8.1 Collisional quenching and Stern-Volmer relationship

Collisional Quenching

Process of collisional quenching

Collisional (or dynamic) quenching happens when a molecule in its excited state bumps into another molecule, called a quencher, and returns to the ground state without emitting a photon. The fluorophore isn't chemically changed in the process. For example, dissolved oxygen can quench tryptophan fluorescence this way.

The underlying mechanism typically involves either energy transfer from the excited fluorophore to the quencher, or electron transfer between them. Either way, the excited state is deactivated before fluorescence can occur.

Several factors control how effective collisional quenching is:

• Temperature: Higher temperature means faster diffusion, so molecules collide more often and quenching increases.
• Viscosity: A more viscous solvent (like glycerol compared to water) slows diffusion and reduces the collision rate, making quenching less efficient.
• Diffusion rates: Both the fluorophore and quencher need to encounter each other during the excited-state lifetime. Larger or slower-diffusing molecules quench less effectively.

The observable result is a decrease in both fluorescence intensity and excited-state lifetime. That lifetime point is critical for distinguishing dynamic quenching from static quenching later on.

Common quenchers include molecular oxygen ($O_2$), halogens and halide ions ($I^-$, $Br^-$), amines, and acrylamide. Each has different selectivity, which makes them useful probes. For instance, iodide is charged and can only quench surface-exposed fluorophores in a protein, while oxygen is small and nonpolar enough to penetrate into hydrophobic regions.

Stern-Volmer relationship in quenching

The Stern-Volmer equation provides a quantitative link between quencher concentration and the reduction in fluorescence:

$F_0/F = 1 + K_{SV}[Q]$

Here, $F_0$ is the fluorescence intensity without quencher, $F$ is the intensity at quencher concentration $[Q]$, and $K_{SV}$ is the Stern-Volmer quenching constant. A larger $K_{SV}$ means the fluorophore is more easily quenched.

If you plot $F_0/F$ on the y-axis against $[Q]$ on the x-axis, purely dynamic quenching gives a straight line with slope $K_{SV}$ and y-intercept of 1.

Applications of this relationship include:

• Quenching efficiency: Using acrylamide to quench tryptophan residues in proteins tells you how exposed those residues are to solvent.
• Accessibility studies: Charged quenchers like iodide only reach surface-exposed fluorophores, so comparing $K_{SV}$ values for different quenchers reveals which fluorophores sit on the protein surface versus buried inside.
• Conformational changes: If a protein unfolds, previously buried tryptophans become exposed, and $K_{SV}$ increases. This makes Stern-Volmer analysis a useful probe of protein structure.
• Membrane permeability: Measuring how efficiently oxygen quenches a probe embedded in a lipid bilayer reports on how easily small molecules penetrate the membrane.

Stern-Volmer Analysis

Analysis of Stern-Volmer plots

The shape of a Stern-Volmer plot tells you what type of quenching is occurring:

1. Dynamic (collisional) quenching produces a linear plot. The quencher deactivates the excited state through diffusion-controlled encounters.
2. Static quenching arises when the quencher forms a non-fluorescent ground-state complex with the fluorophore. This also reduces intensity, but the plot curves upward at higher $[Q]$. When both dynamic and static quenching operate simultaneously, you also see upward curvature.

Two experimental tests distinguish dynamic from static quenching:

• Temperature dependence: For dynamic quenching, raising the temperature increases diffusion, so $K_{SV}$ goes up. For static quenching, heat destabilizes the ground-state complex, so $K_{SV}$ goes down.
• Lifetime measurements: This is the most definitive test. In dynamic quenching, the excited-state lifetime decreases with added quencher, so $\tau_0/\tau = F_0/F$. In static quenching, only complexed fluorophores are removed from the emitting population; the uncomplexed ones still have their normal lifetime, so $\tau_0/\tau = 1$ regardless of $[Q]$.

Applications of the Stern-Volmer equation

The Stern-Volmer constant connects directly to the bimolecular quenching rate constant $k_q$ through the unquenched lifetime $\tau_0$:

$K_{SV} = k_q \tau_0$

This is useful because $k_q$ is the more fundamental quantity. It tells you how fast quenching occurs per molar concentration of quencher, independent of the fluorophore's intrinsic lifetime. You can rearrange to find it:

$k_q = K_{SV} / \tau_0$

For diffusion-controlled quenching in water, $k_q$ is typically around $10^{10} \, M^{-1}s^{-1}$. Values significantly below this suggest steric shielding or limited accessibility.

You can also rearrange the basic equation to solve for unknown quencher concentration if $K_{SV}$ is known:

$[Q] = (F_0/F - 1) / K_{SV}$

For systems where only a fraction of fluorophores are accessible to the quencher (common in proteins with multiple tryptophans), the modified Stern-Volmer equation applies:

$F_0 / (F_0 - F) = 1/(f_a K_{SV}[Q]) + 1/f_a$

Here $f_a$ is the fraction of accessible fluorophores. Plotting $F_0/(F_0 - F)$ versus $1/[Q]$ gives a straight line with y-intercept $1/f_a$ and slope $1/(f_a K_{SV})$.

Finally, when quenching shows slight upward curvature that can't be fully explained by a static complex, a sphere-of-action model is sometimes used:

$F_0/F = (1 + K_{SV}[Q])\exp(V[Q])$

The term $V$ represents the volume around the fluorophore within which any quencher molecule present at the moment of excitation causes immediate quenching. This accounts for quencher molecules that happen to be adjacent to the fluorophore without forming a true ground-state complex.