Revealing Thermodynamics and Kinetics of Lipid Self-Assembly by Markov State Model Analysis

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.

Impact of Nonnative Interactions on the Binding Kinetics of Intrinsically Disordered p53 with MDM2: Insights from All-Atom Simulation and Markov State Model Analysis

Intrinsically disordered proteins (IDPs) lack a well-defined tertiary structure but are essential players in various biological processes. Their ability to undergo a disorder-to-order transition upon binding to their partners, known as the folding-upon-binding process, is crucial for their function. One classical example is the intrinsically disordered transactivation domain (TAD) of the tumor suppressor protein p53, which quickly forms a structured α-helix after binding to its partner MDM2, with clinical significance for cancer treatment. However, the contribution of nonnative interactions between the IDP and its partner to the rapid binding kinetics, as well as their interplay with native interactions, is not well understood at the atomic level. Here, we used molecular dynamics simulation and Markov state model (MSM) analysis to study the folding-upon-binding mechanism between p53-TAD and MDM2. Our results suggest that the system progresses from the nascent encounter complex to the well-structured encounter complex and finally reaches the native complex, following an induced-fit mechanism. We found that nonnative hydrophobic and hydrogen bond interactions, combined with native interactions, effectively stabilize the nascent and well-structured encounter complexes. Among the nonnative interactions, Leu25p53-Leu54MDM2 and Leu25p53-Phe55MDM2 are particularly noteworthy, as their interaction strength is close to the optimum. Evidently, strengthening or weakening these interactions could both adversely affect the binding kinetics. Overall, our findings suggest that nonnative interactions are evolutionarily optimized to accelerate the binding kinetics of IDPs in conjunction with native interactions.

Strategies to reduce the risks of mRNA drug and vaccine toxicity

mRNA formulated with lipid nanoparticles is a transformative technology that has enabled the rapid development and administration of billions of coronavirus disease 2019 (COVID-19) vaccine doses worldwide. However, avoiding unacceptable toxicity with mRNA drugs and vaccines presents challenges. Lipid nanoparticle structural components, production methods, route of administration and proteins produced from complexed mRNAs all present toxicity concerns. Here, we discuss these concerns, specifically how cell tropism and tissue distribution of mRNA and lipid nanoparticles can lead to toxicity, and their possible reactogenicity. We focus on adverse events from mRNA applications for protein replacement and gene editing therapies as well as vaccines, tracing common biochemical and cellular pathways. The potential and limitations of existing models and tools used to screen for on-target efficacy and de-risk off-target toxicity, including in vivo and next-generation in vitro models, are also discussed.

Self-assembly morphology transition mechanism of similar amphiphilic molecules

Molecular self-assembly is a powerful synthesis method for nanomaterials. Promoting the development of self-assembly is not only conducive to the efficient preparation of nanomaterials but also promotes progress in other research fields. Therefore, it is necessary to enhance the advancement of molecular self-assembly, and the key is to deepen the understanding of the correlation between molecular characteristics and self-assembly morphologies. However, some similar amphipihlic molecules self-assemble into assemblies with significant morphology difference, which is challenging to clear the mechanism for experimenters. In this work, we explore the microscopic mechanism of six similar molecules by MD simulations, and the influences of molecular conformation, atomic groups, and polycyclic aromatic hydrocarbons on morphologies are discussed in detail. Our findings enrich the design principles of amphiphilic molecules for self-assembly, which promotes the modular design of molecular self-assembly.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

GraphVAMPnets for uncovering slow collective variables of self-assembly dynamics

Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers, and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenges. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, such as time-structure independent component analysis, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets, which combines graph neural networks with a variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory, which studies Markov processes without forcing detailed balance constraints, which addresses the out-of-equilibrium challenge in the self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: the aggregation of two hydrophobic molecules and the self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely applied to molecular self-assembly.

Nucleotide addition and cleavage by RNA polymerase II: Coordination of two catalytic reactions using a single active site

RNA polymerase II (Pol II) incorporates complementary ribonucleotides into the growing RNA chain one at a time via the nucleotide addition cycle. The nucleotide addition cycle, however, is prone to misincorporation of noncomplementary nucleotides. Thus, to ensure transcriptional fidelity, Pol II backtracks and then cleaves the misincorporated nucleotides. These two reverse reactions, nucleotide addition and cleavage, are catalyzed in the same active site of Pol II, which is different from DNA polymerases or other endonucleases. Recently, substantial progress has been made to understand how Pol II effectively performs its dual role in the same active site. Our review highlights these recent studies and provides an overall model of the catalytic mechanisms of Pol II. In particular, RNA extension follows the two-metal-ion mechanism, and several Pol II residues play important roles to facilitate the catalysis. In sharp contrast, the cleavage reaction is independent of any Pol II residues. Interestingly, Pol II relies on its residues to recognize the misincorporated nucleotides during the backtracking process, prior to cleavage. In this way, Pol II efficiently compartmentalizes its two distinct catalytic functions using the same active site. Lastly, we also discuss a new perspective on the potential third Mg²⁺ in the nucleotide addition and intrinsic cleavage reactions.

Recent Advances of Studies on Cell-Penetrating Peptides Based on Molecular Dynamics Simulations

With the ability to transport cargo molecules across cell membranes with low toxicity, cell-penetrating peptides (CPPs) have become promising candidates for next generation peptide-based drug delivery vectors. Over the past three decades since the first CPP was discovered, a great deal of work has been done on the cellular uptake mechanisms and the applications for the delivery of therapeutic molecules, and significant advances have been made. But so far, we still do not have a precise and unified understanding of the structure-activity relationship of the CPPs. Molecular dynamics (MD) simulations provide a method to reveal peptide-membrane interactions at the atomistic level and have become an effective complement to experiments. In this paper, we review the progress of the MD simulations on CPP-membrane interactions, including the computational methods and technical improvements in the MD simulations, the research achievements in the CPP internalization mechanism, CPP decoration and coupling, and the peptide-induced membrane reactions during the penetration process, as well as the comparison of simulated and experimental results.

Modeling Polyzwitterion-Based Drug Delivery Platforms: A Perspective of the Current State-of-the-Art and Beyond

Drug delivery platforms are anticipated to have biocompatible and bioinert surfaces. PEGylation of drug carriers is the most approved method since it improves water solubility and colloid stability and decreases the drug vehicles’ interactions with blood components. Although this approach extends their biocompatibility, biorecognition mechanisms prevent them from biodistribution and thus efficient drug transfer. Recent studies have shown (poly)zwitterions to be alternatives for PEG with superior biocompatibility. (Poly)zwitterions are super hydrophilic, mainly stimuli-responsive, easy to functionalize and they display an extremely low protein adsorption and long biodistribution time. These unique characteristics make them already promising candidates as drug delivery carriers. Furthermore, since they have highly dense charged groups with opposite signs, (poly)zwitterions are intensely hydrated under physiological conditions. This exceptional hydration potential makes them ideal for the design of therapeutic vehicles with antifouling capability, i.e., preventing undesired sorption of biologics from the human body in the drug delivery vehicle. Therefore, (poly)zwitterionic materials have been broadly applied in stimuli-responsive “intelligent” drug delivery systems as well as tumor-targeting carriers because of their excellent biocompatibility, low cytotoxicity, insignificant immunogenicity, high stability, and long circulation time. To tailor (poly)zwitterionic drug vehicles, an interpretation of the structural and stimuli-responsive behavior of this type of polymer is essential. To this end, a direct study of molecular-level interactions, orientations, configurations, and physicochemical properties of (poly)zwitterions is required, which can be achieved via molecular modeling, which has become an influential tool for discovering new materials and understanding diverse material phenomena. As the essential bridge between science and engineering, molecular simulations enable the fundamental understanding of the encapsulation and release behavior of intelligent drug-loaded (poly)zwitterion nanoparticles and can help us to systematically design their next generations. When combined with experiments, modeling can make quantitative predictions. This perspective article aims to illustrate key recent developments in (poly)zwitterion-based drug delivery systems. We summarize how to use predictive multiscale molecular modeling techniques to successfully boost the development of intelligent multifunctional (poly)zwitterions-based systems.

Accurate and Efficient Estimation of Lennard-Jones Interactions for Coarse-Grained Particles via a Potential Matching Method

The Lennard-Jones (LJ) energy functions are commonly used to describe the nonbonded interactions in bulk coarse-grained (CG) models, which contribute significantly to the stabilization of a local binding configuration or a self-assembly system. In many cases, systematic development of the LJ interaction parameters in a CG model requires a comprehensive sampling of the objective molecules at the all-atom (AA) level, which is therefore extremely time-consuming for large systems. Inspired by the concept of electrostatic potential (ESP), we define the LJ static potential (LJSP), by which the embedding potential energy surface can be constructed analytically. A semianalytic approach, namely, the LJSP matching method, is developed here to derive the CG parameters by minimizing the LJSP difference between the AA and the CG models, which provides a universal way to derive the CG LJ parameters from the AA models without doing presampling. The LJSP matching method is successful not only in deriving the LJ interaction energy landscape in the CG models for proteins, lipids, and DNA but also in reproducing the critical properties such as intermediate structures and enthalpy contributions as exemplified in simulating the self-assembly process of the dipalmitoylphosphatidylcholine (DPPC) lipids.

Nanoparticle cluster formation mechanisms elucidated via Markov state modeling: Attraction range effects, aggregation pathways, and counterintuitive transition rates

Nanoparticle clusters are promising candidates for developing functional materials. However, it is still a challenging task to fabricate them in a predictable and controllable way, which requires investigation of the possible mechanisms underlying cluster formation at the nanoscale. By constructing Markov state models (MSMs) at the microstate level, we find that for highly dispersed particles to form a highly aggregated cluster, there are multiple coexisting pathways, which correspond to direct aggregation, or pathways that need to pass through partially aggregated, intermediate states. Varying the range of attraction between nanoparticles is found to significantly affect pathways. As the attraction range becomes narrower, compared to direct aggregation, some pathways that need to pass through partially aggregated intermediate states become more competitive. In addition, from MSMs constructed at the macrostate level, the aggregation rate is found to be counterintuitively lower with a lower free-energy barrier, which is also discussed.

Molecular View on the Impact of DHA Molecules on the Physical Properties of a Model Cell Membrane

Docosahexaenoic acid (DHA) is a ω-3 polyunsaturated fatty acid, which can be uptaken by cells and is essential for proper neuronal and retinal function. However, the detailed physical impact of DHA molecules on the plasma membrane is still unclear. Hence, in this work, we carried out μs-scale coarse-grained molecular dynamics (MD) simulations to reveal the interactions between DHA molecules and a model cell membrane. As is known, the cell membrane can segregate into liquid-ordered (L_o) and liquid-disordered (L_d) membrane domains due to the differential interactions between lipids and proteins. In order to capture this feature, we adopted the three-component phase-separated lipid membranes and considered both anionic and neutral DHA molecules in the current work. Our results showed that DHA molecules can spontaneously self-assemble into nanoclusters, fuse with lipid membranes, and localize preferably in L_d membrane domains. During the membrane fusion process, DHA molecules can change the intrinsic transmembrane potential of the lipid membrane, and the effects of anionic DHA molecules are much more significant. Besides, the presence of DHA molecules mainly in the L_d membrane domains could regulate the differences in the lipid chain order, membrane thickness, cholesterol preference, and cholesterol flip-flop basically in a concentration-dependent manner, which further promote the stability of the intraleaflet dynamics and inhibit the interleaflet dynamics (or promote membrane domain registration) of the membrane domains. In short, the impact of DHA molecules on the physical properties of a model cell membrane on the molecular level revealed in our work will provide useful insights for understanding the biological functions of DHA molecules.

RPnet: a reverse-projection-based neural network for coarse-graining metastable conformational states for protein dynamics

The Markov State Model (MSM) is a powerful tool for modeling long timescale dynamics based on numerous short molecular dynamics (MD) simulation trajectories, which makes it a useful tool for elucidating the conformational changes of biological macromolecules. By partitioning the phase space into discretized states and estimating the probabilities of inter-state transitions based on short MD trajectories, one can construct a kinetic network model that could be used to extrapolate long-timescale kinetics if the Markovian condition is met. However, meeting the Markovian condition often requires hundreds or even thousands of states (microstates), which greatly hinders the comprehension of the conformational dynamics of complex biomolecules. Kinetic lumping algorithms can coarse grain numerous microstates into a handful of metastable states (macrostates), which would greatly facilitate the elucidation of biological mechanisms. In this work, we have developed a reverse-projection-based neural network (RPnet) to lump microstates into macrostates, by making use of a physics-based loss function that is based on the projection operator framework of conformational dynamics. By recognizing that microstate and macrostate transition modes can be related through a projection process, we have developed a reverse-projection scheme to directly compare the microstate and macrostate dynamics. Based on this reverse-projection scheme, we designed a loss function that allows the effective assessment of the quality of a given kinetic lumping. We then make use of a neural network to efficiently minimize this loss function to obtain an optimized set of macrostates. We have demonstrated the power of our RPnet in analyzing the dynamics of a numerical 2D potential, alanine dipeptide, and the clamp opening of an RNA polymerase. In all these systems, we have illustrated that our method could yield comparable or better results than competing methods in terms of state partitioning and reproduction of slow dynamics. We expect that our RPnet holds promise in analyzing the conformational dynamics of biological macromolecules.

Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning

Markov state models (MSMs) based on molecular dynamics (MD) simulations are routinely employed to study protein folding, however, their application to functional conformational changes of biomolecules is still limited. In the past few years, the field of computational chemistry has experienced a surge of advancements stemming from machine learning algorithms, and MSMs have not been left out. Unlike global processes, such as protein folding, the application of MSMs to functional conformational changes is challenging because they mostly consist of localized structural transitions. Therefore, it is critical to properly select a subset of structural features that can describe the slowest dynamics of these functional conformational changes. To address this challenge, we recommend several automatic feature selection methods such as Spectral-OASIS. To identify states in MSMs, the chosen features can be subject to dimensionality reduction methods such as TICA or deep learning based VAMPNets to project MD conformations onto a few collective variables for subsequent clustering. Another challenge for the application of MSMs to the study of functional conformational changes is the ability to comprehend their biophysical mechanisms, as MSMs built for these processes often require a large number of states. We recommend the recently developed quasi-MSMs (qMSMs) to address this issue. Compared to MSMs, qMSMs encode the non-Markovian dynamics via the generalized master equation and can significantly reduce the number of states. As a result, qMSMs can be built with a handful of states to facilitate the interpretation of functional conformational changes. In the wake of machine learning, we believe that the rapid advancement in the MSM methodology will lead to their wider application in studying functional conformational changes of biomolecules.

Temperature-dependent kinetic pathways of heterogeneous ice nucleation competing between classical and non-classical nucleation

Ice nucleation on the surface plays a vital role in diverse areas, ranging from physics and cryobiology to atmospheric science. Compared to ice nucleation in the bulk, the water-surface interactions present in heterogeneous ice nucleation complicate the nucleation process, making heterogeneous ice nucleation less comprehended, especially the relationship between the kinetics and the structures of the critical ice nucleus. Here we combine Markov State Models and transition path theory to elucidate the ensemble pathways of heterogeneous ice nucleation. Our Markov State Models reveal that the classical one-step and non-classical two-step nucleation pathways can surprisingly co-exist with comparable fluxes at T = 230 K. Interestingly, we find that the disordered mixing of rhombic and hexagonal ice leads to a favorable configurational entropy that stabilizes the critical nucleus, facilitating the non-classical pathway. In contrast, the favorable energetics promotes the formation of hexagonal ice, resulting in the classical pathway. Furthermore, we discover that, at elevated temperatures, the nucleation process prefers to proceed via the classical pathway, as opposed to the non-classical pathway, since the potential energy contributions override the configurational entropy compensation. This study provides insights into the mechanisms of heterogeneous ice nucleation and sheds light on the rational designs to control crystallization processes.