4.4. Determination of Membrane Fluidity Parameters

To study the membrane fluidity, both fluorescence decays and anisotropy decays were measured. In this section, we describe how parameters characterizing the membrane fluidity was determined from the raw measured data.

Fluorescence decay curves were measured through the whole emission range of LAURDAN (400–540 nm, 14 decays, Δλ = 10 nm). In a deconvolution procedure, they were fitted by the 4-exponential function; this gave a satisfying fit at all wavelengths. It was necessary because—over the intrinsic non-exponential decay nature of LAURDAN—there was a strong spectral shift of emission in time, which appeared as complexity of decay. The lifetime components were only proper fitting parameters describing precisely enough this complex decay shape; they were not attributed to any separate emission species. The non-exponential fluorescence decay of LAURDAN at several wavelengths can be described very well using the calculated fitting parameters. With these determined decay parameters, the original fluorescence decay curves of LAURDAN can be reproduced within 0.03%.

From the series of decay curves, Time-Emission Matrices (TEM) were constructed. In the vertical direction of TEM (Time) there are decay curves. In the horizontal direction of TEM (Emission wavelength) there are time-resolved emission spectra that could be constructed from the intensity data of the consecutive decay curves at the same time point.

The speed of solvent relaxation can be described by the time evolution of the Center-of-Gravity [CoG(t)] function of the time-resolved emission spectra [44]. CoG(t) can be calculated with the following equation (Equation (1)):

It is important to mention that the fluorescence decays were collected in wavelength scale; thus the following transformation (Equation (2)) is needed for the precise calculation:

In our calculations, data from all of the measured decays were used (14 decays, 410–540 nm).

A higher value of CoG(t) means faster conformational change of LAURDAN followed by solvent relaxation of neighboring water molecules. This is a consequence of higher membrane stiffness.

Time-resolved spectra show the spectral shapes of the emission of LAURDAN at different time points. The temporal evolution of the shape and spectral position of these spectra reflects the temporal change of energetic distance of the excited and ground states involved in the emission. Time-Resolved Area-Normalized Spectra (TRANES) are special versions of time-resolved spectra and could be used well in spectral analysis [I_AN(λ,t)] [44]. TRANES were constructed from the time-resolved spectra of TEM as their area under the spectra were normalized to the same value. Equation (3) gives the mathematical formula for producing TRANES:

where

If the spectra cross each other at the same point, we have a so-called isoemissive point, which is clear evidence of a two-state reversible process within the excited states of the molecule studied. The lack of the isoemissive point indicates a continuous shift in the excited state rather than a two-state reaction.

To quantify the spectral changes, Generalized Polarization function (GP) is widely used [23,24,33], too. From emission data, we calculated the emission GP function with Equation (5):

where I₄₃₀ and I₅₀₀ stand for the intensities in fluorescence emission spectrum at 430 nm and 500 nm, respectively. These steady-state intensity data were calculated as integrals of fluorescence decays of LAURDAN with Equation (6):

The samples were handled for roughly 3 h as fresh; thus, there was not enough time to measure both time-resolved and steady-state data one after another from the same sample. That is why steady-state intensity data were calculated rather than measured.

The higher value of GP reflects a blue-shifted spectrum, which is an indication of a more restricted motion of LAURDAN in the membrane. The lower value of GP reflects a red-shifted spectrum, and it is an indication of less restricted motion of LAURDAN in the membrane.

Please note that the name “Generalized Polarization” has no connection to any optical polarization. This quantity is widely used in articles and describes spectral changes. Its name just remembers that its definition is analogous to the definition of physical quantity “polarization”; there is just a mathematical similarity of definitions.

Anisotropy decay r(t) was calculated as follows:

where G = I_HV/I_HH is a correction factor [41]. I_VV(t) and I_VH(t) are the emission decays measured in the presence of horizontal and vertical polarizers on excitation and emission sides.

τ_rot was determined from the time-resolved anisotropy decay measurements made at the spectral maximum of the emission (450 nm). It provides information on the mobility of LAURDAN molecules in the phospholipid bilayer, i.e., their confinement in the membrane [35,36].

In the time-resolved anisotropy measurements τ_rot was determined using the following formula (Equation (8)):

where r(t) is the calculated anisotropy decay. This expression can even be applied at hindered rotors when the anisotropy does not decay to zero.

A higher value of τ_rot means slower rotation of LAURDAN, which is clear evidence for increased microviscosity around it within the membrane.

Samples studied were used in fluorescence measurements for not more than three hours after preparation because of the degradation of cells. Under this time window, both treated and control samples had to be measured. It means that there was time only for time-resolved measurements but not for steady-state measurements. That is why steady-state spectra (Figure 6) have been calculated from lifetime and pre-exponential decay parameters as time integral of the decay at a certain wavelength:

where a_n and τ_n are the pre-exponential and the lifetime for the n-th decay component.

Calculated steady-state spectra of LAURDAN. λ_ex = 369 nm.