Introduction

Sodium-protein interactions yield a sodium triple-quantum (TQ) signal, a potential biomarker for cell viability. In general, sodium ions only bind weakly to other molecules. Hence, the correlation time $$$\tau_c$$$ is the result of the combined effect of environmental rotational diffusion and the diffusion of the sodium ion itself. Larger proteins tend to rotate slower and therefore the motional regime of sodium ions shifts to the slow motion regime ($$$\omega_0\tau_c\gtrsim1$$$). This results in bi-exponential relaxation and the creation of TQ coherences¹. For spherical, globular proteins, the rotational correlation time scales with the molecular weight^2,3. A longer correlation time increases the TQ signal and therefore, we propose a TQ signal dependence on the protein size.

This study investigated a correlation of sodium TQ signal with protein size using various globular proteins. Most of the used globular proteins either have been shown to be a suitable model protein for TQ signal⁴ or are well-characterized proteins with knowledge about ion binding sites and affinity for sodium ions^5-7.

Materials and Methods

Measurement data was acquired at a 9.4T preclinical MRI (Bruker Biospec 94/20) equipped with either a linear Bruker ¹H/²³Na volume coil or a quadrature Rapid ¹H/²³Na volume coil combined with a Rapid ²³Na surface coil. Tab.1 lists all used globular proteins. Each samples consisted of 2% w/v protein with 154mM NaCl at pH=7.

A TQ time proportional phase incrementation (TQTPPI) pulse sequence⁸ was used to simultaneously quantify the single-quantum (SQ) and TQ signals (Fig.1a). Simultaneous RF pulse phase and evolution time incrementation enabled a separation and quantification of SQ and TQ signals at distinct frequencies as well as the biexponential $$$T_2$$$ relaxation times. The TQTPPI FID (Fig.1b) was non-linearly fitted using the signal equation⁸:
$$Y(t)=\sin(\omega t+\phi_1)\cdot\left(A_{SQ,1}e^{-t/T_{2f}}+A_{SQ,2}e^{-t/T_{2s}}\right)+A_{TQ}\sin(3\omega t+\phi_2)\left(e^{-t/T_{2f}}-e^{-t/T_{2s}}\right)+DC $$
where $$$Y(t)$$$ is the TQTPPI FID amplitude, $$$A_{SQ,i}$$$ and $$$A_{TQ}$$$ are the SQ and TQ amplitudes, respectively. $$$T_{2s}$$$ and $$$T_{2f}$$$ are the respective slow and fast transverse relaxation time. TQTPPI sequence parameters were: $$$T_R=5\cdot T_1$$$, 20-60 averages, $$$\Delta\tau_{evo} =100-200\mu s$$$, 600-640 phase steps. Monoexponential $$$T_1$$$ relaxation time was determined by a fit, using an inversion recovery pulse sequence.

Results/Discussion

Fig.2 shows the TQ signal for different protein sizes using globular proteins. With the exception of the proteins, Ca depleted α-Lactalbumin (αLA) (14.2kDa), β-lactoglobulin (18kDa), BSA (66.5kDa) and all hemoglobin forms (64.5kDa), the TQ signal increased with protein size. The increased TQ signal indicated a longer correlation time correlating with an increased rotational correlation time of larger proteins. Further increases in protein size result in a rotational correlation time of the protein, which exceeds the diffusional motion of sodium ions. Hence, $$$\tau_c$$$ is now dominated by the diffusional motion and thus, further increases in protein size should have a smaller effect on the TQ signal. This can explain the decreased TQ signal increase for large protein sizes, like thyroglobulin (305kDa) (Fig.2).

At small protein sizes, Ca saturated αLA (14.2kDa) and Myoglobin (17kDa) did not yield a TQ signal. This indicated that sodium ions are in the extreme narrowing regime ($$$\omega_0\tau_c\ll 1$$$). Previous studies observed a similar effect in solutions of Ca saturated αLA, amino acids or small molecules such as glycerol and urea despite the use of high concentrations. In contrast, the small proteins beta-Lactoglobulin (18kDa) and Ca depleted αLA (14.2kDa) yielded one of the largest TQ signals. These two proteins are known for their strong sodium binding^5-7, which resulted in a slow motional regime for sodium ions due to the dominating slow rotational motion of the protein. In the case of αLA, sodium ions bind to the calcium binding site in the absence of calcium ions. Consequently, the strength of sodium binding has a substantial impact on the TQ signal (Fig.3).

BSA (66.5kDa) and ferrous hemoglobin (64.5kDa) both yielded a weaker TQ signal than the slightly smaller protein Ovalbumin (42kDa) and the slightly larger protein Lactoferrin (87kDa). Carr et al.⁶ showed that sodium ions do not bind to both proteins at all. However, there is no evidence that binding to both proteins is substantially weaker than to Ovalbumin and Lactoferrin. In contrast, a paramagnetic form of hemoglobin, methemoglobin, yielded an eight times higher TQ signal and, thus, a large TQ signal for this protein size. The large TQ signal in the presence of a paramagnetism, which usually substantially reduces the TQ signal, may indicate an unknown positive effect on the TQ signal.

Excluding the proteins Ca depleted αLA, β-Lactoglobulin, BSA and hemoglobin, due to the aforementioned effects, the measurements indicate that the TQ signal increases with the size of the protein. This can indicate that the in vivo TQ signal originates mainly from larger proteins, which are generally less frequent in the cell⁹, and sodium binding proteins and. However, further investigations of intracellular proteins and cell lysates are necessary to confirm these results.

Conclusion

The TQ signal of various globular proteins revealed a correlation of TQ signal with protein size and the importance of a strong sodium binding. These results enhance our understanding of the cellular origin of the TQ signal.

Acknowledgements

No acknowledgement found.