How Cell-Penetrating Peptides Behave Differently from Pore-Forming Peptides: Structure and Stability of Induced Transmembrane Pores.

Peptide-induced transmembrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell-penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions, and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore-forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small-angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that although AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

Simulation study of membrane bending by protein crowding: a case study with the epsin N-terminal homology domain.

The mechanisms by which peripheral membrane proteins generate curvature is currently an active area of research. One of the proposed mechanisms is amphipathic insertion or the 'wedge' mechanism in which the protein shallowly inserts an amphipathic helix inside the membrane to drive the curvature. However, recent experimental studies have challenged the efficiency of the 'wedge' mechanism as it requires unusual protein densities. These studies proposed an alternative mechanism, namely 'protein-crowding', in which the lateral pressure generated by the random collisions among the membrane bound proteins drives the bending. In this study, we employ atomistic and coarse-grained molecular dynamics simulations to investigate the effects of amphipathic insertion and protein crowding on the membrane surface. Considering epsin N-terminal homology (ENTH) domain as a model protein, we show that amphipathic insertion is not essential for membrane bending. Our results suggest that ENTH domains can aggregate on the membrane surface by employing another structured region (H3 helix). And this protein crowding decreases the cohesive energy of the lipid tails which causes a significant decrease in the membrane bending rigidity. The ENTH domain can generate a similar degree of membrane curvature irrespective of the activity of its H0 helix. Our results are consistent with the recent experimental results.

Origin of the nonlinear structural and mechanical properties in oppositely curved lipid mixtures.

Structural and mechanical properties of membranes such as thickness, tail order, bending modulus and curvature energetics play crucial role in controlling various cellular functions that depend on the local lipid organization and membrane reshaping. While behavior of these biophysical properties are well understood in single component membranes, very little is known about how do they change in the mixed lipid membranes. Often various properties of the mixed lipid bilayers are assumed to change linearly with the mole fractions of the constituent lipids which, however, is true for "ideal" mixing only. In this study, using molecular dynamics simulations, we show that structural and mechanical properties of binary lipid mixture change nonlinearly with the lipid mole fractions, and the strength of the nonlinearity depends on two factors - spontaneous curvature difference and locally inhomogeneous interactions between the lipid components.

Scission energy and topology of micelles controlled by the molecular structure of additives.

We employ coarse-grained (CG) molecular dynamics simulations (MD) to investigate the effects of the molecular structure of additives on the scission energy and morphology of charged micelles. Considering sodium dodecyl sulfate (SDS) as a representative charged surfactant and taking trimethylphenylammonium chloride (TMPAC) and octyltrimethylammonium bromide (OTAB) as oppositely charged additives, we show that the scission energy and topology of micelles vary significantly depending on the molecular structure of the hydrophobic part of the additives. The cyclic aromatic tail of the TMPAC disrupts the core structure of the SDS micelle and hence decreases the micelle scission energy, whereas the linear alkyl tail of the OTAB packs very well with the micelle core and increases the scission energy. Although both the additives have similar head structures, they lead to very different micelle morphologies because of the difference in the shape of their tail structures; ring-like or toroidal shaped micelles are formed in SDS/TMPAC solution whereas bicelle-like structures are formed in SDS/OTAB solution when the additive to surfactant ratio is higher than a certain value.

Simulation study of domain formation in a model bacterial membrane.

Recent experimental studies revealed that functional membrane microdomains (FMMs) are formed in prokaryotic cells which are structurally and functionally similar to the lipid rafts formed in eukaryotic cells. In this study, we employ coarse-grained molecular dynamics simulations to investigate the mechanism of domain formation and its physiochemical properties in a model methicillin-resistant staphylococcus aureus (MRSA) cell membrane. We find that domains are formed through lateral segregation of staphyloxanthin (STX), a carotenoid which shields the bacteria from the host's immune because of its antioxidant nature. Simulation results suggest that membrane integrity increases with the size of the domain, which is assessed by computing bond order parameter of the lipid tails, membrane expansion modulus and water permeability across the membrane. Various membrane domain proteins such as flotillin-like protein floA and penicillin binding protein (PBP2a) preferentially bind with the STX and accumulate in the membrane domain which is consistent with the recent experimental results.

Protein-induced membrane curvature in coarse-grained simulations.

Using the endosomal sorting complex required for transport (ESCRT)-III membrane remodeling complex as an example, we analyze three popular coarse-grained models (the regular MARTINI, polarizable MARTINI (POL-MARTINI), and big multipole water MARTINI (BMW-MARTINI)) for the description of membrane curvature sensing and generation activities of peripheral proteins. Although the three variants of the MARTINI model provide consistent descriptions for the protein-protein interface in a linear filament model of ESCRT-III, they differ considerably in terms of protein-membrane interface and therefore membrane curvature sensing and generation behaviors. In particular, BMW-MARTINI provides the most consistent description of the protein-membrane interface as compared to all-atom simulations, whereas the regular MARTINI is most consistent with atomistic simulations in terms of the qualitative sign of membrane curvature sensing and generation. With POL-MARTINI, the ESCRT-III model interacts weakly with the membrane and therefore does not exhibit any curvature-sensitive activities. Analysis suggests that the incorrect membrane curvature activities predicted by BMW-MARTINI are due to overestimated insertion depth of an amphipathic helix and incorrect sign for the spontaneous curvature of anionic lipids. These results not only point to ways that coarse-grained models can be improved but also explicitly highlight local lipid composition and insertion depth of protein motifs as essential regulatory factors for membrane curvature sensing and generation.

Molecular Simulation of Mechanical Properties and Membrane Activities of the ESCRT-III Complexes.

The endosomal sorting complex required for transport (ESCRT) machinery carries out the membrane scission reactions that are required for many biological processes throughout cells. How ESCRTs bind and deform cellular membranes and ultimately produce vesicles has been a matter of active research in recent years. In this study, we use fully atomistic molecular dynamics simulations to scrutinize the structural details of a filament composed of Vps32 protomers, a major component of ESCRT-III complexes. The simulations show that both hydrophobic and electrostatic interactions between monomers help maintain the structural stability of the filament, which exhibits an intrinsic bend and twist. Our findings suggest that the accumulation of bending and twisting stresses as the filament elongates on the membrane surface likely contributes to the driving force for membrane invagination. The filament exposes a large cationic surface that senses the negatively charged lipids in the membrane, and the N-terminal amphipathic helix of the monomers not only acts as a membrane anchor but also generates significant positive membrane curvature. Taking all results together, we discuss a plausible mechanism for membrane invagination driven by ESCRT-III.

Modulating Interdendrimer Interactions through Surface Adsorption.

Physical confinement of polymers not only affects their structure but also modifies their effective interaction profiles. In this article, we investigate the nature of graphene-adsorbed poly(amidoamine) (PAMAM) dendrimers' interactions using fully atomistic molecular dynamics simulations. Using the umbrella sampling technique, we calculate the potential of mean force (PMF) profiles for the interaction between two graphene-adsorbed PAMAM dendrimers of generations 3 and 4 as a function of their protonation levels. We find that the attractive PMF profile observed for the interaction between two nonprotonated (high pH) PAMAM dendrimers in bulk becomes repulsive upon adsorption. Also, the repulsive interdendrimer interactions known in bulk for the protonated dendrimers become enhanced for the adsorbed case. We further explain these weakened interactions by explicitly showing that the dendrimer-graphene interaction is an order of magnitude larger than the dendrimer-dendrimer bulk interaction. Using the force integration method, we obtain the contributions from various subinteractions present in the system, that is, dendrimer-water, dendrimer-ions, dendrimer-graphene, and dendrimer-dendrimer to the total PMF. From these contributions, we conclude that the reduced dendrimer-dendrimer interactions in the adsorbed case, as compared to those in bulk, lead to the enhanced repulsive effective interdendrimer interactions. Our PMF profiles fit well with the sum of exponential and Gaussian functions, proposed in the bulk interdendrimer interaction study. We hope the current results provide the microscopic origin of how adsorption weakens the interpolymer interactions in general.

Nonmonotonic Scission and Branching Free Energies as Functions of Hydrotrope Concentration for Charged Micelles.

Using coarse-grained molecular dynamics simulations and an umbrella sampling method that uses local surfactant density as a reaction coordinate, we directly calculate, for the first time, both the scission and branching free energies of a model charged micelle [cationic cetyltrimethylammonium chloride (CTAC)] in the presence of inorganic and organic salts (hydrotropes). We find that while inorganic salt only weakly affects the micelle scission energy, organic hydrotropes produce a strong, nonmonotonic dependence of both scission energy and branching on salt concentration. The nonmonotonicity in scission energy is traced to a competition between electrostatic screening of the repulsions among the surfactant head groups and thinning of the micellar core, which result from attachment of the hydrotropes to the micelle surface. We are able to correlate the nonmonotonicity in the scission energy of CTAC micelles with the peak observed experimentally in viscosity versus hydrotrope concentration and the location of this peak in CTAC solutions.

Stretch and Breakage of Wormlike Micelles under Uniaxial Strain: A Simulation Study and Comparison with Experimental Results.

We use coarse-grained (CG) molecular dynamics simulations to determine the effect of uniaxial strain on the stress, scission stress, and scission energy of solutions of wormlike micelles of cetyltrimethylammonium chloride/sodium salicylate (NaSal). We find that the breaking stress, stretch modulus, and scission energy of the charged micelles are nonmonotonic functions of oppositely charged hydrotrope (NaSal) concentration. While the stretch modulus shows a peak at a value of surfactant-to-hydrotrope concentration ratio ( R) close to unity as expected due to neutralization of head-group charge at R = 1, the breaking stress and scission energy produce a peak at R < 1.0 because of thinning of the micelle diameter with increased R. The breaking stress from the simulations depends on the rate of deformation and roughly agrees with the experimental values of Rothstein ( J. Rheol. 2003 , 47 , 1227 ) after extrapolation to the much lower experimental rates. The method and results can be used to predict the effects of flow and mechanical stress on rates of micellar breakage, which is important in the rheology of wormlike micellar solutions.

Prediction of striped cylindrical micelles (SCMs) formed by dodecyl-ß-d-maltoside (DDM) surfactants.

Using fully atomistic and coarse-grained (CG) molecular dynamics (MD) simulations, we report, for the first time, the self-assembly of initially randomly dispersed dodecyl-ß-d-maltoside (DDM) surfactants into a striped cylindrical micelle (SCM) with lamellae of surfactant heads and tails alternating along the cylindrical axis, with both heads and tails in contact with the water. By changing the interaction strength of the head group with water relative to itself, we find that such micelles are most likely for head groups with marginal solubility in the water solvent. Unlike the surfactants in a regular cylindrical micelle, whose tails are in the fluid micelle interior, the diffusion of DDM surfactants along the micelle body is blocked by the lamellar patterning. As a consequence, branches cannot slide along the micelle body and surfactant molecules cannot exchange between the micelle body and the branch, which should have a significant impact on the rheological properties of these micelles.

Multiscale Computational Modeling of the Nanostructure of Solid Dispersions of Hydroxypropyl Methylcellulose Acetate Succinate (HPMCAS) and Phenytoin.

We recently developed coarse-grained (CG) force fields for hydroxypropyl methylcellulose acetate succinate (HPMCAS) polymers and the model drug molecule phenytoin, and a continuum transport model to study the polymer-drug nanostructures presented during a dissolution test after solvation of solid dispersion particles. We model the polymer-drug interactions that contribute to suppression of drug aggregation, release, and crystal growth during the dissolution process, and we take these as indicators of polymer effectiveness. We find that the size and the intermolecular interaction strength of the functional group and the drug loading concentration are the major factors that impact the effectiveness of the polymeric excipient. The hydroxypropyl acetyl group is the most effective functional group, followed by the acetyl group, while the deprotonated succinyl group is the least effective functional group, except that the deprotonated succinyl group at the 6-position is very effective in slowing down the phenytoin crystal growth. Our simulation results thus suggest HPMCAS with higher acetyl and lower succinyl content is more effective in promoting phenytoin solubility in dissolution media, and polymers become less effective when drug loading becomes high (i.e., 50% of the mass of the polymer/drug solid dispersion), agreeing with previous experimental studies. In addition, our transport model indicates that the drug release time from a solid dispersion particle of 2 µm diameter is less than 10 min, correlating well with the experimental time scale for a typical dissolution profile to reach maximum peak concentration. Our modeling effort, therefore, provides new avenues to understand the dissolution behavior of complex HPMCAS-phenytoin solid dispersions and offers a new design tool to optimize the formulation. Moreover, the systematic and robust approach used in our computational models can be extended to other polymeric excipients and drug candidates.

Computational Modeling of Hydroxypropyl-Methylcellulose Acetate Succinate (HPMCAS) and Phenytoin Interactions: A Systematic Coarse-Graining Approach.

We present coarse-grained (CG) force fields for hydroxypropyl-methylcellulose acetate succinate (HPMCAS) polymers and the drug molecule phenytoin using a bead/stiff spring model, with each bead representing a HPMCAS monomer or monomer side group (hydroxypropyl acetyl, acetyl, or succinyl) or a single phenytoin ring. We obtain the bonded and nonbonded interaction parameters in our CG model using the RDFs from atomistic simulations of short HPMCAS model oligomers (20-mer) and atomistic simulations of phenytoin molecules. The nonbonded interactions are modeled using a LJ 12-6 potential, with separate parameters for each monomer substitution type, which allows heterogeneous polymer chains to be modeled. The cross interaction terms between the polymer and phenytoin CG beads are obtained explicitly from atomistic level polymer-phenytoin simulations, rather than from mixing rules. We study the solvation behavior of 50-mer and 100-mer polymer chains and find chain-length-dependent aggregation. We also compare the phenytoin CG force field developed in this work with that in Mandal et al. (Soft Matter, 2016, 12, 8246-8255) and conclude both are suitable for studying the interaction between polymer and drug in solvated solid dispersion formulation, in the absence of drug crystallization. Finally, we present simulations of heterogeneous HPMCAS model polymer chains and phenytoin molecules. Polymer and drug form a complex in a short period of simulation time due to strong intermolecular interactions. Moreover, the protonated polymer chains are more effective than deprotonated ones in inhibiting the drug aggregation in the polymer-drug complex.

A framework for multi-scale simulation of crystal growth in the presence of polymers.

We present a multi-scale simulation method for modeling crystal growth in the presence of polymer excipients. The method includes a coarse-grained (CG) model for small molecules of known crystal structure whose force field is obtained using structural properties from atomistic simulations. This CG model is capable of stabilizing the molecular crystal structure and capturing the crystal growth from the melt for a wide range of small organic molecules, as demonstrated by application of our method to the molecules isoniazid, urea, sulfamethoxazole, prilocaine, oxcarbazepine, and phenytoin. This CG model can also be used to study the effect of additives, such as polymers, on the inhibition of crystal growth by polymers, as exemplified by our simulation of suppression of the rate of crystal growth of phenytoin, an active pharmaceutical ingredient (API), by a cellulose excipient, functionalized with acetate (Ac), hydroxy-propyl (Hp) and succinate (Su) groups. We show that the efficacy of the cellulosic polymers in slowing crystal growth of small molecules strongly depends on the functional group substitution on the cellulose backbone, with the acetate substituent group slowing crystal growth more than does the deprotonated succinate group, which we confirm by experimental drug supersaturation studies.

Nucleation of urea from aqueous solution: Structure, critical size, and rate.

Using fully atomistic simulations, we find that the structure of the critical urea crystal nucleus (monoclinic, four molecules per unit cell) in an aqueous solution differs from the known crystal structure of bulk urea (orthorhombic, two molecules per unit cell). Following a frequently used "seeding technique" combined with the classical nucleation theory, we also find that at room temperature the critical nucleus is very large (containing ∼530 molecules) and the nucleation rate is very slow (∼5×10-24cm-3s-1), suggesting that the homogeneous nucleation of urea is improbable at room temperature.

Modeling the Hydrophobicity of Nanoparticles and Their Interaction with Lipids and Proteins.

We present a method of modeling nanoparticle (NP) hydrophobicity using coarse-grained molecular dynamics (CG MD) simulations, and apply this to the interaction of lipids with nanoparticles. To model at a coarse-grained level the wettability or hydrophobicity of a given material, we choose the MARTINI coarse-grained force field, and determine through simulation the contact angles of MARTINI water droplets residing on flat regular surfaces composed of various MARTINI bead types (C1, C2, etc.). Each surface is composed of a single bead type in each of three crystallographic symmetries (FCC, BCC, and HCP). While this method lumps together several atoms (for example, one cerium and two oxygens of CeO2) into a single CG bead, we can still capture the overall hydrophobicity of the actual material by choosing the MARTINI bead type that gives the best fit of the contact angle to that of the actual material, as determined by either experimental or all-atom simulations. For different MARTINI bead types, the macroscopic contact angle is obtained by extrapolating the microscopic contact angles of droplets of eight different sizes (containing Nw = 3224-22978 water molecules) to infinite droplet size. For each droplet, the contact angle was computed from a best fit of a circular curve to the droplet interface extrapolated to the first layer of the surface. We then examine how small nanoparticles of differing wettability interact with MARTINI dipalmitoylphosphotidylcholine (DPPC) lipids and SP-C peptides (a component of lung surfactant). The DPPC shows a transition from tails coating the nanoparticle to a hemimicelle coating the water-wet NP, as the contact angle of a water droplet on the surface is lowered below ∼60°. The results are relevant to developing a taxonomy describing the potential nanotoxicity of nanoparticle interactions with components in the lung.

Coarse-grained modeling of crystal growth and polymorphism of a model pharmaceutical molecule.

We describe a systematic coarse-graining method to study crystallization and predict possible polymorphs of small organic molecules. In this method, a coarse-grained (CG) force field is obtained by inverse-Boltzmann iteration from the radial distribution function of atomistic simulations of the known crystal. With the force field obtained by this method, we show that CG simulations of the drug phenytoin predict growth of a crystalline slab from a melt of phenytoin, allowing determination of the fastest-growing surface, as well as giving the correct lattice parameters and crystal morphology. By applying meta-dynamics to the coarse-grained model, a new crystalline form of phenytoin (monoclinic, space group P21) was predicted which is different from the experimentally known crystal structure (orthorhombic, space group Pna21). Atomistic simulations and quantum calculations then showed the polymorph to be meta-stable at ambient temperature and pressure, and thermodynamically more stable than the conventional orthorhombic crystal at high pressure. The results suggest an efficient route to study crystal growth of small organic molecules that could also be useful for identification of possible polymorphs as well.

Nature of the effective interaction between dendrimers.

We have performed fully atomistic classical molecular dynamics simulations to calculate the effective interaction between two polyamidoamine dendrimers. Using the umbrella sampling technique, we have obtained the potential of mean force (PMF) between the dendrimers and investigated the effects of protonation level and dendrimer size on the PMF. Our results show that the interaction between the dendrimers can be tuned from purely repulsive to partly attractive by changing the protonation level. The PMF profiles are well-fitted by the sum of an exponential and a Gaussian function with the weight of the exponential function dominating over that of the Gaussian function. This observation is in disagreement with the results obtained in previous analytic [C. Likos, M. Schmidt, H. Löwen, M. Ballauff, D. Pötschke, and P. Lindner, Macromolecules 34, 2914 (2001)] and coarse-grained simulation [I. Götze, H. Harreis, and C. Likos, J. Chem. Phys. 120, 7761 (2004)] studies which predicted the effective interaction to be Gaussian.

Comparing multifunctional viral and eukaryotic proteins for generating scission necks in membranes.

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is the M2 viroporin, a proton pump from the influenza A virus which is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging Small-Angle X-ray Scattering (SAXS) structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemi-fission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.

Comparing Multifunctional Viral and Eukaryotic Proteins for Generating Scission Necks in Membranes.

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is M2 viroporin, a proton pump from the influenza A virus that is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging small-angle X-ray scattering structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemifission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.