A review of COVID vaccines: success against a moving target.

BACKGROUND: Multiple vaccine platforms against COVID-19 have been developed and found safe and efficacious at a record speed. Although most are effective, they vary in their ease of production and distribution, their potential speed of modification against new variants, and their durability of protection and safety in certain target groups. SOURCES OF DATA: Our discussion is based on published reports of clinical trials and analyses from national and global health agencies. AREAS OF AGREEMENT: The production of neutralizing antibodies against the viral spike protein is protective, and all vaccines for which published data exist have been found to be effective against severe disease caused by the viral strain they target. AREAS OF CONTROVERSY: The degree to which vaccines protect against emerging variants, moderate disease and asymptomatic infection remains somewhat unclear. GROWING POINTS: Knowledge of the duration of protection and its decay is increasing, and discussions of booster frequency and target strains are ongoing. AREAS TIMELY FOR DEVELOPING RESEARCH: The global effort to combat transmission and disease continues to rely upon intense epidemiological surveillance, whilst real-world data and clinical trials shape vaccination schedules and formulae.

A possible scenario for the fragile-to-strong dynamic crossover predicted by the extended mode-coupling theory for glass transition.

It is argued that the extended mode-coupling theory for glass transition predicts a dynamic crossover in the α-relaxation time and in the self-diffusion constant as a general implication of the structure of its equations of motion. This crossover occurs near the critical temperature T(c) of the idealized version of the theory, and is caused by the change in the dynamics from the one determined by the cage effect to that dominated by hopping processes. When combined with a model for the hopping kernel deduced from the dynamical theory for diffusion-jump processes, the dynamic crossover can be identified as the fragile-to-strong crossover (FSC) in which the α-relaxation time and the self-diffusion constant cross over from a non-Arrhenius to an Arrhenius behavior. Since the present theory does not resort to the existence of the so-called Widom line, to which the FSC in confined water has been attributed, it provides a possible explanation of the FSC observed in a variety of glass-forming systems in which the existence of the Widom line is unlikely. In addition, the present theory predicts that the Stokes-Einstein relation (SER) breaks down in different ways on the fragile and strong sides of the FSC, in agreement with the experimental observation in confined water. It is also demonstrated that the violation of the SER in both the fragile and strong regions can be fitted reasonably well by a single fractional relation with an empirical exponent of 0.85.

Evidence of dynamic crossover phenomena in water and other glass-forming liquids: experiments, MD simulations and theory.

In a recent quasi-elastic neutron scattering experiment on water confined in a Portland cement paste, we find that this 3D confined water shows a dynamic crossover phenomenon at T(L) = 227 ± 5 K. The DSC heat-flow scan upon cooling and an independent measurement of specific heat at constant pressure of confined water in silica gel show a prominent peak at the same temperature. We show in this paper that this type of behavior is common to many other glassy liquids, which also show the crossover temperature in coincidence with the temperature of a small specific heat peak. We also demonstrate with MD simulations that the dynamic crossover phenomenon in confined water is an intrinsic property of bulk water, and is not due to the confinement effect. Recently, an extended version of the mode coupling theory (MCT) including the hopping effect was developed. This theory shows that, instead of a structural arrest transition at T(C) predicted by the idealized MCT, a fragile-to-strong dynamic crossover phenomenon takes place instead at T(C), confirming both the experimental and the numerical results. The coherent and incoherent α relaxation times can be scaled with the calculated viscosity, showing the same crossover phenomenon. We thus demonstrated with experiments, simulations and theory that a genuine change of dynamical behavior of both water and many glassy liquids happens at the crossover temperature T(L), which is 10-30% higher than the calorimetric glass transition temperature T(g).

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach.

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.

Structural relaxation in supercooled orthoterphenyl.

We report molecular-dynamics simulation results performed for a model of molecular liquid orthoterphenyl in supercooled states, which we then compare with both experimental data and mode-coupling-theory (MCT) predictions, aiming at a better understanding of structural relaxation in orthoterphenyl. We pay special attention to the wave number dependence of the collective dynamics. It is shown that the simulation results for the model share many features with experimental data for real system, and that MCT captures the simulation results at the semiquantitative level except for intermediate wave numbers connected to the overall size of the molecule. Theoretical results at the intermediate wave number region are found to be improved by taking into account the spatial correlation of the molecule's geometrical center. This supports the idea that unusual dynamical properties at the intermediate wave numbers, reported previously in simulation studies for the model and discernible in coherent neutron-scattering experimental data, are basically due to the coupling of the rotational motion to the geometrical-center dynamics. However, there still remain qualitative as well as quantitative discrepancies between theoretical prediction and corresponding simulation results at the intermediate wave numbers, which call for further theoretical investigation.

Structural relaxation in a system of dumbbell molecules.

The interaction-site-density-fluctuation correlators, the dipole-relaxation functions, and the mean-squared displacements of a system of symmetric dumbbells of fused hard spheres are calculated for two representative elongations of the molecules within the mode-coupling theory for the evolution of glassy dynamics. For large elongations, universal relaxation laws for states near the glass transition are valid for parameters and time intervals similar to the ones found for the hard-sphere system. Rotation-translation coupling leads to an enlarged crossover interval for the mean-squared displacement of the constituent atoms between the end of the von Schweidler regime and the beginning of the diffusion process. For small elongations, the superposition principle for the reorientational alpha process is violated for parameters and time intervals of interest for data analysis, and there is a strong breaking of the coupling of the alpha-relaxation scale for the diffusion process with that for representative density fluctuations and for dipole reorientations.

Mode-coupling theory for structural and conformational dynamics of polymer melts.

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.

Idealized glass transitions for a system of dumbbell molecules.

The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule's constituent atoms as the basic structure variables. The theory is applied to calculate the liquid-glass phase diagram and the form factors for the arrested structure of a system of symmetric dumbbells of fused hard spheres. The static structure factors, which enter the equations of motion as input, are calculated as function of the packing fraction phi and the molecule's elongation zeta within the reference-interaction-site-model and Percus-Yevick theories. The critical packing fraction phi(c) for the glass transition is obtained as nonmonotone function of zeta with a maximum near zeta=0.43. A transition line is calculated separating a small-zeta-glass phase with ergodic dipole motion from a large-zeta-glass phase where also the reorientational motion is arrested. The Debye-Waller factors at the transition are found to be somewhat larger for sufficiently elongated systems than those for the simple hard-sphere system, but the wave-number dependence of the glass-form factors is quite similar. The dipole reorientations for zeta> or =0.6 are arrested as strongly as density fluctuations with wave vectors at the position of the first sharp diffraction peak.

Dynamical transition of myoglobin in a crystal: comparative studies of X-ray crystallography and Mössbauer spectroscopy.

The crystallographic normal mode refinements of myoglobin at a wide range of temperature from 40 K to 300 K were carried out to study the temperature dependence of the internal atomic fluctuations. The refinement method decomposes the mean square displacement from the average position, (deltar2), into the contributions from the internal degrees of freedom and those from the external degrees of freedom. The internal displacements show linear temperature dependence as (deltar2)=alphaT+beta, throughout the temperature range measured here, and exhibit no obvious change in the slope alpha at the dynamical transition temperature (Tc=ca. 180 K). The slope alpha is practically the same as the value predicted theoretically by normal mode analysis. Such linear dependence is considered to be due to the following reason. The crystallographic Debye-Waller factor represents the static distribution caused by convolution of temperature-dependent normal mode motions and a temperature-independent set of the conformational substates. In contrast, Mössbauer absorption spectroscopy shows a clear increase in the gradient alpha at Tc. This difference from X-ray diffraction originates from the incoherent nature of the Mössbauer effect together with its high-energy resolution, which yields the self-correlation, and the temporal behavior of individual Fe atoms in the myoglobin crystal.

Mean-squared displacement of a molecule moving in a glassy system.

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the alpha process, which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The alpha process for molecules with a large elongation is shown to exhibit an anomalously wide crossover interval between the end of the von Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary nonmonotonically as a function of its elongation.

Mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid.

Generalizing the mode-coupling theory for ideal liquid-glass transitions, equations of motion are derived for the correlation functions describing the glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming system. The molecule is described in the interaction-site representation and the equations are solved for a dumbbell molecule consisting of two fused hard spheres in a hard-sphere system. The results for the molecule's arrested position in the glass state and the reorientational correlators for angular-momentum index l=1 and l=2 near the glass transition are compared with those obtained previously within a theory based on a tensor-density description of the molecule in order to demonstrate that the two approaches yield equivalent results. For strongly hindered reorientational motion, the dipole-relaxation spectra for the alpha process can be mapped on the dielectric-loss spectra of glycerol if a rescaling is performed according to a suggestion by Dixon et al. [Phys. Rev. Lett. 65, 1108 (1990)]. It is demonstrated that the glassy dynamics is independent of the molecule's inertia parameters.