In vivo imaging reveals sigmoidal growth kinetic of β-amyloid plaques

Abstract

A major neuropathological hallmark of Alzheimer's disease is the deposition of amyloid plaques in the brains of affected individuals. Amyloid plaques mainly consist of fibrillar β-amyloid, which is a cleavage product of the amyloid precursor protein. The amyloid-cascade-hypothesis postulates Aβ accumulation as the central event in initiating a toxic cascade leading to Alzheimer's disease pathology and, ultimately, loss of cognitive function. We studied the kinetics of β-amyloid deposition in Tg2576 mice, which overexpress human amyloid precursor protein with the Swedish mutation. Utilizing long-term two-photon imaging we were able to observe the entire kinetics of plaque growth in vivo. Essentially, we observed that plaque growth follows a sigmoid-shaped curve comprising a cubic growth phase, followed by saturation. In contrast, plaque density kinetics exhibited an asymptotic progression. Taking into account the fact that a critical concentration of Aβ is required to seed new plaques, we can propose the following kinetic model of β-amyloid deposition in vivo. In the early cubic phase, plaque growth is not limited by Aβ concentration and plaque density increases very fast. During the transition phase, plaque density stabilizes whereas plaque volume increases strongly reflecting a robust growth of the plaques. In the late asymptotic phase, Aβ peptide production becomes rate-limiting for plaque growth. In conclusion, the present study offers a direct link between in vitro and in vivo studies facilitating the translation of Aβ-lowering strategies from laboratory models to patients.

Figure 1

Long-term in vivo imaging of amyloid plaque growth kinetics in Tg2576 mouse model of AD. (a) A young and an old cohort were investigated from 12 to 14 and 18 to 20 months of age, respectively, at a weekly imaging intervals. (b) Time series of 3D volume-rendered images acquired with two-photon fluorescence microscopy showing amyloid plaques and cerebral amyloid angiopathy (CAA). The length of one side of the squares equals 100 μm. (c) Mean volumes of all plaques over time (open circles). The black line indicates a fitted sigmoid function (R² 0.983). Error bars show the 95% confidence intervals (CI). (d) Integrated volume of all plaques over time (open circles). The black line indicates a fitted sigmoid function (R² 0.988). In addition, the temporal development of the plaque density is depicted (gray line) which can be fitted to an exponential function of one phase association (R² 0.975). (e) Integrated volume of the cerebral amyloid angiopathy (open circles) with the corresponding fit of a sigmoid function (R² 0.952).

Figure 2

Illustration of a single plaque over the whole imaging period of 15.5 months. (a) Time series of a single plaque as a surface-rendered object as derived from 3D image analysis. Scale bar represents 100 μm. (b) Volume from the plaque shown in (a) over time (open circles) with the corresponding fit of a sigmoid function (black line). (c) Sigmoid fits of plaque volumes of all imaged plaques in one mouse. Note the considerable variance in plaque volumes.

Figure 3

Summary of plaque densities, radii and growth rates from all imaging cohorts. (a) Representative examples of imaged volumes from the young and old cohort displayed as 3D volume-rendered images. The length of one side of the squares represents 50 μm. (b) Mean plaque densities from the young (12 and 14 months) and old cohorts (18 months). (c) The kinetic of plaque density from long-term imaging (mean from 2 positions) is shown as black line. In addition, plaque densities for each imaged position with their respective means from different cohorts are displayed at the corresponding age. (d) The mean plaque radius and their corresponding cumulative frequency distributions (e) are depicted for each imaging cohort including newly formed plaques from young cohort (two month imaging). For the long-term imaging cohort plaque sizes at 27 months are shown. (f) Box plot for linear plaque growth rates and (g) their corresponding cumulative frequency distributions. Plaque growth from 18 to 20 months of age was significant different from zero (P < 0.0001). Error bars show 95% CI (b-d), Whiskers represent 10th and 90th percentile and outliers are not shown (f). Plaque densities and radii were logarithmized before analysis (b-e). Statistical tests: one-way ANOVA with Tukey-Kramer Post-hoc test (b, d), Kruskal-Wallis test with Dunn’s Post-hoc test (f), Wilcoxon signed-rank test (f, 18 to 20 months), paired t-test (b, 12 vs 14 months). *** P < 0.001, **** P < 0.0001

Figure 4

Bifid analysis of the plaque growth data of long-term imaging. (a) Mean volume over time (error bars, 95% CI). A sigmoid function was fitted to the mean volume (black line). The dotted line indicates the inflection point of the fitted curve dividing the cubic and asymptotic parts of the function. (b) Kinetics of plaque radii. According to the cubic and asymptotic phase of volume growth two linear regressions (black lines) were fit from 12 to 23.3 and 23.5 to 27.5 months of age. This analysis was done for each single plaque. (c) Comparison of the plaque growth rates resulting from the bifid analysis with the values gained from the young and old imaging cohort. Black lines with error bars show medians with interquartile range. Multiple comparisons were performed by Kruskal-Wallis test with Dunn’s Post-hoc test. ***P < 0.001

Figure 5

Correlations between quantitative parameters of plaque growth dynamics. (a) Plaque formation rate as a function of plaque density. Black line, linear regression (slope is significantly different from zero, p = 0.016). Each circle represents one imaged position. (b) Plaque growth rate as a function of plaque density. Error bars show the 95% CI. Black line shows a linear regression of the data. The slope is statistically significant different from zero (p < 0.001). (c) Radius of newly formed plaques at the end of long-term imaging over 15.5 months as a function of the age of the mouse at plaque formation (N = 81 newly formed plaques from 2 positions). (d) Plaque radius at the end of long-term imaging over 15.5 months as a function of plaque growth rate (N = 90 newly formed and preexisting plaques). Black line shows a linear regression of the data. The slope is statistically significant different from zero. Statistical tests: F-test (a, b, d), Spearman correlation (c).

Figure 6

Spatial relationship between growth rates of neighboring plaques. (a) Amyloid plaques are displayed as 3D volume-rendered images. Plaque growth rates are color-coded according to a classification into 5 bins. One square represents 100 μm. (b) Shortest distance to the closest neighboring plaque (90 plaques), calculated from the long-term imaging over 15.5 months. The shortest distances are displayed in the graph with the mean and 95% CI (65.8 μm, 55.3-78.4 μm CI). (c) For each pair of nearest neighbor plaques the difference between their linear plaque growth rates and their shortest distance were calculated (open circles). No relationship between both parameters could be measured by linear regression. The slope was not statistically significant different from zero. Statistical test: F-test (c).

Figure 7

Model for the relationship between plaque density kinetics and amyloid plaque growth in vivo. The term c_critical refers to the minimum critical concentration of Aβ that is necessary to form plaque seeds (a prerequisite discovered by in vitro studies). This initial step of plaque formation was observed by recording the plaque density kinetics in vivo. According to the plaque density kinetics and applying the aforementioned requirement different relations of the Aβ concentrations comparative to the critical minimum concentration can be assigned to the different growth phases.