Coarse-grained models reveal functional dynamics--II. Molecular dynamics simulation at the coarse-grained level--theories and biological applications

Investigation of pH-dependent Paclitaxel delivery mechanism employing Chitosan-Eudragit bioresponsive nanocarriers: a molecular dynamics simulation

Before embarking on any experimental research endeavor, it is advisable to do a mathematical computation and thoroughly examine the methodology. Despite the use of polymeric nanocarriers, the regulation of bioavailability and drug release at the disease site remains insufficient. Several effective methods have been devised to address this issue, including the creation of polymeric nanocarriers that can react to stimuli such as redox potential, temperature, pH, and light. The present study has been utilized all-atom molecular dynamics (AA-MD) and coarse-grained molecular dynamics (CG-MD) methods and illustrated the drug release mechanism, which is influenced by pH, for Chitosan-Eudragit bioresponsive nanocarriers. The aim of current work is to study the molecular mechanism and atomistic interactions of PAX delivery using a Chitosan-Eudragit carrier. The ability of Eudragit polymers to dissolve in various organic solvents employed in the process of solvent evaporation is a crucial benefit in enhancing the solubility of pharmaceuticals. This study investigated the use of Chitosan-Eudragit nanocarriers for delivering an anti-tumor drug, namely Paclitaxel (PAX). Upon analyzing several significant factors affecting the stability of the drug and nanocarrier, it has been shown that the level of stability is more significant in the neutral state than the acidic state. Furthermore, the system exhibits higher stability in the neutral state. The used Chitosan-Eudragit nanocarriers exhibit a stable structure under alkaline conditions, but undergo deformation and release their payloads under acidic conditions. It was demonstrated that the in silico analysis of anti-tumor drugs and carriers' integration could be quantified and validated by experimental results (from previous works) at an acceptable level.

Developing Bonded Potentials for a Coarse-Grained Model of Intrinsically Disordered Proteins

Recent advances in residue-level coarse-grained (CG) computational models have enabled molecular-level insights into biological condensates of intrinsically disordered proteins (IDPs), shedding light on the sequence determinants of their phase separation. The existing CG models that treat protein chains as flexible molecules connected via harmonic bonds cannot populate common secondary-structure elements. Here, we present a CG dihedral angle potential between four neighboring beads centered at Cα atoms to faithfully capture the transient helical structures of IDPs. In order to parameterize and validate our new model, we propose Cα-based helix assignment rules based on dihedral angles that succeed in reproducing the atomistic helicity results of a polyalanine peptide and folded proteins. We then introduce sequence-dependent dihedral angle potential parameters (εd) and use experimentally available helical propensities of naturally occurring 20 amino acids to find their optimal values. The single-chain helical propensities from the CG simulations for commonly studied prion-like IDPs are in excellent agreement with the NMR-based α-helix fraction, demonstrating that the new HPS-SS model can accurately produce structural features of IDPs. Furthermore, this model can be easily implemented for large-scale assembly simulations due to its simplicity.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

An Efficient Timer and Sizer of Biomacromolecular Motions

Life ticks as fast as how proteins move. Computationally expensive molecular dynamics simulation has been the only theoretical tool to gauge the time and sizes of these motions, though barely to their slowest ends. Here, we convert a computationally cheap elastic network model (ENM) into a molecular timer and sizer to gauge the slowest functional motions of structured biomolecules. Quasi-harmonic analysis, fluctuation profile matching, and the Wiener-Khintchine theorem are used to define the "time periods," t, for anharmonic principal components (PCs), which are validated by nuclear magnetic resonance (NMR) order parameters. The PCs with their respective "time periods" are mapped to the eigenvalues (λ_ENM) of the corresponding ENM modes. Thus, the power laws t(ns) = 56.1λ_ENM^-1.6 and σ²(Ų) = 32.7λ_ENM^-3.0 can be established allowing the characterization of the timescales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter.

Dissolution and Hydrolysis of Bleached Kraft Pulp Using Ionic Liquids

Forestry industries in Chile are facing an important challenge-diversifying their products using green technologies. In this study, the potential use of Ionic Liquids (ILs) to dissolve and hydrolyze eucalyptus wood (mix of Eucalyptus nitens and Eucalyptus globulus) kraft pulp was studied. The Bleached Hardwood Kraft Pulp (BHKP) from a Chilean pulp mill was used together with five different ILs: 1-butyl-3-methylimidazolium chloride [bmim][Cl], 1-butyl-3-methylimidazolium acetate [bmim][Ac], 1-butyl-3-methylimidazolium hydrogen sulfate [bmim][HSO4], 1-ethyl-3-methylimidazolium chloride [emim][Cl], 1-ethyl-3-methylimidazolium acetate [emim][Ac]. Experimentally, one vacuum reactor was designed to study the dissolution/hydrolysis process for each ILs; particularly, the cellulose dissolution process using [bmim][Cl] was studied proposing one molecular dynamic model. Experimental characterization using Atomic Force Microscopy, conductometric titration, among other techniques suggest that all ILs are capable of cellulose dissolution at different levels; in some cases, the dissolution evolved to partial hydrolysis appearing cellulose nanocrystals (CNC) in the form of spherical aggregates with a diameter of 40-120 nm. Molecular dynamics simulations showed that the [bmim][Cl] anions tend to interact actively with cellulose sites and water molecules in the dissolution process. The results showed the potential of some ILs to dissolve/hydrolyze the cellulose from Chilean Eucalyptus, maintaining reactive forms.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

Molecular dynamics exploration of poration and leaking caused by Kalata B1 in HIV-infected cell membrane compared to host and HIV membranes

The membrane disruption activities of kalata B1 (kB1) were investigated using molecular dynamics simulations with membrane models. The models were constructed to mimic the lipid microdomain formation in membranes of HIV particle, HIV-infected cell, and host cell. The differences in the lipid ratios of these membranes caused the formation of liquid ordered (lo) domains of different sizes, which affected the binding and activity of kB1. Stronger kB1 disruptive activity was observed for the membrane with small sized lo domain. Our results show that kB1 causes membrane leaking without bilayer penetration. The membrane poration mechanism involved in the disorganization of the lo domain and in cholesterol inter-leaflet translocation is described. This study enhances our understanding of the membrane activity of kB1, which may be useful for designing novel and potentially therapeutic peptides based on the kB1 framework.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Many proteins are nanomachines that perform mechanical or chemical work by changing their three-dimensional shape and cycle between multiple conformational states. Computer simulations of such conformational transitions provide mechanistic insights into protein function but such simulations have been challenging. In particular, it is not clear how to quantitatively compare current simulation methods or to assess their accuracy. To that end, we present a general and flexible computational framework for quantifying transition paths—by measuring mutual geometric similarity—that, compared with existing approaches, requires minimal a-priori assumptions and can take advantage of full atomic detail alongside heuristic information derived from intuition. Using our Path Similarity Analysis (PSA) framework in parallel with several existing quantitative approaches, we examine transitions generated for a toy model of a transition and two biological systems, the enzyme adenylate kinase and diphtheria toxin. Our results show that PSA enables the quantitative comparison of different path sampling methods and aids the identification of potentially important atomistic motions by exploiting geometric information in transition paths. The method has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing macromolecular conformational transitions.

Defining the membrane disruption mechanism of kalata B1 via coarse-grained molecular dynamics simulations

Kalata B1 has been demonstrated to have bioactivity relating to membrane disruption. In this study, we conducted coarse-grained molecular dynamics simulations to gain further insight into kB1 bioactivity. The simulations were performed at various concentrations of kB1 to capture the overall progression of its activity. Two configurations of kB1 oligomers, termed tower-like and wall-like clusters, were detected. The conjugation between the wall-like oligomers resulted in the formation of a ring-like hollow in the kB1 cluster on the membrane surface. Our results indicated that the molecules of kB1 were trapped at the membrane-water interface. The interfacial membrane binding of kB1 induced a positive membrane curvature, and the lipids were eventually extracted from the membrane through the kB1 ring-like hollow into the space inside the kB1 cluster. These findings provide an alternative view of the mechanism of kB1 bioactivity that corresponds with the concept of an interfacial bioactivity model.

Multiscale modeling of cellular actin filaments: from atomistic molecular to coarse-grained dynamics

In this article, we present a computational multiscale model for the characterization of subcellular proteins. The model is encoded inside a simulation tool that builds coarse-grained (CG) force fields from atomistic simulations. Equilibrium molecular dynamics simulations on an all-atom model of the actin filament are performed. Then, using the statistical distribution of the distances between pairs of selected groups of atoms at the output of the MD simulations, the force field is parameterized using the Boltzmann inversion approach. This CG force field is further used to characterize the dynamics of the protein via Brownian dynamics simulations. This combination of methods into a single computational tool flow enables the simulation of actin filaments with length up to 400 nm, extending the time and length scales compared to state-of-the-art approaches. Moreover, the proposed multiscale modeling approach allows to investigate the relationship between atomistic structure and changes on the overall dynamics and mechanics of the filament and can be easily (i) extended to the characterization of other subcellular structures and (ii) used to investigate the cellular effects of molecular alterations due to pathological conditions.

PCDB: a database of protein conformational diversity

PCDB (http://www.pcdb.unq.edu.ar) is a database of protein conformational diversity. For each protein, the database contains the redundant compilation of all the corresponding crystallographic structures obtained under different conditions. These structures could be considered as different instances of protein dynamism. As a measure of the conformational diversity we use the maximum RMSD obtained comparing the structures deposited for each domain. The redundant structures were extracted following CATH structural classification and cross linked with additional information. In this way it is possible to relate a given amount of conformational diversity with different levels of information, such as protein function, presence of ligands and mutations, structural classification, active site information and organism taxonomy among others. Currently the database contains 7989 domains with a total of 36581 structures from 4171 different proteins. The maximum RMSD registered is 26.7 Å and the average of different structures per domain is 4.5.

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions of various biological nanomachines. Coarse-grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse-grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP-driven transitions in three important biological nanomachines (myosin, F(1) ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines.

How to predict diffusion of medium-sized molecules in polymer matrices. From atomistic to coarse grain simulations

The normal diffusion regime of many small and medium-sized molecules occurs on a time scale that is too long to be studied by atomistic simulations. Coarse-grained (CG) molecular simulations allow to investigate length and time scales that are orders of magnitude larger compared to classical molecular dynamics simulations, hence providing a valuable approach to span time and length scales where normal diffusion occurs. Here we develop a novel multi-scale method for the prediction of diffusivity in polymer matrices which combines classical and CG molecular simulations. We applied an atomistic-based method in order to parameterize the CG MARTINI force field, providing an extension for the study of diffusion behavior of penetrant molecules in polymer matrices. As a case study, we found the parameters for benzene (as medium sized penetrant molecule whose diffusivity cannot be determined through atomistic models) and Poly (vinyl alcohol) (PVA) as polymer matrix. We validated our extended MARTINI force field determining the self diffusion coefficient of benzene (2.27·10⁻⁹m² s⁻¹) and the diffusion coefficient of benzene in PVA (0.263·10⁻¹² m² s⁻¹). The obtained diffusion coefficients are in remarkable agreement with experimental data (2.20·10⁻⁹m² s⁻¹ and 0.25·10⁻¹² m² s⁻¹, respectively). We believe that this method can extend the application range of computational modeling, providing modeling tools to study the diffusion of larger molecules and complex polymeric materials.