Computer simulations of a heterogeneous membrane with enhanced sampling techniques.

Computational determination of the equilibrium state of heterogeneous phospholipid membranes is a significant challenge. We wish to explore the rich phase diagram of these multi-component systems. However, the diffusion and mixing times in membranes are long compared to typical time scales of computer simulations. Here, we evaluate the combination of the enhanced sampling techniques molecular dynamics with alchemical steps and Monte Carlo with molecular dynamics with a coarse-grained model of membranes (Martini) to reduce the number of steps and force evaluations that are needed to reach equilibrium. We illustrate a significant gain compared to straightforward molecular dynamics of the Martini model by factors between 3 and 10. The combination is a useful tool to enhance the study of phase separation and the formation of domains in biological membranes.

A mixed alchemical and equilibrium dynamics to simulate heterogeneous dense fluids: Illustrations for Lennard-Jones mixtures and phospholipid membranes.

An algorithm to efficiently simulate multi-component fluids is proposed and illustrated. The focus is on biological membranes that are heterogeneous and challenging to investigate quantitatively. To achieve rapid equilibration of spatially inhomogeneous fluids, we mix conventional molecular dynamics simulations with alchemical trajectories. The alchemical trajectory switches the positions of randomly selected pairs of molecules and plays the role of an efficient Monte Carlo move. It assists in accomplishing rapid spatial de-correlations. Examples of phase separation and mixing are given in two-dimensional binary Lennard-Jones fluid and a DOPC-POPC membrane. The performance of the algorithm is analyzed, and tools to maximize its efficiency are provided. It is concluded that the algorithm is vastly superior to conventional molecular dynamics for the equilibrium study of biological membranes.

Rock climbing: A local-global algorithm to compute minimum energy and minimum free energy pathways.

The calculation of minimum energy or minimum free energy paths is an important step in the quantitative and qualitative studies of chemical and physical processes. The computations of these coordinates present a significant challenge and have attracted considerable theoretical and computational interest. Here we present a new local-global approach to study reaction coordinates, based on a gradual optimization of an action. Like other global algorithms, it provides a path between known reactants and products, but it uses a local algorithm to extend the current path in small steps. The local-global approach does not require an initial guess to the path, a major challenge for global pathway finders. Finally, it provides an exact answer (the steepest descent path) at the end of the calculations. Numerical examples are provided for the Mueller potential and for a conformational transition in a solvated ring system.

Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with Milestoning.

Reaction coordinates are vital tools for qualitative and quantitative analysis of molecular processes. They provide a simple picture of reaction progress and essential input for calculations of free energies and rates. Iso-committor surfaces are considered the optimal reaction coordinate. We present an algorithm to compute efficiently a sequence of isocommittor surfaces. These surfaces are considered an optimal reaction coordinate. The algorithm analyzes Milestoning results to determine the committor function. It requires only the transition probabilities between the milestones, and not transition times. We discuss the following numerical examples: (i) a transition in the Mueller potential; (ii) a conformational change of a solvated peptide; and (iii) cholesterol aggregation in membranes.

Bimodal Phonon Scattering in Graphene Grain Boundaries.

Graphene has served as the model 2D system for over a decade, and the effects of grain boundaries (GBs) on its electrical and mechanical properties are very well investigated. However, no direct measurement of the correlation between thermal transport and graphene GBs has been reported. Here, we report a simultaneous comparison of thermal transport in supported single crystalline graphene to thermal transport across an individual graphene GB. Our experiments show that thermal conductance (per unit area) through an isolated GB can be up to an order of magnitude lower than the theoretically anticipated values. Our measurements are supported by Boltzmann transport modeling which uncovers a new bimodal phonon scattering phenomenon initiated by the GB structure. In this novel scattering mechanism, boundary roughness scattering dominates the phonon transport in low-mismatch GBs, while for higher mismatch angles there is an additional resistance caused by the formation of a disordered region at the GB. Nonequilibrium molecular dynamics simulations verify that the amount of disorder in the GB region is the determining factor in impeding thermal transport across GBs.

Variation of protein corona composition of gold nanoparticles following plasmonic heating.

It is well recognized that the primary interaction of most biological environments with nanoparticles (NPs) is strongly influenced by a long-lived ("hard") protein corona that surrounds the NP and remains strongly adsorbed to its surface. The amount and composition of associated proteins in the corona adsorbed onto the NPs is related to several important factors, including the physicochemical properties of the NPs and the composition of the protein solution. Here, for the first time, it is shown that plasmonic heat induction (by laser activation) leads to significant changes in the composition of the hard protein corona adsorbed on low aspect ratio gold nanorods. Using mass spectrometry, several proteins in the corona were identified whose concentrations change most substantially as a result of photoinduced (plasmonic) heating versus simple thermal heating. Molecular modeling suggests that the origin of these changes in protein adsorption may be the result of protein conformational changes in response to much higher local temperatures that occur near the gold nanorods during photoinduced, plasmonic heating. These results may define new applications in vivo for NPs with hyperthermia capability and better define the likely interactions of cells with NPs after plasmonic heating. Potential changes in the protein corona following hyperthermia treatment may influence the final biological fate of plasmonic NPs in clinical applications and help elucidate safety considerations for hyperthermia applications.

Rigid-body molecular dynamics of DNA inside a nucleosome.

The majority of eukaryotic DNA, about three quarter, is wrapped around histone proteins forming so-called nucleosomes. To study nucleosomal DNA we introduce a coarse-grained molecular dynamics model based on sequence-dependent harmonic rigid base pair step parameters of DNA and nucleosomal binding sites. Mixed parametrization based on all-atom molecular dynamics and crystallographic data of protein-DNA structures is used for the base pair step parameters. The binding site parameters are adjusted by experimental B-factor values of the nucleosome crystal structure. The model is then used to determine the energy cost for placing a twist defect into the nucleosomal DNA which allows us to use Kramers theory to calculate nucleosome sliding caused by such defects. It is shown that the twist defect scenario together with the sequence-dependent elasticity of DNA can explain the slow time scales observed for nucleosome mobility along DNA. With this method we also show how the twist defect mechanism leads to a higher mobility of DNA in the presence of sin mutations near the dyad axis. Finally, by performing simulations on 5s rDNA, 601, and telomeric base pair sequences, it is demonstrated that the current model is a powerful tool to predict nucleosome positioning.

Design of Peptides for Membrane Insertion: The Critical Role of Charge Separation.

A physical understanding of membrane permeation and translocation by small, positively charged molecules can illuminate cell penetrating peptide mechanisms of entry and inform drug design. We have previously investigated the permeation of the doubly charged peptide WKW and proposed a defect-assisted permeation mechanism where a small molecule with +2 charge can achieve a metastable state spanning the bilayer by forming a membrane defect with charges stabilized by phospholipid phosphate groups. Here, we investigate the membrane permeation of two doubly charged peptides, WWK and WWWK, with charges separated by different lengths. Through complementary experiments and molecular dynamics simulations, we show that membrane permeation was an order of magnitude more favorable when charges were separated by an ∼2-3 Šgreater distance on WWWK compared to WWK. These results agree with the previously proposed defect-assisted permeation mechanism, where a greater distance between positive charges would require a less extreme membrane defect to stabilize the membrane-spanning metastable state. We discuss the implications of these results in understanding the membrane permeation of cell-penetrating peptides and other small, positively charged membrane permeants.

Impact of the Protonation State of Phosphatidylinositol 4,5-Bisphosphate (PIP2) on the Binding Kinetics and Thermodynamics to Transient Receptor Potential Vanilloid (TRPV5): A Milestoning Study.

The binding of phosphatidylinositol 4,5-bisphosphate (PIP2) to the ion channel transient receptor potential vanilloid 5 (TRPV5) is critical for its function. We use atomically detailed simulations and the milestoning theory to compute the free energy profile and the kinetics of PIP2 binding to TRPV5. We estimate the rate of binding and the impact of the protonation state on the process. Several channel residues are identified as influential in the association event and will be interesting targets for mutation analysis. Our simulations reveal that PIP2 binds to TRPV5 in an unprotonated state and is protonated in the membrane. The switch between the protonation state of PIP2 is modeled as a diabatic transition and occurs about halfway through the reaction.

Interfacial Dynamics in Lipid Membranes: The Effects of Headgroup Structures.

Phospholipid membranes support essential biochemical processes, yet remain difficult to characterize due to their compositional and structural heterogeneity. The two most common phospholipid headgroup structures in biological membranes are phosphatidylcholine (PC) and phosphatidylethanolamine (PE), but interactions between PC and PE lipids remain underexplored. In this study, we apply ultrafast two-dimensional infrared (2D IR) spectroscopy to quantify the headgroup effects on interfacial dynamics in PC/PE lipid mixtures. Experiments are interpreted through molecular dynamics simulations using the molecular dynamics with alchemical step (MDAS) algorithm for enhanced sampling. Experimental results indicate that the PE content decreases H-bond formation at the ester carbonyl positions near the lipid membrane's hydrophobic core as a result of increased packing density. The observed dehydration is linked to faster molecular dynamics within the interfacial region.

Graphyne-3: a highly efficient candidate for separation of small gas molecules from gaseous mixtures.

Two-dimensional nanosheets, such as the general family of graphenes have attracted considerable attention over the past decade, due to their excellent thermal, mechanical, and electrical properties. We report on the result of a study of separation of gaseous mixtures by a model graphyne-3 membrane, using extensive molecular dynamics simulations and density functional theory. Four binary and one ternary mixtures of H[Formula: see text], CO[Formula: see text], CH[Formula: see text] and C[Formula: see text]H[Formula: see text] were studied. The results indicate the excellence of graphyne-3 for separation of small gas molecules from the mixtures. In particular, the H[Formula: see text] permeance through the membrane is on the order of [Formula: see text] gas permeation unit, by far much larger than those in other membranes, and in particular in graphene. To gain deeper insights into the phenomenon, we also computed the density profiles and the residence times of the gases near the graphyne-3 surface, as well as their interaction energies with the membrane. The results indicate clearly the tendency of H[Formula: see text] to pass through the membrane at high rates, leaving behind C[Formula: see text]H[Formula: see text] and larger molecules on the surface. In addition, the possibility of chemisorption is clearly ruled out. These results, together with the very good mechanical properties of graphyne-3, confirm that it is an excellent candidate for separating small gas molecules from gaseous mixtures, hence opening the way for its industrial use.

Phase Transition in a Heterogeneous Membrane: Atomically Detailed Picture.

Membranes serve diverse functions in biological systems. Variations in their molecular compositions impact their physical properties and lead to rich phase behavior such as switching from the gel to fluid phase and/or separation to micro- and macrodomains with different molecular compositions. We present a combined computational and experimental study of the phase behavior of a mixed membrane of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) molecules. This heterogeneous membrane changes from gel to fluid and shows separate domains as a function of temperature. Atomically detailed simulations provide microscopic information about these molecular assemblies. However, these systems are challenging for computations since approaching equilibrium necessitates exceptionally long molecular dynamics trajectories. We use the simulation method of MDAS (Molecular Dynamics with Alchemical Steps) to generate adequate statistics. Isotope-edited IR spectroscopy of the lipids was used to benchmark the simulations. Together, simulations and experiments provide insight into the structural and dynamical features of the phase diagram.

Long-time methods for molecular dynamics simulations: Markov State Models and Milestoning.

Molecular dynamics (MD) studies of biomolecules require the ability to simulate complex biochemical systems with an increasingly larger number of particles and for longer time scales, a problem that cannot be overcome by computational hardware advances alone. A main problem springs from the intrinsically high-dimensional and complex nature of the underlying free energy landscape of most systems, and from the necessity to sample accurately such landscapes for identifying kinetic and thermodynamic states in the configurations space, and for accurate calculations of both free energy differences and of the corresponding transition rates between states. Here, we review and present applications of two increasingly popular methods that allow long-time MD simulations of biomolecular systems that can open a broad spectrum of new studies. A first approach, Markov State Models (MSMs), relies on identifying a set of configuration states in which the system resides sufficiently long to relax and loose the memory of previous transitions, and on using simulations for mapping the underlying complex energy landscape and for extracting accurate thermodynamic and kinetic information. The Markovian independence of the underlying transition probabilities creates the opportunity to increase the sampling efficiency by using sets of appropriately initialized short simulations rather than typically long MD trajectories, which also enhances sampling. This allows MSM-based studies to unveil bio-molecular mechanisms and to estimate free energy barriers with high accuracy, in a manner that is both systematic and relatively automatic, which accounts for their increasing popularity. The second approach presented, Milestoning, targets accurate studies of the ensemble of pathways connecting specific end-states (e.g., reactants and products) in a similarly systematic, accurate and highly automatic manner. Applications presented range from studies of conformational dynamics and binding of amyloid-forming peptides, cell-penetrating peptides and the DFG-flip dynamics in Abl kinase. As highlighted by the increasing number of studies using both methods, we anticipate that they will open new avenues for the investigation of systematic sampling of reactions pathways and mechanisms occurring on longer time scales than currently accessible by purely computational hardware developments.

The transition between active and inactive conformations of Abl kinase studied by rock climbing and Milestoning.

BACKGROUND: Kinases are a family of enzymes that catalyze the transfer of the ɤ-phosphate group from ATP to a protein's residue. Malfunctioning kinases are involved in many health problems such as cardiovascular diseases, diabetes, and cancer. Kinases transitions between multiple conformations of inactive to active forms attracted considerable interest. METHOD: A reaction coordinate is computed for the transition between the active to inactive conformation in Abl kinase with a focus on the DFG-in to DFG-out flip. The method of Rock Climbing is used to construct a path locally, which is subsequently optimized using a functional of the entire path. The discrete coordinate sets along the reaction path are used in a Milestoning calculation of the free energy landscape and the rate of the transition. RESULTS: The estimated transition times are between a few milliseconds and seconds, consistent with simulations of the kinetics and with indirect experimental data. The activation requires the transient dissociation of the salt bridge between Lys271 and Glu286. The salt bridge reforms once the DFG motif is stabilized by a locked conformation of Phe382. About ten residues are identified that contribute significantly to the process and are included as part of the reaction space. CONCLUSIONS: The transition from DFG-in to DFG-out in Abl kinase was simulated using atomic resolution of a fully solvated protein yielding detailed description of the kinetics and the mechanism of the DFG flip. The results are consistent with other computational methods that simulate the kinetics and with some indirect experimental measurements. GENERAL SIGNIFICANCE: The activation of kinases includes a conformational transition of the DFG motif that is important for enzyme activity but is not accessible to conventional Molecular Dynamics. We propose a detailed mechanism for the transition, at a timescale longer than conventional MD, using a combination of reaction path and Milestoning algorithms. The mechanism includes local structural adjustments near the binding site as well as collective interactions with more remote residues.

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability.

We investigate the thermodynamics and kinetics of the permeation of a potassium ion through a phospholipid membrane. We illustrate that the conventional reaction coordinate (the position of the ion along the normal to the membrane plane) is insufficient to capture essential elements of the process. It is necessary to add coarse variables that measure membrane distortion. New coarse variables are suggested, and a two-dimensional coarse-space is proposed to describe the permeation. We illustrate path splitting and two transition states of comparable barrier heights. The alternative pathways differ by the extent of water solvation of the ion-phosphate pairs. The permeation process cannot be described by a local one-dimensional reaction coordinate, and a network formulation is more appropriate. We use Milestoning with Voronoi tessellation in two dimensions to quantify the equilibrium and rate of the permeation of the positively charged ion. The permeation coefficient is computed and compared favorably to experiment.

Defect-Assisted Permeation Through a Phospholipid Membrane: Experimental and Computational Study of the Peptide WKW.

We investigate membrane permeation by the peptide WKW that is amidated at its C-terminus and therefore carries a positive charge of +2. To facilitate an efficient calculation, we introduce a novel set of simple coarse variables that measure permeation depth and membrane distortion. The phospholipid head groups shift toward the center of the membrane, following the permeating peptide, and create a defect that assists permeation. The Milestoning algorithm was used in the new coarse space to compute the free-energy profile and the mean first passage time. The barrier was lower than expected from a simple continuum estimate. This behavior is consistent with the known behavior of positively charged cell-penetrating peptides, and is explained by a detailed mechanism of defect formation and propagation revealed by the simulations.

Diffusion and self-assembly of C60 molecules on monolayer graphyne sheets.

The motion of a fullerene (C60) on 5 different types of graphyne is studied by all-atom molecular dynamics simulations and compared with former studies on the motion of C60 on graphene. The motion shows a diffusive behavior which consists of either a continuous motion or discrete movements between trapping sites depending on the type of the graphyne sheet. For graphyne-4 and graphyne-5, fullerenes could detach from the surface of the graphyne sheet at room temperature which was not reported for similar cases on graphene sheets. Collective motion of a group of fullerenes interacting with a graphyne studied and it is shown that fullerenes exhibit stable assemblies. Depending on the type of graphyne, these assemblies can have either single or double layers. The mobility of the assembled structures is also dependent on the type of the graphyne sheet. The observed properties of the motion suggests novel applications for the complexes of fullerene and monolayer graphynes.

Modeling and Analysis of Intercalant Effects on Circular DNA Conformation.

The large-scale conformation of DNA molecules plays a critical role in many basic elements of cellular functionality and viability. By targeting the structural properties of DNA, many cancer drugs, such as anthracyclines, effectively inhibit tumor growth but can also produce dangerous side effects. To enhance the development of innovative medications, rapid screening of structural changes to DNA can provide important insight into their mechanism of interaction. In this study, we report changes to circular DNA conformation from intercalation with ethidium bromide using all-atom molecular dynamics simulations and characterized experimentally by translocation through a silicon nitride solid-state nanopore. Our measurements reveal three distinct current blockade levels and a 6-fold increase in translocation times for ethidium bromide-treated circular DNA as compared to untreated circular DNA. We attribute these increases to changes in the supercoiled configuration hypothesized to be branched or looped structures formed in the circular DNA molecule. Further evidence of the conformational changes is demonstrated by qualitative atomic force microscopy analysis. These results expand the current methodology for predicting and characterizing DNA tertiary structure and advance nanopore technology as a platform for deciphering structural changes of other important biomolecules.