Computational Estimation of Microsecond to Second Atomistic Folding Times.

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 µs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τf = 0.8-9 µs), NTL9 at water-like viscosity (τf = 0.2-2 ms), and Protein G at low viscosity (τf = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Nanobubbles, cavitation, shock waves and traumatic brain injury.

Collapse of bubbles, microscopic or nanoscopic, due to their interaction with the impinging pressure wave produces a jet of particles moving in the direction of the wave. If there is a surface nearby, the high-speed jet particles hit it, and as a result damage to the surface is produced. This cavitation effect is well known and intensely studied in case of microscopic sized bubbles. It can be quite damaging to materials, including biological tissues, but it can also be beneficial when controlled, like in case of sonoporation of biological membranes for the purpose of drug delivery. Here we consider recent simulation work performed to study collapse of nanobubbles exposed to shock waves, in order to understand the detailed mechanism of the cavitation induced damage to soft materials, such as biological membranes. We also discuss the connection of the cavitation effect with the traumatic brain injury caused by blasts. Specifically, we consider possible damage to model membranes containing lipid bilayers, bilayers with embedded ion channel proteins like the ones found in neural cells and also protein assemblies found in the tight junction of the blood brain barrier.

Effects of charge and substituent on the S···N chalcogen bond.

Neutral complexes containing a S···N chalcogen bond are compared with similar systems in which a positive charge has been added to the S-containing electron acceptor, using high-level ab initio calculations. The effects on both XS···N and XS(+)···N bonds are evaluated for a range of different substituents X = CH3, CF3, NH2, NO2, OH, Cl, and F, using NH3 as the common electron donor. The binding energy of XMeS···NH3 varies between 2.3 and 4.3 kcal/mol, with the strongest interaction occurring for X = F. The binding is strengthened by a factor of 2-10 in charged XH2S(+)···NH3 complexes, reaching a maximum of 37 kcal/mol for X = F. The binding is weakened to some degree when the H atoms are replaced by methyl groups in XMe2S(+)···NH3. The source of the interaction in the charged systems, like their neutral counterparts, is derived from a charge transfer from the N lone pair into the σ*(SX) antibonding orbital, supplemented by a strong electrostatic and smaller dispersion component. The binding is also derived from small contributions from a CH···N H-bond involving the methyl groups, which is most notable in the weaker complexes.

Conservation and functional importance of carbon-oxygen hydrogen bonding in AdoMet-dependent methyltransferases.

S-adenosylmethionine (AdoMet)-based methylation is integral to metabolism and signaling. AdoMet-dependent methyltransferases belong to multiple distinct classes and share a catalytic mechanism that arose through convergent evolution; however, fundamental determinants underlying this shared methyl transfer mechanism remain undefined. A survey of high-resolution crystal structures reveals that unconventional carbon-oxygen (CH···O) hydrogen bonds coordinate the AdoMet methyl group in different methyltransferases irrespective of their class, active site structure, or cofactor binding conformation. Corroborating these observations, quantum chemistry calculations demonstrate that these charged interactions formed by the AdoMet sulfonium cation are stronger than typical CH···O hydrogen bonds. Biochemical and structural studies using a model lysine methyltransferase and an active site mutant that abolishes CH···O hydrogen bonding to AdoMet illustrate that these interactions are important for high-affinity AdoMet binding and transition-state stabilization. Further, crystallographic and NMR dynamics experiments of the wild-type enzyme demonstrate that the CH···O hydrogen bonds constrain the motion of the AdoMet methyl group, potentially facilitating its alignment during catalysis. Collectively, the experimental findings with the model methyltransferase and structural survey imply that methyl CH···O hydrogen bonding represents a convergent evolutionary feature of AdoMet-dependent methyltransferases, mediating a universal mechanism for methyl transfer.

Preferred configurations of peptide-peptide interactions.

The natural and fundamental proclivities of interaction between a pair of peptide units are examined using high-level ab initio calculations. The NH···O H-bonded structure is found to be the most stable configuration of the N-methylacetamide (NMA) model dimer, but only slightly more so than a stacked arrangement. The H-bonded geometry is destabilized by only a small amount if the NH group is lifted out of the plane of the proton-accepting amide. This out-of-plane motion is facilitated by a stabilizing charge transfer from the CO π bond to the NH σ* antibonding orbital. The parallel and antiparallel stacked dimers are nearly equal in energy, both only slightly less stable than the NH···O H-bonded structure. Both are stabilized by a combination of CH···O H-bonding and a π→π* transfer between the two CO bonds. There are no minima on the surface that are associated with O(lp)→π*(CO) transfers, due in large part to strong electrostatic repulsion between the two O atoms, which resists an approach of a carbonyl O from above the C=O bond of the other amide.

Magnitude and mechanism of charge enhancement of CH··O hydrogen bonds.

Quantum calculations find that neutral methylamines and thioethers form complexes, with N-methylacetamide (NMA) as proton acceptor, with binding energies of 2-5 kcal/mol. This interaction is magnified by a factor of 4-9, bringing the binding energy up to as much as 20 kcal/mol, when a CH3(+) group is added to the proton donor. Complexes prefer trifurcated arrangements, wherein three separate methyl groups donate a proton to the O acceptor. Binding energies lessen when the systems are immersed in solvents of increasing polarity, but the ionic complexes retain their favored status even in water. The binding energy is reduced when the methyl groups are replaced by longer alkyl chains. The proton acceptor prefers to associate with those CH groups that are as close as possible to the S/N center of the formal positive charge. A single linear CH··O hydrogen bond (H-bond) is less favorable than is trifurcation with three separate methyl groups. A trifurcated arrangement with three H atoms of the same methyl group is even less favorable. Various means of analysis, including NBO, SAPT, NMR, and electron density shifts, all identify the (+)CH··O interaction as a true H-bond.

A Suite of Tutorials for the WESTPA 2.0 Rare-Events Sampling Software [Article v2.0].

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations.

Contributions of various noncovalent bonds to the interaction between an amide and S-containing molecules.

N-Methylacetamide, a model of the peptide unit in proteins, is allowed to interact with CH(3) SH, CH(3)SCH(3), and CH(3)SSCH(3) as models of S-containing amino acid residues. All of the minima are located on the ab initio potential energy surface of each heterodimer. Analysis of the forces holding each complex together identifies a variety of different attractive forces, including SH⋅⋅⋅O, NH⋅⋅⋅S, CH⋅⋅⋅O, CH⋅⋅⋅S, SH⋅⋅⋅π, and CH⋅⋅⋅π H-bonds. Other contributing noncovalent bonds involve charge transfer into σ* and π* antibonds. Whereas some of the H-bonds are strong enough that they represent the sole attractive force in several dimers, albeit not usually in the global minimum, charge-transfer-type noncovalent bonds play only a supporting role. The majority of dimers are bound by a collection of several of these attractive interactions. The SH⋅⋅⋅O and NH⋅⋅⋅S H-bonds are of comparable strength, followed by CH⋅⋅⋅O and CH⋅⋅⋅S.

Substituent effects on CL···N, S···N, and P···N noncovalent bonds.

Cl, S, and P atoms have previously been shown as capable of engaging in a noncovalent bond with the N atom on another molecule. The effects of substituents B on the former atoms on the strength of this bond are examined, and it is found that the binding energy climbs in the order B = CH(3) < NH(2) < CF(3) < OH < Cl < NO(2) < F. However, there is some variability in this pattern, particularly for the NO(2) group. The A···N bonds (A = Cl, S, P) can be quite strong, amounting to as much as 10 kcal/mol. The binding energy arises from approximately equal contributions from its induction and electrostatic components, although the former becomes more dominant for the stronger bonds. The induction energy is due in large measure to the transfer of charge from the N lone pair to a B-A σ* antibonding orbital of the electron-acceptor molecule containing Cl, S, or P. These A···N bonds typically represent the lowest-energy structure on each potential energy surface, stronger than H-bonds such as NH···F, CH···N, or SH···N.

Abilities of different electron donors (D) to engage in a P···D noncovalent interaction.

Previous work has documented the ability of the P atom to form a direct attractive noncovalent interaction with a N atom, based in large measure on the charge transfer from the N lone pair into the σ* antibonding orbital of the P-H that is turned away from the N atom. The present work considers whether other atoms, namely, O and S, can also participate as electron donors, and in which bonding environments. Also considered are the π-systems of multiply bonded C atoms. Unlike an earlier observation that the interaction is unaffected by the nature of the electron-acceptor atom, there is strong sensitivity to the donor. The P···D binding energy diminishes in the order D = NH(3) > H(2)CO > H(2)CS > H(2)O > H(2)S, different from the patterns observed in both H and halogen bonds. The P···D interactions are comparable to, and in some cases stronger than, the analogous H-bonds formed by HOH as proton donor. The carbon π systems form surprisingly strong P···D complexes, augmented by the back-donation from the P lone pair to the C-C π* antibond, which surpass the strengths of H-bonds, even some with HF as proton donor.

Comparison of P···D (D = P,N) with other noncovalent bonds in molecular aggregates.

All the minima on the potential energy surfaces of homotrimers and tetramers of PH(3) are identified and analyzed as to the source of their stability. The same is done with mixed trimers in which one PH(3) molecule is replaced by either NH(3) or PFH(2). The primary noncovalent attraction in all global minima is the BP···D (D = N,P) bond which is characterized by the transfer of charge from a lone pair of the donor D to a σ∗ B-P antibond of the partner molecule which is turned away from D, the same force earlier identified in the pertinent dimers. Examination of secondary minima reveals the presence of other weaker forces, some of which do not occur within the dimers. Examples of the latter include PH···P, NH···P, and PH···F H-bonds, and "reverse" H-bonds in which the source of the electron density is the smaller tail lobe of the donor lone pair. The global minima are cyclic structures in all cases, and exhibit some cooperativity, albeit to a small degree. The energy spacing of the oligomers is much smaller than that in the corresponding strongly H-bonded complexes such as the water trimer.

A Suite of Tutorials for the WESTPA Rare-Events Sampling Software [Article v1.0].

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present five tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. Users are expected to already have significant experience with running standard molecular dynamics simulations using the underlying dynamics engine of interest (e.g. Amber, Gromacs, OpenMM). The tutorials range from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding.

Properties of Poloxamer Molecules and Poloxamer Micelles Dissolved in Water and Next to Lipid Bilayers: Results from Computer Simulations.

To study the properties of poloxamer molecules P85 and P188 and micelles containing these poloxamers in bulk water and also next to lipid bilayers, we performed coarse-grained molecular dynamics computer simulations. We used MARTINI force-field and adjusted Lennard-Jones nonbonded interaction strength parameters for poloxamer beads to take into account the presence of polarizable water. Simulations of systems containing poloxamer molecules or micelles solvated in bulk water showed that structural properties, such as radii of gyration of the molecules and micelles, agree with the ones inferred from experiments. We observed that P85 micelle is almost spherical in shape, whereas the P188 micelle is distorted from being spherical. Simulations containing systems with the water-lipid bilayer interface showed that hydrophilic blocks of poloxamers interact with lipid headgroups of the bilayer and remain at the interface, whereas hydrophobic blocks prefer to insert into the central hydrophobic region of the bilayer. Simulations containing poloxamer micelles next to lipid bilayer showed no permeation of these micelles into the bilayer. To study the "healing" properties of P188 poloxamer, we performed simulations on a system containing a P188 micelle next to "damaged" lipid bilayer containing a pore. We observed that hydrophobic chains of poloxamers got inserted into the bilayer through the pore region, ultimately closing the pore.

Behavior of P85 and P188 Poloxamer Molecules: Computer Simulations Using United-Atom Force-Field.

To study the interaction between poloxamer molecules and lipid bilayers using molecular dynamics simulation technique with the united-atom resolution, we augmented the GROMOS force-field to include poloxamers. We validated the force-field by calculating the radii of gyration of two poloxamers, P85 and P188, solvated in water and by considering the poloxamer density distributions at the air/water interface. The emphasis of our simulations was on the study of the interaction between poloxamers and lipid bilayer. At the water/lipid bilayer interface, we observed that both poloxamers studied, P85 and P188, behaved like surfactants: the hydrophilic blocks of poloxamers became adsorbed at the polar interface, while their hydrophobic block penetrated the interface into the aliphatic tail region of the lipid bilayer. We also observed that when P85 and P188 poloxamers interacted with damaged membranes that contained pores, the hydrophobic blocks of copolymers penetrated into the membrane in the vicinity of the pore and compressed the membrane. Due to this compression, water molecules were evacuated from the pore.

Mechanism of membrane poration by shock wave induced nanobubble collapse: a molecular dynamics study.

We performed coarse-grained molecular dynamics simulations in order to understand the mechanism of membrane poration by shock wave induced nanobubble collapse. Pressure profiles obtained from the simulations show that the shock wave initially hits the membrane and is followed by a nanojet produced by the nanobubble collapse. While in the absence of the nanobubble, the shock wave with an impulse of up to 18 mPa s does not create a pore in the membrane, in the presence of a nanobubble even a smaller impulse leads to the poration of the membrane. Two-dimensional pressure maps depicting the pressure distributed over the lateral area of the membrane reveal the differences between these two cases. In the absence of a nanobubble, shock pressure is evenly distributed along the lateral area of the membrane, while in the presence of a nanobubble an unequal distribution of pressure on the membrane is created, leading to the membrane poration. The size of the pore formed depends on both shock wave velocity and shock wave duration. The results obtained here show that these two properties can be tuned to make pores of various sizes.

Opening of the blood-brain barrier tight junction due to shock wave induced bubble collapse: a molecular dynamics simulation study.

Passage of a shock wave across living organisms may produce bubbles in the blood vessels and capillaries. It was suggested that collapse of these bubbles imposed by an impinging shock wave can be responsible for the damage or even destruction of the blood-brain barrier. To check this possibility, we performed molecular dynamics computer simulations on systems that contained a model of tight junction from the blood-brain barrier. In our model, we represent the tight junction by two pairs of interacting proteins, claudin-15. Some of the simulations were done in the absence of a nanobubble, some in its presence. Our simulations show that when no bubble is present in the system, no damage to tight junction is observed when the shock wave propagates across it. In the presence of a nanobubble, even when the impulse of the shock wave is relatively low, the implosion of the bubble causes serious damage to our model tight junction.

Manipulating unconventional CH-based hydrogen bonding in a methyltransferase via noncanonical amino acid mutagenesis.

Recent studies have demonstrated that the active sites of S-adenosylmethionine (AdoMet)-dependent methyltransferases form strong carbon-oxygen (CH···O) hydrogen bonds with the substrate's sulfonium group that are important in AdoMet binding and catalysis. To probe these interactions, we substituted the noncanonical amino acid p-aminophenylalanine (pAF) for the active site tyrosine in the lysine methyltransferase SET7/9, which forms multiple CH···O hydrogen bonds to AdoMet and is invariant in SET domain enzymes. Using quantum chemistry calculations to predict the mutation's effects, coupled with biochemical and structural studies, we observed that pAF forms a strong CH···N hydrogen bond to AdoMet that is offset by an energetically unfavorable amine group rotamer within the SET7/9 active site that hinders AdoMet binding and activity. Together, these results illustrate that the invariant tyrosine in SET domain methyltransferases functions as an essential hydrogen bonding hub and cannot be readily substituted by residues bearing other hydrogen bond acceptors.

First steps in growth of a polypeptide toward ß-sheet structure.

The full conformational energy surface is examined for a molecule in which a dipeptide is attached to the same spacer group as another peptide chain, so as to model the seminal steps of ß-sheet formation. This surface is compared with the geometrical preferences of the isolated dipeptide to extract the perturbations induced by interactions with the second peptide strand. These interpeptide interactions remove any tendency of the dipeptide to form a C5 ring structure, one of its two normally stable geometries. A C7 structure, the preferred conformation of the isolated dipeptide, remains as the global minimum in the full molecule. However, the stability of this structure is highly dependent upon interpeptide H-bonds with the second chain. The latter forces include not only the usual NH···O interaction, but also a pair of CH···O H-bonds. The secondary minimum is also of C7 type and likewise depends in part upon CH···O H-bonds for its stability. The latter interactions also play a part in the tertiary minimum. A two-strand ß-sheet structure is not yet in evidence for this small model system, requiring additional peptide units to be added to each chain.