Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations

Origin and evolution of osmoregulatory mechanisms in blue-green algae as a function of metabolic and structural complexity: Reflections of precambrian paleobiology

Twenty-four of the twenty-nine cyanobacteria proposed for culture were successfully cultured. Betaines are discussed

Theory of commensurable magnetic structures in holmium

The tendency for the period of the helically ordered moments in holmium to lock into values which are commensurable with the lattice is studied theoretically as a function of temperature and magnetic field. The commensurable effects are derived in the mean-field approximation from numerical calculations of the free energy of various commensurable structures, and the results are compared with the extensive experimental evidence collected during the last ten years on the magnetic structures in holmium. In general the stability of the different commensurable structures is found to be in accord with the experiments, except for the tau=5/18 structure observed a few degrees below T_N in a b-axis field. The trigonal coupling recently detected in holmium is found to be the interaction required to explain the increased stability of the tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K, when a field is applied along the c-axis.Comment: REVTEX, 31 pages, 7 postscript figure

Lieb's Theorem and Maximum Entropy Condensates

The maximum entropy steady states which form upon Floquet heating of the ground state of the Hubbard model on unbalanced bi-partite lattices are shown to possess uniform finite off-diagonal long-range order in the thermodynamic limit. For repulsive interactions the induced order corresponds to the formation of a spin-wave condensate, whilst for attractive interactions it instead corresponds to the formation of a superconducting, $\eta$-paired condensate. This creation of a `hot' condensate can occur on any periodically driven unbalanced lattice where the relevant SU(2) symmetry is preserved. Our results provide an understanding of how strong driving can expose order which has been suppressed by the lattice geometry - independent of any microscopic parameters. We discuss the implications of this for recent experiments observing emergent superconductivity in solid-state photoexcited compounds.Comment: 5 pages, 2 figures, comments are welcom

Mathematical modelling of contact dermatitis from nickel and chromium

Dermal exposure to metal allergens can lead to irritant and allergic contact dermatitis (ACD). In this paper we present a mathematical model of the absorption of metal ions, hexavalent chromium and nickel, into the viable epidermis and compare the localised irritant and T-lymphocyte (T-cell) mediated immune responses. The model accounts for the spatial-temporal variation of skin health, extra and intracellular allergen concentrations, innate immune cells, T-cells, cytokine signalling and lymph node activity up to about 6 days after contact with these metals; repair processes associated with withdrawal of exposure to both metals is not considered in the current model, being assumed secondary during the initial phases of exposure. Simulations of the resulting system of PDEs are studied in one-dimension, i.e. across skin depth, and three-dimensional scenarios with the aim of comparing the responses to the two ions in the cases of first contact (no T-cells initially present) and second contact (T-cells initially present). The results show that on continuous contact, chromium ions elicit stronger skin inflammation, but for nickel, subsequent re-exposure stimulates stronger responses due to an accumulation of cytotoxic T-cell mediated responses which characterise ACD. Furthermore, the surface area of contact to these metals has little effect on the speed of response, whilst sensitivity is predicted to increase with the thickness of skin. The modelling approach is generic and should be applicable to describe contact dermatitis from a wide range of allergens

Modelling the enigmatic Late Pliocene Glacial Event: Marine Isotope Stage M2

The Pliocene Epoch (5.2 to 2.58Ma) has often been targeted to investigate the nature ofwarmclimates. However, climate records for the Pliocene exhibit significant variability and show intervals that apparently experienced a cooler than modern climate. Marine Isotope Stage (MIS) M2 (~3.3 Ma) is a globally recognisable cooling event that disturbs an otherwise relatively (compared to present-day) warm background climate state. It remains unclear whether this event corresponds to significant ice sheet build-up in the Northern and Southern Hemisphere. Estimates of sea level for this interval vary, and range from modern values to estimates of 65 m sea level fall with respect to present day. Here we implement plausibleM2 ice sheet configurations into a coupled atmosphere–ocean climate model to test the hypothesis that larger-than-modern ice sheet configurations may have existed at M2. Climate model results are compared with proxy climate data available for M2 to assess the plausibility of each ice sheet configuration. Whilst the outcomes of our data/model comparisons are not in all cases straight forward to interpret, there is little indication that results from model simulations in which significant ice masses have been prescribed in the Northern Hemisphere are incompatible with proxy data from the North Atlantic, Northeast Arctic Russia, North Africa and the Southern Ocean. Therefore, our model results do not preclude thepossibilityof the existenceof larger icemasses duringM2 in the Northern or SouthernHemisphere. Specifically they are not able to discount the possibility of significant icemasses in the Northern Hemisphere during the M2 event, consistent with a global sea-level fall of between 40 m and 60 m. This study highlights the general need for more focused and coordinated data generation in the future to improve the coverage and consistency in proxy records for M2, which will allow these and future M2 sensitivity tests to be interrogated further

Dynamical order and superconductivity in a frustrated many-body system

In triangular lattice structures, spatial anisotropy and frustration can lead to rich equilibrium phase diagrams with regions containing complex, highly entangled states of matter. In this work we study the driven two-rung triangular Hubbard model and evolve these states out of equilibrium, observing how the interplay between the driving and the initial state unexpectedly shuts down the particle-hole excitation pathway. This restriction, which symmetry arguments fail to predict, dictates the transient dynamics of the system, causing the available particle-hole degrees of freedom to manifest uniform long-range order. We discuss implications of our results for a recent experiment on photo-induced superconductivity in ${\rm \kappa - (BEDT-TTF)_{2}Cu[N(CN)_{2}]Br}$ molecules.Comment: Main Text: 7 Pages, 4 Figures, Supplementary: 4 Pages, 3 Figure

A high-density immunoblotting methodology for quantification of total protein levels and phosphorylation modifications

The components of many signaling pathways have been identified and there is now a need to conduct quantitative data-rich temporal experiments for systems biology and modeling approaches to better understand pathway dynamics and regulation. Here we present a modified Western blotting method that allows the rapid and reproducible quantification and analysis of hundreds of data points per day on proteins and their phosphorylation state at individual sites. The approach is of particular use where samples show a high degree of sample-to-sample variability such as primary cells from multiple donors. We present a case study on the analysis of >800 phosphorylation data points from three phosphorylation sites in three signaling proteins over multiple time points from platelets isolated from ten donors, demonstrating the technique's potential to determine kinetic and regulatory information from limited cell numbers and to investigate signaling variation within a population. We envisage the approach being of use in the analysis of many cellular processes such as signaling pathway dynamics to identify regulatory feedback loops and the investigation of potential drug/inhibitor responses, using primary cells and tissues, to generate information about how a cell's physiological state changes over time