Aggregation rate of amyloid beta peptide is controlled by beta-content in monomeric state

Advanced computational approaches to understand protein aggregation

Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.

Exploring Structural Insights of Aβ42 and α-Synuclein Monomers and Heterodimer: A Comparative Study Using Implicit and Explicit Solvent Simulations

Protein misfolding, aggregation, and fibril formation play a central role in the development of severe neurological disorders, including Alzheimer's and Parkinson's diseases. The structural stability of mature fibrils in these diseases is of great importance, as organisms struggle to effectively eliminate amyloid plaques. To address this issue, it is crucial to investigate the early stages of fibril formation when monomers aggregate into small, toxic, and soluble oligomers. However, these structures are inherently disordered, making them challenging to study through experimental approaches. Recently, it has been shown experimentally that amyloid-β 42 (Aβ42) and α-synuclein (α-Syn) can coassemble. This has motivated us to investigate the interaction between their monomers as a first step toward exploring the possibility of forming heterodimeric complexes. In particular, our study involves the utilization of various Amber and CHARMM force-fields, employing both implicit and explicit solvent models in replica exchange and conventional simulation modes. This comprehensive approach allowed us to assess the strengths and weaknesses of these solvent models and force fields in comparison to experimental and theoretical findings, ensuring the highest level of robustness. Our investigations revealed that Aβ42 and α-Syn monomers can indeed form stable heterodimers, and the resulting heterodimeric model exhibits stronger interactions compared to the Aβ42 dimer. The binding of α-Syn to Aβ42 reduces the propensity of Aβ42 to adopt fibril-prone conformations and induces significant changes in its conformational properties. Notably, in AMBER-FB15 and CHARMM36m force fields with the use of explicit solvent, the presence of Aβ42 significantly increases the β-content of α-Syn, consistent with the experiments showing that Aβ42 triggers α-Syn aggregation. Our analysis clearly shows that although the use of implicit solvent resulted in too large compactness of monomeric α-Syn, structural properties of monomeric Aβ42 and the heterodimer were preserved in explicit-solvent simulations. We anticipate that our study sheds light on the interaction between α-Syn and Aβ42 proteins, thus providing the atom-level model required to assess the initial stage of aggregation mechanisms related to Alzheimer's and Parkinson's diseases.

Probing the Conformational Preference to β-Strand during Peptide Self-Assembly

Alanine-rich tetrapeptides like A₃K dominantly exist as polyproline II helices in dilute aqueous solutions. However, during self-assembly, based on the free energy calculation in implicit solvent for various peptide conformations, only the peptides in the β-strand conformation can be packed closely. This necessitates the conformational transition to the β-strand commonly observed during peptide self-assembly such as in amyloid fibril formation. In fact, the closest interpeptide distance of 4.8 Å is consistent with the interstrand distance determined from the X-ray diffraction pattern of many amyloid fibrils. The position of free energy minimum obtained from implicit solvent calculation matches exactly with the explicit solvent simulation through umbrella sampling when the peptide conformations are restrained, demonstrating the applicability of the former for rapid screening of peptide configurations favorable for self-assembly. The barrier in the free energy profile in the presence of water arises out of the entropic restriction on the interstitial water molecules while satisfying the hydrogen bonding of both the peptides by forming water mediated hydrogen bond bridge. Further, the high energy barrier observed for the β-strand suggests that peptides initially tend to self-assemble in the polyproline II structure to mitigate the desolvation energy cost; the transition to the β-strand would happen only in the later stage after crossing the barrier. The umbrella sampling simulations with peptides allowed to change conformations, relative to each other, confirm the dynamic conformational transition during the course of the self-assembly supporting the "dock and lock" mechanism suggested for amyloid fibrillar growth.

Modeling structural interconversion in Alzheimers' amyloid beta peptide with classical and intrinsically disordered protein force fields

A comprehensive understanding of the aggregation mechanism in amyloid beta 42 (Aβ42) peptide is imperative for developing therapeutic drugs to prevent or treat Alzheimer's disease. Because of the high flexibility and lack of native tertiary structures of Aβ42, molecular dynamics (MD) simulations may help elucidate the peptide's dynamics with atomic details and collectively improve ensembles not seen in experiments. We applied microsecond-timescale MD simulations to investigate the dynamics and conformational changes of Aβ42 by using a newly developed Amber force field (ff14IDPSFF). We compared the ff14IDPSFF and the regular ff14SB force field by examining the conformational changes of two distinct Aβ42 monomers in explicit solvent. Conformational ensembles obtained by simulations depend on the force field and initial structure, Aβ42^α-helix or Aβ42^β-strand. The ff14IDPSFF sampled a high ratio of disordered structures and diverse β-strand secondary structures; in contrast, ff14SB favored helicity during the Aβ42^α-helix simulations. The conformations obtained from Aβ42^β-strand simulations maintained a balanced content in the disordered and helical structures when simulated by ff14SB, but the conformers clearly favored disordered and β-sheet structures simulated by ff14IDPSFF. The results obtained with ff14IDPSFF qualitatively reproduced the NMR chemical shifts well. In-depth peptide and cluster analysis revealed some characteristic features that may be linked to early onset of the fibril-like structure. The C-terminal region (mainly M35-V40) featured in-registered anti-parallel β-strand (β-hairpin) conformations with tested systems. Our work should expand the knowledge of force field and structure dependency in MD simulations and reveals the underlying structural mechanism-function relationship in Aβ42 peptides. Communicated by Ramaswamy H. Sarma.

In Silico Analysis of the Antagonist Effect of Enoxaparin on the ApoE4–Amyloid-Beta (Aβ) Complex at Different pH Conditions

Apolipoprotein E4 (ApoE4) is thought to increase the risk of developing Alzheimer’s disease. Several studies have shown that ApoE4-Amyloid β (Aβ) interactions can increment amyloid depositions in the brain and that this can be augmented at low pH values. On the other hand, experimental studies in transgenic mouse models have shown that treatment with enoxaparin significantly reduces cortical Aβ levels, as well as decreases the number of activated astrocytes around Aβ plaques. However, the interactions between enoxaparin and the ApoE4-Aβ proteins have been poorly explored. In this work, we combine molecular dynamics simulations, molecular docking, and binding free energy calculations to elucidate the molecular properties of the ApoE4-Aβ interactions and the competitive binding affinity of the enoxaparin on the ApoE4 binding sites. In addition, we investigated the effect of the environmental pH levels on those interactions. Our results showed that under different pH conditions, the closed form of the ApoE4 protein, in which the C-terminal domain folds into the protein, remains stabilized by a network of hydrogen bonds. This closed conformation allowed the generation of six different ApoE4-Aβ interaction sites, which were energetically favorable. Systems at pH5 and 6 showed the highest energetic affinity. The enoxaparin molecule was found to have a strong energetic affinity for ApoE4-interacting sites and thus can neutralize or disrupt ApoE4-Aβ complex formation.

Computational Models for the Study of Protein Aggregation

Protein aggregation has been studied by many groups around the world for many years because it can be the cause of a number of neurodegenerative diseases that have no effective treatment. Obtaining the structure of related fibrils and toxic oligomers, as well as describing the pathways and main factors that govern the self-organization process, is of paramount importance, but it is also very difficult. To solve this problem, experimental and computational methods are often combined to get the most out of each method. The effectiveness of the computational approach largely depends on the construction of a reasonable molecular model. Here we discussed different versions of the four most popular all-atom force fields AMBER, CHARMM, GROMOS, and OPLS, which have been developed for folded and intrinsically disordered proteins, or both. Continuous and discrete coarse-grained models, which were mainly used to study the kinetics of aggregation, are also summarized.

Examining the Ensembles of Amyloid-β Monomer Variants and Their Propensities to Form Fibers Using an Energy Landscape Visualization Method

The amyloid-β (Aβ) monomer, an intrinsically disordered peptide, is produced by the cleavage of the amyloid precursor protein, leading to Aβ-40 and Aβ-42 as major products. These two isoforms generate pathological aggregates, whose accumulation correlates with Alzheimer's disease (AD). Experiments have shown that even though the natural abundance of Aβ-42 is smaller than that for Aβ-40, the Aβ-42 is more aggregation-prone compared to Aβ-40. Moreover, several single-point mutations are associated with early onset forms of AD. This work analyzes coarse-grained associative-memory, water-mediated, structure and energy model (AWSEM) simulations of normal Aβ-40 and Aβ-42 monomers, along with six single-point mutations associated with early onset disease. We analyzed the simulations using the energy landscape visualization method (ELViM), a reaction-coordinate-free approach suited to explore the frustrated energy landscapes of intrinsically disordered proteins. ELViM is shown to distinguish the monomer ensembles of variants that rapidly form fibers from those that do not form fibers as readily. It also delineates the amino acid contacts characterizing each ensemble. The results shed light on the potential of ELViM to probe intrinsically disordered proteins.

Accelerated Molecular Dynamics to Explore the Binding of Transition Metals to Amyloid-β

We report the accelerated molecular dynamics (aMD) simulation of amyloid-β (Aβ) peptides of four different lengths (16, 28, 40, and 42 residues) and their complexes when bound to Cu(II), Fe(II), or Zn(II). 600 ns equilibrated trajectory data were analyzed for each structure from three independent 200 ns aMD simulations, generating 16 aMD trajectories. We show that the presence of a metal ion leads to reduced size and decreased mobility relative to the free peptide due to the anchoring effect of the ions. The reduced mobility was shown largely to be due to the restricted movement in N-terminal residues, most notably Asp1 and His6 that are involved in the metal-ion coordination in all cases. Significant disruption of the secondary structure and patterns of salt bridge interactions arise on the coordination of metal ions. In this regard, similarities were noted between results for Zn(II) and Fe(II), whereas results for Cu(II) are more comparable to that of the free peptides. Reweighting of free energy surfaces was carried out from aMD data to identify the properties and descriptions of local minima structures.

Amyloid Prefibrillar Oligomers: The Surprising Commonalities in Their Structure and Activity

It has been proposed that a “common core” of pathologic pathways exists for the large family of amyloid-associated neurodegenerations, including Alzheimer’s, Parkinson’s, type II diabetes and Creutzfeldt–Jacob’s Disease. Aggregates of the involved proteins, independently from their primary sequence, induced neuron membrane permeabilization able to trigger an abnormal Ca²⁺ influx leading to synaptotoxicity, resulting in reduced expression of synaptic proteins and impaired synaptic transmission. Emerging evidence is now focusing on low-molecular-weight prefibrillar oligomers (PFOs), which mimic bacterial pore-forming toxins that form well-ordered oligomeric membrane-spanning pores. At the same time, the neuron membrane composition and its chemical microenvironment seem to play a pivotal role. In fact, the brain of AD patients contains increased fractions of anionic lipids able to favor cationic influx. However, up to now the existence of a specific “common structure” of the toxic aggregate, and a “common mechanism” by which it induces neuronal damage, synaptotoxicity and impaired synaptic transmission, is still an open hypothesis. In this review, we gathered information concerning this hypothesis, focusing on the proteins linked to several amyloid diseases. We noted commonalities in their structure and membrane activity, and their ability to induce Ca²⁺ influx, neurotoxicity, synaptotoxicity and impaired synaptic transmission.

Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer's Disease, Parkinson's Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis

Protein misfolding and aggregation is observed in many amyloidogenic diseases affecting either the central nervous system or a variety of peripheral tissues. Structural and dynamic characterization of all species along the pathways from monomers to fibrils is challenging by experimental and computational means because they involve intrinsically disordered proteins in most diseases. Yet understanding how amyloid species become toxic is the challenge in developing a treatment for these diseases. Here we review what computer, in vitro, in vivo, and pharmacological experiments tell us about the accumulation and deposition of the oligomers of the (Aβ, tau), α-synuclein, IAPP, and superoxide dismutase 1 proteins, which have been the mainstream concept underlying Alzheimer's disease (AD), Parkinson's disease (PD), type II diabetes (T2D), and amyotrophic lateral sclerosis (ALS) research, respectively, for many years.

Exploring the Role of Peptide Helical Stability in the Propensity of Uperin 3.x Peptides toward Beta-Aggregation

Antimicrobial peptides of the uperin 3.x family, obtained from the skin secretions of Uperoleia mjobergii, have an inherent ability to form amyloid with possible functional roles and can serve as model peptides to understand mechanistic aspects of amyloidogenesis. The substitution of a positively charged amino acid with a nonpolar alanine residue increased aggregation, fibril content, and propensity for β-sheet formation for the uperin 3.5 R7A variant when compared with the uperin 3.5 wild-type peptides. We use molecular dynamics (MD) simulations and circular dichroism (CD) measurements on three uperin 3.x peptides and their corresponding seventh position alanine variants to understand the effect of substitution of a positively charged amino acid with a nonpolar alanine residue on the process of β-aggregation. Both CD experiments and simulations show that the uperin 3.x wild-type peptides demonstrated lower β-sheet content and propensity than with the corresponding alanine variants. Significantly, simulations of helix-to-coil transitions in individual peptides show an inverse relationship between the helical stability of peptides and their propensity to form structures rich in β-sheets as observed in CD experiments. A simulation scheme based on a conformational search of helix-to-coil transition trajectories to select peptide conformers was used to assemble propagating peptide oligomers. Whereas octamers consisting of lower helical stability peptide conformers evolve into compact aggregates with a large β-sheet component, octamers composed of high helical stability conformers disintegrate and show the least amounts of β-sheet components. The highlight of the current work is that MD simulations are able to predict the correct order of β-sheet propensity among the six peptides derived from the CD experiments and indicate the importance of helical intermediates in the amyloidogenesis pathway for uperin 3.x peptides.

An α-helix mimetic oligopyridylamide, ADH-31, modulates Aβ42 monomer aggregation and destabilizes protofibril structures: insights from molecular dynamics simulations

Alzheimer's disease (AD), an epidemic growing worldwide due to no effective medical aid available in the market, is a neurological disorder. AD is known to be directly associated with the toxicity of amyloid-β (Aβ) aggregates. In search of potent inhibitors of Aβ aggregation, Hamilton and co-workers reported an α-helix mimetic, ADH-31, which acts as a powerful antagonist of Aβ42 aggregation. To identify the key interactions between protein-ligand complexes and to gain insights into the inhibitory mechanism of ADH-31 against Aβ42 aggregation, molecular dynamics (MD) simulations were performed in the present study. The MD simulations highlighted that ADH-31 showed distinct binding capabilities with residues spanning from the N-terminal to the central hydrophobic core (CHC) region of Aβ42 and restricted the conformational transition of the helix-rich structure of Aβ42 into another form of secondary structures (coil/turn/β-sheet). Hydrophobic contacts, hydrogen bonding and π-π interaction contribute to the strong binding between ADH-31 and Aβ42 monomer. The Dictionary of Secondary Structure of Proteins (DSSP) analysis highlighted that the probability of helical content increases from 38.5% to 50.2% and the turn content reduces from 14.7% to 6.2% with almost complete loss of the β-sheet structure (4.5% to 0%) in the Aβ42 monomer + ADH-31 complex. The per-residue binding free energy analysis demonstrated that Arg5, Tyr10, His14, Gln15, Lys16, Val18, Phe19 and Lys28 residues of Aβ42 are responsible for the favourable binding free energy in Aβ42 monomer + ADH-31 complex, which is consistent with the 2D HSQC NMR of the Aβ42 monomer that depicted a change in the chemical shift of residues spanning from Glu11 to Phe20 in the presence of ADH-31. The MD simulations highlighted the prevention of sampling of amyloidogenic β-strand conformations in Aβ42 trimer in the presence of ADH-31 as well as the ability of ADH-31 to destabilize Aβ42 trimer and protofibril structures. The lower binding affinity between Aβ42 trimer chains in the presence of ADH-31 highlights the destabilization of the Aβ42 trimer structure. Overall, MD results highlighted that ADH-31 inhibited Aβ42 aggregation by constraining Aβ peptides into helical conformation and destabilized Aβ42 trimer as well as protofibril structures. The present study provides a theoretical insight into the atomic level details of the inhibitory mechanism of ADH-31 against Aβ42 aggregation as well as protofibril destabilization and could be implemented in the structure-based drug design of potent therapeutic agents for AD.

Plant isoquinoline alkaloids as potential neurodrugs: A comparative study of the effects of benzo[c]phenanthridine and berberine-based compounds on β-amyloid aggregation

Herein we present a comparative study of the effects of isoquinoline alkaloids belonging to benzo[c]phenanthridine and berberine families on β-amyloid aggregation. Results obtained using a Thioflavine T (ThT) fluorescence assay and circular dichroism (CD) spectroscopy suggested that the benzo[c]phenanthridine nucleus, present in both sanguinarine and chelerythrine molecules, was directly involved in an inhibitory effect of Aβ_1-42 aggregation. Conversely, coralyne, that contains the isomeric berberine nucleus, significantly increased propensity for Aβ_1-42 to aggregate. Surface Plasmon Resonance (SPR) experiments provided quantitative estimation of these interactions: coralyne bound to Aβ_1-42 with an affinity (K_D = 11.6 μM) higher than benzo[c]phenanthridines. Molecular docking studies confirmed that all three compounds are able to recognize Aβ_1-42 in different aggregation forms suggesting their effective capacity to modulate the Aβ_1-42 self-recognition mechanism. Molecular dynamics simulations indicated that coralyne increased the β-content of Aβ_1-42, in early stages of aggregation, consistent with fluorescence-based promotion of the Aβ_1-42 self-recognition mechanism by this alkaloid. At the same time, sanguinarine induced Aβ_1-42 helical conformation corroborating its ability to delay aggregation as experimentally proved in vitro. The investigated compounds were shown to interfere with aggregation of Aβ_1-42 demonstrating their potential as starting leads for the development of therapeutic strategies in neurodegenerative diseases.

Lactoferrin-Loaded PEG/PLA Block Copolymer Targeted With Anti-Transferrin Receptor Antibodies for Alzheimer Disease

Last few years, struggles have been reported to develop the nanovesicles for drug delivery via the brain-blood barrier (BBB). Novel drugs, for instance, iAβ5, are efficient to inhibit the aggregates connected to the treatment of Alzheimer disease and are being evaluated, but most of the reports reflect some drawbacks of the drugs to reach the brain in preferred concentrations owing to the less BBB penetrability of the surface dimensions. In this report, we designed and developed a new approach to enhance the transport of drug via BBB, constructed with lactoferrin (Lf)-coated polyethylene glycol-polylactide nanoparticles (Lf-PPN) with superficial monoclonal antibody-functionalized antitransferrin receptor and anti-Aβ to deliver the iAβ5 hooked on the brain. The porcine brain capillary endothelial cells were utilized as BBB typically to examine the framework efficacy and toxicity. The cellular uptake of the immuno-nanoparticles with measured conveyance of the iAβ5 peptide was significantly enhanced and associated with Lf-PPN without monoclonal antibody functionalizations.

Amyloid-β (Aβ42) Peptide Aggregation Rate and Mechanism on Surfaces with Widely Varied Properties: Insights from Brownian Dynamics Simulations

Amyloid-β (Aβ) plaques, which form by aggregation of harmless Aβ peptide monomers into larger fibrils, are characteristic of neurodegenerative disorders such as Alzheimer's disease. Efforts to treat Alzheimer's disease focus on stopping or reversing the aggregation process that leads to fibril formation. However, effective treatments are elusive due to certain unknown aspects of the process. Many hypotheses point to disruption of cell membranes by adsorbed Aβ monomers or oligomers, but how Aβ behaves and aggregates on surfaces of widely varying properties, such as those present in a cell, is unclear. Elucidating the effects of various surfaces on the dynamics of Aβ and the kinetics of the aggregation process from bulk solution to a surface-adsorbed multimer can help identify what drives aggregation, leading to new methods of intervention by inhibitory drugs or other means. In this work, we used all-atom Brownian dynamics simulations to study the association of two distinct Aβ42 monomer conformations with a surface-adsorbed or free-floating Aβ42 dimer. We calculated the association time, surface interaction energy, surface diffusion coefficient, surface residence time, and the mechanism of association on four different surfaces and two different bulk solution scenarios. In the presence of a surface, the majority of monomers underwent a two-dimensional surface-mediated association that depended primarily on an Aβ42 electrostatic interaction with the self-assembled monolayer (SAM) surfaces. Moreover, aggregation could be inhibited greatly by surfaces with high affinity for Aβ42 and heterogeneous charge distribution. Our results can be used to identify new opportunities for disrupting or reversing the Aβ42 aggregation process.

Oligomerization and Conformational Change Turn Monomeric β-Amyloid and Tau Proteins Toxic: Their Role in Alzheimer's Pathogenesis

The structural polymorphism and the physiological and pathophysiological roles of two important proteins, β-amyloid (Aβ) and tau, that play a key role in Alzheimer's disease (AD) are reviewed. Recent results demonstrate that monomeric Aβ has important physiological functions. Toxic oligomeric Aβ assemblies (AβOs) may play a decisive role in AD pathogenesis. The polymorph fibrillar Aβ (fAβ) form has a very ordered cross-β structure and is assumed to be non-toxic. Tau monomers also have several important physiological actions; however, their oligomerization leads to toxic oligomers (TauOs). Further polymerization results in probably non-toxic fibrillar structures, among others neurofibrillary tangles (NFTs). Their structure was determined by cryo-electron microscopy at atomic level. Both AβOs and TauOs may initiate neurodegenerative processes, and their interactions and crosstalk determine the pathophysiological changes in AD. TauOs (perhaps also AβO) have prionoid character, and they may be responsible for cell-to-cell spreading of the disease. Both extra- and intracellular AβOs and TauOs (and not the previously hypothesized amyloid plaques and NFTs) may represent the novel targets of AD drug research.

Impact of the Astaxanthin, Betanin, and EGCG Compounds on Small Oligomers of Amyloid Aβ40 Peptide

There is experimental evidence that the astaxanthin, betanin, and epigallocatechin-3-gallate (EGCG) compounds slow down the aggregation kinetics and the toxicity of the amyloid-β (Aβ) peptide. How these inhibitors affect the self-assembly at the atomic level remains elusive. To address this issue, we have performed for each ligand atomistic replica exchange molecular dynamic (REMD) simulations in an explicit solvent of the Aβ_11-40 trimer from the U-shape conformation and MD simulations starting from Aβ_1-40 dimer and tetramer structures characterized by different intra- and interpeptide conformations. We find that the three ligands have similar binding free energies on small Aβ₄₀ oligomers but very distinct transient binding sites that will affect the aggregation of larger assemblies and fibril elongation of the Aβ₄₀ peptide.

Interactions of a multifunctional di-triazole derivative with Alzheimer's Aβ42monomer and Aβ42protofibril: a systematic molecular dynamics study

The molecular dynamics simulations results highlighted that the multi-target-directed ligand6nstabilizes the native α-helix conformation of the Aβ₄₂monomer and induces a sizable destabilization in the Aβ₄₂protofibril structure.

Molecular Mechanism and Kinetics of Amyloid-β42 Aggregate Formation: A Simulation Study

As an important neuropathological hallmark of Alzheimer's disease (AD), the oligomerization of amyloid-β (Aβ) peptides has been intensively investigated in both theoretical and experimental studies. However, the oligomerization space in terms of the kinetics, molecular mechanism, and oligomer structures remains mysterious to us. An equation that can quantitatively describe the time it takes for Aβ oligomers to appear in the human brain at a given Aβ monomer concentration is extremely vital for us to understand the development and disease progression of AD. In this study, we utilized molecular dynamics (MD) simulations to investigate the oligomerization of Aβ₄₂ peptides at five different monomer concentrations. We have elucidated the formation pathways of Aβ tetramers, characterized the oligomer structures, estimated the oligomerization time for Aβ dimers, trimers, and tetramers, and for the first-time derived equations that could quantitatively describe the relationship between the oligomerization time and the monomer concentration. Applying these equations, our prediction of oligomerization time agrees well with the experimental and clinical findings, in spite of the limitations of our oligomerization simulations. We have found that the Aβ oligomerization time depends on the monomer concentration by a power of -2.4. The newly established equations will enable us to quantitatively estimate the risk score of AD, which is a function of age. Moreover, we have identified the most dominant pathway of forming Aβ tetramers, probably the most important and toxic Aβ oligomer. Our results have shown that the structures of Aβ₄₂ dimer, trimer, and tetramer, which are distinguishable from each other, depend on the monomer concentration at which the oligomers form. Representative oligomer structures, which can serve as potential drug targets, have been identified by clustering analysis. The MD sampling adequacy has been validated by the excellent agreement between the calculated and measured collisional cross section (CCS) parameters (the prediction errors are within 2%). In a conclusion, this study provides the kinetics and structure basis for developing inhibitors to decelerate the Aβ oligomerization process.