Characterization of Frex as an NADH sensor for in vivo applications in the presence of NAD⁺ and at various pH values

Abstract

The fluorescent biosensor Frex, recently introduced as a sensitive tool to quantify the NADH concentration in living cells, was characterized by time-integrated and time-resolved fluorescence spectroscopy regarding its applicability for in vivo measurements. Based on the purified sensor protein, it is shown that the NADH dependence of Frex fluorescence can be described by a Hill function with a concentration of half-maximal sensor response of K _D  ≈ 4 µM and a Hill coefficient of n ≈ 2. Increasing concentrations of NADH have moderate effects on the fluorescence lifetime of Frex, which changes by a factor of two from about 500 ps in the absence of NADH to 1 ns under fluorescence-saturating NADH concentrations. Therefore, the observed sevenfold rise of the fluorescence intensity is primarily ascribed to amplitude changes. Notably, the dynamic range of Frex sensitivity towards NADH highly depends on the NAD⁺ concentration, while the apparent K _D for NADH is only slightly affected. We found that NAD⁺ has a strong inhibitory effect on the fluorescence response of Frex during NADH sensing, with an apparent NAD⁺ dissociation constant of K _I  ≈ 400 µM. This finding was supported by fluorescence lifetime measurements, which showed that the addition of NAD⁺ hardly affects the fluorescence lifetime, but rather reduces the number of Frex molecules that are able to bind NADH. Furthermore, the fluorescence responses of Frex to NADH and NAD⁺ depend critically on pH and temperature. Thus, for in vivo applications of Frex, temperature and pH need to be strictly controlled or considered during data acquisition and analysis. If all these constraints are properly met, Frex fluorescence intensity measurements can be employed to estimate the minimum NADH concentration present within the cell at sufficiently low NAD⁺ concentrations below 100 µM.

Appendix

Model for NADH binding and the derivation of K _d

The binding of two NADH molecules to Frex can be described as

$$\text{Frex}+\text{2NADH}\overset{{{K}_{D,1}}}{\longleftrightarrow}\text{FrexN}+\text{NADH}\overset{{{K}_{D,2}}}{\longleftrightarrow}~\text{Frex}{{\text{N}}_{\text{2}}}~$$

For this process, the macroscopic dissociation constant is a product of two microscopic constants, and we shortly denote this product as K _d  = K _D,1 × K _D,2. In the Hill fit, we determine the averaged single-step dissociation constant K _D (in the absence of NAD⁺), and the highly cooperative character of NADH binding leads to the valid approximation ${{K}_{d}}\,\approx\,K_{D}^{2}$. FrexN and FrexN₂ refer to Frex with one and two bound NADH molecules, respectively.

Derivation of an equation for inhibition

A model for the inhibition of Frex by NAD⁺ is presented in Fig. 6. If we assume that the fluorescence (F) is only emitted by the species FrexN₂, i.e. Frex bound to two NADH molecules, F relates to the fraction of FrexN₂ by

$$F\sim\frac{\left[ \text{Frex}{{\text{N}}_{2}} \right]}{\left[ \text{Frex} \right]+\left[ \text{Frex}{{\text{N}}_{2}} \right]+\left[ \text{Frex}{{\text{N}}^{+}} \right]}.$$

(9)

Expanding by 1/[Frex] leads to

$$F\sim\frac{\frac{\left[ \text{Frex}{{\text{N}}_{2}} \right]}{\left[ \text{Frex} \right]}}{1+\frac{\left[ \text{Frex}{{\text{N}}_{2}} \right]}{\left[ \text{Frex} \right]}+\frac{\left[ \text{Frex}{{\text{N}}^{+}} \right]}{\left[ \text{Frex} \right]}}.$$

(10)

For the two different reactions, the law of mass action yields

$${{K}_{d}}=\frac{\left[ \text{Frex} \right]{{\left[ \text{N} \right]}^{2}}}{\left[ \text{Frex}{{\text{N}}_{2}} \right]}$$

(11)

and

$${{K}_{I}}=\frac{\left[ \text{Frex} \right]\left[ {{\text{N}}^{+}} \right]}{\left[ \text{Frex}{{\text{N}}^{+}} \right]}.$$

(12)

If we substitute the quotients in Eq. 10 by these expressions, we obtain

$$F\sim\frac{\frac{{{\left[ \text{N} \right]}^{2}}}{{{K}_{d}}}}{1+\frac{{{\left[ \text{N} \right]}^{2}}}{{{K}_{d}}}+\frac{\left[ {{\text{N}}^{+}} \right]}{{{K}_{I}}}}.$$

(13)

Expansion with K _d yields

$$F\sim\frac{{{\left[ \text{N} \right]}^{2}}}{{{K}_{d}}+{{\left[ \text{N} \right]}^{2}}+\frac{\left[ {{\text{N}}^{+}} \right]{{K}_{d}}}{{{K}_{I}}}}$$

(14)

and inclusion of a constant to normalize for the maximum fluorescence (F _max) results in Eq. 15, which equals Eq. 5 that was used to fit the fluorescence data shown in Fig. 7 by its linearized variant F _max/F:

$$F=\frac{{{F}_{\max }}{{\left[ \text{N} \right]}^{2}}}{{{K}_{d}}+{{\left[ \text{N} \right]}^{2}}+\frac{\left[ {{\text{N}}^{+}} \right]{{K}_{d}}}{{{K}_{I}}}}.$$

(15)