Imaging β-amyloid fibrils in Alzheimer's disease: a critical analysis through simulation of amyloid fibril polymerization
Introduction
Alzheimer's disease (AD) is defined histologically by the presence of intraneuronal neurofibrillary tangles (NFTs) and extracellular β-amyloid (Aβ) plaques in cerebral cortex [1]. Neurofibrillary tangles are highly insoluble neurofibrils formed by hyperphosphorylation of the cytoskeletal protein tau [2]. Intraneuronal neurofibrillary tangles build-up renders cells ineffective resulting in complete degeneration of affected neurons and appearance of “tombstone” NFTs in the extracellular space [3]. On the other hand, Aβ plaques, are extracellular aggregates of polymeric fibrils which are in turn composed of Aβ peptide monomers. We and others have introduced molecular imaging probes (MIPs) in an effort to quantify Aβ burden in the living brains of individuals afflicted with AD [4], [5], [6], [7], [8], [9], [10], [11]. In this endeavor, it is assumed that the quantitation of Aβ load would parallel the quantitation of neuronal receptor density. In this work, we offer insights on the intricacies of imaging Aβ polymeric aggregates in vivo. We will start with a brief cell biology of Aβ processing as well as theories of Aβ polymerization, which will serve as a basis for the formulation of a mathematical model for the polymerization of Aβ. We use the model to generate tissue time activity curves (TACs) for hypothetical MIPs and draw insights from these simulations to address the efficacy of a particular probe in imaging the pathological progression and therapeutic interventions in AD. We note that the concepts presented in this work may be applicable to the prospect of imaging other polymeric aggregates such as NFTs and prions [12], [13].
One of the characteristics of brains afflicted with AD is the presence of extracellular structural elements referred to as amyloid plaques. Plaques are, in part, composed of masses of filaments which are in turn composed of the insoluble form of the Aβ peptide. The Aβ peptide is formed as a cleavage byproduct of a larger amyloid precursor protein (APP) (Fig. 1) [14], [15]. Amyloid precursor protein is a ubiquitous membrane glycoprotein encoded by a single gene on chromosome 21 [16], [17]. It is cleaved either via the α-secretase or the β-secretase pathway, often referred to as the amyloidogenic pathway (Fig. 1). When APP is cleaved by α-secretase, it produces a large amino-terminal fragment APPα destined for secretion and a smaller carboxyl-terminal fragment. Further processing of the carboxyl-terminal fragment by γ-secretase produces a 22- to 24-residue fragment termed P3, which may or may not be amyloidogenic. Alternatively, when APP is cleaved by β-secretase it produces a soluble amino-terminal fragment, APPβ, and a carboxyl-terminal fragment containing the Aβ peptide. Cleavage of the carboxyl-terminal fragment by γ-secretase results in the formation of multiple Aβ variants of 40–43 amino acids, which are prone to aggregate. Aggregation in the extracellular environment contributes to Aβ fibril (fAβ) assembly through a nuclear-dependent polymerization (NDP) reaction [18] or variations thereof [19], [20], [21]. The plaques seen in the brains of AD patients are structural assemblies made up of fAβ and other extracellular material such as astrocytes and microglial cell residues (see Refs. [22], [23], [24]).
Nuclear-dependent polymerization is characterized by a slow, rate-limiting, nucleation step (Fig. 2A). The formation of a nucleus requires a series of monomeric Aβ (mAβ) association steps, which are thermodynamically unfavorable. Once the nucleus is formed, it extends to form larger polymers. The addition of mAβs at this stage is thermodynamically more favorable. The extension of amyloid fibrils (fAβ) is characterized by a steady-state phase in which the polymeric aggregates (fAβ) and monomeric Aβs (mAβs) are in dynamic equilibrium [18], [25], [26]. The steady-state concentration of mAβ is defined as the critical concentration (XC) for polymer extension, and hence for fAβ formation. Below the critical concentration, there is a lag phase during which mAβ aggregate into β-sheet tapes [27]. With increased concentration of mAβ, the concentration of tapes reaches a level at which the tapes stack — forming ribbons — and extend by the deposition of mAβ [27]. At this stage, the Aβ structures are referred to as protofibrils (or protofilaments, Fig. 2B) [19], [28]. Above the critical concentration XC, protofibrils interweave to form fibrils (Fig. 2C) which further polymerize by the addition of mAβ [29], [30].
Section snippets
Imaging statement
An ideal MIP should be sensitive to changes in the underlying biological processes in the progression of the disease. In imaging neuronal death, for example, an MIP should be sensitive to changes in the concentration, or density, of neuronal receptor binding sites as a function of disease pathology. In contrast to neuronal receptors, however, Aβ formations undergo higher-order growth patterns — one in concentration and another in dimension (maturity) — due to the polymerization and deposition
A mathematical model for Aβ polymerization
In the spirit of previous models of particle polymerization [31], [32], and specifically of Aβ polymerization [33], [34], [35], let X denote the concentration Aβ particles, let N denote the concentration of nucleus particles with n Aβ monomers, and let Fi denote the concentration of fibrils with i monomers (i=n+1, n+2, …) (Fig. 2). The rate of change of X is dictated by the production, consumption and degradation of peptide monomers. Monomers are produced by the net influx of particles at a
Methods
In imaging AD, one would be interested in imaging the total Aβ load, or burden. We define amyloid load as the concentration of mAβ in fibrillary form in order to accommodate various interactions of probes with Aβ structures. By one account the concentration of mAβ in late AD patients can reach as high as 3000 nM (Table 1). The ability of a particular probe to measure the total Aβ burden is a function of the probe's resolution. A probe that binds to every fibrillary mAβ is defined to have a
Results
We will start with some insights drawn from the mathematical model for polymer growth which may parallel events in AD progression. Intuitively, it is expected that the deposition of Aβ peptides would contribute to an overall increase in Aβ burden or load. The question that we seek to address in the simulation of polymer growth is how the dynamics of deposition would influence the probe's binding site concentration as a function of total Aβ load or burden. In Fig. 5A, we depict the concentration
Amyloid load, resolution and the imaging unit
The term amyloid load or amyloid burden is often used to quantify Aβ density (diffuse, senile, hardcore plaques, etc.). At this juncture, quantitation of amyloid load becomes a philosophical matter for it depends on the imaging unit. In imaging neuronal receptor density, the imaging unit is the receptor and probes that target a given receptor share a similar target receptor Bmax. The structural complexity of fAβ, however, changes from immature fibrils to mature fibrils prevalent in dense core
Concluding remarks
The challenge in imaging AD is rooted in characterizing amyloid load in the living patient. Currently, an atomic resolution crystal structure of amyloid fibrils is not available; its availability would allow targeting of periodic fibrillary motifs, which in turn would standardize quantitation of amyloid load as a measure for the pathological progression of AD. In this work, we hypothesized four probes that exemplify possible interactions with fAβs. Interestingly, for a given amyloid pathology,
Uncited reference
[89].
Acknowledgments
This work was supported in part by DOE grant DE-FC0302ER63420. KSJ is a recipient of the UCLA Dissertation Fellowship Award.
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