Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Slowing down a pine invasion despite uncertainty in demography and dispersal

1. Management decisions regarding invasive plants often have to be made quickly and in the face of fragmentary knowledge of their population dynamics. However, recommendations are commonly made on the basis of only a restricted set of parameters. Without addressing uncertainty and variability in model parameters we risk ineffective management, resulting in wasted resources and an escalating problem if early chances to control spread are missed. 2. Using available data for Pinus nigra in ungrazed and grazed grassland and shrubland in New Zealand, we parameterized a stage-structured spread model to calculate invasion wave speed, population growth rate and their sensitivities and elasticities to population parameters. Uncertainty distributions of parameters were used with the model to generate confidence intervals (CI) about the model predictions. 3. Ungrazed grassland environments were most vulnerable to invasion and the highest elasticities and sensitivities of invasion speed were to long-distance dispersal parameters. However, there was overlap between the elasticity and sensitivity CI on juvenile survival, seedling establishment and long-distance dispersal parameters, indicating overlap in their effects on invasion speed. 4. While elasticity of invasion speed to long-distance dispersal was highest in shrubland environments, there was overlap with the CI of elasticity to juvenile survival. In shrubland invasion speed was most sensitive to the probability of establishment, especially when establishment was low. In the grazed environment elasticity and sensitivity of invasion speed to the severity of grazing were consistently highest. Management recommendations based on elasticities and sensitivities depend on the vulnerability of the habitat. 5. Synthesis and applications. Despite considerable uncertainty in demography and dispersal, robust management recommendations emerged from the model. Proportional or absolute reductions in long-distance dispersal, juvenile survival and seedling establishment parameters have the potential to reduce wave speed substantially. Plantations of wind-dispersed invasive conifers should not be sited on exposed sites vulnerable to long-distance dispersal events, and trees in these sites should be removed. Invasion speed can also be reduced by removing seedlings, establishing competitive shrubs and grazing. Incorporating uncertainty into the modelling process increases our confidence in the wide applicability of the management strategies recommended here.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

Forecasting invasions: resource use by mussels informs invasion patterns along the South African coast

Invasive species are often more able to rapidly and efficiently utilise resources than natives, and comparing per capita resource use at different resource densities among invaders and trophically analogous natives could allow for reliable predictions of invasiveness. In South Africa, invasion by the Mediterranean mussel Mytilus galloprovincialis has transformed wave-exposed shores, negatively affecting native mussel species. Currently, South Africa is experiencing a second mussel invasion with the recent detection of the South American Semimytilus algosus. We tested per capita uptake of an algal resource by invading M. galloprovincialis, S. algosus, and the native Aulacomya atra at different algal concentrations and temperatures, representing the west and south coasts of South Africa, to examine whether their per capita resource use could be a predictor of their spread and subsequent invasiveness. Regardless of temperature, M. galloprovincialis was the most efficient consumer, significantly reducing algal cells compared to the other species when the resource was presented in both low and high starting densities. Furthermore, these findings aligned with a greater biomass of M. galloprovincialis on the shore in comparison with the other species. Resource use by the new invader S. algosus was dependent on the density of resource and, although this species was efficient at low algal concentrations at cooler temperatures, this pattern broke down at higher algal densities. This was once more reflected in lower biomass in surveys of this species along the cool west coast. We therefore forecast that S. algosus will be become established along the south coast; however, we also predict that M. galloprovincialis will maintain dominance on these shores.

Explosive invasion of plant mitochondria by a group I intron

Group I introns are mobile, self-splicing genetic elements found principally in organellar genomes and nuclear rRNA genes. The only group I intron known from mitochondrial genomes of vascular plants is located in the cox1 gene of Peperomia, where it is thought to have been recently acquired by lateral transfer from a fungal donor. Southern-blot surveys of 335 diverse genera of land plants now show that this intron is in fact widespread among angiosperm cox1 genes, but with an exceptionally patchy phylogenetic distribution. Four lines of evidence—the intron’s highly disjunct distribution, many incongruencies between intron and organismal phylogenies, and two sources of evidence from exonic coconversion tracts—lead us to conclude that the 48 angiosperm genera found to contain this cox1 intron acquired it by 32 separate horizontal transfer events. Extrapolating to the over 13,500 genera of angiosperms, we estimate that this intron has invaded cox1 genes by cross-species horizontal transfer over 1,000 times during angiosperm evolution. This massive wave of lateral transfers is of entirely recent occurrence, perhaps triggered by some key shift in the intron’s invasiveness within angiosperms.

Pattern and inhibition-dependent invasion of pyramidal cell dendrites by fast spikes in the hippocampus in vivo.

The invasion of sodium spikes from the soma into dendrites was studied in hippocampal pyramidal cells by simultaneous extracellular and intracellular recordings in anesthetized rats and by simultaneous extracellular recordings of the somatic and dendritic potentials in freely behaving animals. During complex-spike patterns, recorded in the immobile or sleeping animal, dendritic invasion of successive spikes was substantially attenuated. Complex-spike bursts occurred in association with population discharge of CA3-CA1 pyramidal cells (sharp wave field events). Synaptic inhibition reduced the amplitude of sodium spikes in the dendrites and prevented the occurrence of calcium spikes. These findings indicate that (i) the voltage-dependent calcium influx into the dendrites is under the control of inhibitory neurons and (ii) the temporal coincidence of synaptic depolarization and activation of voltage-dependent calcium conductances by the backpropagating spikes during sharp wave bursts may be critical for synaptic plasticity in the intact hippocampus.

Interview with Dr. Young-Ki Paik, President of the Human Proteome Organization (HUPO): Pharmacoproteomics and the approaching wave of “Proteomics Diagnostics”

Dr. Young-Ki Paik directs the Yonsei Proteome Research Center in Seoul, Korea and was elected as the President of the Human Proteome Organization (HUPO) in 2009. In the December 2009 issue of the Current Pharmacogenomics and Personalized Medicine (CPPM), Dr. Paik explains the new field of pharmacoproteomics and the approaching wave of “proteomics diagnostics” in relation to personalized medicine, HUPO’s role in advancing proteomics technology applications, the HUPO Proteomics Standards Initiative, and the future impact of proteomics on medicine, science, and society. Additionally, he comments that (1) there is a need for launching a Gene-Centric Human Proteome Project (GCHPP) through which all representative proteins encoded by the genes can be identified and quantified in a specific cell and tissue and, (2) that the innovation frameworks within the diagnostics industry hitherto borrowed from the genetics age may require reevaluation in the case of proteomics, in order to facilitate the uptake of pharmacoproteomics innovations. He stresses the importance of biological/clinical plausibility driving the evolution of biotechnologies such as proteomics,instead of an isolated singular focus on the technology per se. Dr. Paik earned his Ph.D. in biochemistry from the University of Missouri-Columbia and carried out postdoctoral work at the Gladstone Foundation Laboratories of Cardiovascular Disease, University of California at San Francisco. In 2005, his research team at Yonsei University first identified and characterized the chemical structure of C. elegans dauer pheromone (daumone) which controls the aging process of this nematode. He is interviewed by a multidisciplinary team specializing in knowledge translation, technology regulation, health systems governance, and innovation analysis.

Osteryoung square wave voltammetric determination of lactose in food samples by a derivative procedure

A method for determination of lactose in food samples by Osteryoung square wave voltammetry (OSWV) was developed. It was based on the nucleophilic addition reaction between lactose and aqua ammonia. The carbonyl group of lactose can be changed into imido group, and this increases the electrochemical activity in reduction and the sensitivity. The optimal condition for the nucleophilic addition reaction was investigated and it was found that in NH4Cl–NH3 buffer of pH 10.1, the linear range between the peak current and the concentration of lactose was 0.6–8.4 mg L−1, and the detection limits was 0.44 mg L−1. The proposed method was applied to the determination of lactose in food samples and satisfactory results were obtained.

How well are Australian infants and children aged 4 to 5 years doing? Findings from the Longitudinal Study of Australian Children Wave 1

This report presents an analysis of the data from the first wave of the Longitudinal Study of Australian Children (LSAC) to explore the wellbeing of 5,107 children in the infant cohort of the study and the 4,983 children, aged 4 to 5 years, in the child cohort. Wave 1 of LSAC includes measures of multiple aspects of children’s early development. These developmental measures are summarised in the LSAC Outcome Index, a composite measure which includes an overall index as well as three separate domain scores, tapping physical development, social and emotional functioning, and learning and cognitive development.