Single-molecule FRET and molecular diffusion analysis characterize stable oligomers of amyloid-β 42 of extremely low population

Abstract

Soluble oligomers produced during protein aggregation have been thought to be toxic species causing various diseases. Characterization of these oligomers is difficult because oligomers are a heterogeneous mixture, which is not readily separable, and may appear transiently during aggregation. Single-molecule spectroscopy can provide valuable information by detecting individual oligomers, but there have been various problems in determining the size and concentration of oligomers. In this work, we use a newly-developed method to analyze single-molecule fluorescence burst data of freely diffusing molecules in solution based on molecular diffusion theory and maximum likelihood method. We demonstrate that the photon count rate, diffusion time, population, and FRET efficiency can be accurately determined from simulated data and the experimental data of a known oligomerization system, the tetramerization domain of p53. We used this method to characterize the oligomers of the 42-residue amyloid β peptide (Aβ42). Combining peptide incubation in a plate reader and single-molecule free diffusion experiments allows for the detection of stable oligomers appearing at various stages of aggregation. We find that the average size of these oligomers is 70-mer and their overall population is very low, less than 1 nM, in the early and middle stages of aggregation of 1 μM Aβ42 peptide. Based on their average size and long diffusion time, we predict the oligomers have a highly elongated rod-like shape.

Unraveling Burst Selection Bias in Single-Molecule FRET of Species with Unequal Brightness and Diffusivity

“…The normalization factor Z in eq is obtained by integrating eq with respect to all possible interphoton times τ i and summing over colors c i = D, A and the total numbers of photons N : , Z = p f T M N th − 1 false( bold-italicI − bold-scriptM ) − 1 bold-scriptN p in where I is the identity matrix. The time integral matrix bold-scriptM is bold-scriptM = ∫ 0 τ th normald τ bold-scriptN e false( bold-scriptL − bold-scriptN false) τ The normalization factor Z and the initial, p in , and final, p f , vectors take burst selection into account and involve the threshold number of photons, N th , and the threshold time, τ th .…”

“…Now, let us consider a burst of photons that can be emitted by a molecule of species 1 (with population p 1 ) or 2 (with population p 2 = 1 – p 1 ). The corresponding likelihood function for a mixture of two species can be presented as the weighted sum of the likelihoods of individual species: L = p 1 b L 1 + p 2 b L 2 Here, L 1 is the likelihood functions in eq for species 1 (with parameters n 01 , D 1 , and E 1 ), and L 2 is for species 2 (with n 02 , D 2 , and E 2 ), p 1 b and p 2 b are the probabilities to have a burst of photons emitted by species 1 and 2 (also referred to as burst fractions): p 1 b = p 1 Z 1 p 1 Z 1 + p 2 Z 2 = 1 − p 2 b where Z 1 and Z 2 are the normalization factors for species 1 and 2 in eq . These factors depend on the species count rates and diffusion coefficients, but they are independent of the FRET efficiencies.…”

“…The boundary of the discreatized coordinate q max = r max / a should be positioned far enough so that the molecule does not reach the boundary during interphoton times, r max 2 > D τ th , which corresponds to q max 2 > D τ th / a 2 . In our calculations involving the effective isotropic laser spot approximation, we used q max = 4 and J = 50 and J = 100 for the analysis of the simulated and experimental data, respectively. For the Gaussian laser spot in eq , the elements of the diagonal matrices of the acceptor ( N A ), donor ( N D ), and total false( bold-scriptN false) count rates are .25ex2ex false[ N A ] j j = n 0 E e − 2 q j 2 + b A false[ N D ] j j = n 0 false( 1 − E false) e − 2 q j 2 + b D false[ bold-scriptN ] j j = n 0 e − 2 q j 2 + b A + b D where b A and b D are the background count rates. The vector p 0 in eq has elements 4π q j 2 and appears due to the entropic factor in the spherically symmetric problem, 4π r 2 .…”

“…For the Gaussian laser spot in eq , the elements of the diagonal matrices of the acceptor ( N A ), donor ( N D ), and total false( bold-scriptN false) count rates are .25ex2ex false[ N A ] j j = n 0 E e − 2 q j 2 + b A false[ N D ] j j = n 0 false( 1 − E false) e − 2 q j 2 + b D false[ bold-scriptN ] j j = n 0 e − 2 q j 2 + b A + b D where b A and b D are the background count rates. The vector p 0 in eq has elements 4π q j 2 and appears due to the entropic factor in the spherically symmetric problem, 4π r 2 .…”

Carlos Gutiérrez-Merino: Synergy of Theory and Experimentation in Biological Membrane Research

“…Additionally, a new dimension of FRET has been opened with hybrid/integrative modeling, where bio-macromolecular systems are studied simultaneously through a combination of experimental techniques (such as small-angle neutron and small-angle X-ray scatterings, along with NMR, EPR, and FRET spectroscopies), as reviewed in [ 115 ]. Single-molecule fluorescence spectroscopy is an emerging field in which FRET is a necessary partner, as demonstrated in a recent study characterizing the coexistence of stable oligomers of amyloid-β 42 within a heterogeneous and dynamic sample [ 116 ].…”