Studies were found from a literature search of Web of Science and Google Scholar and had to meet the following criteria to merit inclusion: they had to be from 2005 onward to assure their methodology, and measurements were somewhat current with the standards in the field, they had to include data about the regional distribution of amyloid pathology from at least 5 different regions, and they had to be from mouse models using the APPswe mutation and had to assess endogenous pathology development, rather than pathology development induced from exogenous amyloidogenic seeds. We note that this criterion excludes some important studies, such as Ye et al. (24), but uses it nonetheless for consistency in our analyses. Amyloidopathy data here come from Harris et al. (25) (seven total regions and three timepoints), Bero et al. (26) (five total regions, one timepoint), and Lim et al. (29) (five total regions and one timepoint). Tau data cited for comparison purposes in Figure 2 came from Ahmed et al. (12) (5 total regions, 1 timepoint), Bolmont et al. (30) (5 total regions, 1 timepoint), and Clavaguera et al. (11) (11 total regions, 3 timepoints, only the final one used); please refer to the original citations for specific methodological questions about any of the above studies.

Connectivity and spatial distance data were taken from the supplementary dataset published along with the mesoscale mouse connectome from the ABI (31). Total projection volume between regions was generated by multiplying element-wise by the rows the connectivity matrix times the number of voxels in each seeding region. Regional distances used were the Cartesian distances between the centers of mass of any region pairs. For an anatomical illustration of the brain represented as a connectivity graph, see Figure 1A; directional connectivity from to and from the entorhinal cortex (EC), used as an example region, can be seen in Figure 1B. For an example of a spatial distance graph as a matrix, see Figure 1C.

For a given connectivity C or distance matrix S, we define a Normalized Laplacian Matrix, as in Raj et al. (2), L: L=I−Dr⋅C⋅Dc

where D_r and D_c are diagonal degree matrices of the sum totals of the rows and columns, respectively, and I signifies the identity matrix. In our notation for the connectivity matrices, C represents the retrograde transmission mode, and the corresponding anterograde mode is then simply given by C^T, and the bidirectional mode by (C + C^T)/2. The distance matrix was obtained from a separate dataset appended to Ref. (31) and is referred to in this manuscript using S. Normalized Laplacian matrices were generated for each mode with the above equation.

A previous graph theoretic model of pathology spread in AD throughout a brain network was shown to be predictive of future patterns of disease progression (2). The principle is to seed a graph node corresponding to a brain region with an arbitrary value and then model the diffusion of the disease factor throughout the network via the Network Diffusion equation: (1)X(t) = exp(−βLt)⋅X(0).

This models the long-range patterns of spread of the protein pathology at any time t as a product of the initial seeding pattern X(0), and the so-called diffusion kernel exp (−βtL), with diffusion constant, β (2).

The major differences with previous network diffusion model are twofold: (1) we are for the first time using this model with a directed brain network and (2) we are interested in total pathology accumulation over time, which we model as a summative process: (2)X(i)=exp(−βLΔt)⋅X(i−1)+X(i−1).

We use Eq. 2 to calculate, for any point in time, the deposition of tau, amyloid, and neuronal atrophy across the brain regions represented in the network. The Eq. 1 in the present study will be referred to as the standard undirected network diffusion model, or NT, while our modified directional version in Eq. 2 will be referred to as directed network transmission, or DNT. We discuss this equation modeling spatial pathology diffusion in the Section “Spatial Diffusion Modeling As an Alternative Model to Network Diffusion.”

We additionally created a spatial diffusion model as a comparison or alternative hypothesis to the network diffusion model. The spatial diffusion model was based on the same fundamental network diffusion Eq. 2 explicitly stated above. The difference between DNT (and NT) and spatial diffusion in the present study is that the network for spatial diffusion is a matrix where each entry in the matrix S_i,j is the reciprocal of the Cartesian distance between the center of mass of each GM region included in the Allen Institute’s mouse connectivity atlas. Using this distance matrix, S, rather than the connectivity matrix C, we ran the diffusion equation stated above in (2) to get a model approximating diffusion based on spatial proximity, which will be referred to as SPD.

We ran the network and spatial diffusion Eq. 2, through the number of iterations, in months, given in each study. If a study measured pathology at 6 months, we ran the model through 6 iterations, and if a study measured pathology at 9 months, we ran the model through 9 iterations. The implicit assumption here is that amyloidopathy spreads in all datasets at the same rate. While these datasets were obtained with different mouse models potentially exhibiting different amyloid strains, we do not have enough data to assess the kinetics or speed of amyloid pathology spread in individual cases. Hence, we decided to impose a minimal and general set of assumptions across the board. In these iterations, we used Δt = 1 month and modified β to achieve the optimal match with the data, as the empirical diffusion constant for various pathologies in AD is a priori unknown. Example, βt curves for a range of β values, where the model both shows behavior that is predictive of proteinopathy spread and non-predictive of proteinopathy spread can be seen in Figure 1C. We show anatomical examples of a graph that is the basis of NT/DNT in Figure 1A, and a model of the brain demonstrating the locations of regional centers of mass, which form the basis of the network used in SPD, in Figure 1B. To compare whether DNT/NT or SPD performed better at recapitulating amyloid-β pathology, we calculate Δr-squared values, which are the difference between the r-squared value between the amyloidopathic seed (no diffusion) and empirical amyloidopathy, and the same r-squared value calculated between the best fit value of the βt model constants of diffusion time and empirical amyloid-β pathology. An example of this calculation can be seen in Figure 1C. Given the relatively small sample size of regions quantified from Harris et al. (25), we performed an additional assessment for the significance of regressions that were significant at an alpha of p < 0.05: we randomized either the connectivity or interregional distance matrices from the ABA 1,000 times and ran our models to produce simulated data generated with randomized networks, generating a distribution r²-values to use as a comparison with r²-values from our models run using empirical networks or distances. An example of the results of this process can be found in Figure 1D.

Prior use of the brain connectome graph metrics and models (such as DNT and NT) have successfully, characterized the spatiotemporal development of regional volume loss (2) and metabolic deficits (3) in patients, and the spatiotemporal proliferation of tau pathology in mouse models (16). We use the first two eigenvectors of the mouse brain connectome to assess whether amyloid-β pathology can be recapitulated by the properties of mouse brain wiring in a way that resembles the accurate characterization of tau pathology. We find that, while, accordant with prior research (16) relative regional severities of tau pathology across all three studies highlighted here [Figures 2A–C,G,H; Table 1; (11, 12, 30)] are all strongly recapitulated by at least one the first two eigenvectors of all of the mouse connectomes used (anterograde, retrograde, and bidirectional), only one study regionally quantifying amyloid pathology produced any such significant results [Figures 2D,G,H; Table 1; (26)]. The results comparing the eigenvectors from our mouse connectomes with our other two amyloid datasets (25, 29) showed no significant match between where, based on transsynaptic spread, one would expect the most severe amyloid pathology and where the empirical dataset indicated the most severe pathology, across all mouse connectomes (Figures 2E–H; Table 1). The present results confirm our prior analyses that tau pathology patterns in mouse models can be well characterized using mouse connectomes but also reveal that no such strong relationship exists between amyloid-β pathology patterns in mouse models and the mouse connectomes.

We next assess how well our connectivity based DNT/NT model recapitulates the longitudinal spatiotemporal development of amyloid-β pathology in our one multi-timepoint mouse amyloid dataset from Harris et al. (25). We find that, at no measured timepoint either early or late, does anterograde or retrograde DNT or bidirectional NT successfully predict amyloid pathology patterns (Table 2). In fact, at all timepoints, including the final measured timepoint, DNT and NT fail to add any information beyond the EC seeding reported by Harris et al. (25) for predicting the development of amyloid-β pathology (Figure 3A). The regional slopes of pathology severity increase show an identical pattern of results (Figure 3B).

However, the amyloid-β pathology patterns at all timepoints, including the final measured timepoint, are significantly recreated using the SPD model of pathology spread, which is based on spatial proximity to the EC, where pathology initiated (Figures 3A,C; Table 2). Moreover, the regional slopes of amyloid-β pathology severity increase are also significantly predicted by SPD (Figures 3B,D; Table 2). Due to the relatively small sample size of mice and quantified regions from Harris et al. (25), we tested whether the results from the SPD model were due to chance by assessing whether significant results could be obtained using randomized distances between regions; we found that for the final measured timepoint of amyloid-β pathology, SPD using empirical distances between brain regions outperformed 91% of the 1,000 randomizations, and 93% of the randomization when predicting the regional severities of rate of amyloid-β pathology increase (Figures 3E,F).

The data from Harris et al. (25) also includes regional quantification of amyloid-β precursor protein (APP) levels using anti-hAPP antibody. While we find that amyloid-β pathology proliferation is not well explained by connectome-based spread models, but rather by spatial proximity-based models, we want to test whether regional levels of APP can be predicted using the connectome. However, our results again indicate that, while retrograde DNT does give a significant prediction of APP levels (Figures 4A,B), anterograde DNT and bidirectional NT do not, and SPD outperforms even retrograde DNT at recreating relative regional levels of APP (Figures 4A,C; Table 2). Furthermore, the significant match between the predictions of retrograde DNT and regional APP levels appears to be driven by a single outlier region (Figure 4B), calling the validity of these results into question. Akin to our results about the spatiotemporal development of amyloid-β pathology in the subsection above, we find that regional levels of APP are again best predicted by a model of diffusion based on spatial proximity with regions exhibiting high APP levels, more accordant with extracellular diffusion mechanisms than connectivity based or transsynaptic based proliferation. To emphasize the above results, we also include an anatomical illustration of the regional rates of suspected pathology increase, from the measurement of regional APP levels until the final quantification of amyloid-β pathology can be seen in Figure 4D; note that SPD is a better model for spatiotemporal amyloid-β pathology patterns than is DNT/NT.

The present analysis shows results suggestive of amyloid-β pathology spread being predominantly extracellular, rather than intracellular. Modeling assuming transsynaptic spread failed to significantly recapitulate empirical patterns of amyloid-β pathology (Figures 2–4; Tables 1 and 2), while modeling based on spatial proximity significantly recreated observed spatiotemporal amyloid-β pathology development patterns (Figures 3 and 4; Table 2). While prior studies implicate transsynaptic amyloid-β pathology transmission (25, 26), these findings are contradicted by other research demonstrating a lack of evidence for transsynaptic or even any form of intracellular transneuronal and transregional spread (24, 29). By contrast, studies of other pathological protein species’ mechanisms of spread, such as pathological tau, consistently implicate transsynaptic spread (11–16) with little evidence for other mechanisms.

Extracellular diffusion resulting in amyloid-β pathology transmission to the areas of the brain most spatially proximal to those already exhibiting amyloidopathy fits with the known characteristics of amyloid-β as a protein. First, APP, the precursor protein for amyloid-β, is a transmembrane protein with a large extracellular domain, and it is from this large extracellular domain that amyloid-β is formed as a cleavage product from APP (34). Post-cleavage, amyloid-β generally exists in the extracellular space, even as a healthy protein (35). Finally, amyloid-β in its pathological states also forms plaques almost exclusively extracellularly (36). None of this is to say that pathological amyloid-β might not gain capabilities of becoming internalized into neuron or spreading transneuronally or transsynaptically, as some authors have suggested (25). But given our meta-analytic results suggesting no mathematical basis for transsynaptic spread or any spread based on the brain’s connectivity network, and suggesting that pathology is more likely to spread into regions spatially close to rather than heavily interconnected with already affected areas, we posit that our present work, strongly implies some mechanism of pathology spread that is extracellular. We hope that our work serves as a starting point for more heavily quantitative investigations of amyloid-β pathology transmission with an aim toward clearing up the inconsistent results about how and where amyloid-β progresses around the brain.

Given that amyloid patterns are known to depend on exogenous seeding site (32, 33), a purely spatial mode of spread would suggest a radial distribution of pathology spread, which was not observed in our data. However, there is very little evidence that initial amyloid seeding is in fact focal; instead early amyloid pathology is found diffusely in the neocortex and then spreads to subcortical areas (8). Quite likely, amyloid pathology could be caused or initiated by metabolic deficits that target particular regions, leading to amyloid initiation in broad areas of the brain, for instance in the default mod network (9). Due to broad initiation, a radial spread from a focal source may not be manifested under spatial spread. Nonetheless, it is unlikely that spatial spread via extracellular spaces is the only process involved in amyloid pathology ramification. Several additional factors might play a role beyond pure spatial spread, and future research will be needed to identify and assess them.

Also of note is that our SPD model accurately recreated regional APP levels from Harris et al. (25). Given that APP is a transmembrane protein (34), spread based on spatial proximity, such as through the extracellular space, seems unlikely. First, it is possible that the anti-hAPP antibody used in the study (25) bound to a non-Aβ fragment of APP following cleavage, sAPPα, which akin to Aβ is also often released into the extracellular space (34) and could therefore plausibly spread into spatially proximal regions. Aβ also has known reactions with full-length transmembrane APP (34), and so spatially spreading pathological Aβ could influence regional APP levels by upregulating APP expression or by inducing the release of transmembrane APP into the extracellular space. These hypotheses for why a model of diffusion into spatially proximal regions accurately captured empirical APP levels, however, are conjecture at this point. Akin to the discussion of factors beyond spatial proximity contributing to the spatiotemporal development of Aβ pathology, above, elucidating why APP levels mirror Aβ pathology spread patterns in at least a pathological mouse model, will require careful future research.

Deficits in cellular function directly attributable to amyloid-β in mouse models are generally synaptic deficits (37, 38). Given the propensity for amyloid-β plaques to accrue at synapses (39), it is not surprising that such an accumulation of misfolded protein species would causes deficits in the ability to transmit and receive action potentials (37, 38). However, our findings implying extracellular spread based on spatial proximity to already affected regions, coupled with the above work demonstrating the propensity for amyloid-β pathology to cause synaptic and cell-signaling deficits raise an important question: why should misfolded amyloid-β, if it is spreading and circulating extracellularly, preferentially cause issues at synapses, rather than at other areas along the very large neuronal membranes?

Work whose data are used in the present analysis regarding spatiotemporal amyloid-β pathology development provides a possible explanation. Some recent studies demonstrate amyloid-β pathology appears more likely to accrue in more active regions (26) close to those already exhibiting pathology. Furthermore, this work suggests electrical signaling between neurons may act as an attractant for pathological amyloid-β (26), inducing more amyloid-β to accumulate and therefore form plaques at cellular locations where electrical current leakage is the greatest: at the synapse (39). If, as our results indicate, amyloid-β pathology follows a pattern of transiting to spatially proximal, rather than interconnected areas, likely via some form of extracellular diffusion, then electrical current leakage from the synapse could bias amyloid-β pathology spread toward those regions that are both spatially proximal and more likely to have high signaling (and therefore electrical) activity. This could further explain why, even though SPD consistently outperformed DNT/NT, it was still not as strong a model for predicting spatiotemporal amyloid-β pathology development as DNT/NT are for modeling tau pathology (16). Amyloid-β pathology spread patterns might be best explained by a model incorporating both spatial proximity with already affected regions and the average signaling activity of those spatially proximal regions; our research suggests this as a topic for further study in elucidating amyloid-β transmission.

While amyloid-β is mainly an extracellular protein, other protein pathologies known to be comorbid with amyloid-β pathology are caused by intracellular proteins tau and synuclein. A potential complication for the model of extracellular spread of amyloid-β pathology into the most spatially proximal regions is complicated by evidence demonstrating potential interactions between amyloid-β and tau (30, 40, 41) and known co-occurrence of misfolded amyloid-β plaques embedded within Lewy Bodies composed primarily of misfolded synuclein (42). Synuclein is almost exclusively present at synaptic terminals and tau is an almost exclusively axonal protein, so given the prior work cited above showcasing known amyloid-β propensity for accumulating around and causing issues at synapses (37–39), a predominantly extracellular mechanism of misfolded amyloid-β spread does not necessarily negate the possibility of the interaction of these proteins. However, our present work does not provide a satisfying explanation as to how pathological proteins that are on the one hand predominantly intracellular and on the other are the likely extracellular transiting amyloid-β are likely to interact. We nonetheless feel it is important to point out the limitation to our current work and to encourage future research to pursue this question.