Noriyuki Yoshii

A molecular dynamics study of free energy of micelle formation for sodium dodecyl sulfate in water and its size distribution

Free energy of micelle formation has been evaluated for spherical sodium dodecyl sulfate (SDS) in water by a thermodynamic integration method combined with a series of large-scale molecular dynamics calculations following the chemical species model. In particular, free energy change delta mu(n+1)0 with respect to the addition of one surfactant molecule to the spherical micelle of size n was obtained as a function of n. The free energy profile showed a minimum followed by a maximum, which corresponds to a peak in the size distribution. The calculated peak size n = 57 near its critical micelle concentration is in good agreement with the experimental averaged aggregation number n = 55-75 of the SDS micelle. The distribution showed a rather sharp peak, indicating that the size is almost a monodisperse one. The size is likely to be insensitive to the total concentration of the surfactant.

MODYLAS: A Highly Parallelized General-Purpose Molecular Dynamics Simulation Program for Large-Scale Systems with Long-Range Forces Calculated by Fast Multipole Method (FMM) and Highly Scalable Fine-Grained New Parallel Processing Algorithms

Our new molecular dynamics (MD) simulation program, MODYLAS, is a general-purpose program appropriate for very large physical, chemical, and biological systems. It is equipped with most standard MD techniques. Long-range forces are evaluated rigorously by the fast multipole method (FMM) without using the fast Fourier transform (FFT). Several new methods have also been developed for extremely fine-grained parallelism of the MD calculation. The virtually buffering-free methods for communications and arithmetic operations, the minimal communication latency algorithm, and the parallel bucket-relay communication algorithm for the upper-level multipole moments in the FMM realize excellent scalability. The methods for blockwise arithmetic operations avoid data reload, attaining very small cache miss rates. Benchmark tests for MODYLAS using 65 536 nodes of the K-computer showed that the overall calculation time per MD step including communications is as short as about 5 ms for a 10 million-atom system; that is, 35 ns of simulation time can be computed per day. The program enables investigations of large-scale real systems such as viruses, liposomes, assemblies of proteins and micelles, and polymers.

All-atom molecular dynamics calculation study of entire poliovirus empty capsids in solution.

Small viruses that belong, for example, to the Picornaviridae, such as poliovirus and foot-and-mouth disease virus, consist simply of capsid proteins and a single-stranded RNA (ssRNA) genome. The capsids are quite stable in solution to protect the genome from the environment. Here, based on long-time and large-scale 6.5 × 10(6) all-atom molecular dynamics calculations for the Mahoney strain of poliovirus, we show microscopic properties of the viral capsids at a molecular level. First, we found equilibrium rapid exchange of water molecules across the capsid. The exchange rate is so high that all water molecules inside the capsid (about 200,000) can leave the capsid and be replaced by water molecules from the outside in about 25 μs. This explains the capsids tolerance to high pressures and deactivation by exsiccation. In contrast, the capsid did not exchange ions, at least within the present simulation time of 200 ns. This implies that the capsid can function, in principle, as a semipermeable membrane. We also found that, similar to the xylem of trees, the pressure of the solution inside the capsid without the genome was negative. This is caused by coulombic interaction of the solution inside the capsid with the capsid excess charges. The negative pressure may be compensated by positive osmotic pressure by the solution-soluble ssRNA and the counter ions introduced into it.

All-atom molecular dynamics study of a spherical micelle composed of N-acetylated poly(ethylene glycol)-poly(gamma-benzyl L-glutamate) block copolymers: a potential carrier of drug delivery systems for cancer.

An all-atom molecular dynamics simulation of a spherical micelle composed of amphiphilic N-acetylated poly(ethylene glycol)-poly(gamma-benzyl L-glutamate) (PEG-PBLG-Ac) block copolymers was performed in aqueous solution at 298.15 K and 1 atm. Such copolymers have received considerable attention as carriers in drug delivery systems. In this study, we used copolymers consisting of 11 EG units and 9 BLG units as models. Starting from the copolymers arranged spherically, the calculation predicted an equilibrium state consisting of a slightly elliptical micelle structure with a hydrophobic PBLG inner core and a hydrophilic PEG outer shell. The micelle structure was dynamically stable during the simulation, with the PEG blocks showing a compact helical conformation and the PBLG blocks an alpha-helix form. Multiple hydrogen bonds with solvent water molecules stabilized the helical conformation of the PEG blocks, leading to their hydration as shown by longer residence times of water molecules near the PEG ether oxygen atoms compared with that of bulk water. Some water molecules have also been found distributed within the hydrophobic core; they showed continuous exchange with bulk water during the simulation. Those molecules existed mostly as a cluster in spaces between the copolymers, forming hydrogen bonds among themselves as well as with the hydrophobic core through hydrophilic groups such as esters and amides. The water molecules forming hydrogen bonds with the micelle may play an important role in the stabilization of the micelle structure.

Free energy profiles for penetration of methane and water molecules into spherical sodium dodecyl sulfate micelles obtained using the thermodynamic integration method combined with molecular dynamics calculations

The free energy profiles, ΔG(r), for penetration of methane and water molecules into sodium dodecyl sulfate (SDS) micelles have been calculated as a function of distance r from the SDS micelle to the methane and water molecules, using the thermodynamic integration method combined with molecular dynamics calculations. The calculations showed that methane is about 6-12 kJ mol(-1) more stable in the SDS micelle than in the water phase, and no ΔG(r) barrier is observed in the vicinity of the sulfate ions of the SDS micelle, implying that methane is easily drawn into the SDS micelle. Based on analysis of the contributions from hydrophobic groups, sulfate ions, sodium ions, and solvent water to ΔG(r), it is clear that methane in the SDS micelle is about 25 kJ mol(-1) more stable than it is in the water phase because of the contribution from the solvent water itself. This can be understood by the hydrophobic effect. In contrast, methane is destabilized by 5-15 kJ mol(-1) by the contribution from the hydrophobic groups of the SDS micelle because of the repulsive interactions between the methane and the crowded hydrophobic groups of the SDS. The large stabilizing effect of the solvent water is higher than the repulsion by the hydrophobic groups, driving methane to become solubilized into the SDS micelle. A good correlation was found between the distribution of cavities and the distribution of methane molecules in the micelle. The methane may move about in the SDS micelle by diffusing between cavities. In contrast, with respect to the water, ΔG(r) has a large positive value of 24-35 kJ mol(-1), so water is not stabilized in the micelle. Analysis showed that the contributions change in complex ways as a function of r and cancel each other out. Reference calculations of the mean forces on a penetrating water molecule into a dodecane droplet clearly showed the same free energy behavior. The common feature is that water is less stable in the hydrophobic core than in the water phase because of the energetic disadvantage of breaking hydrogen bonds formed in the water phase. The difference between the behaviors of the SDS micelles and the dodecane droplets is found just at the interface; this is caused by the strong surface dipole moment formed by sulfate ions and sodium ions in the SDS micelles.

Drug binding and mobility relating to the thermal fluctuation in fluid lipid membranes

Drug binding and mobility in fluid lipid bilayer membranes are quantified in situ by using the multinuclear solution NMR combined with the pulsed-field-gradient technique. One-dimensional and pulsed-field-gradient (19)F and (1)H NMR signals of an anticancer drug, 5-fluorouracil (5FU) are analyzed at 283-313 K in the presence of large unilamellar vesicles (LUVs) of egg phosphatidylcholine (EPC) as model cell membranes. The simultaneous observation of the membrane-bound and free 5FU signals enables to quantify in what amount of 5FU is bound to the membrane and how fast 5FU is moving within the membrane in relation to the thermal fluctuation of the soft, fluid environment. It is shown that the mobility of membrane-bound 5FU is slowed down by almost two orders of magnitude and similar to the lipid movement in the membrane, the movement closely related to the intramembrane fluidity. The mobility of 5FU and EPC is, however, not similar at 313 K; the 5FU movement is enhanced in the membrane as a result of the loose binding of 5FU in the lipid matrices. The membrane-bound fraction of 5FU is approximately 0.1 and almost unaltered over the temperature range examined. It is also independent of the 5FU concentration from 2 to 30 mM with respect to the 40-50 mM LUV. The free energy of the 5FU binding is estimated at -4 to -2 kJ/mol, the magnitude always close to the thermal fluctuation, 2.4-2.6 kJ/mol.

Free energy of water permeation into hydrophobic core of sodium dodecyl sulfate micelle by molecular dynamics calculation.

In our previous analysis of the structural stability of a sodium dodecyl sulfate (SDS) micelle based on molecular dynamics calculation, vacancies were found in the center of the micelles [N. Yoshii and S. Okazaki, Chem. Phys. Lett.425, 58 (2006)]. It is very interesting to clarify whether a water molecule is expected in the vacancy in thermodynamic equilibrium at room temperature. In order to investigate the stability of water in the core of micelle, free energy of transfer of water from bulk to the core has been calculated for the SDS micelle in water for two micelle sizes, N=61 and 121, at temperature T=300 K and pressure P=1 atm. The calculated free energy of transfer, ΔGc←b, from the bulk to the core is about 28±4 kJ∕mol and 26±4 kJ∕mol for the micelle of the size N=61 and 121, respectively, where the corresponding Boltzmann factor, exp(−ΔGc←b∕kT), is in the order of one over several ten thousands. Thus, a water molecule hardly permeates into the core of the micelle.

Molecular dynamics study of solubilization of immiscible solutes by a micelle: Free energy of transfer of alkanes from water to the micelle core by thermodynamic integration method

Free energy of transfer, DeltaG(w-->m), from water phase to a sodium dodecyl sulfate (SDS) micelle core has been calculated for a series of hydrophobic solutes originally immiscible with water by thermodynamic integration method combined with molecular dynamics calculations. The calculated free energy of transfer is in good correspondence to the experiment as well as the theoretical free energy of transfer. The calculated DeltaG(w-->m)s are all negative, implying that the alkane molecules are more stable in the micelle than in the water phase. It decreases almost linearly as a function of the number of carbon atoms of the alkanes longer than methane with a decrement of 3.3 kJ mol(-1) per one methylene group. The calculated free energy of transfer indicates that, for example, at the micelle concentration of 50 CMC (critical micelle concentration), about only 1 of 6 micelles or 1 of 32 000 micelles does not contain a solute methane or n-octane molecule, respectively.

Binding of hydrophobic fluorinated bisphenol A to large unilamellar vesicles of egg phosphatidylcholine.

The kinetics of membrane binding and dissociation of fluorinated bisphenol A (FBPA, (CF(3))(2)C(C(6)H(4)OH)(2)) is quantified by 1D (19)F NMR spectra in situ. Although the bound and free components are in fast exchange, the rate constants and bound fraction is nonetheless determined from an analysis of the spectra. The analysis relies on the expression of 1D NMR signal intensity by a set of Bloch equations with exchange terms. The time span of the binding and dissociation of hydrophobic FBPA to large unilamellar vesicles of egg phosphatidylcholine (EPC) is 10(-3) to 10(-2) s. The rates of FBPA binding and dissociation are kept constant per EPC molecule even at different concentrations of the vesicle. The free energy of FBPA transfer is -20 ± 2 kJ/mol at 303 K. The process is entropy-driven. The efficiency of FBPA transfer is enhanced by a factor of 7 × 10(4), as compared with the hydrophilic 5-fluorouracil.

Lateral diffusion of lipids separated from rotational and translational diffusion of a fluid large unilamellar vesicle.

A new method to separate lateral diffusion of lipids in spherical large unilamellar vesicles from the rotational and the translational diffusion of the vesicle as a whole is proposed. The lateral diffusion coefficient DL is obtained as a time-dependent part of the observed diffusion coefficient in vesicles of 800-nm diameters, by systematically changing the diffusion time interval of the high-field-gradient NMR measurement. Although the lipid is in a confined space, the DL of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine is (1.5±0.6)×10(-11) m(2) s(-1) in the fluid state at 45°C, more than one order of magnitude faster than the rotational and the translational diffusion coefficients of the vesicle by the hydrodynamic continuum model. The method provides a potential for quantifying the lateral diffusion of lipids and proteins in fluid bilayer vesicles as model cell membranes in a natural manner.