Mathematical models for cell-matrix interactions during dermal wound healing

This paper contains a review of our recent work on the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing. The models are of partial differential equation type and allow us to investigate in detail how various mechanochemical effects may be responsible for certain wound healing disorders such as fibrocontractive and fibroproliferative diseases. We also present a model for wound healing angiogenesis. The latter has several features in common with angiogenesis during cancer tumour growth and spread so a deeper understanding of the phenomenon in the context of wound healing may also help in the treatment of certain cancers

Travelling waves in wound healing

We illustrate the role of travelling waves in wound healing by considering three different cases. Firstly, we review a model for surface wound healing in the cornea and focus on the speed of healing as a function of the application of growth factors. Secondly, we present a model for scar tissue formation in deep wounds and focus on the role of key chemicals in determining the quality of healing. Thirdly, we propose a model for excessive healing disorders and investigate how abnormal healing may be controlled

A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis

Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic conditions. In wound healing, new capillaries deliver vital metabolites such as amino acids and oxygen to the cells in the wound which are involved in a complex sequence of repair processes. The key cellular constituents of these new capillaries are endothelial cells: their interactions with soluble biochemical and insoluble extracellular matrix (ECM) proteins have been well documented recently, although the biological mechanisms underlying wound-healing angiogenesis are incompletely understood. Considerable recent research, including some continuum mathematical models, have focused on the interactions between endothelial cells and soluble regulators (such as growth factors). In this work, a similar modelling framework is used to investigate the roles of the insoluble ECM substrate, of which collagen is the predominant macromolecular protein. Our model consists of a partial differential equation for the endothelial-cell density (as a function of position and time) coupled to an ordinary differential equation for the ECM density. The ECM is assumed to regulate cell movement (both random and directed) and proliferation, whereas the cells synthesize and degrade the ECM. Analysis and numerical solutions of these equations highlights the roles of these processes in wound-healing angiogenesis. A nonstandard approximation analysis yields insight into the travel ling-wave structure of the system. The model is extended to two spatial dimensions (parallel and perpendicular to the plane of the skin), for which numerical simulations are presented. The model predicts that ECM-mediated random motility and cell proliferation are key processes which drive angiogenesis and that the details of the functional dependence of these processes on the ECM density, together with the rate of ECM remodelling, determine the qualitative nature of the angiogenic response. These predictions are experimentally testable, and they may lead towards a greater understanding of the biological mechanisms involved in wound-healing angiogenesis

Quantum field effects in coupled atomic and molecular Bose-Einstein condensates

This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive-P representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The model includes all interactions between the particles, background gas losses, two-body losses and the numerical simulations are performed in three dimensions. It is found that it is possible to differentiate the quantum and semiclassical behaviour when the particle density is sufficiently low and the coupling is sufficiently strong.Comment: 4 postscript figure

Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures, in direct analogy to the position and momentum correlations originally considered by EPR.Comment: Final published version (corrections in Ref. [32], updated references

The labor market regimes of Denmark and Norway – one Nordic model?

The literature on the Danish and Norwegian labor market systems emphasizes the commonalities of the two systems. We challenge this perception by investigating how employers in multinational companies in Denmark and Norway communicate with employees on staffing changes. We argue that the development of ‘flexicurity’ in Denmark grants Danish employers considerably greater latitude in engaging in staffing changes than its Nordic counterpart, Norway. Institutional theory leads us to suppose that large firms located in the Danish setting will be less likely to engage in employer–employee communication on staffing plans than their Norwegian counterparts. In addition, we argue that in the Danish context indigenous firms will have a better insight into the normative and cognitive aspects to flexicurity than foreign-owned firms, meaning that they are more likely to engage in institutional entrepreneurialism than their foreign owned counterparts. We supplement institutional theory with an actor perspective in order to take into account the role of labor unions. Our analysis is based on a survey of 203 firms in Norway and Denmark which are either indigenous multinational companies or the subsidiaries of foreign multinational companies. The differences we observe cause us to conclude that the notion of a common Nordic model is problematic

SIGAME simulations of the [CII], [OI] and [OIII] line emission from star forming galaxies at z ~ 6

Of the almost 40 star forming galaxies at z>~5 (not counting QSOs) observed in [CII] to date, nearly half are either very faint in [CII], or not detected at all, and fall well below expectations based on locally derived relations between star formation rate (SFR) and [CII] luminosity. Combining cosmological zoom simulations of galaxies with SIGAME (SImulator of GAlaxy Millimeter/submillimeter Emission) we have modeled the multi-phased interstellar medium (ISM) and its emission in [CII], [OI] and [OIII], from 30 main sequence galaxies at z~6 with star formation rates ~3-23Msun/yr, stellar masses ~(0.7-8)x10^9Msun, and metallicities ~(0.1-0.4)xZsun. The simulations are able to reproduce the aforementioned [CII]-faintness at z>5, match two of the three existing z>~5 detections of [OIII], and are furthermore roughly consistent with the [OI] and [OIII] luminosity relations with SFR observed for local starburst galaxies. We find that the [CII] emission is dominated by the diffuse ionized gas phase and molecular clouds, which on average contribute ~66% and ~27%, respectively. The molecular gas, which constitutes only ~10% of the total gas mass is thus a more efficient emitter of [CII] than the ionized gas making up ~85% of the total gas mass. A principal component analysis shows that the [CII] luminosity correlates with the star formation activity as well as average metallicity. The low metallicities of our simulations together with their low molecular gas mass fractions can account for their [CII]-faintness, and we suggest these factors may also be responsible for the [CII]-faint normal galaxies observed at these early epochs.Comment: 24 pages, 14 figures. Accepted for publication in the Astrophysical Journa

Delta Self-Consistent Field as a method to obtain potential energy surfaces of excited molecules on surfaces

We present a modification of the $\Delta$SCF method of calculating energies of excited states, in order to make it applicable to resonance calculations of molecules adsorbed on metal surfaces, where the molecular orbitals are highly hybridized. The $\Delta$SCF approximation is a density functional method closely resembling standard density functional theory (DFT), the only difference being that in $\Delta$SCF one or more electrons are placed in higher lying Kohn-Sham orbitals, instead of placing all electrons in the lowest possible orbitals as one does when calculating the ground state energy within standard DFT. We extend the $\Delta$SCF method by allowing excited electrons to occupy orbitals which are linear combinations of Kohn-Sham orbitals. With this extra freedom it is possible to place charge locally on adsorbed molecules in the calculations, such that resonance energies can be estimated. The method is applied to N$_2$, CO and NO adsorbed on different metallic surfaces and compared to ordinary $\Delta$SCF without our modification, spatially constrained DFT and inverse-photoemission spectroscopy (IPES) measurements. This comparison shows that the modified $\Delta$SCF method gives results in close agreement with experiment, significantly closer than the comparable methods. For N$_2$ adsorbed on ruthenium (0001) we map out a 2-dimensional part of the potential energy surfaces in the ground state and the 2$\pi$-resonance. Finally we compare the $\Delta$SCF approach on gas-phase N$_2$ and CO, to higher accuracy methods. Excitation energies are approximated with accuracy close to that of time-dependent density functional theory, and we see very good agreement in the minimum shift of the potential energy surfaces in the excited state compared to the ground state.Comment: 11 pages, 7 figure

Spectroscopic Observations of Optically Selected Clusters of Galaxies from the Palomar Distant Cluster Survey

We have conducted a redshift survey of sixteen cluster candidates from the Palomar Distant Cluster Survey (PDCS) to determine both the density of PDCS clusters and the accuracy of the estimated redshifts presented in the PDCS catalog (Postman et. al. 1996). We find that the matched-filter redshift estimate presented in the PDCS has an error sigma_z = 0.06 in the redshift range 0.1 < z < 0.35 based on eight cluster candidates with three or more concordant galaxy redshifts. We measure the low redshift (0.1 < z < 0.35) space density of PDCS clusters to be 31.3^{+30.5}_{-17.1} * E-06 h^3 Mpc^-3 (68% confidence limits for a Poisson distribution) for Richness Class 1 systems. We find a tentative space density of 10.4^{+23.4}_{-8.4}* E-06 h^3 Mpc^-3 for Richness Class 2 clusters. These densities compare favorably with those found for the whole of the PDCS and support the finding that the space density of clusters in the PDCS is a factor of ~5 above that of clusters in the Abell catalog (Abell 1958; Abell, Corwin, and Olowin 1989). These new space density measurements were derived as independently as possible from the original PDCS analysis and therefore, demonstrate the robustness of the original work. Based on our survey, we conclude that the PDCS matched-filter algorithm is successful in detecting real clusters and in estimating their true redshifts in the redshift range we surveyed.Comment: 23 pages with 4 figures and 3 seperate tables. To be published in the November Issue of the Astronomical Journa