AT-specific DNA visualization revisits the directionality of bacteriophage λ DNA ejection.

In this study, we specifically visualized DNA molecules at their AT base pairs after in vitro phage ejection. Our AT-specific visualization revealed that either end of the DNA molecule could be ejected first with a nearly 50% probability. This observation challenges the generally accepted theory of Last In First Out (LIFO), which states that the end of the phage λ DNA that enters the capsid last during phage packaging is the first to be ejected, and that both ends of the DNA are unable to move within the extremely condensed phage capsid. To support our observations, we conducted computer simulations that revealed that both ends of the DNA molecule are randomized, resulting in the observed near 50% probability. Additionally, we found that the length of the ejected DNA by LIFO was consistently longer than that by First In First Out (FIFO) during in vitro phage ejection. Our simulations attributed this difference in length to the stiffness difference of the remaining DNA within the phage capsid. In conclusion, this study demonstrates that a DNA molecule within an extremely dense phage capsid exhibits a degree of mobility, allowing it to switch ends during ejection.

The effects of asymmetry in active noises on the efficiency of single colloidal Stirling engines with active noises.

Molecular machines, which operate in highly fluctuating environments far from equilibrium, may benefit from their non-equilibrium environments. It is, however, a topic of controversy how the efficiency of the microscopic engines can be enhanced. Recent experiments showed that microscopic Stirling engines in bacterial reservoirs could show high performance beyond the equilibrium thermodynamics. In this work, we perform overdamped Langevin dynamics simulations for microscopic Stirling heat engines in bacterial reservoirs and show that the temperature dependence of the magnitude of active noises should be responsible for such high efficiency. Only when we introduce temperature-dependent active noises, the efficiency of the microscopic Stirling engines is enhanced significantly as in experiments.

The effects of defects on the transport mechanisms of lithium ions in organic ionic plastic crystals.

Organic ionic plastic crystals (OIPCs) consist of molecular ions of which interactions are strong enough to maintain crystalline order but are weak enough to allow the rotations of the molecular ions at sufficiently high temperatures. When defects such as Schottky vacancies and grain boundaries are introduced into OIPCs, the defects facilitate the transport of dopants such as Li+ ions, for which OIPCs are considered as strong candidates for solid electrolytes. The transport mechanism of dopant ions in OIPCs with defects, however, remains elusive at a molecular level partly because it is hard in experiments to track the dopant ions and control the types of defects systematically. In this work, we perform molecular dynamics simulations for 1,3-dimethylimidazolium hexafluorophosphate ([MMIM][PF6]) OIPCs with Li+ ions doped and show that the transport mechanism of Li+ ions depends on the types and concentrations of defects. A high concentration of Schottky vacancies enhance the overall ion conduction, but decrease the transference number. The transference numbers of Li+ ions in [MMIM][PF6] with grain boundaries are similar to that in [MMIM][PF6] with 0.78 mol% point vacancies. We also find that the transport of ions in OIPCs is strongly heterogeneous and the time scales of the dynamic heterogeneity of the ions are sensitive to the types of defects.

The effects of the shape of a capsid on the ejection rate of a single polymer chain through a nanopore.

The shape of a viral capsid affects the equilibrium conformation of DNA inside the capsid: the equilibrium DNA conformation inside a spherical capsid is a concentric spool while the equilibrium conformation inside an elongated capsid is a twisted toroid. The conformation of DNA, jammed inside the capsid due to high internal pressure, influences the ejection kinetics of the DNA from the capsid. Therefore, one would expect that the DNA ejection kinetics would be subject to the shape of the viral capsid. The effects of the capsid shape on the ejection, however, remain elusive partly due to a plethora of viral capsid shapes. In this work, we perform Langevin dynamics simulations for the ejection of a polymer chain from three different types of viral capsids: (1) spherical, (2) cubic, and (3) cuboid capsids. We find that the ejection rate of the polymer chain from the spherical capsid is much faster than that from either cubic or cuboid capsids. The polymer chain in the spherical capsid may undergo collective rotational relaxation more readily such that the polymer chain becomes more mobile inside the spherical capsid, which enhances the ejection kinetics. On the other hand, a threading motion is dominant inside cubic and cuboid capsids. We also find that the effects of the collective rotational motion become more significant for a more rigid chain inside a capsid.

Effects of alkali ion dopants on the transport mechanisms and the thermal stabilities of imidazolium-based organic ionic plastic crystals.

Various dopant alkali ions have been introduced into organic ionic plastic crystals (OIPCs) in order to design solid electrolytes with the desired thermal stability and ionic conductivity. We performed extensive molecular dynamics simulations to investigate at the molecular level how dopant alkali ions affect the rotational and the translational diffusion of ions and the thermal stability of OIPCs. We introduced lithium (Li+), sodium (Na+), and potassium (K+) ions as dopants into 1-methyl-3-methylimidazolium hexafluorophosphate ([MMIM][PF6]) OIPCs at the molecular level. We found that as smaller alkali ions are doped, larger domains of the crystals are disrupted. This makes it harder for OIPCs doped with smaller alkali ions to maintain their crystal structure such that the melting temperature of OIPCs decreases and phase transitions between rotator phases change. The size of dopant alkali ions also affects the rotational diffusion of matrix ions of [MMIM]+ and PF6-: the rotational diffusion of matrix ions near Li+ ions becomes more heterogeneous and facilitated than those near other kinds of alkali ions. We also find that alkali ions of different kinds diffuse translationally in OIPCs via different transport mechanisms: while the Li+ ion undergoes continuous (anion-associated) diffusion through an amorphous region, the K+ ion hops between neighbor lattice sites. To investigate the effects of the relative size between matrix cations and dopant ions on translational diffusions, we also simulate OIPCs with longer alkyl chains such as 1-ethyl-3-methylimidazolium hexafluorophosphate ([EMIM][PF6]) and 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) crystals. We find that as the size of imidazolium cations increases, the hopping diffusion of the K+ ion becomes suppressed and the K+ ion is more likely to diffuse through amorphous domains.

The effects of polarization on the rotational diffusion of ions in organic ionic plastic crystals.

Organic ionic plastic crystals (OIPCs), which consist of organic molecular ions, are considered excellent candidates for solid electrolytes due to their high ionic conductivity in solid phases. Molecular ions undergo either rotational or conformational relaxation at certain temperatures in OIPCs. There have been molecular simulations to understand the rotational motion. The polarizability of ions was, however, often ignored in simulations due to the high computational cost. Since the polarizability may affect the translational diffusion, the ionic conductivity, and the phase transition of ionic liquids, it should be of interest to investigate how the polarizability would affect the rotational diffusion of ions in solid phases. In this work, we perform extensive atomistic molecular dynamics simulations for two different kinds of OIPCs, 1-methyl-3-methylimidazolium hexafluorophosphate ([MMIM][PF6]) and 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]). We employ various simulation models for ions by turning on and off the polarization in their interaction potentials. We find that the polarizability hardly affects the density, the crystalline structure, and the phase transition of both OIPCs. However, a certain rotational motion, especially the rotational diffusion of PF6 - in [MMIM][PF6] OIPCs, is enhanced by a factor of up to four when the polarizability is turned on. The PF6 - in [MMIM][PF6] OIPCs undergoes rotational hopping motions more significantly due to polarizability. We find that the rotational diffusion of a certain ion can be enhanced only when the polarization results in a significant change in the dipole moment of the neighboring ions around the ion.

Transport dynamics of complex fluids.

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate subdiffusive, and long-time diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a challenging problem. Here, we present a transport equation and its solutions, which yield a unified quantitative explanation of the mean-square displacement (MSD), the non-Gaussian parameter (NGP), and the displacement distribution of complex fluids. In our approach, the environment-coupled diffusion kernel and its time correlation function (TCF) are the essential quantities that determine transport dynamics and characterize mobility fluctuation of complex fluids; their time profiles are directly extractable from a model-free analysis of the MSD and NGP or, with greater computational expense, from the two-point and four-point velocity autocorrelation functions. We construct a general, explicit model of the diffusion kernel, comprising one unbound-mode and multiple bound-mode components, which provides an excellent approximate description of transport dynamics of various complex fluidic systems such as supercooled water, colloidal beads diffusing on lipid tubes, and dense hard disk fluid. We also introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents an unexplored direction for quantitative understanding of transport and transport-coupled processes in complex disordered media.

The effects of vacancies and their mobility on the dynamic heterogeneity in 1,3-dimethylimidazolium hexafluorophosphate organic ionic plastic crystals.

Organic ionic plastic crystals (OIPCs) are the crystals of electrolytes with a long-range translational order. The rotational modes of ions in OIPCs are, however, activated even in solid phases such that the diffusion of dopants such as lithium ions may be facilitated. OIPCs have been, therefore, considered as good candidates for solid electrolytes. Recent experiments and theoretical studies have suggested that both the translational and the rotational diffusion of ions are quite heterogeneous: the diffusion of some ions are quite fast while other ions of the same kind hardly diffuse, either rotationally or translationally. Such dynamic heterogeneity would be a key to the transport mechanism of dopants in solid state electrolytes. In this work, we investigate the effects of defects on the dynamic heterogeneity of OIPCs. We perform atomistic molecular dynamics simulation of 1,3-dimethylimidazolium hexafluorophosphate ([MMIM][PF6]) with a pair of cation and anion vacancies. At low temperature, vacancies undergo hopping motions toward each other and form a charge-neutral cluster. At high temperature, two vacancies act like a loosely bonded molecule and diffuse together via hopping motions. We find that the translational diffusion of ions is correlated strongly with the vacancy diffusion and becomes heterogeneous when the vacancies hop. The rotation of ions also becomes active when the ions are close to vacancies such that the rotational dynamic heterogeneity strengthens.

The effects of the lipid type on the spatial arrangement and dynamics of cholesterol in binary component lipid membranes.

Intermolecular interactions between cholesterol and lipids in cell membranes, which play critical roles in cellular processes such as the formation of nano-domains, depend on the molecular structure of the lipids. The diffusion and the spatial arrangement of cholesterol within the lipid membranes also change with the type of lipids. For example, the flip-flop, an important transport mechanism for cholesterol in the membranes, can be facilitated significantly by the presence of unsaturated lipids. However, how the structure of lipids affects the spatial arrangement and the dynamics of cholesterol remains elusive at a molecular level. In this study, we investigate the effects of lipid-cholesterol interactions on the spatial arrangement and the dynamics of cholesterol. We perform molecular dynamics simulations for the binary component membranes of lipids and cholesterol. We employ seven different kinds of lipids by changing either the degree of a saturation level or the length of lipid tails. We find from our simulations that the rate of cholesterol flip-flop is enhanced as the lipids are either less saturated or shorter, which is consistent with previous studies. Interestingly, when the lipid tails are fully saturated and sufficiently long, the center in between two leaflets becomes metastable for cholesterol to stay at. Because the cholesterol at the membrane center diffuses faster than that within leaflets, regardless of the lipid type, such an emergence of the metastable state (in terms of the cholesterol position) complicates the cholesterol diffusion significantly.

One-photon VUV-MATI and two-photon IR+VUV-MATI spectroscopic determination of oxetane cation ring-puckering vibrations and conformation.

The conformational structures of heterocyclic compounds are of considerable interest to chemists and biochemists as they are often the constituents of natural products. Among saturated four-membered heterocycles, the conformational structure of oxetane is known to be slightly puckered in equilibrium because of a low interconversion barrier in its ring-puckering potential, unlike cyclobutane and thietane. We measured the one-photon vacuum ultraviolet mass-analyzed threshold ionization (VUV-MATI) and two-photon IR+VUV-MATI spectra of oxetane for the first time to determine the ring-puckering potential of the oxetane cation and hence its conformational structure in the D0 (ground) state. Remarkably, negative anharmonicity and large amplitudes were observed for the ring-puckering vibrational mode progression in the low-frequency region of the observed MATI spectra. We were able to successfully analyze the progression in the MATI spectra through the Franck-Condon simulations, using modeled potential energy functions for the ring-puckering modes in the S0 and D0 states. Considering that the interconversion barrier and puckered angle for the ring-puckering potential on the S0 state were found to be 15.5 cm-1 and 14°, respectively, the cationic structure is expected to be planar with C2v symmetry. Our results revealed that the removal of an electron from the nonbonding orbitals on the oxygen atom in oxetane induced the straightening of the puckered ring in the cation owing to an increase in ring strain. Consequently, we conclude that this change in the conformational structure upon ionization generated the ring-puckering vibrational mode progression in the MATI spectra.

The non-classical kinetics and the mutual information of polymer loop formation.

The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (kloop) of the loop formation would be inversely proportional to viscosity (η), i.e., kloop ∼ η-1. Experiments and simulations showed, however, that kloop showed the fractional viscosity dependence of kloop ∼ η-ß with ß < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully.

A Theoretical Model for the Cell Cycle and Drug Induced Cell Cycle Arrest of FUCCI Systems with Cell-to-Cell Variation during Mitosis.

PURPOSE: Since the molecular mechanism of the cell cycle was established, various theoretical models of this process have been developed. A recent study revealed significant variability in cell cycle duration between mother and daughter cells, but this observation has not been incorporated into the theoretical models. METHODS: We used fluorescent ubiquitination-based cell cycle indicator (FUCCI) systems and live-monitored the heterogeneity of cell cycle progression within daughter cells, which accounts for dephasing synchrony. To incorporate the variable cell cycle durations into a model, we modified a two-ordinary differential equation (ODE) model based on reciprocal activation between CDK1 and APC. RESULTS: Our model reproduced the experimental population profile, in which cell cycle synchrony dephased due to variability. Based on this model, we determined parameters for CDK1 and APC in the cell cycle profile after treatment with antimitotic drugs and associated the parameters with the drugs' mode of action as cell cycle inhibitors. CONCLUSION: This suggests that this model is useful for determining the mode of action of unknown small molecules on the cell cycle.

The breakdown of the local thermal equilibrium approximation for a polymer chain during packaging.

The conformational relaxation of a polymer chain often slows down in various biological and engineering processes. The polymer, then, may stay in nonequilibrium states throughout the process such that one may not invoke the local thermal equilibrium (LTE) approximation, which has been usually employed to describe the kinetics of various processes. In this work, motivated by recent single-molecule experiments on DNA packaging into a viral capsid, we investigate how the nonequilibrium conformations and the LTE approximation would affect the packaging of a polymer chain into small confinement. We employ a simple but generic coarse-grained model and Langevin dynamics simulations to investigate the packaging kinetics. The polymer segments (both inside and outside the confinement) stay away from equilibrium under strong external force. We devise a simulation scheme to invoke the LTE approximation during packaging and find that the relaxation of nonequilibrium conformations plays a critical role in regulating the packaging rate.

Effects of solvent quality and non-equilibrium conformations on polymer translocation.

The conformation and its relaxation of a single polymer depend on solvent quality in a polymer solution: a polymer collapses into a globule in a poor solvent, while the polymer swells in a good solvent. When one translocates a polymer through a narrow pore, a drastic conformational change occurs such that the kinetics of the translocation is expected to depend on the solvent quality. However, the effects of solvent quality on the translocation kinetics have been controversial. In this study, we employ a coarse-grained model for a polymer and perform Langevin dynamics simulations for the driven translocation of a polymer in various types of solvents. We estimate the free energy of polymer translocation using steered molecular dynamics simulations and Jarzynski's equality and find that the free energy barrier for the translocation increases as the solvent quality becomes poorer. The conformational entropy contributes most to the free energy barrier of the translocation in a good solvent, while a balance between entropy and energy matters in a poor solvent. Interestingly, contrary to what is expected from the free energy profile, the translocation kinetics is a non-monotonic function of the solvent quality. We find that for any type of solvent, the polymer conformation stays far away from the equilibrium conformation during translocation due to an external force and tension propagation. However, the degree of tension propagation differs depending on the solvent quality as well as the magnitude of the external force: the tension propagation is more significant in a good solvent than in a poor solvent. We illustrate that such differences in tension propagation and non-equilibrium conformations between good and poor solvents are responsible for the complicated non-monotonic effects of solvent quality on the translocation kinetics.

Bernal stacking-assisted shear exfoliation of nanoplate bilayers.

Nanoplates such as graphene and MoS2 are promising materials due to their excellent electronic and mechanical properties. The preparation of such nanoplates is, however, still challenging due to the large free energy barrier that multilayer nanoplates need to overcome during exfoliation. In the case of a Bernal-stacked bilayer graphene, the binding energy between two graphene layers is about 17.8 meV per atom such that harsh chemical and/or mechanical treatment is usually necessary. In this paper, we perform extensive molecular dynamics simulations for a generic model of nanoplates and illustrate that when the shear is applied to the nanoplate bilayer solution, the nanoplate bilayer may exfoliate readily. In our simulations, the free energy barrier that two nanoplate layers need to overcome reaches up to 21.8kBT, where kB and T denote the Boltzmann constant and temperature, respectively. This implies that without external stimuli, the nanoplate bilayer would hardly exfoliate. Upon the application of shear, however, the transition between different Bernal stacked conformations occurs, which provides multiple intermediate states for exfoliation and facilitates the shear exfoliation. We also find that if one were to increase the affinity between the solvent and nanoplates slightly, the free energy barrier would be decreased significantly.

Fractional Viscosity Dependence of Reaction Kinetics in Glass-Forming Liquids.

The diffusion of molecules in complex systems such as glasses and cell cytoplasm is slow, heterogeneous, and sometimes nonergodic. The effects of such intriguing diffusion on the kinetics of chemical and biological reactions remain elusive. In this Letter, we report that the kinetics of the polymer loop formation reaction in a Kob-Andersen (KA) glass forming liquid is influenced significantly by the dynamic heterogeneity. The diffusion coefficient D of a KA liquid deviates from the Stokes-Einstein relation at low temperatures and D shows a fractional dependence on the solvent viscosity η_{s}, i.e., D∼η_{s}^{-ξ_{D}} with ξ_{D}=0.85. The dynamic heterogeneity of a KA liquid affects the rate constant k_{rxn} of the loop formation and leads to the identical fractional dependence of k_{rxn} on η_{s} with k_{rxn}∼η_{s}^{-ξ} and ξ=ξ_{D}, contrary to reactions in dynamically homogeneous solutions where k_{rxn}∼η_{s}^{-1}.

The glass transition and interfacial dynamics of single strand fibers of polymers.

We investigate the glass transition and interfacial dynamics of single strand fibers of flexible polymers by employing molecular dynamics (MD) simulations along with a coarse grained model. While the polymer fiber has drawn significant attention due to its applicability in tissue engineering and stretchable electronics, its dynamic properties, especially the glass transition temperature (Tg), are yet to be understood at the molecular level. For example, there has been a controversy on the effect of the polymer fiber radius (R) on Tg: Tg decreased with a decrease in R for some polymer fibers, whereas Tg of other polymer fibers was not sensitive to R. In this article, we estimate the bond relaxation time of polymers and evaluate both Tg and fragility (m) as a function of R. We illustrate that Tg of the polymer fiber decreased with a decrease in R monotonically and also that the values of Tg follow faithfully the empirical equation proposed by Keddie et al. as a function of R, which was successfully employed to fit the values of Tg of both polyvinyl alcohol (PVA) fibers and polyethylene (PE) fibers. We also find that the dynamics of polymers at the interface between a polymer fiber and air is faster than that of polymers at the center. By employing Adam-Gibbs theory, we show that the fast interface dynamics of polymer fibers should influence the cooperative motion of monomers, which should be responsible for the decrease in Tg for smaller values of R. Near the interface there are more mobile monomers that participate in the cooperative motions of polymers. Interesting is that due to the curved surface (unlike flat polymer films) the cooperative motion of monomers is anisotropic in polymer fibers.

The spatial arrangement of a single nanoparticle in a thin polymer film and its effect on the nanoparticle diffusion.

The spatial arrangement of nanoparticles (NPs) within thin polymer films may influence their properties such as the glass transition temperature. Questions regarding what may affect the spatial arrangement of NPs, however, still remain unanswered at a molecular level. In this work, we perform molecular dynamics simulations for a free-standing thin polymer film with a single NP. We find from simulations that depending on the NP size and the inter-particle interaction between the NP and polymers, one may control the spatial arrangement of the NP. When the interaction between the NP and polymers is sufficiently attractive (repulsive), the NP is likely to be placed at the center (at the surface) of the thin film in equilibrium. Interestingly, for a moderate interaction between the NP and polymers, the first-order transition occurs in the spatial arrangement of the NP as one increases the NP size: a small NP prefers the surface of the polymer film whereas a large NP prefers the center. Such a first-order transition is corroborated by calculating the free energy of the NP as a function of the position and can be understood in terms of a sixth-order Landau free energy. More interestingly, the diffusion of the NP also changes drastically due to the first-order transition in the spatial arrangement. The NP diffusion is enhanced drastically (more than expected in bulk polymer melts) as the NP is shifted to the polymer film surface.

Observation of the Ring-Puckering Vibrational Mode in Thietane Cation.

We have measured the high-resolution vibrational spectra of a thietane (trimethylene sulfide) cation in the gas phase by employing the vacuum ultraviolet mass-analyzed threshold ionization (VUV-MATI) spectroscopic technique. Peaks in the low-frequency region of the observed MATI spectrum of thietane originate from a progression of the ring-puckering vibrational mode (typical in small heterocyclic molecules), which is successfully reproduced by quantum-chemical calculations with 1D symmetric double-well potentials along the ring puckering coordinates on both the S0 and D0 states, the ground electronic states of neutral and cation of thietane, respectively. The values of the interconversion barrier and the ring-puckering angle on the S0 state, the parameters used for the quantum-chemical calculations, were assumed to be 274 cm-1 and 26°. The barrier and the angle on the D0 state, however, are found to be 48.0 cm-1 and 18.2°, respectively, where such small barrier height and puckering angle for the cation suggest that the conformation of thietane cation on the D0 state should be more planar than that of the thietane neutral.

Translation-rotation decoupling of tracers of locally favorable structures in glass-forming liquids.

Particles in glass-forming liquids may form domains of locally favorable structures (LFSs) upon supercooling. Whether and how the LFS domains would relate to the slow relaxation of the glass-forming liquids have been issues of interest. In this study, we employ tracers of which structures resemble the LFS domains in Wahnström and Kob-Andersen (KA) glass-forming liquids and investigate the translation-rotation decoupling of the tracers. We find that the tracer structure affects how the translation and the rotation of tracers decouple and that information on the local mobility around the LFS domains may be gleaned from the tracer dynamics. According to the Stokes-Einstein relation and the Debye-Stokes-Einstein relation, the ratio of the translational (DT) and rotational (DR) diffusion coefficients is expected to be a constant over a range of T/η, where η and T denote the medium viscosity and temperature, respectively. In supercooled liquids and glasses, however, DT and DR decouple due to dynamic heterogeneity, thus DT/DR not being constant any more. In Wahnström glass-forming liquids, icosahedron LFS domains are the most long-lived ones and the mobility of neighbor particles around the icosahedron LFS domain is suppressed. We find from our simulations that the icosahedron tracers, similar in size and shape to the icosahedron LFS domains, experience drastic translation-rotation decoupling upon cooling. The local mobility of liquid particles around the icosahedron tracers is also suppressed significantly. On the other hand, tracers of FCC and HCP structures do not show translation-rotation decoupling in the Wahnström liquid. In KA glass-forming liquids, bicapped square antiprism LFS domains are the most long-lived LFS domains but are not correlated significantly with the local mobility. We find from our simulations that DT and DR of bicapped square antiprism tracers, also similar in size and shape to the bicapped square antiprism LFS domains, do not decouple significantly similarly to tracers of other structures, thus reflecting that the local mobility would not be associated strongly with LFS domains in the KA liquid.