules. Instead, proteins are said to have only one adsorption and one desorption (when it is eluted). You don't say that such and such small molecule elutes at some % of acetonitrile. However, I can say that BSA, for instance, elutes near 45% acetonitrile on a particular system. Below 45% and no elution.

Peptides are said to behave like a hybrid between the two.

Does this change the discussion any?

[Uwe Neue]

It does not change the discussion substantially. The S value is between 50 and 60 for your peptides, which means G is 5 to 6 times larger, and the entire plot shifts towards longer gradient times. However, the equation does not change, and you just need to plug in the new numbers.
For a gradient with a G of 1.5, you will still see substantial improvements when you increase the run time.

While the elution of peptides and proteins is very steep, it is NOT a one step on/off mechanism.

[HW Mueller]

We have discused the narrow range of equilbration for proteins before. My experience: The nanopeptides, vasopressin and oxytocin (MW just over 1000g/mol) behaved more like amino acids, so did ANP (atrial natriuretic peptide, ~40000) once conditions were found which did not use TFA. Monoclonal antibodies (~150000) were not amenable to isocratic HPLC.
I suspect the elution behavior strongly depends on how complicated the (non-primary) structure is.

[JA]

...The nanopeptides...

I have an irrational hatred of that word already. What is a nanopeptide?

[HW Mueller]

Sorry, some mistakes crept in: Should be nona (9 for 9 amino acids) not nano (10^-9). Also, ANP has about 28 amino acids so the molecular weigth should be below 4000, not 40000.