Effect of micro-viscosity on the rotational diffusion: pulsed laser-based time-resolved single-molecule study

Even single-molecule spectroscopy emerged in the 1970s by Magde and Elson (Douglas 1972, 1974; Elson 1974), but the last two decades witnessed much more effective yields of single-molecule, time-resolved, and super-resolution laser spectroscopy, especially in life science research (Rosenkranz 2009; Fitter 2011; Forkey 2003; Möckl 2014; Atta 2016). The novelty of this emerging laser spectroscopy technique is the ability to follow the observations in real-time of biochemical reactions (Atta et al. 2015; Atta and Okasha 2015; Katranidis 2009).

Since its discovery in the 1950s of the last century, lasers have succeeded in enhancing spectroscopic analysis in many aspects, like Raman microscopy and photoluminescence spectroscopy (Atta 2022a, 2022b; El Hameed 2022; Elbanna 2022; Refaat 2019). The advances in semi-conductors (Degheidy and Elkenany 2012, 2015; Ghoniem 2023) encouraged the researchers to developed new category of lasers that could be considered as a corner stone in the laser spectroscopy science, moreover the vast research in nano-science (Elashmawi 2013; Abdelghany and ElBatal 2013; El-kader 2019; Abdelghany et al. 2024) increases the sensitivity of the detectors. The confocal microscope (CM), particularly the time-resolved transition contribution mapping (TCM) kind, is a powerful instrument in laser spectroscopy. Single-molecule investigations based on such CM depend on ultra-small focused laser beams forming the so-called confocal volume. Those methods and techniques of measurement depend on diffusing molecules such as FCS, Forester resonance energy transfer (FRET), and time decay fluorescence anisotropy. The only counted photons are those that come from the diffused fluorophores through the confocal volume. Hence, the observation time depends on the time at which the molecules remain in the confocal volume, or, in other words, the diffusion time (τ_D) (Atta 2023; Das 2021).

Once the diffusion time is very effective on the measurements, the parameters affecting the molecular diffusion speed, like the local viscosity and temperature, become controlling parameters for the diffusion process. The time decay anisotropy measurements are the proper tool to study several life sciences aspects, such as hydrodynamic properties as well as the structural dynamics of proteins and enzymes. Because viscosity influences molecular diffusion through the confocal volume, it is critical to investigate the effect of buffer concentration on the value of time decay anisotropy, which is strong evidence about molecule diffusion freedom and rotational diffusion of the protein under investigation.

For single-molecule studies, it is required to link such fluorescent molecules through a linker that could be attached to one of the side chain groups of the protein polypeptide chain. As the tertiary and quaternary structure of every protein is a fingerprint, the accessibility of the targeted amino acid should be calculated to confirm the probability of staining reaction success (Atta 2019).

This work aims to clarify the effect of changing the buffer concentration on the anisotropy decay on a single molecule level. In this regime, PGK labeled with Atto-647 has been utilized as an example of such two-domain proteins.

Each of the substances was obtained from Sigma Aldrich, while the Atto-647-NHS was obtained from ATTO-TEC GmbH, Siegen, Germany.

UV–Vis spectrophotometry has been carried out using a spectrophotometer from Jasco-Japan, model V730. The FCS and lifetime measurements have been carried out using a time-resolved confocal microscope equipped with a 650 nm picosecond pulsed laser from ISS-USA. The time decay anisotropy has been measured by using a time-resolved spectrofluorometer model FS5 from Edinburgh, UK, equipped with a TCSPC module, a Glan–Thompson polarizer, and a picosecond pulsed laser with a wavelength of 640 nm.

Single-molecule analysis depends mainly on fluorescence techniques. While only fluorescence is what we measure, the tested molecules must be linked either to a single dye molecule or not. Single-labeling could be done by two methods: one by staining only a single specific amino acid in the protein sequence (Atta and Okasha 2015; Elbanna 2022), which costs much time and money. The other method is to have the majority of the labeled molecules stained with a single dye. If the location of the dye molecule on the protein chain does not matter, the second method could be a better choice.

Performing the second method could be done by following such a statistical method. One could use Poisson statistics (Elson 1974; Atta et al. 2015, 2023).where μ is the average number of dyes per protein, and P (N, µ) is the probability of finding a protein with N dyes if the average number of dyes per protein is µ.

It is found in much literature that the best value for single labeling occurs if P (N, µ) = 0.6. In this regime, the labeling ratio should be around 0.6 dyes per protein molecule.

Hence, the labeling conditions have been optimised to achieve this labeling ratio, which has been found to be a threefold dye excess with an incubation time of 1 h and a 7.4 PH value.

As it is clear in Fig. 1b, the autocorrelation curve interception with the Y-axis (G (0)) could be used to calculate the average number of stained protein molecules that have been diffused through the confocal volume of the confocal microscope according to the following relation:

So, as it is clear in the figure, avoiding the fast events (events faster than 10–5 ms), which could be fluorescence blinking or fluorophores in triplet state, the value of G (0) is approximately 1.1.

The average number of freely diffused labeled proteins travelling through the confocal volume will then be:this value assures that for every laser pulse, either we have single-molecule or no molecules have been diffused through the confocal volume during the pulse period. This confirms that the prepared samples are running through the analysis as single-molecules.

Additional information could be extracted from the FCS curve about the translational diffusion time, which is in the middle of the exponential decay part. In this case, the diffusion time (t) is around 0.065 ms, or 65 µs.

While the relationship between lateral diffusion (D) and diffusion time (τ) could be provided by:where ω_o is the semi minor axis of the confocal volume of the microscope, which in our case equals 0.15 microns (the confocal volume is a constant geometrical parameter related to the optical setup itself, the used fluorophore, and the puffer). By applying Eq. 3, the diffusion coefficient has been found to be 86.53 µm²/s.

From the average number of diffused molecules and the geometrical parameters of the laser focus (lateral and transversal radii), one could easily calculate the average concentration of the sample in molar terms according to the following relation:where V is the confocal volume and N_A is the Avogadro’s number.

Applying Eq. 3, It has been determined that the typical concentration is 8.2 nM.

Hence, it is clear that the viscosity altered the single-molecule dynamics by affecting the translational diffusion of the single-molecule, but what about the rotational diffusion and the freedom of the enzyme?

If molecular dynamics is the issue under investigation, it is better to start with measuring the lifetime of the used fluorophore. In this regime, the confocal microscope has been utilized to measure the time decay of the stained protein. Figure 2 shows the time decay of the stained protein and the tail fitting, which has been found to be 2.7 ns, this is somewhat greater than the dye catalogue's declared value of 2.4 ns; this change could be attributed to a slight change in the PH value of the used buffer.

The angle between the incident wave's plane of polarization and the system's total dipole moment determines to what extent that level system could be excited. In this regime, the degree of freedom of the rotational diffusion acts an important role in the photoluminescence of the diffused molecule.

While changing the number of the soluble salt molecules in the buffer solvent affects the viscosity of the buffer, that viscosity affects the degree of freedom of the rotational diffusion, which affects the dye emission, which alters the dynamics measurements like FRET and photo-induced electron transfer (PET).

Time decay anisotropy measurements (time decay polarization) could answer the question of the degree of freedom, especially if the excitation wave was a highly pure Gaussian laser beam.

For this purpose, different concentrations of Na₂CO₃ (transferring buffer) have been prepared. To do this, a time-resolved spectrofluorometer has been utilized after installing the polarizer-analyzer pair and a 635 nm pico second laser in both polarization directions (horizontal and vertical).

Analyzing the original data that were presented in Fig. 3, requires applying some fitting models to extract useful information. The best fitting model for the enzyme in its native form is the wobbling in-a-cone model (Douglas 1974; Rosenkranz 2009), which is connected to the initial anisotropy (r_o), limiting anisotropy (r_∞), and rotational correlation diffusion time across the laser beam (τ_c) as follows:

According to the mentioned information before one could describe the dynamics of the tested enzyme as follows: even the increase in buffer concentration alters the rotational diffusion time, but even the slower one could make complete rotations during every single photon emission from the dye. The Atto-647 lifetime is in the order of 2.7 ns, i.e., the lifetime of the used dye is approximately 4 times the complete rotation of the enzyme.

This means that if the conformation of the enzyme were the point of investigation, the effect of the micro-viscosity around the diffused molecules should be taken into consideration; for example, during any FRET or PET measurement, additional wave front splitting should be done according to the plane of polarization simultaneously with the splitting according to the wavelength, to have evidence about the angle between the total dipole moment and the laser plane of polarization, and correlating the donor–acceptor emission intensity with the degree of freedom to be able to calibrate for the micro-viscosity effect.

In single-molecule studies of the different proteins affected by the buffer concentrations, increasing the amount of solutes in the buffer solvent should consequently increase the buffer viscosity. It is well known that in any bulky solution, any changes in the viscosity affect the diffusion directly, but what about single-molecule diffusion? Through this work, PGK labeled with Atto-647 has been investigated on the single-molecule level while it diffuses in Na₂CO₃ buffer at concentrations that vary between 10 mg/l up to 50 mg/l. While time-resolved measurements are the target, the lifetime of the dye molecule will be a crucial value, so the life time of PGK_Atto-647 in the highest buffer concentration has been measured, and it was found to be 2.7 ns, which is the same as the recorded one for the Atto-647 free dye. This means that the changes in the buffer concentration did not affect the time decay of the dye. The FCS of the diffused protein has also been measured for the highest concentration of the puffer, and it confirms that the used samples are at the single-molecule level. To study the effect of buffer concentration on the molecular dynamics at the single-molecule level, time decay fluorescence anisotropy was done, and the results confirmed that there is a clear effect on the molecular translational and rotational diffusion even with slight changes in the buffer concentration. It is concluded from the current study that the local viscosity should be taken into consideration and all single-molecule time-resolved measurements should be calibrated for the difference in the buffer concentration or even the protein concentration to achieve more accurate results about the protein dynamics, such as the conformational changes or folding unfolding reactions of any enzyme. It is strongly recommended to spend more efforts on the affecting parameters of the single-molecule and the calibration, not only for the viscosity, which should be done. The confocal volume, which is theoretically an ellipsoid, suffers from deformation according to many optical parameters and the sample itself (Rüttinger 2008). Also, looking for the best buffer for every protein could be done using molecular modeling (Osman 2015). The distribution of the electromagnetic potential could have an effect on the diffusion and the molecular reactions, and some corrections may be needed to overcome the artifacts on the diffusion values (Farrage 2019a, 2019b).