Computer Simulation Studies of Aβ37–42 Aggregation Thermodynamics and Kinetics in Water and Salt Solution

Novel Insights into the Catalytic Mechanism of Collagenolysis by Zn(II)-Dependent Matrix Metalloproteinase-1

Collagen hydrolysis, catalyzed by Zn(II)-dependent matrix metalloproteinases (MMPs), is a critical physiological process. Despite previous computational investigations into the catalytic mechanisms of MMP-mediated collagenolysis, a significant knowledge gap in understanding remains regarding the influence of conformational sampling and entropic contributions at physiological temperature on enzymatic collagenolysis. In our comprehensive multilevel computational study, employing quantum mechanics/molecular mechanics (QM/MM) metadynamics (MetD) simulations, we aimed to bridge this gap and provide valuable insights into the catalytic mechanism of MMP-1. Specifically, we compared the full enzyme-substrate complex in solution, clusters in solution, and gas-phase to elucidate insights into MMP-1-catalyzed collagenolysis. Our findings reveal significant differences in the catalytic mechanism when considering thermal effects and the dynamic evolution of the system, contrasting with conventional static potential energy surface QM/MM reaction path studies. Notably, we observed a significant stabilization of the critical tetrahedral intermediate, attributed to contributions from conformational flexibility and entropy. Moreover, we found that protonation of the scissile bond nitrogen occurs via proton transfer from a Zn(II)-coordinated hydroxide rather than from a solvent water molecule. Following C-N bond cleavage, the C-terminus remains coordinated to the catalytic Zn(II), while the N-terminus forms a hydrogen bond with a solvent water molecule. Subsequently, the release of the C-terminus is facilitated by the coordination of a water molecule. Our study underscores the pivotal role of protein conformational dynamics at physiological temperature in stabilizing the transition state of the rate-limiting step and key intermediates, compared to the corresponding reaction in solution. These fundamental insights into the mechanism of collagen degradation provide valuable guidance for the development of MMP-1-specific inhibitors.

Markov State Models Reveal How Folding Kinetics Influence Absorption Spectra of Foldamers

Self-assembly of platinum(II) complex foldamers is an essential approach to fabricate advanced luminescent materials. However, a comprehensive understanding of folding kinetics and their absorption spectra remains elusive. By constructing Markov state models (MSMs) from large-scale molecular dynamics simulations, we reveal that two largely similar dinuclear alknylplatinum(II) terpyridine foldamers, Pt-PEG and Pt-PE with slightly different bridges, exhibit distinctive folding kinetics. Particularly, Pt-PEG bears bridge-dominant, plane-dominant, and cooperative pathways, while Pt-PE only prefers the plane-dominant pathway. Such preference originates from their difference in intrabridge electrostatic interactions, leading to contrastive distributions of metastable states. We also found that the bridge-dominant pathway for Pt-PEG becomes more favorable when lowering the temperature. Interestingly, based on the comprehensive conformation ensembles from our MSMs, we reveal the conformation-dependent absorption spectra of Pt-PEG and Pt-PE. Our theoretical spectra not only align with experimental results but also reveal the contributions of diverse conformations to the overall absorption bands explicitly, facilitating the rational design of stimuli-responsive smart luminescent molecules.

Pathways of hLL-3717-29 Aggregation Give Insight into the Mechanism of α-Amyloid Formation

α-amyloids present a novel self-assembly principle that can be utilized to prepare functional biomaterials. Evidence of α-amyloid formation in the active core of the human LL-37 protein (comprising residues 17 to 29) was associated with this peptide's membranolytic property. Though mechanistic pathways of β-amyloid formation are known, such studies are scarce in α-amyloids. Modern computational techniques allow such mechanistic studies in molecular detail. Here, we propose aggregation pathways in hLL-3717-29 through molecular dynamics simulations. We first identified oligomers among peptides based on a distance criterion. The distribution of oligomers was then used to build Markov state models from which pathways were obtained using the framework of transition path theory. We checked the structural stability of the peptides during oligomerization, which is crucial from their functional point of view. We also investigated the key residues that participate in oligomer formation, the interactions between them, and the effect of residue mutations on the binding free energy of the peptides. Our findings suggest that larger oligomers are produced from the association of smaller and intermediate oligomers. The peptides retain their helical structure during aggregation with transient occurrences of 3-10 helix and turns. Hydrophobic interactions are vital in the aggregation of these peptides with Ile24 playing a crucial role. Mutation of this residue to alanine decreases the peptides' binding free energy, resulting in reduced aggregation tendency.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

The α-Synuclein Monomer May Have Different Misfolding Mechanisms in the Induction of α-Synuclein Fibrils with Different Polymorphs

The aggregation of alpha-synuclein (α-Syn) is closely related to the occurrence of some neurodegenerative diseases such as Parkinson's disease. The misfolding of α-Syn monomer plays a key role in the formation of aggregates and extension of fibril. However, the misfolding mechanism of α-Syn remains elusive. Here, three different α-Syn fibrils (isolated from a diseased human brain, generated by in vitro cofactor-tau induction, and obtained by in vitro cofactor-free induction) were selected for the study. The misfolding mechanisms of α-Syn were uncovered by studying the dissociation of the boundary chains based on the conventional molecular dynamics (MD) and Steered MD simulations. The results showed that the dissociation paths of the boundary chains in the three systems were different. According to the reverse process of dissociation, we concluded that in the human brain system, the binding of the monomer and template starts from the C-terminal and gradually misfolds toward the N-terminal. In the cofactor-tau system, the monomer binding starts from residues 58-66 (contain β3), followed by the C-terminal coil (residues 67-79). Then, the N-terminal coil (residues 36-41) and residues 50-57 (contain β2) bind to the template, followed by residues 42-49 (contain β1). In the cofactor-free system, two misfolding paths were found. One is that the monomer binds to the N/C-terminal (β1/β6) and then binds to the remaining residues. The other one is that the monomer binds sequentially from the C- to N-terminal, similar to the human brain system. Furthermore, in the human brain and cofactor-tau systems, electrostatic interactions (especially from residues 58-66) are the main driving force during the misfolding process, whereas in the cofactor-free system, the contributions of electrostatic and van der Waals interactions are comparable. These results may provide a deeper understanding for the misfolding and aggregation mechanism of α-Syn.

Exploring the folding process of human βB2-crystallin using multiscale molecular dynamics and the Markov state model

Adequate knowledge of protein conformations is crucial for understanding their function and their association properties with other proteins. The cataract disease is correlated with conformational changes in key proteins called crystallins. These changes are due to mutations or post-translational modifications that may lead to protein unfolding, and thus the formation of aggregate states. Human βB2-crystallin (HβB2C) is found in high proportion in the eye lens, and its mutations are related to some cataracts. HβB2C also associates into dimers, tetramers, and other higher-order supramolecular complexes. However, it is the only protein of the βγ-crystallin family that has been found in an extended conformation. Therefore, we hypothesize that the extended conformation is not energetically favourable and that HβB2C may adopt a closed (completely folded) conformation, similar to the other members of the βγ-crystallin family. To corroborate this hypothesis, we performed extensive molecular dynamics simulations of HβB2C in its monomeric and dimeric conformations, using all-atom and coarse-grained scales. We employed Markov state model (MSM) analysis to characterize the conformational and kinetically relevant states in the folding process of monomeric HβB2C. The MSM analysis clearly shows that HβB2C adopts a completely folded structure, and this conformation is the most kinetically and energetically favourable one. In contrast, the extended conformations are kinetically unstable and energetically unfavourable. Our MSM analysis also reveals a key metastable state, which is particularly interesting because it is from this state that the folded state is reached. The folded state is stabilized by the formation of two salt bridges between the residue-pairs E74-R187 and R97-E166 and the two hydrophobic residue-pairs V59-L164 and V72-V151. Furthermore, free energy surface (FES) analysis revealed that the HβB2C dimer with both monomers in a closed conformation (face-en-face dimer) is energetically more stable than the domain-swapped dimer (crystallographic structure). The results presented in this report shed light on the molecular details of the folding mechanism of HβB2C in an aqueous environment and may contribute to interpreting different experimental findings. Finally, a detailed knowledge of HβB2C folding may be key to the rational design of potential molecules to treat cataract disease.

Disclosing the Template-Induced Misfolding Mechanism of Tau Protein by Studying the Dissociation of the Boundary Chain from the Formed Tau Fibril Based on a Steered Molecular Dynamics Simulation

The level of tau aggregation into neurofibrillary tangles, including paired helical filament (PHF) and straight filament (SF), is closely associated with Alzheimer's disease. Despite the pathological importance of misfolding and aggregation of tau, the corresponding mechanism remains unclear. Therefore, to uncover the misfolding mechanism of the tau monomer upon induction of formed PHF and SF, in this study, a conventional molecular dynamics simulation combined with a steered molecular dynamics simulation was performed to study the dissociation of the boundary chain. Interestingly, our results show that the dissociation mechanisms of the boundary chain in PHF and SF are different. In PHF, the boundary chain begins to dissociate from regions β2 and β3 and ends at β8. However, in SF, it is simultaneously dissociated from β1 and β8 and ends at β5. The dissociation of the boundary chain is the reverse of template-induced misfolding of the monomer. Therefore, we can deduce the misfolding mechanism of the monomer upon induction of the template. For PHF, β8 first interacts with the template by hydrophobic interaction. Then β7, β6, β5, β4, and β1 sequentially bind to the template by electrostatic and hydrophobic interactions. After β1 binds to the template, β2 and β3 very quickly bind to the template through hydrophobic interaction. For SF, β5 of the monomer first interacts with the template by electrostatic attraction. Then β4 and β6, β3 and β7, and β2 and β8 bind to the template in turn. Finally, β1 and β8 are fully bound to the template by hydrophobic interaction. The obtained results will be vital for understanding the earlier events during misfolding and aggregation of tau.

Improving the productivity of monodisperse polyhedral cages by the rational design of kinetic self-assembly pathways

Hollow polyhedral cages hold great potential for application in nanotechnological and biomedical fields. Understanding the formation mechanism of these self-assembled structures could provide guidance for the rational design of the desired polyhedral cages. Here, by constructing kinetic network models from extensive coarse-grained molecular dynamics simulations, we elucidated the formation mechanism of the dodecahedral cage, which is formed by the self-assembly of patchy particles. We found that the dodecahedral cage is formed through increasing the aggregate size followed by structure rearrangement. Based on this mechanistic understanding, we improved the productivity of the dodecahedral cage through the rational design of the patch arrangement of patchy particles, which promotes the structural rearrangement process. Our results demonstrate that it should be a feasible strategy to achieve the rational design of the desired nanostructures via the kinetic analysis. We anticipate that this methodology could be extended to other self-assembly systems for the fabrication of functional nanomaterials.

Harnessing complexity in molecular self-assembly using computer simulations

In molecular self-assembly, hundreds of thousands of freely-diffusing molecules associate to form ordered and functional architectures in the absence of an actuator. This intriguing phenomenon plays a critical role in biology and has become a powerful tool for the fabrication of advanced nanomaterials. Due to the limited spatial and temporal resolutions of current experimental techniques, computer simulations offer a complementary strategy to explore self-assembly with atomic resolution. Here, we review recent computational studies focusing on both thermodynamic and kinetic aspects. As we shall see, thermodynamic approaches based on modeling and statistical mechanics offer initial guidelines to design nanostructures with modest computational effort. Computationally more intensive analyses based on molecular dynamics simulations and kinetic network models (KNMs) reach beyond it, opening the door to the rational design of self-assembly pathways. Current limitations of these methodologies are discussed. We anticipate that the synergistic use of thermodynamic and kinetic analyses based on computer simulations will provide an important contribution to the de novo design of self-assembly.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.

Efficient sampling over rough energy landscapes with high barriers: A combination of metadynamics with integrated tempering sampling

In order to efficiently overcome high free energy barriers embedded in a complex energy landscape and calculate overall thermodynamics properties using molecular dynamics simulations, we developed and implemented a sampling strategy by combining the metadynamics with (selective) integrated tempering sampling (ITS/SITS) method. The dominant local minima on the potential energy surface (PES) are partially exalted by accumulating history-dependent potentials as in metadynamics, and the sampling over the entire PES is further enhanced by ITS/SITS. With this hybrid method, the simulated system can be rapidly driven across the dominant barrier along selected collective coordinates. Then, ITS/SITS ensures a fast convergence of the sampling over the entire PES and an efficient calculation of the overall thermodynamic properties of the simulation system. To test the accuracy and efficiency of this method, we first benchmarked this method in the calculation of ϕ - ψ distribution of alanine dipeptide in explicit solvent. We further applied it to examine the design of template molecules for aromatic meta-C-H activation in solutions and investigate solution conformations of the nonapeptide Bradykinin involving slow cis-trans isomerizations of three proline residues.

Peptide self-assembly: thermodynamics and kinetics

Self-assembling systems play a significant role in physiological functions and have therefore attracted tremendous attention due to their great potential for applications in energy, biomedicine and nanotechnology. Peptides, consisting of amino acids, are among the most popular building blocks and programmable molecular motifs. Nanostructures and materials assembled using peptides exhibit important potential for green-life new technology and biomedical applications mostly because of their bio-friendliness and reversibility. The formation of these ordered nanostructures pertains to the synergistic effect of various intermolecular non-covalent interactions, including hydrogen-bonding, π-π stacking, electrostatic, hydrophobic, and van der Waals interactions. Therefore, the self-assembly process is mainly driven by thermodynamics; however, kinetics is also a critical factor in structural modulation and function integration. In this review, we focus on the influence of thermodynamic and kinetic factors on structural assembly and regulation based on different types of peptide building blocks, including aromatic dipeptides, amphiphilic peptides, polypeptides, and amyloid-relevant peptides.

Automatic state partitioning for multibody systems (APM): an efficient algorithm for constructing Markov state models to elucidate conformational dynamics of multibody systems

The conformational dynamics of multibody systems plays crucial roles in many important problems. Markov state models (MSMs) are powerful kinetic network models that can predict long-time-scale dynamics using many short molecular dynamics simulations. Although MSMs have been successfully applied to conformational changes of individual proteins, the analysis of multibody systems is still a challenge because of the complexity of the dynamics that occur on a mixture of drastically different time scales. In this work, we have developed a new algorithm, automatic state partitioning for multibody systems (APM), for constructing MSMs to elucidate the conformational dynamics of multibody systems. The APM algorithm effectively addresses different time scales in the multibody systems by directly incorporating dynamics into geometric clustering when identifying the metastable conformational states. We have applied the APM algorithm to a 2D potential that can mimic a protein-ligand binding system and the aggregation of two hydrophobic particles in water and have shown that it can yield tremendous enhancements in the computational efficiency of MSM construction and the accuracy of the models.