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

Flight experience with lightweight, low-power miniaturized instrumentation systems

Engineers at the NASA Dryden Flight Research Facility (NASA-Dryden) have conducted two flight research programs with lightweight, low-power miniaturized instrumentation systems built around commercial data loggers. One program quantified the performance of a radio-controlled model airplane. The other program was a laminar boundary-layer transition experiment on a manned sailplane. NASA-Dryden personnel's flight experience with the miniaturized instrumentation systems used on these two programs is reported. The data loggers, the sensors, and the hardware and software developed to complete the systems are described. How the systems were used is described and the challenges encountered to make them work are covered. Examples of raw data and derived results are shown as well. Finally, future plans for these systems are discussed. For some flight research applications where miniaturized instrumentation is a requirement, the authors conclude that commercially available data loggers and sensors are viable alternatives. In fact, the data loggers and sensors make it possible to gather research-quality data in a timely and cost-effective manner

Space and time on the membrane:modelling Type VI secretion system dynamics as a state-dependent random walk

The type six secretion system (T6SS) is a transmembrane protein complex that mediates bacterial cell killing. The T6SS comprises three main components (transmembrane, baseplate and sheath/tube complexes) that are sequentially assembled in order to enable an attacking cell to transport payloads into neighbouring cells. A T6SS attack disrupts the function of essential cellular components of target cells, typically resulting in their death. While the assembled T6SS adopts a fixed position in the cell membrane of the attacking cell, the location of the firing site varies between firing events. In Serratia marcescens, a post-translational regulatory network regulates the assembly and firing kinetics of the T6SS in a manner that affects the attacking cell's ability to kill target cells. Moreover, when the ability of membrane complexes to reorient is reduced, an attacking cell's competitiveness is also reduced. In this study, we will develop a mathematical model that describes both the spatial motion and assembly/disassembly of a firing T6SS. The model represents the motion of a T6SS on the cell membrane as a state-dependent random walk. Using the model, we will explore how both spatial and temporal effects can combine to give rise to different firing phenotypes. Using parameters inferred from the available literature, we show that variation in estimated diffusion coefficients is sufficient to give rise to either spatially local or global firers.</p

Star formation in galaxy mergers with realistic models of stellar feedback and the interstellar medium

We use hydrodynamic simulations with detailed, explicit models for stellar feedback to study galaxy mergers. These high-resolution (∼1 pc) simulations follow the formation and destruction of individual giant molecular clouds (GMC) and star clusters. We find that the final starburst is dominated by in situ star formation, fuelled by gas which flows inwards due to global torques. The resulting high gas density results in rapid star formation. The gas is self-gravitating, and forms massive (≲10¹⁰ M_⊙) GMC and subsequently super star clusters (with masses up to 10⁸ M_⊙). However, in contrast to some recent simulations, the bulk of new stars which eventually form the central bulge are not born in super-clusters which then sink to the centre of the galaxy. This is because feedback efficiently disperses GMC after they turn several per cent of their mass into stars. In other words, most of the mass that reaches the nucleus does so in the form of gas. The Kennicutt–Schmidt law emerges naturally as a consequence of feedback balancing gravitational collapse, independent of the small-scale star formation microphysics. The same mechanisms that drive this relation in isolated galaxies, in particular radiation pressure from infrared photons, extend, with no fine-tuning, over seven decades in star formation rate (SFR) to regulate star formation in the most extreme starburst systems with densities ≳10⁴ M_⊙ pc⁻². This feedback also drives super-winds with large mass-loss rates; however, a significant fraction of the wind material falls back on to the discs at later times, leading to higher post-starburst SFRs in the presence of stellar feedback. This suggests that strong active galactic nucleus feedback may be required to explain the sharp cut-offs in SFR that are observed in post-merger galaxies. We compare the results to those from simulations with no explicit resolution of GMC or feedback [‘effective equation-of-state’ (EOS) models]. We find that global galaxy properties are similar between EOS and resolved-feedback models. The relic structure and mass profile, and the total mass of stars formed in the nuclear starburst are quite similar, as is the morphological structure during and after mergers (tails, bridges, etc.). Disc survival in sufficiently gas rich mergers is similar in the two cases, and the new models follow the same scalings as derived for the efficiency of disc re-formation after a merger as derived from previous work with the simplified EOS models. While the global galaxy properties are similar between EOS and feedback models, subgalaxy-scale properties and the SFRs can be quite different: the more detailed models exhibit significantly higher star formation in tails and bridges (especially in shocks), and allow us to resolve the formation of super star clusters. In the new models, the star formation is more strongly time-variable and drops more sharply between close passages. The instantaneous burst enhancement can be higher or lower, depending on the details of the orbit and initial structural properties of the galaxies; first-passage bursts are more sensitive to these details than those at the final coalescence

From Individual-based Mechanical Models of Multicellular Systems to Free-boundary Problems

In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered whereby: (i) every cell is identified by the position of its centre; (ii) mechanical interactions between cells are described via generic nonlinear force laws; and (iii) cell proliferation is contact inhibited. We formally show that the continuum counterpart of this discrete model is given by a free-boundary problem for the cell densities. The results of the derivation demonstrate how the parameters of continuum mechanical models of multicellular systems can be related to biophysical cell properties. We prove an existence result for the free-boundary problem and construct travelling-wave solutions. Numerical simulations are performed in the case where the cellular interaction forces are described by the celebrated Johnson-Kendall-Roberts model of elastic contact, which has been previously used to model cell-cell interactions. The results obtained indicate excellent agreement between the simulation results for the individual-based model, the numerical solutions of the corresponding free-boundary problem and the travelling-wave analysis

The clockfront and wavefront model revisited

The currently accepted interpretation of the clock and wavefront model of somitogenesis is that a posteriorly moving molecular gradient sequentially slows the rate of clock oscillations, resulting in a spatial readout of temporal oscillations. However, while molecular components of the clocks and wavefronts have now been identified in the pre-somitic mesoderm (PSM), there is not yet conclusive evidence demonstrating that the observed molecular wavefronts act to slow clock oscillations. Here we present an alternative formulation of the clock and wavefront model in which oscillator coupling, already known to play a key role in oscillator synchronisation, plays a fundamentally important role in the slowing of oscillations along the anterior–posterior (AP) axis. Our model has three parameters which can be determined, in any given species, by the measurement of three quantities: the clock period in the posterior PSM, somite length and the length of the PSM. A travelling wavefront, which slows oscillations along the AP axis, is an emergent feature of the model. Using the model we predict: (a) the distance between moving stripes of gene expression; (b) the number of moving stripes of gene expression and (c) the oscillator period profile along the AP axis. Predictions regarding the stripe data are verified using existing zebrafish data. We simulate a range of experimental perturbations and demonstrate how the model can be used to unambiguously define a reference frame along the AP axis. Comparing data from zebrafish, chick, mouse and snake, we demonstrate that: (a) variation in patterning profiles is accounted for by a single nondimensional parameter; the ratio of coupling strengths; and (b) the period profile along the AP axis is conserved across species. Thus the model is consistent with the idea that, although the genes involved in pattern propagation in the PSM vary, there is a conserved patterning mechanism across species

HIV-1 capsid uncoating initiates after the first strand transfer of reverse transcription

BACKGROUND: Correct disassembly of the HIV-1 capsid shell, called uncoating, is increasingly recognised as central for multiple steps during retroviral replication. However, the timing, localisation and mechanism of uncoating are poorly understood and progress in this area is hampered by difficulties in measuring the process. Previous work suggested that uncoating occurs soon after entry of the viral core into the cell, but recent studies report later uncoating, at or in the nucleus. Furthermore, inhibiting reverse transcription delays uncoating, linking these processes.RESULTS: Here, we have used a combined approach of experimental interrogation of viral mutants and mathematical modelling to investigate the timing of uncoating with respect to reverse transcription. By developing a minimal, testable, model and employing multiple uncoating assays to overcome the disadvantages of each single assay, we find that uncoating is not concomitant with the initiation of reverse transcription. Instead, uncoating appears to be triggered once reverse transcription reaches a certain stage, namely shortly after first strand transfer.CONCLUSIONS: Using multiple approaches, we have identified a point during reverse transcription that induces uncoating of the HIV-1 CA shell. We propose that uncoating initiates after the first strand transfer of reverse transcription.</p

Effects of carbon dioxide on the searching behaviour of the root-feeding clover weevil <i>Sitona lepidus</i> (Coleoptera: Curculionidae)

The respiratory emission of CO2 from roots is frequently proposed as an attractant that allows soil-dwelling insects to locate host plant roots, but this role has recently become less certain. CO2 is emitted from many sources other than roots, so does not necessarily indicate the presence of host plants, and because of the high density of roots in the upper soil layers, spatial gradients may not always be perceptible by soil-dwelling insects. The role of CO2 in host location was investigated using the clover root weevil Sitona lepidus Gyllenhall and its host plant white clover (Trifolium repens L.) as a model system. Rhizochamber experiments showed that CO2 concentrations were approximately 1000 ppm around the roots of white clover, but significantly decreased with increasing distance from roots. In behavioural experiments, no evidence was found for any attraction by S. lepidus larvae to point emissions of CO2, regardless of emission rates. Fewer than 15% of larvae were attracted to point emissions of CO2, compared with a control response of 17%. However, fractal analysis of movement paths in constant CO2 concentrations demonstrated that searching by S. lepidus larvae significantly intensified when they experienced CO2 concentrations similar to those found around the roots of white clover (i.e. 1000 ppm). It is suggested that respiratory emissions of CO2 may act as a ‘search trigger’ for S. lepidus, whereby it induces larvae to search a smaller area more intensively, in order to detect location cues that are more specific to their host plant.<br/