[WalterFaber]

Hey everyone,

I was wondering if someone here has experience with the analysis of fluorescence titration experiments.

I have synthesized some bis(aminomethylene) acridines that work as turn-on sensors for Zn²⁺ ions based on the PET effect.
To compare the different sensors I want to obtain the association constants with Zn²⁺ in DMF and THF as solvents. I prepared a 10 µM solution of the sensor and added aliquots of a solution containing 100 µM ZnBr₂ as well as 10 µM sensor (to circumvent dilution effects).

The resulting titration curves showed the expected saturation behavior at high Zn²⁺ concentrations. However, overall the shape of the curves was a bit sigmoidal rather than hyperbolical. The same curve shape was obtained with NMR titrations (the concentrations of the solutions were 100x higher compared to the ones used for fluorescence)

Non-linear least squares fitting with various software suites produced mixed results: A simple 1:1 model could be fitted to the data, however the association constant has a value of around 100-300 L/mol, which seems very low for my chelating ligand. Also the residuals of the fit show a very systematic distribution.
A 1:2 model (2 Zn²⁺ ions per ligand) resulted in a random distribution of the residuals and sensible association constants, but the reported erros were 2-3 magnitudes greater than the association constants themselves.

Up to this point all other data pointed to a 1:1 complexation model: xray crystal structures, DOSY nmr and ESI-TOF mass spectra are in agreement.

I redid the titration experiments but this time didn't prevent dilution: A 10 µM solution of the sensor simply was titrated with a 100 µM ZnBr₂ solution without added sensor. This time the curves don't show any saturation even with 30 equivalents of Zn²⁺ added. After the initial hyperbolical increase in fluorescence intensity it continued to rise in a linear fashion with increased Zn²⁺ concentration.

The titrations were repeated at 10x and 100x greater concentrations and gave the same results.

Nonetheless these curves can easily be fitted to a model that describes 1:1 complexation with additional non-specific binding (similar to http://www.graphpad.com/guides/prism/6/curve-fitting/reg_one_site_total.htm). The resulting association constants (the model on the linked website uses dissociation constants instead) seem reasonable.

Do you have ideas why the titration curves show distinctly different behavior in the two described cases? I'm very grateful for every little bit of advice!

[Corribus]

It's hard to interpret data without actually seeing it.

I'm also not following when you write, "I prepared a 10 µM solution of the sensor and added aliquots of a solution containing 100 µM ZnBr2 as well as 10 µM sensor (to circumvent dilution effects)."

So, to a solution of your sensor, you added a solution containing your zinc source and more sensor?

[WalterFaber]

So, to a solution of your sensor, you added a solution containing your zinc source and more sensor?

Exactly, that way the concentration of the sensor remained at 10 µM over the course of the titration.

Attached are two graphs of the fluorescence intensity vs the added concentration of Zn²⁺ and the ratio of Zn²⁺ to the sensor. The first one shows the result when 100 µM Zn²⁺+10 µM sensor is added.

The second shows the steadily increasing curve when pure 100 µM Zn²⁺ is used instead. I also included a possible fit.

[Corribus]

Attached are two graphs of the fluorescence intensity vs the added concentration of Zn²⁺ and the ratio of Zn²⁺ to the sensor. The first one shows the result when 100 µM Zn²⁺+10 µM sensor is added.

The second shows the steadily increasing curve when pure 100 µM Zn²⁺ is used instead. I also included a possible fit.

It's of course always potentially dangerous to render an opinion with only a cursory explanation of what someone is doing, but the first scenario seems like a rather unconventional way to go about things. As long as you're not working over enormous volume ranges, it is usually a simple matter to compensate for the dilution effect by adjusting the signal intensity by the effective concentration change. This requires that we make the assumption that the dependence of signal intensity on concentration is linear, but it's typically not a bad assumption, and one that is easily checked simply by diluting one of your samples with your solvent and seeing if the PL intensity scales accordingly.

I'm not entirely sure what's going on in scenario 1. Maybe a more descriptive account of what you're doing would help. But conceptually, I'm inclined to expect strange behavior based on what you seem to be doing. You have a solution of sensor (call it A), which fluoresces in the presence of B. You want to analyze this process, so you add B to A in various relative concentrations. But you are afraid of the dilution effect, so instead of just adding B to A, you add mixtures of B+A to A. The mixtures of B+A are already going to be "turned on", though. So what you're effectively doing is adding a mixture of activated A-B complex to unactivated A. This is potentially a different physical situation than simply adding B to A and measuring the formation of complex. For one thing, we don't know much about the reversibility of the process or what types of intermediates there are, and the reversibility of various steps in the process (hard to say without knowing much about A). E.g., if both 1:1 and 1:2 ratio are possible, you may have two very different association constants. A --> AB --> AB2. These complexes may have different fluorescence intensities and thermodynamic stabilities, which could result in the plot changing shape depending on the order in which you add the various reactants. That's just speculation, of course.

All things being equal I think your second process is the better way to go about things, provided you adjust for the effective concentration after the fact. Your sensor isn't a neutral spectator, so I think it is strange to add it along with your analyte to your titrating solution. You are asking for trouble.

[mjc123]

I don't understand where you get your concentration values from - if I've understood your procedure correctly.
Graph 1 has a point at cM = 100 µM, and graph 2 goes to over 200 µM. Yet if you add a 100 µM solution to something with no zinc, the zinc concentration will only ever asymptotically approach 100 µM, and never exceed it.
The cM/cL axes look wrong too - in graph 1, cM/cL is not 1 at cM = 0, and in graph 2, cM/cL will not vary linearly with cM. (I assume these are the analytical concentrations, not the actual concentrations after complexing.) What have you actually plotted - cM or cM/cL?
I suggest you go over all your calculations again very carefully.

[WalterFaber]

I don't understand where you get your concentration values from - if I've understood your procedure correctly.
Graph 1 has a point at cM = 100 µM, and graph 2 goes to over 200 µM. Yet if you add a 100 µM solution to something with no zinc, the zinc concentration will only ever asymptotically approach 100 µM, and never exceed it.
The cM/cL axes look wrong too - in graph 1, cM/cL is not 1 at cM = 0, and in graph 2, cM/cL will not vary linearly with cM. (I assume these are the analytical concentrations, not the actual concentrations after complexing.) What have you actually plotted - cM or cM/cL?
I suggest you go over all your calculations again very carefully.

You're right, the cM/cL axes are wrong. I will have to look over those again. What is plotted is Intensity vs. cM (the cL/cM were only included as a comparison)

In the first case the last datapoint at cM=100 µM was obtained by measuring the zinc/sensor solution itself, without adding it to the sensor solution.

I didn't describe the procedure for the second graph very well: As no saturation was observed when adding a 100 µM zinc solution I used a 1 mM solution.

I hope this clears things up.

the first scenario seems like a rather unconventional way to go about things

As far as I know this is the usual way to do titrations with supramolecular host-guest systems (cf http://pubs.rsc.org/en/content/articlepdf/2011/CS/C0CS00062K , end of section 5.1 for example). I wondered whether this method was suitable for my system since it's not a typical host-guest complex, but ultimately stuck with it. The points you raised are very good and I also trust the second process more.

[Corribus]

As far as I know this is the usual way to do titrations with supramolecular host-guest systems (cf http://pubs.rsc.org/en/content/articlepdf/2011/CS/C0CS00062K , end of section 5.1 for example). I wondered whether this method was suitable for my system since it's not a typical host-guest complex, but ultimately stuck with it. The points you raised are very good and I also trust the second process more.

It may be perfectly fine. I just haven't personally doesn't a fluorescence titration like this before - although admittedly my experience is mostly with quenching expts.

[Yggdrasil]

You may be having issues with ligand depletion at low ligand concentrations (i.e. the binding depends on the amount of free ligand in solution, which is different than the total amount of ligand if a significant fraction of your ligand gets bound by your receptor).  You could try fitting your curve to an equation that takes ligand depletion into account (e.g. see Equation 7.8B in the following pdf):
https://tools.thermofisher.com/downloads/FP7.pdf

[WalterFaber]

I'm sure that ligand depletion is important, the sensor does bind very well to zinc. The fit equation in the picture above was only for preliminary testing. The model I'm currently using contains the equation you mentioned as well as an additional linear term to account for the continuing fluorescence increase at high zinc concentrations.