A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Modelling the effects of Transforming Growth Factor-β on extracellular matrix alignment in dermal wound repair

We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of transforming growth factor-β (TGFβ.) Our work extends a previously developed model which considers the interactions between fibroblasts and an extracellular matrix composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix directs the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGFβ to alter the properties of the fibroblasts. Thus we are able to simulate experiments which alter the TGFβ profile. Within this model framework we find that most of the known effects of TGFβ, i.e., changes in cell motility, cell proliferation and collagen production, are of minor importance to matrix alignment and cannot explain the anti-scarring properties of TGFβ. However, we find that by changing fibroblast reorientation rates, consistent with experimental evidence, the alignment of the regenerated tissue can be significantly altered. These data provide an explanation for the experimentally observed influence of TGFβ on scarring

Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair

We deveiop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a continuous extracellular matrix composed of collagen and a fibrin based blood clot. There are four basic interactions assumed in the model: fibroblasts orient the collagen matrix, fibroblasts produce and degrade collagen and fibrin and the matrix directs the fibroblasts and determines the speed of the cells. Several factors which influence the alignment of collagen are examined and related to current anti-scarring therapies using transforming growth factor ß. The most influential of these factors are cell speed and, more importantly for wound healing, the influx of fibroblasts from surrounding tissue

Mathematical modelling of signalling in Dictyostelium discoideum

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Understanding Streaming in Dictyostelium discoideum: Theory versus Experiments

Recent experimental work involving Dictyostelium discoideum seems to contradict several theoretical models. Experiments suggest that localization of the release of the chemoattractant cyclic adenosine monophosphate to the uropod of the cell is important for stream formation during aggregation. Yet several mathematical models are able to reproduce streaming as the cells aggregate without taking into account localization of the chemoattractant. A careful analysis of the experiments and the theory suggests the two major features of the system which are important to stream formation are random cell motion and chemotaxis to regions of higher cell density. Random cell motion acts to reduce streaming, whereas chemotaxis to regions of higher cell density reinforces streaming. With this understanding, the experimental results can be explained in a manner consistent with the theoretical results. In all the experiments, alterations in the two main factors of random motion and chemotaxis to regions of higher cell density, not the localization of the release of the chemoattractant, can explain the results as they relate to streaming. Additionally, a comparison of results from a mathematical model that simulates cells which localize the chemoattractant and cells which do not shows little difference in the streaming patterns

A FORCE BASED MODEL OF INDIVIDUAL CELL MIGRATION WITH DISCRETE ATTACHMENT SITES AND RANDOM SWITCHING TERMS

ABSTRACT A force based model of cell migration is presented which gives new insight into the importance of the dynamics of cell binding to the substrate. The main features of the model are the focus on discrete attachment dynamics, the treatment of the cellular forces as springs, and an incorporation of the stochastic nature of the attachment sites. One goal of the model is to capture the effect of the random binding and unbinding of cell attachments on global cell motion. Simulations reveal one of the most important factor influencing cell speed is the duration of the attachment to the substrate. The model captures the correct velocity and force relationships for several cell types

Using a mathematical model of cadherin-based adhesion to understand the function of the actin cytoskeleton

The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move and the end results are similar. For adherent cells, simulations suggest that the actin cytoskeleton must play an active role for the cells to establish cell-cell contact regions similar to those observed in vitro

Streaming instability of slime mold amoebae: An analytical model

During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed

Models of Dictyostelium discoideum aggregation

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