Experimental Diffusion Constants Research Articles

Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment.

Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.

Dynamic ionic radius of alkali metal ions in aqueous solution: a pulsed-field gradient NMR study

The dynamic behavior of alkali metal ions, Li+, Na+, K+, Rb+ and Cs+ in aqueous solutions is one of the most important topics in solution chemistry. Since these alkali metals contain nuclear magnetic resonance (NMR) active nuclei, it is possible to directly measure the diffusion constants of the alkali metal ions using the pulsed field gradient (PFG) NMR method. In this paper, the 7Li, 23Na, 87Rb, 133Cs and 1H resonances are observed for diffusion constants in aqueous solution and the solvent H2O. Until now, the values of the diffusion constant have been lacking when discussing hydration effects around alkali metal ions. It is known that the static ionic radius (Rion) increases with increasing the atomic number, and the experimental diffusion constants also increase with increasing the atomic number, which is opposite to the Stokes–Einstein (SE) relation. It suggests that alkali metal ions diffuse through a space of 10−6 m accompanying the hydrated spheres with a time interval of 10−3 s. For each alkali metal ion, the dynamic ionic radius is evaluated.

Can Polarity-Inverted Surfactants Self-Assemble in Nonpolar Solvents?

We investigate the self-assembly process of a surfactant with inverted polarity in water and cyclohexane using both all-atom and coarse-grained hybrid particle-field molecular dynamics simulations. Unlike conventional surfactants, the molecule under study, proposed in a recent experiment, is formed by a rigid and compact hydrophobic adamantane moiety, and a long and floppy triethylene glycol tail. In water, we report the formation of stable inverted micelles with the adamantane heads grouping together into a hydrophobic core and the tails forming hydrogen bonds with water. By contrast, microsecond simulations do not provide evidence of stable micelle formation in cyclohexane. Validating the computational results by comparison with experimental diffusion constant and small-angle X-ray scattering intensity, we show that at laboratory thermodynamic conditions the mixture resides in the supercritical region of the phase diagram, where aggregated and free surfactant states coexist in solution. Our simulations also provide indications as to how to escape this region to produce thermodynamically stable micellar aggregates.

Surface Shear Viscosity and Interleaflet Friction from Nonequilibrium Simulations of Lipid Bilayers.

Nonequilibrium simulation protocols based on shear deformations are applied to determine the surface viscosity and interleaflet friction of lipid bilayers. At high shear rates, a non-Newtonian shear thinning regime is observed, but lower shear rates yield a Newtonian plateau and results that are consistent with equilibrium measurements based on fluctuation-dissipation theorems. Application to all-atom bilayers modeled with the CHARMM36 parameter set yields values for the surface viscosity that are consistent with microscopic measurements based on membrane protein diffusion but are approximately 10 times lower than more macroscopic experimental measurements. The interleaflet friction is about 10 times lower than experimental measurements. Trends across different lipids, temperatures, and ternary liquid-disordered phase mixtures produce results that are consistent with experimental diffusion constants. Application of the protocol to the liquid-ordered phase fails to yield a Newtonian plateau, suggesting more complex rheology.

Increased stability of nitroxide radicals in ionic liquids: more than a viscosity effect.

Radical stability has been subject to continuous research due to its importance in polymerization as well as in all-organic batteries. Recently, the SOMO-HOMO conversion was identified as the main factor in controlling the stability of distonic radicals, for which the negative charge resides on the same molecule. Based on this finding, the idea of ionic liquids stabilizing radicals was hypothesized in this study. A series of ionic liquids were tested in EPR measurements of the 3-carboxy-2,2,5,5-tetramethyl-pyrroline-1-oxyl. Unusually high rotational diffusion constants (τR), 4 times larger compared to conventional media such as dichloromethane (DCM), were recorded at room temperature. This finding could only be explained by a strong interaction existing between the radical and ionic liquid ions, which was confirmed with quantum chemical calculations, with interaction energies falling between -17.1 kJ mol-1 for tetramethylphosphonium tetrafluoroborate and -85.6 kJ mol-1 for 1,3-dimethylimidazolium triflate. Elevated temperature measurements performed at 80 °C reduced the viscosity of the ionic liquids to that of DCM, while the τR values remained relatively high, thus further confirming that the rotational hindrance occurred due to radical-ionic liquid interactions. The calculated interaction energies between the radical and ionic liquids ions were also found to correlate well with experimental rotational diffusion constants, thus offering us a valuable tool in tailoring ionic liquids for enhanced stability of nitroxide radicals. The findings of this study showcase the ability of ionic liquids to reduce reactivity of nitroxides without the need for any chemical modification of the radical.

Development of Divide-and-Conquer Density-Functional Tight-Binding Method for Theoretical Research on Li-Ion Battery.

The density-functional tight-binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear-scaling divide-and-conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium-ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC-DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.

Lateral diffusion of peripheral membrane proteins on supported lipid bilayers is controlled by the additive frictional drags of (1) bound lipids and (2) protein domains penetrating into the bilayer hydrocarbon core

Peripheral membrane proteins bound to lipids on bilayer surfaces play central roles in a wide array of cellular processes, including many signaling pathways. These proteins diffuse in the plane of the bilayer and often undergo complex reactions involving the binding of regulatory and substrate lipids and proteins they encounter during their 2D diffusion. Some peripheral proteins, for example pleckstrin homology (PH) domains, dock to the bilayer in a relatively shallow position with little penetration into the bilayer. Other peripheral proteins exhibit more complex bilayer contacts, for example classical protein kinase C isoforms (PKCs) bind as many as six lipids in stepwise fashion, resulting in the penetration of three PKC domains (C1A, C1B, C2) into the bilayer headgroup and hydrocarbon regions. A molecular understanding of the molecular features that control the diffusion speeds of proteins bound to supported bilayers would enable key molecular information to be extracted from experimental diffusion constants, revealing protein–lipid and protein–bilayer interactions difficult to study by other methods. The present study investigates a range of 11 different peripheral protein constructs comprised by 1–3 distinct domains (PH, C1A, C1B, C2, anti-lipid antibody). By combining these constructs with various combinations of target lipids, the study measures 2D diffusion constants on supported bilayers for 17 different protein–lipid complexes. The resulting experimental diffusion constants, together with the known membrane interaction parameters of each complex, are used to analyze the molecular features correlated with diffusional slowing and bilayer friction. The findings show that both (1) individual bound lipids and (2) individual protein domains that penetrate into the hydrocarbon core make additive contributions to the friction against the bilayer, thereby defining the 2D diffusion constant. An empirical formula is developed that accurately estimates the diffusion constant and bilayer friction of a peripheral protein in terms of its number of bound lipids and its geometry of penetration into the bilayer hydrocarbon core, yielding an excellent global best fit (R2 of 0.97) to the experimental diffusion constants. Finally, the observed additivity of the frictional contributions suggests that further development of current theory describing bilayer dynamics may be needed. The present findings provide constraints that will be useful in such theory development.

IMPORTANCE OF EXCLUDED VOLUME AND HYDRODYNAMIC INTERACTIONS ON MACROMOLECULAR DIFFUSION IN VIVO.

The interiors of all living cells are highly crowded with macromolecules, which results in a considerable difference between the thermodynamics and kinetics of biological reactions in vivo from that in vitro. To begin to elucidate the principles of intermolecular dynamics in the crowded environment of cells, employing Brownian dynamics (BD) simulations, we examined possible mechanism(s) responsible for the great reduction in diffusion constants of macromolecules in vivo from that at infinite dilution. In an E. coli cytoplasm modelcomprised of 15 different macromolecule types at physiological concentrations, where macromolecules were represented by spheres with their Stokes radii, BD simulations were performed with and without hydrodynamic interactions (HI). Without HI, the calculated diffusion constant of green fluorescent protein (GFP) is much larger than experiment. On the other hand, when HI were considered, the in vivo experimental GFP diffusion constant is almost reproduced without adjustable parameters. In addition, HI give rise to significant, size independent intermolecular dynamic correlations. These results suggest that HI play an important role on macromolecular dynamics in vivo.

Membrane Diffusion of Tethered Dimer and Trimer Systems

We have used molecular dynamics simulations to investigate the diffusion of tethered dimer and trimer systems in lipid bilayers. Coarse-grained (CG) models of DPPC dimers were simulated in a DPPC bilayer with the MARTINI model, and single-lipid diffusion constants compared to those obtained for dimmers and trimers at various tether lengths. The ratio of diffusion constants matches well with theoretical predictions of a simple bead model. A full theoretical model of the translational and rotational diffusion of tethered dimers and trimers was developed at the Saffman-Delbruck level, and results were compared to the simple bead model. The ratios of diffusion constants from the theoretical and CG models were then compared to experimental diffusion constants of pleckstrin homology (PH) domains bound to lipids with a PIP3 (phosphatidylinositol (3,4,5)-trisphosphate) head group. Excellent agreement between all systems was found, indicating that the frictional contributions of multiple, coupled but well-separated lipids are additive, analogous to the free-draining limit for isotropic fluids.

Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion

To begin to elucidate the principles of intermolecular dynamics in the crowded environment of cells, employing brownian dynamics (BD) simulations, we examined possible mechanism(s) responsible for the great reduction in diffusion constants of macromolecules in vivo from that at infinite dilution. In an Escherichia coli cytoplasm model comprised of 15 different macromolecule types at physiological concentrations, BD simulations of molecular-shaped and equivalent sphere representations were performed with a soft repulsive potential. At cellular concentrations, the calculated diffusion constant of GFP is much larger than experiment, with no significant shape dependence. Next, using the equivalent sphere system, hydrodynamic interactions (HI) were considered. Without adjustable parameters, the in vivo experimental GFP diffusion constant was reproduced. Finally, the effects of nonspecific attractive interactions were examined. The reduction in diffusivity is very sensitive to macromolecular radius with the motion of the largest macromolecules dramatically slowed down; this is not seen if HI dominate. In addition, long-lived clusters involving the largest macromolecules form if attractions dominate, whereas HI give rise to significant, size independent intermolecular dynamic correlations. These qualitative differences provide a testable means of differentiating the importance of HI vs. nonspecific attractive interactions on macromolecular motion in cells.

Electronic Energy Migration on Different Time Scales: Concentration Dependence of the Time-Resolved Anisotropy and Fluorescence Quenching of Lumogen Red in Poly(methyl methacrylate)

Electronic energy transfer plays an important role in many types of organic electronic devices. Forster-type theories of exciton diffusion provide a way to calculate diffusion constants and lengths, but their applicability to amorphous polymer systems must be evaluated. In this paper, the perylenediimide dye Lumogen Red in a poly(methyl methacrylate) host matrix is used to test theories of exciton motion over Lumogen Red concentrations (C(LR)'s) ranging from 1 x 10(-4) to 5 x 10(-2) M. Two experimental quantities are measured. First, time-resolved anisotropy decays in films containing only Lumogen Red provide an estimate of the initial energy transfer rate from the photoexcited molecule. Second, the Lumogen Red lifetime decays in mixed systems where the dyes Malachite Green and Rhodamine 700 act as energy acceptors are measured to estimate the diffusive quenching of the exciton. From the anisotropy measurements, it is found that theory accurately predicts both the C(LR)(-2) concentration dependence of the polarization decay time tau(pol), as well as its magnitude to within 30%. The theory also predicts that the diffusive quenching rate is proportional to C(LR)(alpha), where alpha ranges between 1.00 and 1.33. Experimentally, it is found that alpha = 1.1 +/- 0.2 when Malachite Green is used as an acceptor, and alpha = 1.2 +/- 0.2 when Rhodamine 700 is the acceptor. On the basis of the theory that correctly describes the anisotropy data, the exciton diffusion constant is projected to be 4-9 nm(2)/ns. By use of several different analysis methods for the quenching data, the experimental diffusion constant is found to be in the range of 0.32-1.20 nm(2)/ns. Thus the theory successfully describes the early time anisotropy data but fails to quantitatively describe the quenching experiments which are sensitive to motion on longer time scales. The data are consistent with the idea that orientational and energetic disorder leads to a time-dependent exciton migration rate, suggesting that simple diffusion models cannot accurately describe exciton motion within this system.

Simulation of equivalent weight dependence of Nafion morphologies and predicted trends regarding water diffusion

Microphase separation within hydrated Nafion ® membranes was simulated using Dissipative Particle Dynamics (DPD). Morphologies were obtained at branching densities corresponding with equivalent weights ranging from ∼800 to ∼1400 (g/mole SO 3) and water percentage volume contents ([H 2O]) varying between 10% and 30%. All cases showed pronounced microphase separation involving a hydrophobic Teflon phase and a hydrophilic phase in which water is associated with SO 3 groups that are located near the phase boundaries. Pore morphologies were found to depend strongly on water content and branching density. The average pore radius ( R pore) and the distance between the pores ( D cl-cl) were found to increase with water content obeying the relations R pore = 1.3 + α[H 2O] (nm), and D cl-cl = 3.2 + β[H 2O] (nm). The values of the expansion coefficients α and β decrease linearly with branching density with α = 5.3 × 10 −5 × (EW-450) and β = 1.3 × 10 −4 × (EW-450) nm/vol%. For decreasing branching density the pores obtain a more spherical character. The consequence of this on water diffusion is estimated by employing Monte Carlo trajectory calculations in which we assume that water movement is confined within the hydrophilic phase and local water mobility to be equal to that of pure water. The estimated diffusion constants increase linearly with branching density (i.e. linear decrease with equivalent weight). Experimental water diffusion constants obtained from literature for Nafion1100 membrane are in good agreement with our calculations. A counterintuitive picture evolves in which smaller pores lead to enhanced water diffusion.

Langevin Network Model of Myosin

Langevin mode theory and the coarse-grained elastic network model (ENM) for proteins are combined to yield the Langevin network model (LNM). Hydrodynamic radii of 6 A were assigned to each alpha-carbon on the basis of matching experimental translational and rotational diffusion constants of lysozyme, myoglobin, and hemoglobin with those calculated using a rigid body bead model with hydrodynamic interactions described by the Rotne-Prager tensor. LNM analysis of myosin II indicates that all ENM-like modes are overdamped at water viscosities. The low-frequency LNM modes in the pre-power stroke structure (PDB code: 1VOM) are substantially less mixed than the corresponding modes of the post-power stroke structure (1Q5G). Results from a four-bead model of the myosin "lever arm" indicate that coupling between modes increases as the array departs from linearity and are consistent with the results for 1VOM and 1Q5G. The decay times for all overdamped Langevin modes are shorter than the calculated rotational tumbling times found for lysozyme and myosin.

Molecular Dynamics Simulation of Benzene Diffusion in MOF‐5: Importance of Lattice Dynamics

Doing the locomotion: When benzene molecules diffuse through the metal organic framework MOF-5, they accumulate in pockets (see picture). Molecular dynamics simulations reveal that the correlated lattice motion increases this binding. Only when the the lattice dynamics are considered in the simulation, can the experimental diffusion constants be reproduced.

Role of Loop Residues and Cations on the Formation and Stability of Dimeric DNA G-Quadruplexes

Formation of guanine-quadruplexes by four DNA oligonucleotides with common sequence dG4-loop-dG4 has been studied by a combination of NMR and UV spectroscopy. The loops consisted of 1',2'-dideoxyribose, propanediol, hexaethylene glycol, and thymine residues. The comparison of data on modified and parent oligonucleotides gave insight into the role of loop residues on formation and stability of dimeric G-quadruplexes. All modified oligonucleotides fold into dimeric fold-back G-quadruplexes in the presence of sodium ions. Multiple structures form in the presence of potassium and ammonium ions, which is in contrast to the parent oligonucleotide with dT4 loop. 15N-filtered 1H NMR spectra demonstrate that all studied G-quadruplexes exhibit three 15NH4(+) ion binding sites. Topology of intermolecular G-quadruplexes was evaluated by NMR measurements and diffusion experiments. The spherical, prolate-ellipsoid and symmetric cylinder models were used to interpret experimental translational diffusion constants in terms of diameters and lengths of unfolded oligonucleotides and their respective G-quadruplexes. UV melting and annealing curves show that oligonucleotides with non-nucleosidic loop residues fold faster, exhibit no hysteresis, and are less stable than dimeric d(G4T4G4)2 which can be attributed to the absence of H-bonds, stacking between loop residues and the outer G-quartets as well as cation-pi interactions. Oligonucleotide consisting of hexaethylene glycol linkage with only two phosphate groups in the loop exhibits higher melting temperature and more negative deltaH(o) and deltaG(o) values than oligonucleotides with four 1',2'-dideoxyribose or propanediol residues.

Boundary element modeling of biomolecular transport

The boundary element (BE) methodology has emerged as a powerful tool in modeling a broad range of different transport phenomena of biomolecules in dilute solution. These include: sedimentation, diffusion (translational and rotational), intrinsic viscosity, and free solution electrophoresis. Modeling is carried out in the framework of the continuum primitive model where the biomolecule is modeled as an arbitrary array of solid platelets that contains fixed charges within. The surrounding fluid is modeled as a electrodynamic/hydrodynamic continuum which obeys the Poisson and low Reynolds number Navier–Stokes equations. Ion relaxation (the distortion of the ion atmosphere from equilibrium) can also be accounted for by solving the coupled ion transport equation (for each mobile ion species present), Poisson, and Navier–Stokes equations in tandem. Several examples are presented in this work. It is first applied to a detailed model of 20 bp DNA and it is concluded that it is not necessary to include a layer of bound water to reconcile experimental and model translational diffusion constants. With regards to diffusion, the BE approach is also applied to a 375-bp supercoiled DNA model (without ion relaxation), and also 20–60-bp DNA fragments with ion relaxation included in order to assess the magnitude of the electrolyte friction effect under a number of different salt/buffer conditions. Attention is then turned to modeling the electrophoretic mobility of three different cases. First of all, we consider a sphere with a central charge large enough in magnitude to insure that ion relaxation is significant. Excellent agreement with independent theory is obtained. Finally, it is applied to modeling short DNA fragments in KCl and Tris acetate salts. Quantitative agreement is achieved when the salt is KCl, but the calculated (absolute) mobility in Tris acetate is substantially higher than the experimental value. The interpretation of this is that there is an association between Tris + and DNA (perhaps hydrogen bonding) not accounted for in our modeling that is responsible for this discrepancy.

26] Transient electric birefringence for determining global conformations of nonhelix elements and protein-induced bends in RNA

This chapter describes the transient electric birefringence (TEB) that determines the global conformations of nonhelix elements and protein-induced bends in RNA. TEB is a sensitive method for characterizing both the conformations and the flexibilities of RNA molecules in solution. In its application to the study of RNA conformation, it is fundamentally a hydrodynamic method; RNA helices with central bends undergo more rapid rotational diffusion than do their linear counterparts, because the bent molecules experience less frictional resistance. Because rotational diffusion is much more sensitive to changes in overall helix conformation than is translational diffusion and the relationship between the experimental diffusion constants and hydrodynamic theory is more straightforward, TEB has proven to be quite useful for quantifying both intrinsic and protein-induced bends in RNA. Another important distinction between rotational and translational diffusion pertains to the magnitude of the direct frictional contribution of a bound protein or element of RNA tertiary structure. For centrally placed elements, rotational diffusion is relatively insensitive to the frictional surface of the added protein or RNA structure because such elements lie close to the center of rotation. In a typical TEB experiment, an element of interest is placed at the center of an otherwise duplex RNA molecule. By comparing the birefringence decay time of the heteroduplex (or protein-bound) molecule to a linear control, a measure of the effective angle between the helix arms is obtained.

Transport coefficients of liquid transition metals: A computer simulation study using the embedded atom model

Using the Voter and Chen version of the embedded atom model, we carried out molecular dynamics simulations to compute the diffusion constants and shear viscosities of liquid Pd, Pt, Cu, Ag, and Au as representative of single-particle and collective dynamic properties, respectively. The generally good agreement between the calculated values and available experimental data is evidence that the Voter and Chen embedded atom model allows a reliable description of the dynamic properties of liquid transition metals in spite of being derived from solid-state data and the properties of the diatomic molecule. The discrepancy between the reported experimental diffusion constant of liquid Cu and the values calculated in this work, together with the consistency of these latter, suggests that the reported experimental value may be in error.

Phase separation studies on poly(vinylidene fluoride) and poly(methyl methacrylate) quenched blends

AbstractA combined study by SAXS and DSC on quenched blends of PVDF and PMMA is presented. Attention is focused on the first stage of the phase separation process during annealing that is shown to be mainly determined by the diffusion of the PVDF molecules from the amorphous blend phase towards the crystals growth front. The experimental monomer diffusion constants at T > Tg are compared with those expected theoretically using the approximation of the fast model process and the WLF equation for the relaxation frequency of the monomer. The nature and composition of the crystal interphase are discussed in terms of the SAXS invariant for the whole system and the calorimetric data derived from the Tg transitions observed.

Cation dependence of the ionic dynamics in computer simulated molten nitrates

In order to study the cation dependence of the ionic dynamics in molten nitrates, molecular dynamics simulations including vibrational degrees of freedom were carried out for molten LiNO3, NaNO3, and RbNO3. Coulomb pair potential with Born-type repulsion was adopted for the interionic interaction. The simulated diffusion coefficient was smaller for a larger cation, and that of nitrate ions did not change with changing cation species. The mean squared charge displacements showed that the static conductivity decreased considerably as the cation size increased from Li+ to Rb+. The simulated orientational correlation function of nitrate ions decayed more quickly as the cation size increased. Far infrared absorption spectrum simulated from the time evolution of the dipole moment (or the current) of the system showed that the peak shifted to the low energy side and the intensity decreased as the cation size increased. Results of the simulation were compared with the experimental diffusion constants, static and dynamic conductivities, and rotational behavior revealed by Raman spectroscopy. The simulated vibrational correlation functions and the power spectra of NO3− could reproduce the observed cation dependence of the peak frequencies of the ν1(A′1) and ν2(A″2) modes. However, the assumed interionic potentials in the present simulation were found to result in too slow vibrational dephasing of the ν1 mode and too fast dephasing of the ν2 mode as compared with the infrared and isotropic Raman spectra. Strong correlation between radial and angular distributions of cations was found in the first coordination spheres of nitrate ions in the simulated molten nitrates.