A model for mesoscale patterns in motile populations

Experimental observations of cell migration often describe the presence of mesoscale patterns within motile cell populations. These patterns can take the form of cells moving as aggregates or in chain-like formation. Here we present a discrete model capable of producing mesoscale patterns. These patterns are formed by biasing movements to favor a particular configuration of agent–agent attachments using a binding function f(K), where K is the scaled local coordination number. This discrete model is related to a nonlinear diffusion equation, where we relate the nonlinear diffusivity D(C) to the binding function f. The nonlinear diffusion equation supports a range of solutions which can be either smooth or discontinuous. Aggregation patterns can be produced with the discrete model, and we show that there is a transition between the presence and absence of aggregation depending on the sign of D(C). A combination of simulation and analysis shows that both the existence of mesoscale patterns and the validity of the continuum model depend on the form of f. Our results suggest that there may be no formal continuum description of a motile system with strong mesoscale patterns.

Computing with motile bio-agents

We describe a model of computation of the parallel type, which we call 'computing with bio-agents', based on the concept that motions of biological objects such as bacteria or protein molecular motors in confined spaces can be regarded as computations. We begin with the observation that the geometric nature of the physical structures in which model biological objects move modulates the motions of the latter. Consequently, by changing the geometry, one can control the characteristic trajectories of the objects; on the basis of this, we argue that such systems are computing devices. We investigate the computing power of mobile bio-agent systems and show that they are computationally universal in the sense that they are capable of computing any Boolean function in parallel. We argue also that using appropriate conditions, bio-agent systems can solve NP-complete problems in probabilistic polynomial time.

Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Cell invasion with proliferation mechanisms motivated by time-lapse data

Cell invasion involves a population of cells which are motile and proliferative. Traditional discrete models of proliferation involve agents depositing daughter agents on nearest- neighbor lattice sites. Motivated by time-lapse images of cell invasion, we propose and analyze two new discrete proliferation models in the context of an exclusion process with an undirected motility mechanism. These discrete models are related to a family of reaction- diffusion equations and can be used to make predictions over a range of scales appropriate for interpreting experimental data. The new proliferation mechanisms are biologically relevant and mathematically convenient as the continuum-discrete relationship is more robust for the new proliferation mechanisms relative to traditional approaches.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Ureaplasma parvum and ureaplasma urealyticum detected in semen after washing prior to assisted reproductive technology procedures

Objective: This study investigated: (i) the prevalence of ureaplasmas in semen and washed semen and (ii) the effect of ureaplasmas on semen andrology parameters. Design: Prospective study. Setting: IVF unit -private hospital, Brisbane, Australia. Patient(s): Three hundred and forty three men participating in an assisted reproductive technology (ART) treatment cycle. Intervention(s): Semen and washed semen tested by culture, PCR assays and indirect immunofluorescent antibody assays. Statistical differences were determined by a t-test, Wilcoxon or Pearson’s Chi- square test where appropriate. Main Outcome Measure(s): The prevalence of ureaplasmas in semen and washed semen and the effect of these microorganisms on semen andrology parameters. Result(s): Ureaplasmas were detected in 73/343 (22%) semen samples and 29/343 (8.5%) washed semen samples. Ureaplasmas adherent to the surface of spermatozoa were demonstrated by indirect immunofluorescent antibody testing. U. parvum serovar 6 (36.6%) and U. urealyticum (30%) were the most prevalent isolates in washed semen. A comparison of the semen andrology parameters of washed semen ureaplasma positive and negative groups demonstrated a lower proportion of non-motile sperm in the washed semen ureaplasma positive group. Conclusion(s): Ureaplasmas are not always removed from semen by a standard ART washing procedure and can remain adherent to the surface of spermatozoa.

Experimental and modelling investigation of monolayer development with clustering

Standard differential equation–based models of collective cell behaviour, such as the logistic growth model, invoke a mean–field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, which aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean–field model to both data sets. Our results indicate that the mean–field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean–field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.

Do pioneer cells exist?

Most mathematical models of collective cell spreading make the standard assumption that the cell diffusivity and cell proliferation rate are constants that do not vary across the cell population. Here we present a combined experimental and mathematical modeling study which aims to investigate how differences in the cell diffusivity and cell proliferation rate amongst a population of cells can impact the collective behavior of the population. We present data from a three–dimensional transwell migration assay which suggests that the cell diffusivity of some groups of cells within the population can be as much as three times higher than the cell diffusivity of other groups of cells within the population. Using this information, we explore the consequences of explicitly representing this variability in a mathematical model of a scratch assay where we treat the total population of cells as two, possibly distinct, subpopulations. Our results show that when we make the standard assumption that all cells within the population behave identically we observe the formation of moving fronts of cells where both subpopulations are well–mixed and indistinguishable. In contrast, when we consider the same system where the two subpopulations are distinct, we observe a very different outcome where the spreading population becomes spatially organized with the more motile subpopulation dominating at the leading edge while the less motile subpopulation is practically absent from the leading edge. These modeling predictions are consistent with previous experimental observations and suggest that standard mathematical approaches, where we treat the cell diffusivity and cell proliferation rate as constants, might not be appropriate.

Cells Tissues Organs : preface

This volume stems from the 1st International Conference on Epithelial-Mesenchymal Transitions (EMT), which was convened by the editors on October 5–8, 2003 in the beautiful setting of Port Douglas, Queensland, Australia. EMT, the name given to the transformation of cells arranged in a coherent layer – epithelial cells – to more individualistic and potential motile cells – mesenchymal cells – was recognized decades ago by Prof. Elisabeth (Betty) Hay (Harvard Medical School, Boston, Mass., USA) as a primary mechanism in embryogenesis for remodelling tissues. More recently EMT has been seen as crucial to the spread and invasion of carcinoma, and more recently still, EMT-like changes have been detected in various pathologies marked by fi brosis. Despite the basic and clinical importance of EMT, this extremely rapidly growing fi eld had never previously had a conference devoted to it, and indeed the disciplines of developmental biology, cancer and pathology rarely interact although they have much to share. The chapters assembled for this volume encompass these three major themes of the meeting, development, pathology and cancer, and further highlight the commonality in terms of mechanisms and outcomes among them...

Epithelial-mesenchymal transitions - new insights into signaling, development and pathogenesis

This 2nd special edition of Cells Tissues Organs on epithelial-mesenchymal transitions (EMT) stems from the 2nd International Conference on EMT, which was convened by Shoukat Dedhar and Raghu Kalluri on October 1–3, 2005, in Vancouver, B.C., Canada. EMT – the transformation of epithelial cells which are usually arranged in a coherent layer and sessile, into more individualistic and motile cells, mesenchymal cells – is well recognized as an important primary mechanism in embryogenesis for remodeling tissues, as is the reverse transition. This has obvious implications in numerous pathophysiologies, and in particular EMT has emerged as an important feature of fibrosis in a growing number of organ types. It is now clear that about a third of the fibroblasts in the setting of organ fibrosis are likely derived from the epithelium. Cancer EMT remains topical, and although EMT has been reported in many cancer studies, this meeting was held against a backdrop of controversy in the cancer community as to the prevalence of EMT in clinical scenarios [Tarin et al.: Cancer Res 2005;65:5996–6000; Thompson et al.: Cancer Res 2005;65:5991–5995]...

MicroRNA regulation of epithelial-to-mesenchymal transition during re-epithelialisation: Assessing an open wound

It is becoming increasing clear that microRNAs contribute to the regulation of many biological processes, including wound healing. After injury, keratinocytes need to undergo what is known as an epithelial-to-mesenchymal transition (EMT) to initiate re-epithelialisation. During this process, keratinocytes reduce their attachment to the underlying matrix, extend membrane protrusions, become motile and migrate over the wound bed, affecting wound closure. MicroRNAs that regulate EMT are aberrantly upregulated in keratinocytes at the edge of non-healing wounds and potentially play a role in the chronicity of these wounds. In vitro and in vivo, downregulation of these microRNAs promotes EMT and migration, facilitating re-epithelialisation in wound models. This review will focus on the role of microRNAs that regulate or have potential to regulate EMT and re-epithelialisation during wound healing

The role of H4 flagella in Escherichia coli ST131 virulence

Escherichia coli sequence type 131 (ST131) is a globally dominant multidrug resistant clone associated with urinary tract and bloodstream infections. Most ST131 strains exhibit resistance to multiple antibiotics and cause infections associated with limited treatment options. The largest sub-clonal ST131 lineage is resistant to fluoroquinolones, contains the type 1 fimbriae fimH30 allele and expresses an H4 flagella antigen. Flagella are motility organelles that contribute to UPEC colonisation of the upper urinary tract. In this study, we examined the specific role of H4 flagella in ST131 motility and interaction with host epithelial and immune cells. We show that the majority of H4-positive ST131 strains are motile and are enriched for flagella expression during static pellicle growth. We also tested the role of H4 flagella in ST131 through the construction of specific mutants, over-expression strains and isogenic mutants that expressed alternative H1 and H7 flagellar subtypes. Overall, our results revealed that H4, H1 and H7 flagella possess conserved phenotypes with regards to motility, epithelial cell adhesion, invasion and uptake by macrophages. In contrast, H4 flagella trigger enhanced induction of the anti-inflammatory cytokine IL-10 compared to H1 and H7 flagella, a property that may contribute to ST131 fitness in the urinary tract.

Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient),D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculateDdirectly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.