Development and applications of a model for cellular response to multiple chemotactic cues

The chemotactic response of a cell population to a single chemical species has been characterized experimentally for many cell types and has been extensively studied from a theoretical standpoint. However, cells frequently have multiple receptor types and can detect and respond chemotactically to more than one chemical. How these signals are integrated within the cell is not known, and we therefore adopt a macroscopic phenomenological approach to this problem. In this paper we derive and analyze chemotactic models based on partial differential (chemotaxis) equations for cell movement in response to multiple chemotactic cues. Our derivation generalizes the approach of Othmer and Stevens [29], who have recently developed a modeling framework for studying different chemotactic responses to a single chemical species. The importance of such a generalization is illustrated by the effect of multiple chemical cues on the chemotactic sensitivity and the spatial pattern of cell densities in several examples. We demonstrate that the model can generate the complex patterns observed on the skin of certain animal species and we indicate how the chemotactic response can be viewed as a form of positional indicator

A chemotactic model for the advance and retreat of the primitive streak in avian development

The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective endodermal, mesodermal and ectodermal tissue. During streak formation a specialized group of cells first moves anteriorly as a coherent column, beginning from the posterior end of the prospective anterior-posterior axis (a process called progression), and then reverses course and returns to the most posterior point on the axis (a process called regression). To date little is known concerning the mechanisms controlling either progression or regression. Here we develop a model in which chemotaxis directs the cell movement and which is capable of reproducing the principal features connected with progression and regression of the primitive streak. We show that this model exhibits a number of experimentally-observed features of normal and abnormal streak development, and we propose a number of experimental tests which may serve to illuminate the mechanisms. This paper represents the first attempt to model the global features of primitive streak formation, and provides an initial stage in the development of a more biologically-realistic discrete cell model that will allow for variation of properties between cells and control over movement of individual cells

From microscopic to macroscopic descriptions of cell\ud migration on growing domains

Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs

Reaction mechanism of the direct gas phase synthesis of H2O2 catalyzed by Au3

The gas phase reaction of molecular oxygen and hydrogen catalyzed by a Au3cluster to yield H2O2 was investigated theoretically using second order Z-averaged perturbation theory, with the final energies obtained with the fully size extensive completely renormalized CR-CC(2,3) coupled clustertheory. The proposed reaction mechanism is initiated by adsorption and activation of O2 on the Au3cluster. Molecular hydrogen then binds to the Au3O2 global minimum without an energy barrier. The reaction between the activated oxygen and hydrogen molecules proceeds through formation of hydroperoxide (HO2) and a hydrogen atom, which subsequently react to form the product hydrogen peroxide. All reactants, intermediates, and product remain bound to the goldcluster throughout the course of the reaction. The steps in the proposed reaction mechanism have low activation energy barriers below 15kcal∕mol. The overall reaction is highly exothermic by ∼30kcal∕mol

Pattern formation in Turing systems with mixed boundary conditions

A central issue in developmental biology is the formation of pattern and form in the early embryo. From the apparently homogeneous mass of dividing cells that exists in the earliest stages of development emerges the vast range of pattern and structure observed in the adult. The formation of structure is termed morphogenesis, and pattern generation models are known as morphogenetic models. The role of modelling in morphogenesis is to suggest possible scenarios as to how various physical and chemical processes conspire to produce pattern

Steady-state patterns in a reaction diffusion system with mixed boundary conditions

A number of models for pattern formation and regulation are based on the hypothesis that a diffusible morphogen supplies positional information that can interpreted by cells. Such models fall into two main classes:- those in which pattern arises from distributed sources and/or sinks of the morphogens, and those which can spontaneously produce pattern via the interaction of reaction and transport. In source-sink models, specialized cells maintain the concentration of the morphogen at fixed levels, and given a suitable distribution of sources and sinks, a tissue can be proportioned into any number of cell types with a threshold interpretation mechanism. However, the spatial pattern established is strongly dependent on the distances between the sources and sinks, and additional hyoptheses must be invoked to ensure that the pattern is invariant under changes in the scale of the system

Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source

This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source

Models of Dictyostelium discoideum aggregation

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Multiscale models for movement in oriented environments and their application to hilltopping in butterflies

Hilltopping butterflies direct their movement in response to topography, facilitating mating encounters via accumulation at summits. In this paper, we take hilltopping as a case study to explore the impact of complex orienteering cues on population dynamics. The modelling employs a standard multiscale framework, in which an individual's movement path is described as a stochastic 'velocity-jump' process and scaling applied to generate a macroscopic model capable of simulating large populations in landscapes. In this manner, the terms and parameters of the macroscopic model directly relate to statistical inputs of the individual-level model (mean speeds, turning rates and turning distributions). Applied to hilltopping in butterflies, we demonstrate how hilltopping acts to aggregate populations at summits, optimising mating for low-density species. However, for abundant populations, hilltopping is not only less effective but also possibly disadvantageous, with hilltopping males recording a lower mating rate than their non-hilltopping competitors. © 2013 Springer Science+Business Media Dordrecht