Early warning signals in plant disease outbreaks

Infectious disease outbreaks in plants threaten ecosystems, agricultural crops and food trade. Currently, several fungal diseases are affecting forests worldwide, posing a major risk to tree species, habitats and consequently ecosystem decay. Prediction and control of disease spread are difficult, mainly due to the complexity of the interaction between individual components involved. In this work, we introduce a lattice-based epidemic model coupled with a stochastic process that mimics, in a very simplified way, the interaction between the hosts and pathogen. We studied the disease spread by measuring the propagation velocity of the pathogen on the susceptible hosts. Our quantitative results indicate the occurrence of a critical transition between two stable phases: local confinement and an extended epiphytotic outbreak that depends on the density of the susceptible individuals. Quantitative predictions of epiphytotics are performed using the framework early-warning indicators for impending regime shifts, widely applied on dynamical systems. These signals forecast successfully the outcome of the critical shift between the two stable phases before the system enters the epiphytotic regime. Our study demonstrates that early-warning indicators could be useful for the prediction of forest disease epidemics through mathematical and computational models suited to more specific pathogen–host-environmental interactions. Our results may also be useful to identify a suitable planting density to slow down disease spread and in the future, design highly resilient forests

L\'evy flights and self-similar exploratory behaviour of termite workers: beyond model fitting

Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties --including L\'evy flights-- in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.Comment: 13 pages, 11 figures. Unrevised version. Final version to appear in Plos ON

Correlated random walks of human embryonic stem cells in vitro

We perform a detailed analysis of the migratory motion of human embryonic stem cells in two-dimensions, both when isolated and in close proximity to another cell, recorded with time-lapse microscopic imaging. We show that isolated cells tend to perform an unusual locally anisotropic walk, moving backwards and forwards along a preferred local direction correlated over a timescale of around 50 min and aligned with the axis of the cell elongation. Increasing elongation of the cell shape is associated with increased instantaneous migration speed. We also show that two cells in close proximity tend to move in the same direction, with the average separation of m or less and the correlation length of around 25 μm, a typical cell diameter. These results can be used as a basis for the mathematical modelling of the formation of clonal hESC colonies

Seeding hESCs to achieve optimal colony clonality

Human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) have promising clinical applications which often rely on clonally-homogeneous cell populations. To achieve this, it is important to ensure that each colony originates from a single founding cell and to avoid subsequent merging of colonies during their growth. Clonal homogeneity can be obtained with low seeding densities; however, this leads to low yield and viability. It is therefore important to quantitatively assess how seeding density affects clonality loss so that experimental protocols can be optimised to meet the required standards. Here we develop a quantitative framework for modelling the growth of hESC colonies from a given seeding density based on stochastic exponential growth. This allows us to identify the timescales for colony merges and over which colony size no longer predicts the number of founding cells. We demonstrate the success of our model by applying it to our own experiments of hESC colony growth; while this is based on a particular experimental set-up, the model can be applied more generally to other cell lines and experimental conditions to predict these important timescales

Seeding hESCs to achieve optimal colony clonality

Human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) have promising clinical applications which often rely on clonally-homogeneous cell populations. To achieve this, cross-contamination and merger of colonies should be avoided. This motivates us to experimentally study and quantitatively model the growth of hESC colonies. The colony population is unexpectedly found to be multi-modal. We associate these sub-populations with different numbers of founding cells, and predict their occurrence by considering the role of cell-cell interactions and cell behaviour on randomly seeded cells. We develop a multi-population stochastic exponential model for the colony population which captures our experimental observations, and apply this to calculate the timescales for colony merges and over which colony size no longer predicts the number of founding cells. These results can be used to achieve the best outcome for homogeneous colony growth from different cell seeding densities

Quantification of the morphological characteristics of hESC colonies

The maintenance of the undifferentiated state in human embryonic stem cells (hESCs) is critical for further application in regenerative medicine, drug testing and studies of fundamental biology. Currently, the selection of the best quality cells and colonies for propagation is typically performed by eye, in terms of the displayed morphological features, such as prominent/abundant nucleoli and a colony with a tightly packed appearance and a well-defined edge. Using image analysis and computational tools, we precisely quantify these properties using phase-contrast images of hESC colonies of different sizes (0.1–1.1 mm2) during days 2, 3 and 4 after plating. Our analyses reveal noticeable differences in their structure influenced directly by the colony area A. Large colonies (A > 0.6 mm2) have cells with smaller nuclei and a short intercellular distance when compared with small colonies (A  0.6 mm2) due to the proliferation of the cells in the bulk. This increases the colony density and the number of nearest neighbours. We also detect the self-organisation of cells in the colonies where newly divided (smallest) cells cluster together in patches, separated from larger cells at the final stages of the cell cycle. This might influence directly cell-to-cell interactions and the community effects within the colonies since the segregation induced by size differences allows the interchange of neighbours as the cells proliferate and the colony grows. Our findings are relevant to efforts to determine the quality of hESC colonies and establish colony characteristics database

Quantification of the morphological characteristics of hESC colonies

The maintenance of the pluripotent state in human embryonic stem cells (hESCs) is critical for further application in regenerative medicine, drug testing and studies of fundamental biology. Currently, the selection of the best quality cells and colonies for propagation is typically performed by eye, in terms of the displayed morphological features, such as prominent/abundant nucleoli and a colony with a tightly packed appearance and a well-defined edge. Using image analysis and computational tools, we precisely quantify these properties using phase-contrast images of hESC colonies of different sizes (0.1 -- 1.1$\, \text{mm}^2$) during days 2, 3 and 4 after plating. Our analyses reveal noticeable differences in their structure influenced directly by the colony area $A$. Large colonies ($A > 0.6 \, \text{mm}^2$) have cells with smaller nuclei and a short intercellular distance when compared with small colonies ($A < 0.2 \, \text{mm}^2$). The gaps between the cells, which are present in small and medium sized colonies with $A \le 0.6 \, \text{mm}^2$, disappear in large colonies ($A > 0.6 \, \text{mm}^2$) due to the proliferation of the cells in the bulk. This increases the colony density and the number of nearest neighbours. We also detect the self-organisation of cells in the colonies where newly divided (smallest) cells cluster together in patches, separated from larger cells at the final stages of the cell cycle. This might influence directly cell-to-cell interactions and the community effects within the colonies since the segregation induced by size differences allows the interchange of neighbours as the cells proliferate and the colony grows. Our findings are relevant to efforts to determine the quality of hESC colonies and establish colony characteristics database

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation