The supersaturation perspective on the amyloid hypothesis

Development of therapeutic interventions for Alzheimer's over the past three decades has been guided by the amyloid hypothesis, which puts Aβ deposition as the initiating event of a pathogenic cascade leading to dementia. In the current form, the amyloid hypothesis lacks a comprehensive framework that considers the complex nature of Aβ aggregation. The explanation of how Aβ deposition leads to downstream pathology, and how reducing Aβ plaque load via anti-amyloid therapy can lead to improvement in cognition remains insufficient. In this perspective we integrate the concept of Aβ supersaturation into the amyloid hypothesis, laying out a framework for the mechanistic understanding and therapeutic intervention of Alzheimer's disease. We discuss the important distinction between in vitro and in vivo patterns of Aβ aggregation, the impact of different aggregation stages on therapeutic strategies, and how future investigations could integrate this concept in order to produce a more thorough understanding and better treatment for Alzheimer's and other amyloid-related disorders.

some common properties such as binding to thioavin T 4,5 or cross-b structures. 6,7Recent breakthroughs in cryo-EM have led to the elucidation of the structures of many amyloid proteins, showing a diverse structural landscape. 7,80][11][12] Ab protein is produced from the sequential cleavage of amyloid precursor protein by band g-secretases. 13The g-secretase cleavage generates two main types of Ab proteins: the 40-residue Ab40 and the 42-residue Ab42, with Ab42 having two extra amino acids at the C-terminus.Although the overall concentration of Ab40 is several fold more than that of Ab42, 14,15 the main component of the senile plaques is Ab42. 16,17n 1992, Hardy and Higgins 18 presented the amyloid hypothesis, which states that Ab, "the main component of the plaques, is the causative agent of Alzheimer's pathology, and that the neurobrillary tangles, cell loss, vascular damage, and dementia follow as a direct result of this deposition."Over the years, the amyloid hypothesis has been constantly re-evaluated in light of new experimental discoveries, [19][20][21] and has remained as the prevailing theory guiding therapeutic development for Alzheimer's disease. 22,23One notable development is the inclusion of Ab oligomers in the amyloid hypothesis. 24Mechanistic understanding of Ab aggregation in terms of primary and secondary nucleation suggests that amyloid brils catalyze the formation of oligomers, 25 linking oligomers to the overall process of Ab aggregation.
While earlier failures of anti-Ab clinical trials have led to criticism of the amyloid hypothesis, the full FDA approval of anti-Ab antibody lecanemab (marketed as Leqembi) in July 2023 was a turning point in Alzheimer's research. 26Unlike the controversial aducanumab (Aduhelm), 27,28 the ndings of lecanemab are straightforward and robust.In the phase 3 trial, lecanemab slowed cognitive decline by 27% on the primary endpoint and also met all key secondary endpoints. 29The data from the lecanemab trial are widely considered as a validation of targeting Ab aggregates as a disease-modifying therapy. 30,31he phase 3 trial data of donanemab, an antibody targeting pyroglutamated Ab, show that donanemab treatment slowed clinical decline by 35% and met all secondary endpoints, further demonstrating the clinical benets of anti-amyloid therapy. 32

Basic concepts of supersaturation in the context of Ab aggregation
Supersaturation is a well-known concept in the eld of protein crystallization, which, like protein aggregation, 33 is a nucleation-dependent polymerization process. 34,35Supersaturation is a non-equilibrium state in which protein concentration exceeds the solubility limit.Equilibrium is restored when aggregates or crystals are formed and the protein concentration reaches the solubility limit.Through a series of elegantly designed experiments, Goto and colleagues have demonstrated that protein aggregation is driven by the same principle of supersaturation. 36,37Vendruscolo and colleagues 38,39 examined cellular protein concentrations relative to their solubility limit and found that neurodegeneration-related pathways are enriched in proteins at supersaturated concentrations.
Fig. 1 depicts an Ab phase diagram in the context of aggregation.The Ab solubility curve divides the phase diagram into two regions: undersaturation and supersaturation.The supersaturation region is further divided into two zones: metastable zone and nucleation zone.The boundary between the nucleation and metastable zones corresponds to the "critical concentration" for Ab aggregation. 40,41Below we describe seven key points of Ab aggregation in the framework of supersaturation.
(i) Ab aggregation requires a supersaturated solution.Protein aggregation involves two distinct steps: bril nucleation and growth.Fibril nucleation requires overcoming of a kinetic or energy barrier to form structurally ordered bril nuclei and is thus the rate-limiting step.Fibril growth is an energetically favorable reaction.Both bril nucleation and growth require supersaturation.Changes in solution pH and addition of salts, ions, or polymers are oen used to alter the properties of proteins, the chemical potential of the solution, or interactions between proteins to achieve supersaturation.In a typical in vitro aggregation experiment, Ab stock solutions in denaturing buffers such as urea or organic solvents such as dimethyl sulfoxide are mixed with a native buffer to immediately create a supersaturated solution.Depending on the concentration, Ab would aggregate immediately or aer a lag time. 33ii) To spontaneously aggregate, Ab concentration needs to be in the nucleation zone of supersaturation.When Ab concentration exceeds the solubility limit, it does not immediately form the stable bril nucleus.The energy barrier for nucleation allows Ab concentrations to increase further from the solubility limit and into the zone of supersaturation.The supersaturation zone that results in spontaneous nucleation of Ab brils is referred to as the nucleation zone.For in vitro aggregation, Hellstrand et al. 40 reported that there was no spontaneous Ab42 aggregation when Ab concentration was between 10 and 200 nM.Ab42 aggregation was observed at Ab42 concentrations higher than 260 nM, which denes the boundary between the nucleation zone and metastable zone under their aggregation conditions. 40iii) Within the nucleation zone, higher Ab concentrations lead to faster nucleation rates.The further away from the solubility limit, the higher energy Ab accumulates.As a result, Ab at higher concentrations aggregate at a faster rate.Hellstrand et al. 40 studied the aggregation of Ab42 at a wide range of concentrations, and found that Ab concentration has a linear relationship with the logarithmic value of the aggregation lag time.Ab42 at 0.26 mM has a lag time of ∼24 h, whereas Ab42 concentrations at >5 mM observe almost no lag time.
(iv) Ab in the metastable zone of supersaturation does not spontaneously initiate aggregation, but can aggregate in the presence of pre-formed aggregates, oen referred to as "bril seeds".While spontaneous bril nucleation needs to overcome an energy barrier, bril-seeded aggregation is a much more energetically favorable reaction.Cohen et al. 25 showed that Ab aggregation in the presence of even small amounts of amyloid brils is dominated by bril-catalyzed secondary nucleation reactions, rather than the classical mechanism of primary nucleation.
(v) Once aggregation starts, it will continue until the protein concentration reaches the solubility limit.Because the supersaturation is a non-equilibrium state, initiation of protein aggregation will restore the equilibrium state of saturation, where solubilization of Ab from brils and brillization of Ab from monomers reach equilibrium.Hellstrand et al. 40 found that, with starting concentrations ranging from 0.2 to 10 mM, the soluble Ab concentration at the end of aggregation converge to approximately 15 nM, suggesting that Ab42 solubility is approximately 10-20 nM for the specic aggregation conditions of their study.For in vivo Ab concentrations, Portelius et al. 42 found that the Ab42 concentrations in the cerebrospinal uid of familial Alzheimer's patients are similar to the sporadic Alzheimer's patients, even though this familial mutation has been shown to increase plasma Ab42 levels at preclinical stage. 43The implications of these studies are that even though familial mutations of Alzheimer's disease changed the Ab concentrations and thus result in increased aggregation propensity, the Ab aggregation in the post-amyloid stage is similar to that in sporadic Alzheimer's patients because the Ab solubility for these patients are similar.
(vi) An Ab solution in the presence of aggregates can no longer maintain supersaturation.Due to the presence of seeded aggregation, an increase in Ab concentration above the solubility limit will lead to aggregation.As a result, Ab concentration can no longer maintain supersaturation.A direct in vivo implication of this point is that Ab concentrations in amyloidpositive individuals cannot reach the same level as amyloidnegative individuals.Aer injecting isotopically-labeled Ab into the interstitial uid, Hong et al. 44 found that the recovered Ab from plaque-rich mice is only 45% of that from plaque-free mice, supporting the notion that most of the newly produced Ab proteins deposit to amyloid plaques.
(vii) In the presence of a large amount of aggregates, Ab concentration cannot become undersaturated, because the aggregates can be solubilized when protein concentration reaches below the solubility limit.For individuals that are amyloidpositive, this means that the Ab clearance pathway will not be able to lower Ab concentrations as much as in amyloid-negative individuals.It has been shown that, in plaque-free mice, acute inhibition of g-secretase activity led to rapid decline of Ab42 concentration. 44In contrast, plaque-rich mice showed signicantly less concentration reduction, supporting the role of amyloid plaques as a reservoir of soluble Ab. 44

Difference in the Ab phase diagram for in vitro and in vivo conditions
The exact parameters that dene the Ab phase diagram under in vitro and in vivo conditions are vastly different.The extensive study by Hellstrand et al. 40 of Ab42 aggregation in vitro at a wide range of Ab42 concentrations put Ab42 solubility at approximately 10-20 nM and Ab42 critical aggregation concentrations at approximately 200-400 nM.For in vivo conditions, it is not possible to perform any controlled aggregation studies.However, some parameters of the phase diagram can be implicated from biomarker studies in Alzheimer's patients.Because Ab solubility is dened as the Ab concentration in the presence of amyloid plaques, we used the cerebrospinal uid (CSF) Ab42 concentrations in the amyloid-positive individuals as an approximation of Ab42 solubility and CSF Ab42 concentrations in the amyloid-negative individuals as an approximation of Ab42 critical concentrations.With these assumptions, the Ab42 solubility in vivo was estimated to be 50-100 pM and Ab critical concentration was estimated to be 150-300 pM. 15,45,46he Ab42 concentration for in vitro aggregation differs from in vivo aggregation by approximately three orders of magnitude.Part of the reason for the extremely low critical concentration of in vivo Ab42 aggregation may be the presence of aggregationpromoting factors such as lipids, membrane surfaces, and interacting proteins.
We note that each individual may have a distinct in vivo phase diagram that determines their individualized Ab aggregation behavior.The Ab solubility and the boundary of the nucleation zone are determined by the local concentrations of proteins, lipids, and metabolites.A wide range of Ab concentrations have been observed in amyloid-positive individuals. 15,45ased on the supersaturation theory, Ab concentrations in the presence of amyloid plaques correspond to the solubility limit, and thus these results suggest a wide range of Ab in vivo solubility in different individuals.
Ab40 modies the phase diagram of Ab42 aggregation by interacting with Ab42.As a result, Ab42/Ab40 ratio is a more reliable descriptor of Ab42 aggregation propensity than the absolute Ab42 concentration alone. 47,48In a comprehensive study of 138 pathogenic presenilin-1 mutations, Sun et al. 49 found that a quarter of the presenilin-1 variants increased production of Ab42, and most variants producing lower levels of Ab42 exhibited a compromised ability to produce Ab40, leading to a higher Ab42/Ab40 ratio.The work of Sun et al. 49 suggests that familial Alzheimer's disease mutations modulate the phase diagram of Ab42 aggregation through not only Ab42 concentrations, but also Ab42/Ab40 ratio.

Comparison between in vivo and in vitro Ab aggregation
In vitro Ab aggregation kinetics are typically represented by a sigmoidal curve, 33,50 which consists of three phases: nucleation, growth, and stationary (Fig. 2A).The rate of in vitro aggregation can be measured by the length of the nucleation phase, also called "lag time".Using chemical kinetics and mathematical modeling, Dear et al. 51 show that oligomers are transiently formed during the process of brillization and disappear towards the end of the aggregation reaction.The secondary nucleation process 50 also leads to the formation of toxic oligomers, suggesting that oligomer formation may be an integral part of the overall Ab aggregation process. 52Cryo-EM studies have revealed mechanistic insights into the brilcatalyzed secondary nucleation. 53ccumulation of Ab plaques in vivo appears to show a similar sigmoidal curve 21,54 (Fig. 2B), but the nature of the in vivo Ab aggregation curve is fundamentally different from the in vitro aggregation curve.In vitro Ab aggregation is a closed system, transitioning from a non-equilibrium state consisting of a supersaturated solution to a nal equilibrium state consisting of Ab brils and a saturated Ab solution.In vivo Ab aggregation, on the other hand, is an open system, constantly replenishing and removing Ab through production and clearance pathways.Because Ab production and clearance is under the control of the 24-hour circadian clock, Ab aggregation in vivo likely also has a circadian rhythm, with a daily sigmoidal aggregation curve (Fig. 2C).Ab oligomers, due to their association with the Ab aggregation process, are also produced as part of the daily aggregation process.

In vivo Ab concentration dynamics in the framework of Ab supersaturation
Based on the framework of Ab supersaturation, the Ab concentrations of two imaginary individuals are plotted in Fig. 3A.One is an amyloid-negative individual, who never develops amyloid and dies amyloid-free.][57] The Ab concentration of this amyloid-negative individual stays in the metastable zone.The other imaginary person is an amyloidpositive individual who develops amyloid deposition later in life.The age-dependent changes of Ab concentration over the amyloid-positive individual's adult lifetime can be divided into four phases: soluble phase, burst phase, reduction phase, and stationary phase (Fig. 3A).The burst phase is a prediction based on the framework of supersaturation because spontaneous Ab

Chemical Science
Perspective aggregation requires Ab concentration to be in the nucleation zone.This can be achieved by an accelerated increase in Ab concentration, a "burst", where Ab concentration crosses the threshold into the nucleation zone (moving up along the Y-axis of Fig. 1).This could also be achieved by lowering the boundary of the nucleation zone because variations in in vivo environments can modulate the boundaries between the two zones of the supersaturation and even the solubility limit of Ab (moving right along the X-axis of Fig. 1).The reduction phase is when spontaneous Ab aggregation starts and eventually leads to a lower Ab concentration.The stationary phase can be classied as the stage when the Ab concentration reaches a steady-state.Mild cognitive impairment and dementia appear years or decades into the stationary phase. 58Studies have been performed to compare the amyloid-positive group and amyloid-negative group in the stationary phase, and show that the Ab concentration in the amyloid-positive group is markedly lower than that in the amyloid-negative group. 15,59In addition to lowered Ab concentration, amyloid formation also leads to a reduction in the amplitude of Ab circadian uctuations (Fig. 3E).

Post-amyloid Ab dynamics and circadian rhythm
Ab concentration has a circadian rhythm. 52Amyloid formation leads to reduced overall Ab42 concentration and reduced amplitude of the Ab42 circadian rhythm.Since Ab can no longer maintain supersaturation in the presence of plaques, the postamyloid Ab concentration is close to Ab ′ s in vivo solubility.For the same individual, the post-amyloid Ab concentration is likely lower than the pre-amyloid Ab concentration.Bateman and colleagues 15 studied the circadian dynamics of Ab concentration and found that the circadian amplitude in amyloid-negative group is 15.6 pM, almost 3-fold higher than the circadian amplitude of the amyloid-positive group (6.3 pM).Both the lowered Ab42 concentration and diminished circadian rhythm over a long period of time may be pathogenic and contribute to cognitive decline and dementia.Ab is an evolutionarily conserved protein, 60 although its precise physiological function has not been conclusively established. 61The reduced amplitude in Ab circadian rhythm may underlie the sleep disturbances associated with amyloid deposition. 62In an analysis of 598 amyloid-positive individuals, Sturchio et al. 63 found that normal cognition is associated with preservation of soluble Ab42 concentrations, suggesting that sufficient Ab42 concentrations are critical for cognition.In a cellular model, Zhou et al. 64 showed that restoring physiological amounts of Ab in APP-deleted neurons elevated synapse number and synaptic transmission, supporting a positive role of Ab in synapse function.

Implications for therapeutic development
In considering the daily production and clearance of Ab proteins in vivo, therapeutic treatments must be designed so as to address the constant cycle of Ab aggregation.

Non-linear effects of plaque removal
One important implication of the supersaturation framework is that the effect of plaque removal on Ab aggregation and the subsequent effect on cognitive function is not linear.Due to the ability of the large aggregates to act as both bril seeds for aggregation and reservoirs for soluble monomers, we expect that cognitive impairement would be mitigated only aer a large proportion of the accumulated plaques have been cleared.Ab aggregation in the presence of plaques versus in the absence of plaques is fundamentally different: one being spontaneous aggregation and the other seeded aggregation.In the framework of Ab supersaturation, the success of the antiamyloid therapy depends on the removal of most seedingcompetent plaques so that aggregation is no longer driven by bril seeds.By examining clinical trial data of four anti-Ab antibodies, Karran and De Strooper 23 reached a similar conclusion that amyloid plaque needs to be reduced to a low level to show signicant clinical benet.

Anti-Ab treatment
Several anti-Ab monoclonal antibodies have advanced to late stage clinical trials or gained FDA approval as treatment options.The main mechanism of action for these antibodies is the reduction of plaque load.Surprisingly, an enormous amount of resources has been poured into developing antiamyloid therapies, but there are no well-explained biochemical pathways that would lead from plaque reduction to cognitive improvement.Likewise, there is no clear biochemical rationalization as to how plaque reduction would lead to reduced toxic oligomer production.The supersaturation framework points to the removal of seeded Ab aggregation as the main benet of plaque removal, which restores Ab42 concentration to a higher level and reduces the daily toxic assault of Ab oligomer formation.

Modulation of Ab concentration
Lowering monomer Ab concentration has long been considered as a therapeutic strategy.This can be achieved using inhibitors or modulators of b-secrease 65 and g-secretase. 66Alternatively, antibodies that bind soluble Ab can also be used to lower Ab levels.Recent development in this area has been reviewed in Long and Holtzman. 67As a standalone strategy, this approach is likely most effective in the burst phase (Fig. 3A), when an increase in Ab concentration poses the greatest risk of initiating amyloid formation.Once amyloid is formed, the mechanism of aggregation shis from spontaneous aggregation to seeded aggregation, and Ab concentration plays a lesser role in the rate of aggregate formation.In the scenario where the majority of plaques and seeding-competent components have been removed, Ab concentration will return to a supersaturated state, which can be monitored with CSF or plasma Ab measurements.

Personalized Ab biomarkers
Measurements of Ab42 in human CSF show a wide range of concentrations.Although the amyloid-positive and amyloid-negative groups can be distinguished using a cutoff of Ab42 concentration, a large number of individuals, for example, 8% of cases in Palmqvist et al., 59 do not show agreement between Ab42 concentration and amyloid imaging.This is likely due to large inter-individual differences in Ab42 concentrations.One solution to this problem is to establish Ab concentration as a personalized biomarker.Then changes in Ab concentration can be compared to the past levels of the same individual.It has been shown that the Ab42 concentrations in amyloid-positive and amyloid-negative cohorts differ by 2-3 fold. 15,59A change of this magnitude would be readily detected using the same individual's history of Ab concentration.The personal history of Ab concentration will be particularly useful to detect if Ab supersaturation is restored aer a therapeutic intervention that has cleared the amyloid plaques.

Aggregation inhibitors
An additional personalized treatment strategy would be tailored to the specic pattern of aggregation exhibited by the patient.Due to the difference between spontaneous and seeded aggregation, two types of aggregation inhibitors may be needed.Spontaneous aggregation inhibitors are most important in the burst phase before a signicant amount of amyloids have built up.Once the seeded aggregation becomes the dominant mechanism, inhibitors for seeded aggregation will work more effectively.

Toxicity blockers
Proteins or small molecules that bind directly to toxic species can serve as toxicity blockers.This class of therapeutic molecules would be effective throughout the course of Alzheimer's disease.It may be particularly helpful in combination with antiamyloid therapy, which by itself does not eliminate the toxicity of soluble Ab.However, these types of potential drugs are also the most elusive due to a lack of understanding of both mechanisms of toxicity and the structures of the toxic Ab species.

Different therapeutic windows call for different treatment strategies
Due to the high degree of variations in Ab aggregation behavior at different stages of pathogenesis, therapeutic strategies will need to be adjusted accordingly.In the soluble and burst phase, the most effective way to reduce the risk of Ab aggregation is to keep Ab levels away from the nucleation zone.This can be done either by reduction of soluble Ab concentration (e.g., band g-secretase inhibitors, Ab immunization) or modulate the Ab phase diagram by increasing the boundary concentration between metastable and nucleation zones.In the reduction phase, Ab aggregation has started and the presence of small amounts of amyloid plaques provides the best opportunity for anti-amyloid therapy.Reduction of soluble Ab concentration is likely not effective in the reduction phase because Ab aggregation is driven by bril-catalyzed secondary nucleation.Because oligomer formation is associated with the overall aggregation process, toxicity blockers will also be desired to limit damage to synaptic connections and neuronal cells.The stationary phase is the least desired treatment window because the effect of treatment will only be felt aer the vast majority of plaques have been removed.

Issues of interest for future investigations
In order to further our understanding of Alzheimer's disease and other amyloid-related disorders, in the light of the supersaturation framework, future investigation could expand on the following ideas.First, there is a wide range of Ab42 concentrations in amyloid-negative individuals.It is important to distinguish whether a higher Ab concentration means a higher risk of imminent aggregation or if it indicates that the individual has a higher tolerance to Ab aggregation, in other words, a higher boundary for the nucleation zone.It is conceivable that different individuals have their unique combination of aggregationpromoting and inhibiting factors and some may be more tolerant to higher Ab concentrations than others.Identifying these aggregation-inhibiting factors may provide a new form of therapeutic intervention.Second, Ab40 has been shown to be an important and likely the best-characterized inhibitor of in vivo Ab42 aggregation.Mutations in familial Alzheimer's disease oen lead to an increase in Ab42/Ab40 ratio, not simply increased Ab42 concentrations.In sporadic Alzheimer's disease, Ab42/Ab40 ratio is a better predictor of Alzheimer's risk than the absolute Ab42 concentration.It is likely that this modulation of the Ab42 phase diagram is a result of a direct interaction with Ab40.Therefore, exploring the potential use of Ab40 or another Ab variant as a modulator of Ab42 aggregation deserves further investigation.Third, as a consequence of Ab42 aggregation, the net concentration of Ab42 is lowered as it is no longer able to maintain supersaturation.Although the exact physiological function of Ab42 is not clear, the reduction in both absolute Ab42 concentration and its circadian amplitude may have a negative effect on cognition, especially over a long period of time.While replenishment of Ab42 is out of the question due to seeded aggregation, identication of a functionally equivalent and nonaggregating form of Ab42 may provide another disease-modifying treatment.

Chemical Science Perspective
which inspired the conceptualization of this work.thank the members of the Guo group for insightful discussions.This work was supported by the National Institutes of Health (Grant number R01AG050687).

Fig. 1 A
Fig.1A phase diagram of Ab supersaturation.Both Ab concentration and environmental factors affect the phase diagram.In the undersaturation zone, Ab exists mostly as monomers.The area of supersaturation consists of a metastable zone and a nucleation zone.In the metastable zone, Ab exists as monomers and transient oligomers, and does not spontaneously aggregate but can aggregate in the presence of aggregate seeds.In the nucleation zone, Ab can aggregate spontaneously and exists as a mixture of soluble Ab monomers, stable oligomers, fibril nuclei, and fibrils.

Fig. 2
Fig. 2 In vivo and in vitro Ab aggregation curves.(A) Ab aggregation in vitro leading to fibril formation (brown line) shows a typical sigmoidal curve with three phases: nucleation, growth, and stationary.Oligomers (green line) first appear in the nucleation phase but disappear towards the end of the aggregation process.(B) Ab aggregation in vivo displays a similar sigmoidal curve of fibril formation as the in vitro system, but with fundamentally different features.(C) In vivo day-to-day Ab aggregation shows a sigmoidal curve and oligomer formation.

Fig. 3
Fig. 3 In vivo Ab dynamics in the framework of supersaturation.(A) Two imaginary individuals are considered here: one eventually becomes amyloid-positive (red line) and the other one remains amyloid-negative (blue line).The Ab concentration in the amyloid-negative individual has a slow linear increase but never goes into the nucleation zone.For the amyloid-positive individual, Ab concentration can be divided into four phases: soluble, burst, reduction, and stationary.(B) Before amyloid formation, the amyloid-positive individual and the amyloid-negative individual display highly similar circadian fluctuations.(C and D) Daily modulation of soluble Ab42 in amyloid-negative (C) and amyloid-positive (D) individuals.(E) After amyloid formation, the amyloid-positive individual has a dramatically reduced circadian amplitude as a result of amyloid formation.