Formation of amyloid loops in brain tissues is controlled by the flexibility of protofibril chains

Neurodegenerative diseases, such as Alzheimer’s Disease (AD), are associated with protein misfolding and aggregation into amyloid fibrils. Increasing evidence suggests that soluble, low molecular weight aggregates play a key role in disease-associated toxicity. Within these aggregates, protofibrillar loop-like structures have been observed for a variety of amyloid systems and their presence in brain tissues is associated with high levels of neuropathology. However, their mechanism of formation and relationship with mature fibrils has largely remained challenging to elucidate. Here, we use atomic force microscopy and statistical theory of biopolymers to characterise amyloid ring structures derived from the brains of AD patients. We analyse the bending fluctuations of protofibrils and show that the process of loop formation is governed by the mechanical properties of their chains. We conclude that ex vivo protofibril chains possess greater flexibility than that imparted by hydrogen-bonded networks characteristic of mature amyloid fibrils, such that they are able to form end-to-end connections. Furthermore, we show that these findings can be extended to several amyloid systems, giving a general framework relating the mechanical properties of assemblies and the conditions in which they can form loop structures. These results explain the diversity in the structures formed from protein aggregation and sheds light on the links between early forms of flexible ring-forming aggregates and their role in disease.

Introduction 1 by atomic force microscopy (AFM) and transmission electron microscopy (TEM). Then, additionally using amyloid assemblies 23 formed by bovine α-lactalbumin as a model system, we measure the arc-length distribution of filament and loop structures 24 and show that a theory of semi-flexible polymers quantitatively predicts the range over which the formation of closed rings is 25 expected to be favoured over open protofibril chains. Finally, we demonstrate that this type of model can be extended to other 26 systems and provides a general framework which links the mechanical properties with the morphology and toxicity of amyloid 27 structures.

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Characterisation of amyloid loops 30 We first induced the formation of amyloid protofibrils and rings from recombinant α-lactalbumin in vitro (Fig. 1 A) Conditions 31 were selected to destabilise the native state of the protein, namely low pH (2.0) and high temperature (50 • C). Initially non-32 fibrillar aggregates were observed, followed by the formation of chain-like aggregates after 2 h of incubation (Fig. S1 A). 33 Amyloid loops and open chain protofibrils were identified after incubation times ranging from 5 to 14 h (Fig. S1 B and C). After rings were observed after 1 day of incubation at 37 • C and after 1 month of incubation at -5 • C. This contains information on the 40 combined nucleation and growth rates, giving an order of magnitude estimate which is comparable to that measured for the 41 growth of insulin fibrils 14 . For the sake of simplicity, protofibrils formed from α-lactalbumin will henceforth be referred to as We then extracted and characterised soluble aggregates from the hippocampus of post-mortem Alzheimer's disease brains. 44 Briefly, brain homogenate was subjected to successive rounds of buffer soaking and centrifugation, then the soluble fraction was 45 retrieved and deposited on a mica surface and characterised using AFM 5, 15 . We observe heterogeneous structures, including  Having established the presence of ring-like structures for the in vitro and ex vivo samples, we sought to define their length 50 distribution. Over 1000 individual structures from over 200 AFM maps were individually traced (Fig. 2) using a semi-automatic 51 algorithm (Materials and methods), and the arc-lengths were measured from the digitized contours using fitted splines.

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Additionally, the height was measured for the same structures by considering the maximal height from the local average 53 background from sections perpendicular to the tangent of the spline following the contour of the filament (Fig. S2). These 54 measurements allow us to understand the mechanical properties of protofibrils, such as the persistence length l p which can be 55 calculated directly from AFM maps using the mean square end-to-end distance R as a function of contour length L (Fig. 2E): p is a surface parameter, which has a value of 2 for chains that have equilibrated on the 2D surface and 1.5 ± 0.5 for those

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The groups we selected are 0-3nm, 3-6nm, 6-9nm, and 9-12nm, which corresponds with the height of protofilament chains  k R→F ( j) are the first order rates for ring closure and opening. 79 We first consider the ring closure rate: k F→R ( j) = k 0 F→R g( j) whereby the j dependence is in the circularisation probability g( j), and the constant factor k 0 O→F ( j) contains information about the diffusion coefficient of the ends of the polymer as well as about the reaction cross-sections. The circularisation probability for semi-flexible chains has been explored theoretically by Stockmayer and Yamakawa 23 and more recently by Liverpool and Edwards 24 and is very generally given by the sum of the Boltzmann weights corresponding to different configurations of the bond vectors {⃗ u 1 . . .⃗ u j } which satisfy the loop closure condition ∑ n j=1 ⃗ u i = 0: with the semi-flexible Hamiltonian: We take here the result based on perturbation theory derived by 23 , which enables an approximate value of the circularisation probability to be derived for semi-flexible chains in the continuum limit; the result can be expressed as a simple function of a scaled dimensionless arc length, q = s 2βC B : where the approximate numeric values of the dimensionless constants are σ = 0.96, C 0 = 1.51 · 10 3 , C 1 = −0.81 and A = 7.026. 80 We furthermore include the possibility for the two ends of the chain to break apart again, and this process can be modelled

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The values of the bending rigidity reported here are also below that which is typically measured for elongated amyloid fibrils, 95 suggesting that the in vitro and ex vivo protofibrils have a lower level of structural organisation than that which is generally 96 found in amyloid fibrils.

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The present measurements also enable us to investigate the energetics of the ring closure. There is an enthalpic energy 98 cost of ∆H = 2C B π/d > 0 to bring the two ends of the chain together, and therefore the energy gain from the ligation of the 99 ends must exceed this value for this state to be significantly populated. We observe loops down to a diameter of approximately Where the ratio between persistence length and arc length is below one (indicated by black line), loop structures may form.
for a single toxic species in AD may be a fruitless one, and that rather a heterogeneous, dynamic population of low molecular 119 weight structures are involved in disease pathogenesis 6 .

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While we have not investigated the mechanism of action of soluble protofibrils, this has been investigated in previous work,