Implicit Solvent Molecular Dynamics Simulations Research Articles

Exact Analytical Algorithm for the Solvent-Accessible Surface Area and Derivatives in Implicit Solvent Molecular Simulations on GPUs.

In this paper, we present differentiable solvent-accessible surface area (dSASA), an exact geometric method to calculate SASA analytically along with atomic derivatives on GPUs. The atoms in a molecule are first assigned to tetrahedra in groups of four atoms by Delaunay tetrahedralization adapted for efficient GPU implementation, and the SASA values for atoms and molecules are calculated based on the tetrahedralization information and inclusion-exclusion method. The SASA values from the numerical icosahedral-based method can be reproduced with >98% accuracy for both proteins and RNAs. Having been implemented on GPUs and incorporated into AMBER, we can apply dSASA to implicit solvent molecular dynamics simulations with the inclusion of this nonpolar term. The current GPU version of GB/SA simulations has been accelerated up to nearly 20-fold compared to the CPU version, outperforming LCPO, a commonly used, fast algorithm for calculating SASA, as the system size increases. While we focus on the accuracy of the SASA calculations for proteins and nucleic acids, we also demonstrate stable GB/SA MD mini-protein simulations.

Prediction of the surface chemistry of calcium aluminosilicate glasses

We have used a combination of density functional theory, the implicit solvent model COSMO-RS and molecular dynamics simulations to predict the pKa of surface groups on calcium aluminosilicate glasses. We found that the average of pKa for deprotonation and protonation for silanols agrees well with the point of zero charge for pure silica materials. Similarly, the average of pKa for deprotonation and protonation for aluminols agrees well with the point of zero charge for pure alumina. We identified trends in the pKa related to the hydrogen bonding of the surface groups, as well as the influence of tri-briding oxygen defects.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1), using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed state simulations, we find much more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated theta temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role for condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions which are significantly lower compared to typical combinations of immiscible simple liquids.

Conformations and Solvation of Synthetic Polymers in Water by Generalized Born Implicit-Solvent Molecular Dynamics Simulations: Stereoisomers of Poly(acrylic acid) and Poly(methacrylic acid)

We present the GB-OBC model as an approach for implicit-solvent MD simulations of a synthetic macromolecule in water. The model is tested and found to be successful in reproducing the chain dimensions and predicting the free energy of solvation of carboxylic acid vinyl polymers. The influence of stereochemistry and the hydrophobic nature of the polymer was investigated as a function of chain length (20 < N < 600) for poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMA). The dimensionless parameters of the GB-OBC model were parameterized to be applicable to PAA and PMA. Scaling relations for chain dimensions obtained using implicit-solvent MD simulations in this study are in good agreement with those from experiments, theory of solvated chains in good solvents, and all-atom MD simulations in explicit water. Results show that ⟨Rg2⟩/NL2 is greater for the atactic chain as compared to the isotactic chain, for PAA as well as PMA. ⟨Rg2⟩/NL2 values of chains attain constancy in water for N = 200, with the values being greater for PMA. The PMA chain is conformationally more perturbed than the PAA chain, for both isotactic and atactic stereochemistry. The solvation free energy ΔGhyd of PAA and PMA in water is negative for all chain lengths (N = 20-600) and becomes more favorable with an increase in molecular weight. The ΔGhyd values for isotactic and atactic chains are identical at lower values of N but differ slightly for N > 300. Irrespective of the hydrophobic nature of the polymer, the atactic chain is thermodynamically more soluble in water as compared to the isotactic chain. The isotactic chain is less hydrophilic as compared to the atactic chain due to the closer proximity of the COOH groups along the backbone. This implicit solvent method is an effective way to accurately simulate the configurational properties and solvation of synthetic polymers in water.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1) using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with an increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed-state simulations, we find many more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated θ-temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role in condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions, which are significantly lower compared to typical combinations of immiscible simple liquids.

A Transfer Free Energy Based Implicit Solvent Model for Protein Simulations in Solvent Mixtures: Urea-Induced Denaturation as a Case Study.

We developed a method for implicit solvent molecular dynamics simulations of proteins in solvent mixtures (model with implicit solvation thermodynamics, MIST). The MIST method introduces experimental group transfer free energies to the generalized Born formulation for generating molecular trajectories without the need for developing rigorous explicit-solvent force fields for multicomponent solutions. As a test case, we studied the urea-induced denaturation of the Trp-cage miniprotein in water. We demonstrate that our method allows efficient exploration of the conformational space of the protein in only a few hundreds of nanoseconds of all-atom unbiased simulations. Furthermore, selective implementation of the transfer free energies of specific peptide groups, backbone, and side chains enables us to decouple their specific energetic contributions to the conformational changes of the protein. The approach herein developed can readily be extended to the investigation of complex matrices as well as to the characterization of protein aggregation. The MIST method is implemented in Plumed (ver. 2.8) as a separate module called SASA.

NMDA Receptor Opening and Closing-Transitions of a Molecular Machine Revealed by Molecular Dynamics.

We report the first complete description of the molecular mechanisms behind the transition of the N-methyl-d-aspartate (NMDA) receptor from the state where the transmembrane domain (TMD) and the ion channel are in the open configuration to the relaxed unliganded state where the channel is closed. Using an aggregate of nearly 1 µs of unbiased all-atom implicit membrane and solvent molecular dynamics (MD) simulations we identified distinct structural states of the NMDA receptor and revealed functionally important residues (GluN1/Glu522, GluN1/Arg695, and GluN2B/Asp786). The role of the “clamshell” motion of the ligand binding domain (LBD) lobes in the structural transition is supplemented by the observed structural similarity at the level of protein domains during the structural transition, combined with the overall large rearrangement necessary for the opening and closing of the receptor. The activated and open states of the receptor are structurally similar to the liganded crystal structure, while in the unliganded receptor the extracellular domains perform rearrangements leading to a clockwise rotation of up to 45 degrees around the longitudinal axis of the receptor, which closes the ion channel. The ligand-induced rotation of extracellular domains transferred by LBD–TMD linkers to the membrane-anchored ion channel is responsible for the opening and closing of the transmembrane ion channel, revealing the properties of NMDA receptor as a finely tuned molecular machine.

Stratification Dynamics in Drying Colloidal Mixtures.

Stratification in binary colloidal mixtures was investigated using implicit-solvent molecular dynamics simulations. For large particle size ratios and film Péclet numbers greater than unity, smaller colloids migrated to the top of the film, while big colloids were pushed to the bottom, creating an "inverted" stratification. This peculiar behavior was observed in recent simulations and experiments conducted by Fortini et al. [ Phys. Rev. Lett. 2016 , 116 , 118301 ]. To rationalize this behavior, particle size ratios and drying rates spanning qualitatively different Péclet number regimes were systematically studied, and the dynamics of the inverted stratification were quantified in detail. The stratified layer of small colloids was found to grow faster and to larger thicknesses for larger size ratios. Interestingly, inverted stratification was observed even at moderate drying rates where the film Péclet numbers were comparable to unity, but the thickness of the stratified layer decreased. A model based on dynamical density functional theory is proposed to explain the observed phenomena.

Molecular dynamics simulations of β2-microglobulin interaction with hydrophobic surfaces.

Hydrophobic surfaces are known to adsorb and unfold proteins, a process that has been studied only for a few proteins. Here we address the interaction of β2-microglobulin, a paradigmatic protein for the study of amyloidogenesis, with hydrophobic surfaces. A system with 27 copies of the protein surrounded by a model cubic hydrophobic box is studied by implicit solvent molecular dynamics simulations. Most proteins adsorb on the walls of the box without major distortions in local geometry, whereas free molecules maintain proper structures and fluctuations as observed in explicit solvent molecular dynamics simulations. The major conclusions from the simulations are as follows: (i) the adopted implicit solvent model is adequate to describe protein dynamics and thermodynamics; (ii) adsorption occurs readily and is irreversible on the simulated timescale; (iii) the regions most involved in molecular encounters and stable interactions with the walls are the same as those that are important in protein-protein and protein-nanoparticle interactions; (iv) unfolding following adsorption occurs at regions found to be flexible by both experiments and simulations; (v) thermodynamic analysis suggests a very large contribution from van der Waals interactions, whereas unfavorable electrostatic interactions are not found to contribute much to adsorption energy. Surfaces with different degrees of hydrophobicity may occur in vivo. Our simulations show that adsorption is a fast and irreversible process which is accompanied by partial unfolding. The results and the thermodynamic analysis presented here are consistent with and rationalize previous experimental work.

A computational approach for studying antibody-antigen interactions without prior structural information: the anti-testosterone binding antibody as a case study.

Given the increasing exploitation of antibodies in different contexts such as molecular diagnostics and therapeutics, it would be beneficial to unravel the atomistic level properties of antibody-antigen complexes with the help of computational modeling. Thus, here we have studied the feasibility of computational tools to gather atomic scale information regarding the antibody-antigen complexes solely starting from an amino acid sequence. First, we constructed a homology model for the anti-testosterone binding antibody based on the knowledge based classification of complementary determining regions (CDRs) and implicit solvent molecular dynamics simulations. To further examine whether the generated homology model is suitable for studying antibody-antigen interactions, docking calculations were carried out followed by binding free-energy simulations. Our results indicate that with the antibody modeling approach presented here it is possible to construct accurate homology models for antibodies which correctly describes the antibody-antigen interactions, and produces absolute binding free-energies that are comparable with experimental values. In addition, our simulations suggest that the conformations of complementary determining regions (CDRs) may considerably change from the X-ray configuration upon solvation. In conclusion, here we have introduced an antibody modeling workflow that can be used in studying the interactions between antibody and antigen solely based on an amino acid sequence, which in turn provides novel opportunities to tune the properties of antibodies in different applications. Proteins 2017; 85:322-331. © 2016 Wiley Periodicals, Inc.

Static polarizability effects on counterion distributions near charged dielectric surfaces: A coarse-grained Molecular Dynamics study employing the Drude model

Coarse-grained implicit solvent Molecular Dynamics (MD) simulations have been used to investigate the structure of the vicinal layer of polarizable counterions close to a charged interface. The classical Drude oscillator model was implemented to describe the static excess polarizability of the ions. The electrostatic layer correction with image charges (ELCIC) method was used to include the effects of the dielectric discontinuity between the aqueous solution and the bounding interfaces for the calculation of the electrostatic interactions. Cases with one or two charged bounding interfaces were investigated. The counterion density profile in the vicinity of the interfaces with different surface charge values was found to depend on the ionic polarizability. Ionic polarization effects are found to be relevant for ions with high excess polarizability near surfaces with high surface charge.

Surface Reconfiguration of Binary Lipid Vesicles via Electrostatically Induced Nanoparticle Adsorption.

We demonstrate the adsorption of nanoparticles (NPs) with charged patches onto a binary vesicle encompassing polar neutral and polar zwitterionic lipids via an implicit solvent coarse-grained model and molecular dynamics simulations. Our investigations on the interactions between NPs and a binary vesicle demonstrate that the adsorption of charged NPs onto a binary vesicle surface can induce structural reorganization of the lipid bilayer. The approach of the NP to the vesicle surface is accompanied by spatial reorganization of the zwitterionic lipids, and the degree of reorganization is found to depend on the NP patch size. Interfacial adsorption of the NP is observed to promote a group of zwitterionic lipids to cluster at the adsorption site. Spatial reorganization of the zwitterionic lipids is activated by favorable electrostatic interactions with the NP and not between the lipids. The favorable electrostatic interaction between oppositely charged lipid headgroup moieties increases and assists the clustering process as the NP approaches the vesicle surface. In addition, the availability of zwitterionic lipids in the vesicle affects the adsorption dynamics of multiple NPs. Our results can be used for the design of reconfigurable biomaterials for applications in drug delivery, sensing, and imaging.

Sequence dependent interaction of single stranded DNA with graphitic flakes: atomistic molecular dynamics simulations

ABSTRACTIn an attempt to understand the structure and dynamics of ssDNA on graphene based surfaces, we performed all-atom implicit solvent molecular dynamics simulations of ssDNA on graphene and graphene oxide (GO) surfaces. Simulations indicate that adsorption of poly(A), poly(T) and poly (AT) have similar mechanisms of adsorption to free standing graphitic flakes, which are governed by a surface oxygen content. Specifically, higher oxygen content of a surface leads to decrease in persistence length of ssDNA. However, the role of DNA sequence on the physisorption mechanism is minimal.

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li(+) with two anions have been studied using quantum-chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute-ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum-chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations.

Insights into the mechanism of C5aR inhibition by PMX53 via implicit solvent molecular dynamics simulations and docking.

BackgroundThe complement protein C5a acts by primarily binding and activating the G-protein coupled C5a receptor C5aR (CD88), and is implicated in many inflammatory diseases. The cyclic hexapeptide PMX53 (sequence Ace-Phe-[Orn-Pro-dCha-Trp-Arg]) is a full C5aR antagonist of nanomolar potency, and is widely used to study C5aR function in disease.ResultsWe construct for the first time molecular models for the C5aR:PMX53 complex without the a priori use of experimental constraints, via a computational framework of molecular dynamics (MD) simulations, docking, conformational clustering and free energy filtering. The models agree with experimental data, and are used to propose important intermolecular interactions contributing to binding, and to develop a hypothesis for the mechanism of PMX53 antagonism.ConclusionThis work forms the basis for the design of improved C5aR antagonists, as well as for atomic-detail mechanistic studies of complement activation and function. Our computational framework can be widely used to develop GPCR-ligand structural models in membrane environments, peptidomimetics and other chemical compounds with potential clinical use.

Bioinspired vesicles encompassing two-tail phospholipids: self-assembly and phase segregation via implicit solvent coarse-grained molecular dynamics.

Via implicit solvent molecular dynamics simulations, we demonstrate the self-assembly of stable single and binary vesicles composed of two-tail phospholipid molecules. The amphiphilic lipid molecules are composed of a hydrophilic headgroup and two hydrophobic tails and are represented by a reduced coarse-grained model which effectively captures the key chemical and geometric attributes of phospholipid molecules. We report our measurements of the bilayer thickness to be consistent with experimental values reported in the literature. We have probed the role of temperature on the physical properties of single component lipid vesicles and found our results to concur with experimental results. Our investigations on the phase segregation in binary vesicles demonstrate that the degree of distinction between the tail groups of the lipid species can be used to tune their phase segregation in the vesicle bilayer. Finally, our measurements of the scaling exponents for macroscopically phase-segregated systems have been found to be in good agreement with theoretical and simulation studies. Our results can be used for the design of responsive biomaterials for applications in drug delivery, sensing, and imaging.

Long range Debye-Hückel correction for computation of grid-based electrostatic forces between biomacromolecules.

BackgroundBrownian dynamics (BD) simulations can be used to study very large molecular systems, such as models of the intracellular environment, using atomic-detail structures. Such simulations require strategies to contain the computational costs, especially for the computation of interaction forces and energies. A common approach is to compute interaction forces between macromolecules by precomputing their interaction potentials on three-dimensional discretized grids. For long-range interactions, such as electrostatics, grid-based methods are subject to finite size errors. We describe here the implementation of a Debye-Hückel correction to the grid-based electrostatic potential used in the SDA BD simulation software that was applied to simulate solutions of bovine serum albumin and of hen egg white lysozyme.ResultsWe found that the inclusion of the long-range electrostatic correction increased the accuracy of both the protein-protein interaction profiles and the protein diffusion coefficients at low ionic strength.ConclusionsAn advantage of this method is the low additional computational cost required to treat long-range electrostatic interactions in large biomacromolecular systems. Moreover, the implementation described here for BD simulations of protein solutions can also be applied in implicit solvent molecular dynamics simulations that make use of gridded interaction potentials.

How Kinetics within the Unfolded State Affects Protein Folding: An Analysis Based on Markov State Models and an Ultra-Long MD Trajectory

Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 μs explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultralong MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ≤40 ns, compared with the folding time of ∼5 μs. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90% of the unfolded states are sampled within the first 40 μs of the ultralong MD trajectory, which on average explores ∼27% of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into "tubes", and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that, when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with nonuniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently, leading to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded state is constructed which reveals that different unfolded populations have almost the same probability to fold along any of the multiple folding paths. We are investigating whether the results for the kinetics in the unfolded state of the 20-residue Trp-cage is representative of larger single domain proteins.

Motion of a Disordered Polypeptide Chain as Studied by Paramagnetic Relaxation Enhancements,15N Relaxation, and Molecular Dynamics Simulations: How Fast Is Segmental Diffusion in Denatured Ubiquitin?

Molecular dynamics (MD) simulations have been widely used to analyze dynamic conformational equilibria of folded proteins, especially in relation to NMR observables. However, this approach found little use in the studies of disordered proteins, where the sampling of vast conformational space presents a serious problem. In this paper, we demonstrate that the latest advances in computation technology make it possible to overcome this limitation. The experimentally validated (calibrated) MD models allow for new insights into structure/dynamics of disordered proteins. As a test system, we have chosen denatured ubiquitin in solution with 8 M urea at pH 2. High-temperature MD simulations in implicit solvent have been carried out for the wild-type ubiquitin as well as MTSL-tagged Q2C, D32C, and R74C mutants. To recalibrate the MD data (500 K) in relation to the experimental conditions (278 K, 8 M urea), the time axes of the MD trajectories were rescaled. The scaling factor was adjusted such as to maximize the agreement between the simulated and experimental (15)N relaxation rates. The resulting effective length of the trajectories, 311 μs, ensures good convergence properties of the MD model. The constructed MD model was validated against the array of experimental data, including additional (15)N relaxation parameters, multiple sets of paramagnetic relaxation enhancements (PREs), and the radius of gyration. In each case, a near-quantitative agreement has been obtained, suggesting that the model is successful. Of note, the MD-based approach rigorously predicts the quantities that are inherently dynamic, i.e., dependent on the motional correlation times. This cannot be accomplished, other than in empirical fashion, on the basis of static structural models (conformational ensembles). The MD model was further used to investigate the relative translational motion of the MTSL label and the individual H(N) atoms. The derived segmental diffusion coefficients proved to be nearly uniform along the peptide chain, averaging to D = 0.49-0.55 × 10(-6) cm(2)/s. This result was verified by direct analysis of the experimental PRE data using the recently proposed Ullman-Podkorytov model. In this model, MTSL and H(N) moieties are treated as two tethered spheres undergoing mutual diffusion in a harmonic potential. The fitting of the experimental data involving D as a single adjustable parameter leads to D = 0.45 × 10(-6) cm(2)/s, in good agreement with the MD-based analyses. This result can be compared with the range of estimates obtained from the resonance energy transfer experiments, D = 0.2-6.0 × 10(-6) cm(2)/s.

Merging Implicit with Explicit Solvent Simulations: Polyethylene Glycol

We constructed an accurate polyether force field for implicit solvent (IS) molecular dynamics (MD) simulations that matches local and global conformations of 1,2-dimethoxy-ethane (DME) and polyethylene glycol (PEG), respectively. To make appropriate force field adjustments for IS models of PEG, we used long-term MD simulation data of 1 μs in explicit solvent (ES) based on the most recent CHARMM35 ether force field that includes adjustments for PEG in explicit water. In IS models, competition of attractive van der Waals (vdW) interactions between solute-solute and solute-solvent atom pairs is often not considered explicitly. As a consequence, the attractive vdW interactions between solute atom pairs that remain in IS models explicitly can yield equilibrium structures that are too compact. This behavior was observed in the present study comparing MD simulation data of the DME and PEG ES model with corresponding IS models that use generalized Born (GB) electrostatics combined with positive surface energy terms favoring compact structures. To regain balance of attractive vdW interactions for IS models, we considered the IS generalized Born with simple switching (GBSW) model in detail, where we turned off surface energy terms and reduced attractive vdW interactions to 90%, or we used alternatively even slightly negative surface energies. However, to obtain quantitatively the same local and global distributions of PEG conformers as in ES, we needed additional force field adjustments involving torsion potentials and 1-4 and 1-5 atom pair Coulomb interactions. This CHARMM ether force field, specifically optimized for IS simulation conditions, is equally valid for dimeric and polymeric ethylene glycol. To explore the conformational space of PEG with MD simulations, an IS GBSW model requires 2 orders of magnitude less CPU time than the corresponding ES model. About a factor of 5 of this gain in efficiency is due to the lack of solvent viscosity in IS models.