A structured model for COVID-19 spread: modelling age and healthcare inequities.

We use a stochastic branching process model, structured by age and level of healthcare access, to look at the heterogeneous spread of COVID-19 within a population. We examine the effect of control scenarios targeted at particular groups, such as school closures or social distancing by older people. Although we currently lack detailed empirical data about contact and infection rates between age groups and groups with different levels of healthcare access within New Zealand, these scenarios illustrate how such evidence could be used to inform specific interventions. We find that an increase in the transmission rates among children from reopening schools is unlikely to significantly increase the number of cases, unless this is accompanied by a change in adult behaviour. We also find that there is a risk of undetected outbreaks occurring in communities that have low access to healthcare and that are socially isolated from more privileged communities. The greater the degree of inequity and extent of social segregation, the longer it will take before any outbreaks are detected. A well-established evidence for health inequities, particularly in accessing primary healthcare and testing, indicates that Maori and Pacific peoples are at a higher risk of undetected outbreaks in Aotearoa New Zealand. This highlights the importance of ensuring that community needs for access to healthcare, including early proactive testing, rapid contact tracing and the ability to isolate, are being met equitably. Finally, these scenarios illustrate how information concerning contact and infection rates across different demographic groups may be useful in informing specific policy interventions.

Effective rate constant for nanostructured heterogeneous catalysts.

There is a great deal of interest in the use of nanostructured heterogeneous catalysts, particularly those based on expensive precious metals, in order to maximise the surface to volume ratio of the catalyst, potentially reducing the cost without sacrificing performance. When there is an abundance of reactants available, the effective reactivity will depend on the surface density of the catalytically active sites. However, under diffusion-limited conditions, catalytically active sites may compete for reactants, potentially leading to diminishing returns from the use of nanostructures. In this paper we apply a mathematical homogenization approach to investigate the effect of scale and patterning on the effective activity of catalytic sites on a heterogeneous catalyst operating under diffusion-limited conditions. We test these theoretical results numerically using Monte Carlo simulations, and show that in the continuum limit the theory works well. In particular, in the limit where the mean free path is much less than the scale of patterning of catalytically active sites, the effective rate constant is found to be equal to the area-weighted harmonic mean of the rate constants on the surface. However, as the length scale of the patterns becomes comparable to the mean free path length, the simulations show that the effective activity of the system can exceed the theoretical limit suggested by the continuum theory.

Degenerate Ising model for atomistic simulation of crystal-melt interfaces.

One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level.

Filling a nanoporous substrate by dewetting of thin films.

Following a simple thermodynamic model, which predicts that an array of non-wettable pores can be filled by dewetting of sufficiently thin films, we use molecular dynamics to simulate the rupture of nanometre-thick liquid Au films on nanoporous substrates. Our simulations clearly exhibit spinodal dewetting and hole nucleation, and some of the metal is indeed absorbed by non-wettable pores solely as a virtue of the Laplace pressure acting on dewetted droplets and rivulet-like structures. Finally, we show that the fraction of absorbed Au can be increased through patterning of the initial film.

Uptake and withdrawal of droplets from carbon nanotubes.

We give an account of recent studies of droplet uptake and withdrawal from carbon nanotubes using simple theoretical arguments and molecular dynamics simulations. Firstly, the thermodynamics of droplet uptake and release is considered and tested via simulation. We show that the Laplace pressure acting on a droplet assists capillary uptake, allowing sufficiently small non-wetting droplets to be absorbed. We then demonstrate how the uptake and release of droplets of non-wetting fluids can be exploited for the use of carbon nanotubes as nanopipettes. Finally, we extend the Lucas-Washburn model to deal with the dynamics of droplet capillary uptake, and again test this by comparison with molecular dynamics simulations.

Effective slip lengths for flows over surfaces with nanobubbles: the effects of finite slip.

We consider effective slip lengths for flows of simple liquids over surfaces contaminated by gaseous nanobubbles. In particular, we examine whether the effects of finite slip over the liquid-bubble interface are important in limiting effective slip lengths over such surfaces. Using an expression that interpolates between the perfect slip and finite slip regimes for flow over bubbles, we conclude that for the bubble dimensions and coverages typically reported in the literature the effects of finite slip are secondary, reducing effective slip lengths by only 10%. Further, we find that nanobubbles do not significantly increase slip lengths beyond those reported for bare hydrophobic surfaces.

Molecular dynamics study of the melting of a supported 887-atom Pd decahedron.

We employ classical molecular dynamics simulations to investigate the melting behaviour of a decahedral Pd(887) cluster on a single layer of graphite (graphene). The interaction between Pd atoms is modelled with an embedded-atom potential, while the adhesion of Pd atoms to the substrate is approximated with a Lennard-Jones potential. We find that the decahedral structure persists at temperatures close to the melting point, but that just below the melting transition, the cluster accommodates to the substrate by means of complete melting and then recrystallization into an fcc structure. These structural changes are in qualitative agreement with recently proposed models, and they verify the existence of an energy barrier preventing softly deposited clusters from 'wetting' the substrate at temperatures below the melting point.

Dynamics of capillary absorption of droplets by carbon nanotubes.

We consider the capillary absorption of liquid metal droplets by carbon nanotubes using molecular dynamics simulations and the steady-state flow model due to Marmur [A. Marmur, J. Colloid Interface Sci. 122, 209 (1988)]. We find an exact solution to Marmur's evolution equation for the height of the absorbed liquid column as a function of time, and show that this reproduces the dynamics observed in the simulations well. The simulations show that the flow of the metal exhibits a large degree of slippage at the tube walls, with slip lengths of up to 10 nm depending on the wettability of the nanotube. The results support the use of the Lucas-Washburn approach for modeling capillary absorption at the nanoscale.

Capillary absorption of metal nanodroplets by single-wall carbon nanotubes.

We present a simple model that demonstrates the possibility of capillary absorption of nonwetting liquid nanoparticles by carbon nanotubes (CNTs) assisted by the action of the Laplace pressure due to the droplet surface tension. We test this model with molecular dynamics simulation and find excellent agreement with the theory, which shows that for a given nanotube radius there is a critical size below which a metal droplet will be absorbed. The model also explains recent observations of capillary absorption of nonwetting Cu nanodroplets by carbon nanotubes. This finding has implications for our understanding of the growth of CNTs from metal catalyst particles and suggests new methods for fabricating composite metal-CNT materials.

Effective slip boundary conditions for flows over nanoscale chemical heterogeneities.

We study slip boundary conditions for simple fluids at surfaces with nanoscale chemical heterogeneities. Using a perturbative approach, we examine the flow of a Newtonian fluid far from a surface described by a heterogeneous Navier slip boundary condition. In the far field, we obtain expressions for an effective slip boundary condition in certain limiting cases. These expressions are compared to numerical solutions which show they work well when applied in the appropriate limits. The implications for experimental measurements and for the design of surfaces that exhibit large slip lengths are discussed.

Reentrant adhesion behavior in nanocluster deposition.

We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of incident kinetic energy, we find a transition from adhesion to reflection at low kinetic energies. We also identify a second adhesive regime at intermediate kinetic energies, where strong deformation of the cluster leads to an increase in contact area and adhesive energy.

Superheating and solid-liquid phase coexistence in nanoparticles with nonmelting surfaces.

We present a phenomenological model of melting in nanoparticles with facets that are only partially wet by their liquid phase. We show that in this model, as the solid nanoparticle seeks to avoid coexistence with the liquid, the microcanonical melting temperature can exceed the bulk melting point and that the onset of coexistence is a first-order transition. We show that these results are consistent with molecular dynamics simulations of aluminum nanoparticles which remain solid above the bulk melting temperature.

Transition from icosahedral to decahedral structure in a coexisting solid-liquid nickel cluster.

We have used molecular dynamics simulations to construct a microcanonical caloric curve for a 1415 atom Ni icosahedron. Prior to melting, the Ni cluster exhibits static solid-liquid phase coexistence. Initially, a partial icosahedral structure coexists with a partially wetting melt. However, at energies very close to the melting point the icosahedral structure is replaced by a truncated decahedral structure that is almost fully wet by the melt. This structure remains until the cluster fully melts. The transition appears to be driven by a preference for the melt to wet the decahedral structure.

Static, transient, and dynamic phase coexistence in metal nanoclusters.

Molecular dynamics simulations are used to examine static and dynamic coexistence between solid and liquid phases in nanoscale silver, copper, and nickel clusters. We find static coexistence in the 561-atom copper icosahedron, the 561-atom silver icosahedron, and the 923-atom nickel icosahedron, and in cluster sizes above these thresholds, but not in smaller clusters. Nonetheless, in smaller clusters we typically observe either dynamic coexistence between fully solid and liquid states or transient coexistence which is essentially dynamic coexistence between a fully solid state and a solid-liquid state.

Effect of patterned slip on micro- and nanofluidic flows.

We consider the flow of a Newtonian fluid in a nano- or microchannel with walls that have patterned variations in slip length. We formulate a set of equations to describe the effects on an incompressible Newtonian flow of small variations in slip and solve these equations for slow flows. We test these equations using molecular dynamics simulations of flow between two walls which have patterned variations in wettability. Good qualitative agreement and a reasonable degree of quantitative agreement is found between the theory and molecular dynamics simulations. The results of both analyses show that patterned wettability can be used to induce complex variations in flow. Finally we discuss the implications of our results for the design of microfluidic mixers using slip.

Two classes of androgen receptor elements mediate cooperativity through allosteric interactions.

Genes uniquely regulated by the androgen receptor (AR) typically contain multiple androgen response elements (AREs) that in isolation are of low DNA binding affinity and transcriptional activity. However, specific combinations of AREs in their native promoter context result in highly cooperative DNA binding by AR and high levels of transcriptional activation. We demonstrate that the natural androgen-regulated promoters of prostate specific antigen and probasin contain two classes of AREs dictated by their primary nucleotide sequence that function to mediate cooperativity. Class I AR-binding sites display conventional guanine contacts. Class II AR-binding sites have distinctive atypical sequence features and, upon binding to AR, the DNA structure is dramatically altered through allosteric interactions with the receptor. Class II sites stabilize AR binding to adjacent class I sites and result in synergistic transcriptional activity and increased hormone sensitivity. We have determined that the specific nucleotide variation within the AR binding sites dictate differential functions to the receptor. We have identified the role of individual nucleotides within class II sites and predicted consensus sequences for class I and II sites. Our data suggest that this may be a universal mechanism by which AR achieved unique regulation of target genes through complex allosteric interactions dictated by primary binding sequences.

Determinants of DNA sequence specificity of the androgen, progesterone, and glucocorticoid receptors: evidence for differential steroid receptor response elements.

While androgen, progesterone, and glucocorticoid receptors perform distinct physiological functions by regulating unique sets of genes, in vitro they can transactivate a common high-affinity DNA-binding target. Naturally occurring steroid response elements display nucleotide divergence that lowers binding affinity in comparison to the optimal binding element, but enhances receptor-type specificity. We investigated the role of nucleotide deviations within the DNA-binding site for contribution to steroid receptor specificity. We hypothesized that receptor specificity drives the evolution of binding site sequence, rather than strictly receptor-binding affinity. Receptor-selective targets can evolve by some nucleotides selected on the basis of additional bond energy, and others may be selected by differential tolerance to discourage binding from inappropriate receptors. To identify receptor-specific binding sites, we mimicked these dual selection pressures in a receptor-competitive environment in which DNA binding sites for the androgen or progesterone receptors were selected in the presence of the glucocorticoid receptor. These analyses also demonstrated that steroid receptors strongly select nucleotides in the spacer and flanking regions of the half-site and do so in an asymmetric fashion, indicating that steroid receptors interact with DNA in an allosteric manner that affects the transcriptional activation potential.

Retinoid X receptor alters the determination of DNA binding specificity by the P-box amino acids of the thyroid hormone receptor.

Nuclear hormone receptors bind to hormone response elements in DNA consisting of two half-sites of 6 base pairs. The P-box amino acids of each receptor determine the identities of the central nucleotides of the half-site. 57 P-box variants of the human thyroid hormone receptor (hT3Rbeta) were used to demonstrate the relationship between P-box sequence and DNA binding specificity by homodimers and heterodimers formed with the retinoid X receptor (RXR). In general, the formation of heterodimers relieved many of the constraints on the compatibility of hT3Rbeta P-box sequences with DNA binding. Effects were most dramatic for heterodimers bound to a direct repeat spaced by four base pairs. RXR also overrides the P-box-derived DNA binding specificity of hT3Rbeta when heterodimers are bound to inverted or everted repeat elements. These effects of RXR are most pronounced on AGGTCA half-sites but are squelched when the RXR partner of the heterodimer is bound to an AGGACA half-site. The influence of RXR on hT3Rbeta DNA binding specificity varies with the orientation of half-sites in the element, the identity of the fourth base pair of the half-site, and the spacing between the half-sites of direct repeats. These differences suggest that the DNA binding domains of RXR-hT3Rbeta heterodimers are not positioned equivalently on the various elements, affecting the manner in which the P-box amino acids of hT3Rbeta interact with base pairs within the half-site.

Relationship between P-box amino acid sequence and DNA binding specificity of the thyroid hormone receptor. The effects of half-site sequence in everted repeats.

The three P-box amino acids in the DNA recognition alpha-helix of steroid/thyroid hormone receptors participate in the discrimination of the central base pairs of the hexameric half-sites of receptor response elements in DNA. A series of 57 variants of the beta isoform of the human thyroid hormone receptor were constructed in which the 19 possible amino acid substitutions were incorporated at each of the three P-box positions. The effects of these substitutions on the sequence specificity of the DNA binding activity of the receptor were analyzed using 16 everted repeat elements which differed in sequence in the two central base pairs of the hexameric half-sites. Only receptors with glutamate or aspartate as the first P-box amino acid had detectable DNA binding affinity on everted repeats with AGGNCA half-sites. Only those receptors with alanine, glycine, serine, or proline in the second P-box position were able to bind to this same group of everted repeat elements. In contrast, many of the variant receptors with substitutions at the third P-box position were capable of binding to the AGGNCA group of repeat elements. The actual substitutions at the third P-box position that were compatible with binding depended upon the identity of the fourth base pair of the AGGNCA half-sites. Of the remaining 12 everted repeat sequences, only those with AGTTCA or AGTCCA half-sites were able to bind any of the receptors. In addition to wild type receptor, several variant receptors with amino acid substitutions in either the first or third P-box position were able to bind to the everted repeat with AGTTCA half-sites. The everted repeat with AGTCCA half-sites was bound by receptors with a DGG, NGG, or EGQ P-box sequence, but not the wild type receptor which has an EGG P-box sequence. These data demonstrate that all three P-box positions of the thyroid hormone receptor function to discriminate between half-sites that differ in sequence at the third and fourth base pairs.

Relationship between P-box amino acid sequence and DNA binding specificity of the thyroid hormone receptor. The effects of sequences flanking half-sites in thyroid hormone response elements.

The three P-box amino acids in the DNA recognition alpha-helix of steroid/thyroid hormone receptors participate in the discrimination of the central base pairs of the hexameric half-sites of receptor response elements in DNA. Using a series of variant receptors incorporating all 19 possible substitutions for each individual P-box amino acid of the human thyroid hormone receptor (hT3R beta), we demonstrated that the first P-box position must have a glutamate, and the second P-box position must have either an alanine or a glycine for high affinity binding to everted repeat elements with half-site sequences of AGGNCA. In the present study, the influence of half-site flanking sequence on the compatibility of P-box amino acids in hT3R beta with DNA binding was investigated. When a 5' sequence of CTG flanked AGGNCA half-sites in an everted repeat, several additional P-box variant receptors were able to bind to the DNA that were not able to bind when the half-sites were flanked with the 5' sequence CAG. Flanking sequence had the most dramatic effects on amino acid substitutions at the first P-box position, with smaller effects observed at the second P-box position and only subtle effects observed at the third P-box position. Expansion of the number of P-box sequences compatible with binding of hT3R beta to thyroid hormone response elements required the thymidine in the CTG flanking sequence, an everted repeat of the AGGNCA half-sites, and an intermolecular interaction in the C terminus of the receptor.