α-Synuclein-induced deformation of small unilamellar vesicles

α-Synuclein is a small neuronal protein that reversibly associates with lipid membranes. The membrane interactions are believed to be central to the healthy function of this protein involved in synaptic plasticity and neurotransmitter release. α-Synuclein has been speculated to induce vesicle fusion as well as fission, processes which are analogous to each other but proceed in different directions and involve different driving forces. In the current work, we analyse α-synuclein-induced small unilamellar vesicle deformation from a thermodynamics point of view. We show that the structures interpreted in the literature as fusion intermediates are in fact a stable deformed state and neither fusion nor vesicle clustering occurs. We speculate on the driving force for the observed deformation and put forward a hypothesis that α-synuclein self-assembly on the lipid membrane precedes and induces membrane remodelling.

The theory and fundamental principles of Inverse FCS (iFCS) and Inverse FCCS (iFCCS) have been described previously [1,2]. Since in iFCCS, a high fluorescence signal of several MHz is recorded from the fluorophores surrounding the particles of interest and cross-talk mainly occurs from the green to the red channel, it can be advantageous to use red dyes for the surrounding solution and green labeled particles of interest. Though this reduces the amount of cross-talk, it still exists and needs to be corrected for.
Below, the relationship between the particle volume and the amplitude of the iFCCS function is derived.
The amplitude of the cross-correlation function is given by:

S2
where I g and I r are the mean detected fluorescence intensities in the green and the red channels, and dI g and dI r are the deviations from those mean values. The detected fluorescence intensity in the red channel is given by: where I r,tot is the red fluorescence intensity when there are no particles in the detection volume, N p,r is the number of particles in the red detection volume, V p is the volume of a particle, V r is the red detection volume, V g is the green detection volume, q p,g is the brightness of the particles in the green channel, and CT (cross-talk) is the fraction of the total detected green signal that is detected in the red channel. Derivation with respect to N p,r gives: Since the fluctuations of the particle number is a Poissonian process it follows that ∆N p,r = (N p,r ) 1 2 and: The detected fluorescence intensity in the green channel, I g , is given by: where N p,g is the number of particles in the green detection volume, which equals N p,r V g /V r from scaling with the ratio of the two detection volumes. Derivation with respect to N p,r gives: S3 and with ∆N p,r = (N 1 2 p,r ) it follows that: Inserting equations (2), (4), (5), and (7) into equation (1) gives: which after after simplification becomes: Since 1-N p,r V q ≈ 1 and I r,tot >> N p,r Vg Vr q p,g CT , equation (9) can be approximated by: In our measurements, Vg Vr = 0.6, q p,g =50 kHz, CT =0.01, and I r,tot ≈ 3000 kHz. Thus: Vr q p,g CT I r,tot − (G cc (0)) − 1) = 0.6 · 50 · 0.01 3000 − (G cc (0) − 1) = 10 −4 − (G cc (0) − 1) As an example, the amplitude of the curve in figure 4B is -0.0017 (0.9983-1) and -0.00221 after correction for detector dead time (see section below). Together with V r =0.3 · 10 −15 L, this gives that V p =7.0 · 10 −19 L. For spherical particles this corresponds to a mean radius of 55 nm.

S4
iFCS dead time correction As has been described previously [3], the fact that the photon detectors are not linear at count rates of several MHz affects the amplitude of the auto-and cross-correlation curves, and thereby the estimated particle volumes. This is because the signal when there are no particles in the focus is higher, and therefore the detector is more saturated, compared to when a particle is in the focus, and this affects the observed depth of the negative intensity spikes. The GaAsP detectors used in the Zeiss 780 and 980 LSMs have a dead time of 66 ns, and the corrected count rate is described by: where CR 0 is the corrected count rate, CR is the measured count rate, and t d is the detector dead time. In our measurements we kept the total count rate in the red channel as close to 3 MHz as possible. At this count rate the corrected amplitude of the cross-correlation curve in iFCCS (and thereby the particle volume) is 30 % larger than that observed.