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Biological and Environmental Phenomena at the Interface
Kinetics of Surface-Mediated Fibrillization of Amyloid-# (12-28) Peptides Yi-Chih Lin, Chen Li, and Zahra Fakhraai Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02744 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018
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Kinetics of Surface-Mediated Fibrillization of Amyloid-β β (12-28) Peptides Yi-Chih Lin, Chen Li, and Zahra Fakhraai* Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, Pennsylvania 19104-6323, United States *Corresponding Author: Zahra Fakhraai Email:
[email protected] Abstract Surfaces or interfaces have been considered as key factors in facilitating the formation of amyloid fibrils under physiological conditions. In this report, we study the kinetics of surfacemediated fibrillization (SMF) of amyloid-β fragment (Aβ12-28) on mica substrate. We employ a spin-coating based drying procedure to control the exposure time of the substrate to a lowconcentrated peptide solution, and then monitor the fibril growth as a function of time via atomic force microscopy (AFM). The evolution of surface-mediated fibril growth is quantitatively characterized in terms of the length histogram of imaged fibrils and their surface concentration. A two-dimensional (2D) kinetic model is proposed to numerically simulate the length evolution of surface-mediated fibrils by assuming a diffusion-limited aggregation (DLA) process along with size-dependent rate constants. We find that both monomer and fibril diffusions on the surface are required to obtain length histograms as a function of time that resemble those observed in experiments. The best-fit simulated data can accurately describe the key features of experimental length histograms, and suggests that the mobility of loosely-bound amyloid species is crucial in regulating the kinetics of SMF. We determine that the mobility exponent for the size-dependence on the DLA rate constants is α=0.55±0.5, which suggests that the diffusion of loosely-bound surface fibrils roughly depends on the inverse of the square-root of their size. ACS Paragon Plus Environment
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These studies elucidate the influence of deposition rate and surface diffusion on the formation of amyloid fibrils through SMF. The method used here can be broadly adopted to study diffusion and aggregation of peptides or proteins on various surfaces to investigate the role of chemical interactions in the two-dimensional fibril formation and diffusion.
Keywords: Surface-Mediated Fibrillization, Amyloid Fibrils, Atomic Force Microscopy, Amyloid Beta Peptide, Alzheimer’s Disease, Diffusion Limited Aggregation, Surface Diffusion, Surface Driven Self-Assembly
Introduction. Self-assembly of amyloid proteins has been widely associated with neurodegenerative diseases (e.g. Alzheimer's disease, Parkinson's disease, and Huntington's disease) and nonneuropathic localized diseases (e.g. Type II diabetes).1,2 In particular, amyloid-beta (Aβ) peptide and its relationship to the Alzheimer’s disease has been extensively studied for more than two decades.3–5 Recent studies suggest that fibrillization of Aβ peptides can accumulate insoluble fibrils in the extracellular space of various tissues to form the amyloid deposits in the brains of Alzheimer's patients.6–10 In 2013, Alzheimer's disease was reported as the sixth leading cause of death in the U.S. and an estimated 5.1 million Americans suffered from symptoms of cognitional disabilities.11,12 Therefore, it is crucial to understand the formation mechanisms of Aβ fibrils, which may help the development of pathogenesis investigations and therapeutic strategies for the Alzheimer’s disease.5,13,14 Several mechanisms have been proposed to explain the aggregation pathways from soluble proteins to insoluble amyloid fibrils.5,15–21 When the peptide concentration is high (> the critical concentration for Aβ aggregation22, e.g. 17.5 µM for Aβ40 peptide23), nucleation-limited
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polymerization governs the formation of amyloid fibrils in the solution phase.17,18,21 However, the concentration of Aβ peptide in physiological fluids is several orders of magnitude lower than this critical concentration.24 This disparity suggests that other mechanisms may control the formation of amyloid fibrils in vivo. In recent years, the effects of surfaces and interfaces on the growth of amyloid fibrils have been studied for their role in catalyzing fibrillization.25–35 For example, hydrophobic nanoparticles28 and the air-water interface31 have been shown to facilitate the formation of amyloid fibrils. A few studies focused on surface-mediated fibrillization (SMF) under low protein concentration conditions (below the critical concentration).36–40 These studies demonstrated that enhanced fibril formation and aggregation rates under low solution concentration require mobile surface precursors36, high surface concentration37, and a preferred orientation of the adsorbed proteins39. These features are similar to the membrane-assisted fibril formation which has been recognized as the potential mechanism in vivo.5,15,16,41 As such, it is worthwhile to further investigate the details of surface-mediated fibrilization mechanism. However, simultaneously tracking the formation of heterogeneous nano-structures is still a challenge for most of current imaging techniques with nanometer spatial resolution. There is a trade-off between temporal and spatial resolution due to instrumental or systematic limitations. Recently developed fast-scanning AFMs can be used to study dynamic processes in nanoscale42 in limited conditions where the fibrils themselves are immobile on the surface. Most other studies rely on images that reflect a steady-state growth or snapshots of a time-lapsed process. This approach allows for high-resolution imaging of small species such as oligomers, but the mobility of oligomers and fibrils on the surface during drying can cause potential artifacts.22 We have recently demonstrated that a slow-spinning drying procedure can be used to prevent artifact formation on the surface and allows us to capture accurate snapshots of the SMF process after drying the samples at different incubation periods.22,37 This approach is particularly beneficial for cases where the adsorbed fibrils and oligomers have high diffusivity on the surface. Using this ACS Paragon Plus Environment
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technique, we demonstrated that the fragment of amyloid beta peptide, Aβ12-28, can rapidly selfassemble into amyloid fibrils on a mica surface within 30 minutes, when the bulk concentration of the peptide is well below the critical concentration. In this report, we employ the same protocol to investigate the kinetics of SMF in more detail and elucidate the important role of mobile surface species in enhancing the SMF rate. Analysis of fibrillar structures observed in AFM images of Aβ12-28 on mica indicates that rapid fibrillization originates from peptide adsorption and subsequent surface-mediated aggregation. Therefore, we propose a 2D diffusion-limited aggregation (DLA) model that allows us to numerically model the evolution of the lengths of surface-mediated fibrils and their distribution during the SMF process. We demonstrate the accuracy of this model by predicting the outcome when varying bulk peptide concentration. The best-fit simulated results suggest that both surface concentration and surface mobility of amyloid species formed during SMF can modulate the kinetics of fibril formation. In the case of Aβ12-28 aggregation on mica, fibrils are mobile on the surface with a negative mobility exponent α=0.55 which significantly enhances the SMF process. This implies that the diffusion coefficient of SFM fibrils on mica surface roughly follows an inverse square root dependence on the fibril size.
Experimental Results Evolution of SMF fibrils Figure 1A shows representative AFM images of samples prepared by incubating a 10 µM Aβ12-28 peptide solution on mica substrate for various periods of time before drying by spincoating. At the low peptide concentration and short incubation times used in this study, there is no evidence of bulk fibril formation as demonstrated in our previous studies.22 As such, the imaged morphologies were produced by SMF.22,37 More AFM images of these samples are
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provided in Figures S1 and S2 of supporting information (SI). The AFM images taken after 5-10 minutes show that at early times the structures are predominantly small structures with maximum heights in the range of 0.3-0.5 nm. Using volume analysis, the small features displayed in the 5min AFM image of Figure 1A can be assigned as monomers, dimers, trimers, and other short oligomers, as indicated by the labeled numbers. Some short fibrillar structures with length < 200 nm are also found in both 5- and 10-min samples. When the incubation time is increased to above 20 mins, the small globular structures gradually disappear and fibrils became the predominant morphologies. These SMF fibrils are elongated with time, but their height does not change, and remains within 0.4-0.5 nm. This is a strong indication that the SFM process for the Aβ12-28 peptide on mica is strictly two-dimensional, as fibrils are only one monomer thick and never cross each other. To quantitatively describe the evolution of the SMF process, the size (length) of the surface species as well as their size distribution was analyzed using multiple AFM images at each incubation time. The normalized length histograms are plotted in Figure 1B. The length histograms further confirm that at the early time stage (5-10 min) small-sized monomers and oligomers are the most probable species, evolving into short fibrils (20-50 nm in length) after 20 minutes. The peak and the breadth of the length distribution rapidly increases with time, showing a shift of the most probable length from 22.5 nm to near 200 nm after only 30 minutes of incubation. AFM images, such as those shown in Figure 1A, can also provide the peptide quantity using the volumetric analysis described in our previous report.37 Since all fibrils are only one peptide thick, the volume of each fibril strand is proportional to its length. In Figure 2, the number density of Aβ12-28 peptides at each time point is plotted as a function of time. The number density reaches a plateau after 20 minutes of incubation time. This data suggests that the adsorption and desorption of Aβ12-28 peptides on mica substrate reaches equilibrium. Considering ACS Paragon Plus Environment
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a simple two-state system composed of Aβ12-28 peptides either remaining in the solution or bound to the surface, Equations 1 and 2 (derived from uni-molecular reactions) can be used to illustrate the evolution of Aβ12-28 peptide concentration on the surface. [] {1 − }
[] =
(1)
[] =
[ ]
(2)
Here and are the adsorption and desorption rates of peptides on the surface, respectively. ! = 0.67 Lm-2 (L is liter) is a volume to surface ratio between the solution volume used during incubation (1.5×10-4 L) and the mica surface area (2.25×10-4 m2). The red dashed line in Figure 2 is the best fit curve to Equation 1, which suggests the equilibrium surface concentration (number of peptides per unit area) is [] = 2.7 × 10( µm-2 (4.5 × 10+ mol/m2) and + = 3.0 × 10( s-1. Based on Equation 2, and are determined to be = 2.0 × 10. s-1 and = 3.0 × 10( s-1, respectively. For the ease of comparison between AFM data, we report surface concentration as the number of peptides per unit area as opposed to the molar concentration for the rest of this manuscript. We note that such AFM analysis does not include size information of the adsorbed species, thus, the derived adsorption and desorption rates ( and ) represent the accumulation of all possible aggregate species, e.g. monomers, dimers, trimers, or oligomers. Proposed Model for SMF Figure 3A displays the proposed model to describe the origins of rapid fibrillization during SMF. While it is possible for dimers and other species to adsorb on the surface, we make a simplification and assume that only monomers are adsorbed to the surface. This is in-line with previous studies5,15,16,41 where the mica substrate is considered as a template to accumulate peptides through monomer adsorption/desorption, after which the motion of the peptides are confined to the two-dimensional surface. This is strengthened by the fact that the fibrils are never ACS Paragon Plus Environment
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observed to be thicker than a single peptide (0.4-0.5 nm) and never cross one another. Based on this assumption, the aggregated status for adsorption/desorption mentioned in the previous section can be as assumed to be the number of monomers. This suggests that the surface concentration observed in Figure 2 represents the monomer adsorption/desorption behaviors. We also note that, in the proposed model, we do not expect peptide binding constant to be significantly affected by the aggregation, specially once dimer and trimers are formed. We provide more evidence for the validity of this assumption in the SI by considering models with dimer adsorption. The mobility of surface-species enables diffusion-limited aggregation (DLA) and regulates the rate of fibril formation and elongation. Since fibrils are formed by hydrogen bonding of Aβ peptides, we assume that the rate of fragmentation19 or shrinkage43 is much slower than the elongation rate and can be ignored in our analysis. Furthermore, we don’t observe any experimental evidence of such fragmentation or shrinkage occurring as the length distribution continuously and rapidly grows as seen in Figure 1B. Figure 3A schematically outlines the elementary growth steps needed for the size evolution of fibrils during DLA in our proposed model. The mass balance equation can be expressed as Equation 3: /0 ,2 /
= ! ∙ ∙ [ ] ∙ ∙ 52, +261, 7 − 18, 18, 7 − 1 − 261, 78, 18, 7 2
+ ∑; 6:, 7 − :8, :8, 7 − : − ∑< 67, 8, 78,
(3a) (3b) (3c)
Here, 8, 7 denotes the surface concentration of 7 -mers at time 8 . 6, is a kinetic rate constant for the DLA of two reactants with size and ( -mers and -mers). Under the assumption that only monomers adsorb/desorb on the surface, the first term (3a) is the first derivative of Equation 1, as previously determined by the fit to Figure 2. This term represents the change in the surface concentration of monomers and has no free fit parameters. The physical ACS Paragon Plus Environment
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meaning of and in Equation (3a) becomes the adsorption and desorption rates of monomers on the surface, respectively. The terms in (3b) illustrate the population gain and loss of the 7-mers due to the monomer addition (linear growth in length), where the factor of 2 indicates the two active ends for the fibril elongation. The final terms in (3c) describe the population changes of larger structures by nonlinear elongation due to the fusion of two oligomeric or fibrillar reactants with sizes larger than a monomer (7 ≥ 2). In this model, all oligomers and fibrils are assumed to be products of the DLA on the surface and only the monomer adsorption is assumed. This is an appropriate assumption given that the concentrations used in this study are below the critical concentration for aggregation in solution. The DLA rate constant, 6, , can be referred to as a generalized sum kernel and expressed as Equation 444,45: 6, = > ? + ? (4) Here > is a composite factor that is a monotonically increasing function of the monomer’s diffusion coefficient. The negative size exponent, @, can be considered as a mobility exponent corresponding to the inverse of fractal dimension (A0 ). This expression infers that a large reactant (oligomer or fibril) contributes to a smaller 6, due to slower surface diffusion. Therefore, the surface diffusion slows with the fibril or oligomer size (length) to the power of −@ . If two reactants are considerably different in size (e.g. monomers and 100-mers), the diffusion of the smaller reactant will govern the aggregation rate as it will be the faster moving species. While this simplified model does not explicitly include any details of fibril diffusion, as detailed below, we find that it adequately describes the aggregation properties of the system studied here. The generalized sum kernels simplify the mass balance equation (Equation 3), where only two free fitting parameters (@ and > ) remain unknown. It is important to note that Equations 3b, 3c and 4 assume that the fibrils themselves are mobile on the surface. As discussed later in this manuscript this assumption is an important factor in obtaining numerical functions ACS Paragon Plus Environment
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that properly predict the asymmetric shape of the length histograms shown in Figure 1, as well as the rapid rate of fibril formation. Numerical Simulation for the Evolution of SMF To estimate the kernels for SMF that predict the experimental observations, a leapfrog method was used to simulate the evolution of length histograms with time using various combinations of @ and > values based on Equation 3 and 4 (details are provided in SI). The simulated length distributions were then compared with the experimental histograms (Figure 1B) to determine the best-fit parameters. Figure 3B displays the contour map of the square error (∆ ) between experimental and simulated length histograms for samples prepared with the 10 µM solution as a function of @ and > . The black crosses in this map are the data with ∆ ≤ 2. The set of parameters for these local minima are summarized in Table S1. For the range of values of @ and > considered here, the two variables do not seem to be completely independent. A larger value of @ requires a larger value of > to reasonably resemble the experimental data. This is not very surprising as a large @ value means that the diffusion of fibrils is considerably slowed with their increasing size, requiring faster monomer diffusion to produce elongated fibrils. A simple example of the @ and > effects on the shape of predicted length distributions is demonstrated in the Figure S5 of SI. The best-fit simulated length distributions for the 10 µM sample are obtained at @ = 0.55, > = 7.5 × 10. µm2 /s, and a mean square error of ∆ = 1.33. The results of this fit are plotted along with the experimental data at all experimental time points in Figure 1B as black, dashed lines. It can be seen in this figure that this prediction describes the asymmetric shape of the experimental histograms and the kinetics of the length evolution at all time points remarkably well. The consistency between experimental and simulated histograms supports our assumptions for including DLAs and size-dependent kernels of 6, in the mass balance equation
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(Equation 3). It is important to note that if we did not consider the nonlinear elongation in the DLA process, by eliminating line (3c) from Equation 3, the numerical modeling would result in considerably different length histograms as shown in Figure S6. In particular, the asymmetry in the shape of the histogram is missing in the absence of the DLA term. This confirms our previous experimental evidence that the fibrils themselves are mobile on the mice surface. The rapid growth of fibrils observed after 20-min incubation is distinctly related to the fibril diffusion on the mica surface and the fibril size-dependence as determined by the exponent @. Effects of bulk concentration on the SMF To further examine the robustness of the best-fit parameters determined in the 10 µM samples, the effects of bulk concentration on the evolution of SMF was monitored using a 5 µM solution. Figure 4A displays a representative AFM snapshot of surface-mediated fibrils formed at 30 mins using 5 µM Aβ12-28 sample solution. Compared to the 10 µM samples, the 5 µM solution forms shorter fibrils for the same incubation time and exhibits a slower evolution in the length histogram (Figure 4B). In the numerical simulation, it suffices to only change the [ ] from 10 µM to 5 µM in Equation 3, and then simulate the length evolution using various sets of @ and > . Like the 10 µM samples, the comparison between simulated and experimental histogram provides the contour plots of the mean square error, ∆ (Figure S3), where the best fit data of each @ value has been plotted in Figure 4C. For the 5 µM sample, both @ = 0.55 and 0.60 can provide reasonable values of simulated length histogram with ∆ = 0.06. As shown in Figure 4C, the best-fit data between 10 µM (black points) and 5 µM sample (red points) has an intersection at @ = 0.55 ± 0.05 and > = 7.5 × 10. ( ± 0.8 × 10. , minimum value of step size in numerical simulation) µm2/s, which is the same set of values as predicted by the 10 µM measurements, and is also the same set of values that independently minimize ∆ for the 5 µM sample. This remarkable agreement between two independent
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measurements further confirms the reliability of the simple mass-balance equation chosen here. This control experiment determines the global @ and > for the DLA rate constants in SMF. Furthermore, it also highlights that the bulk concentration can regulate the surface concentration, and thus modulate the kinetics of fibril’s formation on the surface, increasing the SMF rate with increasing bulk concentration.
Discussions In our previous reports22,37, we have demonstrated that the used Aβ12-28 peptide solution will not form fibrils in solution via cryo-electron microscopy images, as well as several solution samples dried without incubation. Aβ12-28 fibrils formed through SMF mechanisms on mica surface are one-peptide thick (~0.5 nm), without crossover points, and lack complex geometry and morphological heterogeneity (polymorphism) observed in amyloid fibrils formed in solution. This is a strong indication that the process of SMF is a strictly two-dimensional. The evolution of surface concentration indicates that an equilibrium is reached for the peptide concentration between the solution and the surface, preventing a second layer of peptides from adhering to the surface and mainlining the strictly two-dimensional process. We hypothesize that this is due to changes in the effective surface energy as peptides are adsorbed on mica surface, which will be explored in our future publications. Surface fibrils grow rapidly within an hour, with no significant lag time for the nucleation step. As demonstrate in Figure 1, the asymmetric shape of the length histogram at intermediate and long times, along with the rapid growth of the most probable fibril length as a function of time suggests that SMF has a distinctly different mechanism compared to the fibril elongation in solution phase.43 Unlike solution phase growth, no critical nucleation or distinct nuclei size is
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observed during the SMF process. In contrast, the length distributions are the products of multiple kinetic processes, which can be used to explore the detailed mechanism of SMF. Based on experimental results, a model was developed based on diffusion limited aggregation (DLA) with a mass balance equation (Equation 3) to elucidate the mechanism of rapid fibrillization on the surface. In this model, two assumptions were made for (a) the equilibrium behavior of monomer’s adsorption/desorption on the surface and (b) size-dependent DLA rate constant, implying fibril mobility on the surface. A generalized sum kernel, 6, (Equation 4), was used to represent the DLA rate constant that involves the size-dependent diffusivity due to effective island diffusion.44 This is supported by the distinct shape of the length distribution when this term is added, as can be seen in comparison between data in Figure 1 and the simulated histograms shown in Figure S6. This conclusion is also consistent with our previous studies22,37, where we demonstrated that surface mediated fibrils are loosely bound to mica and could be easily removed from the substrate, orientated, or packed parallel to each other by the liquid stream or air flow,22 or due to drying of droplets37. Shen et al.36,40 also have shown that the existence of mobile precursors can determine the formation of surface-mediated fibrils. Using a leap-frog method to numerically simulate the length evolution, we predicted the two fitting parameters @ and > to be @ = 0.55 ± 0.05 and > = 7.5 × ±0.8 × 10. µm2/s, which fits the data at two solution concentrations of 5 µM (Figure 4B) and 10 µM samples (Figure 1B) equally well. This is important as it hints that the simple sum kernel used here is adequate in describing the experimental observations, even though it does not include the potential anisotropies in the diffusion coefficients along and normal to the fibril length nor does it include any specific diffusion model for the islands. More sophisticated kernels and diffusion models have been used in the past for the DLA processes as well as bulk aggregation of amyloid fibrils.19,21,46,47 However, since the current model works reasonably well, it is unlikely that we have the resolution in the experiments to justify the need to employ more specific models for the ACS Paragon Plus Environment
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specific system studied here. SMF processes on other surfaces or using other peptides may require improvements to this model. Another simplification assumed in this work is the choice not to include fibril shrinkage in the DLA model. We note that fragmentation has been used in other forms of kernels for studying protein aggregation in solution phase.44,45 However, there is no experimental evidence in our study for the fibril length shrinkage. We hypothesize that this is due to strong hydrogen bonding between peptides in the fibril strands, as well as the peptidesubstrate interactions, which generates high barrier to shrinkage. The best-fit simulated results can also reveal the detailed structural evolution during SMF that cannot be achieved in static AFM measurements. Figure 5 displays the evolution of the population of monomers (j=1), oligomers (j=2-50) and fibrils (j>50) as a function of time using the best-fit result of the simulations for the 10 µM sample. Unlike static AFM measurements, the numerical simulation provides detailed footprints on the structural evolution, in which two characteristic features can be recognized in SMF. First, the spatial confinement facilitates the rate of oligomerization. The surface oligomers rapidly form once monomers are deposited on the surface without significant lag time. Moreover, the fibril formation progresses as rapidly as the accumulation of the surface oligomers, as indicated by the blue arrows in Figure 5. Second, the decrease of bulk concentration slows down the formation of oligomers and fibrils. These results rule out the role of oligomerization as a rate determining step for surface mediated fibrilization. Instead, the surface concentration of oligomers plays an important role to regulate the formation of µm-long surface-mediated fibrils by participating in the fibril elongation through oligomer fusion. Such rapid fibrillization requires high surface peptide concentration and the mobility of surface species, which can facilitate the aggregation rate and quickly shift the population towards longer species. We note that the rapid DLAs can be attributed to the effects of 2D confinement on the adsorbed amyloid species, which includes the dimensional reduction in translational and rotational motions. In the extreme limit of high initial surface concentration, when either the bulk ACS Paragon Plus Environment
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concentration or adsorption rates are high, local rearrangement of peptides can suffice to form extended fibrils in a very short amount of time. Furthermore, the formation of hydrogen bonds along the backbone of amyloid peptides can also help lower the activation energy for aggregation. While the experiments and the model used here do not directly measure the diffusion coefficient of Aβ12-28 fibrils on mica, the exponent @ can elucidate the physical origins and the processes governing the size-dependence of their surface diffusivity. One approach is to consider @ as the inverse of the fractal dimension (A0 ) of the reactants. A0 is a measure of compactness of the fibrils. In a strictly 2D geometry, stiff, extended rods have a dimension of A0 = 1, while in compact discs A0 = 2. Based on the best-fit @ value, the effective A0 of the surface reactants is determined to be A0 = 1.8 ± 0.2, which is closer to a disc-shaped object, meaning that the diffusion is roughly two dimensional despite the long length of the fibrils. In contrast, direct evaluation of the fractal dimension of the fibrils using AFM image analysis of images shown in Figure 1A, as detailed in the Experimental Details and Data Analysis section, yields a fractal dimension of A0,FGH ~ 1.6 ±0.2, which is slightly smaller, but within the error of the value obtained from the fit to @ . Schreck et al.44 have previously demonstrated that A0 ~1.35 for amyloid fibrils formed in solution, which is closer to the expected dimensionality of long, but semi-flexible fibrils. To rationalize this data, it is important to note that the simplified form of 6, used this study is more sensitive to the properties of smaller reactants than the larger species. As the species become larger they diffuse more slowly and play a smaller role in the value of the generalized sum kernel, 6, . The A0 = 1.8 implies that small species rotate at time scales that are faster or comparable to their translational diffusion, and as such can attach to another larger island at almost all incoming orientations. Another possibility for the observed value of @ is the possibility of a hoping mechanism in the diffusion process. Schwartz et al.48,49 showed that the effective surface diffusion
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coefficient of polyethylene glycol (PEG) is proportional to the J K , where the J is the number of PEG monomers and L is the size-dependent exponent. Their single-molecule tracking experiments demonstrated L = −0.6 ± 0.2 and an intermittent-hopping mechanism of polymer surface diffusion. This can potentially explain the subtle balance between the molecule-substrate interactions and our best-fit @ value for the DLA rate constants. We note that this is unlikely given that based on our modeled results the probability of desorption, even for dimers is low (See discussions on dimer’s adsorption/desorption and size-dependent exponent @, and Figure S7-S8 in SI). Direct measurements of peptide diffusion are necessary to explore this possibility. However, such measurements would require fluorescence tagging of Aβ12-28 which can potentially change the subtle molecule-substrate interactions on the substrate and vary both > and @. We note that the method used in this paper is robust and does not require fluorescent tagging. As such, our AFM-based technique would be able to measure such variations directly, which as important strength of this label-free technique. In the best-fit DLA rate constant, the > value, 7.5 ± 0.8 × 10. µm2/s, is a composite factor related to the monomer’s diffusivity. The relation between diffusivities and reaction rate constants have been studied for the reactions M + M → M or M + O → MO.50–54 In 3D, continuum mechanics can provide a steady-state DLA rate constant corresponding to the diffusion coefficient of reactants. When the dimensionality falls into 2D, the kinetics become more complex due to the inflow and outflow of materials via adsorption and desorption. It is shown that a pure 2D model of surface reactions yields no steady state rate constant. After considering the influence of adsorption and desorption, Freeman et al.51 and Agmon54 have demonstrated the steady-state DLA rate constant for surface reaction under different scenarios. However, we are unable to use their results to determine the monomer’s diffusivity from > , by simply considering the case of the monomer’s DLA on the surface (which results in the formation of dimers). The major challenge here is that sequential reactions can occur rapidly and within a few ACS Paragon Plus Environment
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minutes, which disturbs the mean-field approximation. Therefore, the best-fit > derived in our simulated results may reflect a time-average DLA rate constant depending on the monomer’s diffusivity.
Conclusions In summary, we have monitored the formation of surface-mediated fibrils by controlling the peptide incubation time on the mica substrate using an artifact-free drying procedure. Through AFM image analysis, the AFM snapshots of surface-mediated fibrils were used to provide quantitative assessments of the evolution of peptide surface concentration and fibril length evolution. Using a simple proposed DLA model and numerical simulations, we demonstrated that the formation of surface-mediated fibrils on mica are controlled by two elementary processes, adsorption/desorption of monomers and two-dimensional diffusion-limited aggregation of monomers and fibrils. We demonstrated that the mobility of loosely-bound surface species can initiate the monomer addition, as well as the nonlinear elongation of fibrils. The latter helps significantly expedite the fibril growth. Besides surface mobility, the surface concentration of these mobile precursors is also a crucial factor in regulating the kinetics of SMF. From the best-fit simulated parameter, the critical exponent (@ = 0.55 ± 0.05) and the kinetic rate constant associated with monomer’s diffusivity ( > = 7.5 ± 0.8 × 10. µm2/s) were determined. While the system studied here represents a model system of Aβ12-28 diffusion on mica, this label-free method is robust and can be easily adopted to study peptide or biopolymer diffusion on various surfaces. The simple proposed kinetic model can be adopted to study the role of various parameters, such as surface diffusion, fibril-fibril fusion, and bulk concentration on the formation of amyloid fibrils at various interfaces. More complicated diffusion models can be employed if necessary.
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Experimental Details and Data Analysis. Sample Preparation. Sample solutions were prepared using the same procedures described in our previous publications and in SI.22,37 To monitor the SMF, 150 µL solution of Aβ12-28 peptide solution at different concentrations was placed on fresh-cleaved mica, and incubated for various periods of time (between 5 to 60 minutes) prior to the drying process. A spin coater (WS650 MZ-23, Laurell Technologies Corp.) was used to remove excess solution and dry the samples using 1000 RPM speed and an acceleration of 250 RPM/s without further water-raising process. This speed was previously determined to be below the rupture threshold of the droplet, allowing for stain-free, artifact-free drying of the surface as demonstrated in our previous work.22 Atomic Force Microscopy (AFM). Samples prepared at various drying times were imaged in tapping mode (93% of free amplitude) using AFM (Keysight Technologies, 5500 AFM) equipped with a XYZ closed-loop scanner (for most of samples) or a high-resolution scanner (for 5-min samples). Rotated silicon probes with aluminum reflex coating (Budget Sensors, Tap300G, resonance frequency ~300 kHz, tip radius
