Models of collective cell spreading with variable cell aspect ration: a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models

A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices

Unique metabolic features of pancreatic cancer stroma: relevance to the tumor compartment, prognosis, and invasive potential.

Pancreatic ductal adenocarcinoma (PDAC) has a dismal prognosis. The aggressiveness and therapeutic recalcitrance of this malignancy has been attributed to multiple factors including the influence of an active desmoplastic stroma. How the stromal microenvironment of PDAC contributes to the fatal nature of this disease is not well defined. In the analysis of clinical specimens, we observed diverse expression of the hypoxic marker carbonic anhydrase IX and the lactate transporter MCT4 in the stromal compartment. These stromal features were associated with the epithelial to mesenchymal phenotype in PDAC tumor cells, and with shorter patient survival. Cultured cancer-associated fibroblasts (CAFs) derived from primary PDAC exhibited a high basal level of hypoxia inducible factor 1a (HIF1α) that was both required and sufficient to modulate the expression of MCT4. This event was associated with increased transcription and protein synthesis of HIF1α in CAFs relative to PDAC cell lines, while surprisingly the protein turnover rate was equivalent. CAFs utilized glucose predominantly for glycolytic intermediates, whereas glutamine was the preferred metabolite for the TCA cycle. Unlike PDAC cell lines, CAFs were resistant to glucose withdrawal but sensitive to glutamine depletion. Consistent with the lack of reliance on glucose, CAFs could survive the acute depletion of MCT4. In co-culture and xenograft studies CAFs stimulated the invasive potential and metastatic spread of PDAC cell lines through a mechanism dependent on HIF1α and MCT4. Together, these data indicate that stromal metabolic features influence PDAC tumor cells to promote invasiveness and metastatic potential and associate with poor outcome in patients with PDAC

A two-compartment mechanochemical model of the roles of\ud transforming growth factor β and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor−β (TGFβ) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGFβ and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGFβ in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGFβ significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures

A fibrocontractive mechanochemical model of dermal wound\ud closure incorporating realistic growth factor kinetics

Fibroblasts and their activated phenotype, myofibroblasts, are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct processes: the cells are stimulated to change phenotype by the combined actions of transforming growth factor β (TGFβ) and mechanical tension. This observation indicates a need for a detailed exploration of the effect of the strong interactions between the mechanical changes and growth factors in dermal wound healing. We review the experimental findings in detail and develop a model of dermal wound healing that incorporates these phenomena. Our model includes the interactions between TGFβ and collagenase, providing a more biologically realistic form for the growth factor kinetics than those included in previous mechanochemical descriptions. A comparison is made between the model predictions and experimental data on human dermal wound healing and all the essential features are well matched

SPOCS User Guide

SPOCS implements a graph-based ortholog prediction method to generate a simple tab-delimited table of orthologs, and in addition, html files that provide a visualization of the ortholog/paralog relationships to which gene/protein expression metadata may be overlaid

A critical role for the chromatin remodeller CHD7 in anterior mesoderm during cardiovascular development

CHARGE syndrome is caused by spontaneous loss-of-function mutations to the ATP-dependant chromatin remodeller chromodomain-helicase-DNA-binding protein 7 (CHD7). It is characterised by a distinct pattern of congenital anomalies, including cardiovascular malformations. Disruption to the neural crest lineage has previously been emphasised in the aetiology of this developmental disorder. We present evidence for an additional requirement for CHD7 activity in the Mesp1-expressing anterior mesoderm during heart development. Conditional ablation of Chd7 in this lineage results in major structural cardiovascular defects akin to those seen in CHARGE patients, as well as a striking loss of cardiac innervation and embryonic lethality. Genome-wide transcriptional analysis identified aberrant expression of key components of the Class 3 Semaphorin and Slit-Robo signalling pathways in Chd7(fl/fl);Mesp1-Cre mutant hearts. CHD7 localises at the Sema3c promoter in vivo, with alteration of the local chromatin structure seen following Chd7 ablation, suggestive of direct transcriptional regulation. Furthermore, we uncover a novel role for CHD7 activity upstream of critical calcium handling genes, and demonstrate an associated functional defect in the ability of cardiomyocytes to undergo excitation-contraction coupling. This work therefore reveals the importance of CHD7 in the cardiogenic mesoderm for multiple processes during cardiovascular development