Model-based Bayesian inference of the ventilation distribution in patients with cystic fibrosis from multiple breath washout, with comparison to ventilation MRI.

BACKGROUND: Indices of ventilation heterogeneity (VH) from multiple breath washout (MBW) have been shown to correlate well with VH indices derived from hyperpolarised gas ventilation MRI. Here we report the prediction of ventilation distributions from MBW data using a mathematical model, and the comparison of these predictions with imaging data. METHODS: We developed computer simulations of the ventilation distribution in the lungs to model MBW measurement with 3 parameters: σV, determining the extent of VH; V0, the lung volume; and VD, the dead-space volume. These were inferred for each individual from supine MBW data recorded from 25 patients with cystic fibrosis (CF) using approximate Bayesian computation. The fitted models were used to predict the distribution of gas imaged by 3He ventilation MRI measurements collected from the same visit. RESULTS: The MRI indices measured (I1/3, the fraction of pixels below one-third of the mean intensity and ICV, the coefficient of variation of pixel intensity) correlated strongly with those predicted by the MBW model fits (r=0.93,0.88 respectively). There was also good agreement between predicted and measured MRI indices (mean bias ± limits of agreement: I1/3:-0.003±0.118 and ICV:-0.004±0.298). Fitted model parameters were robust to truncation of MBW data. CONCLUSION: We have shown that the ventilation distribution in the lung can be inferred from an MBW signal, and verified this using ventilation MRI. The Bayesian method employed extracts this information with fewer breath cycles than required for LCI, reducing acquisition time required, and gives uncertainty bounds, which are important for clinical decision making.

Collagen fibril assembly: New approaches to unanswered questions.

Collagen fibrils are essential for metazoan life. They are the largest, most abundant, and most versatile protein polymers in animals, where they occur in the extracellular matrix to form the structural basis of tissues and organs. Collagen fibrils were first observed at the turn of the 20th century. During the last 40 years, the genes that encode the family of collagens have been identified, the structure of the collagen triple helix has been solved, the many enzymes involved in the post-translational modifications of collagens have been identified, mutations in the genes encoding collagen and collagen-associated proteins have been linked to heritable disorders, and changes in collagen levels have been associated with a wide range of diseases, including cancer. Yet despite extensive research, a full understanding of how cells assemble collagen fibrils remains elusive. Here, we review current models of collagen fibril self-assembly, and how cells might exert control over the self-assembly process to define the number, length and organisation of fibrils in tissues.

Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis.

Distinct mechanisms involving cell shape and mechanical force are known to influence the rate and orientation of division in cultured cells. However, uncoupling the impact of shape and force in tissues remains challenging. Combining stretching of Xenopus tissue with mathematical methods of inferring relative mechanical stress, we find separate roles for cell shape and mechanical stress in orienting and cueing division. We demonstrate that division orientation is best predicted by an axis of cell shape defined by the position of tricellular junctions (TCJs), which align with local cell stress rather than tissue-level stress. The alignment of division to cell shape requires functional cadherin and the localization of the spindle orientation protein, LGN, to TCJs but is not sensitive to relative cell stress magnitude. In contrast, proliferation rate is more directly regulated by mechanical stress, being correlated with relative isotropic stress and decoupled from cell shape when myosin II is depleted.

A Mechanosensitive RhoA Pathway that Protects Epithelia against Acute Tensile Stress.

Adherens junctions are tensile structures that couple epithelial cells together. Junctional tension can arise from cell-intrinsic application of contractility or from the cell-extrinsic forces of tissue movement. Here, we report a mechanosensitive signaling pathway that activates RhoA at adherens junctions to preserve epithelial integrity in response to acute tensile stress. We identify Myosin VI as the force sensor, whose association with E-cadherin is enhanced when junctional tension is increased by mechanical monolayer stress. Myosin VI promotes recruitment of the heterotrimeric Gα12 protein to E-cadherin, where it signals for p114 RhoGEF to activate RhoA. Despite its potential to stimulate junctional actomyosin and further increase contractility, tension-activated RhoA signaling is necessary to preserve epithelial integrity. This is explained by an increase in tensile strength, especially at the multicellular vertices of junctions, that is due to mDia1-mediated actin assembly.

Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model.

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted.

Early gene regulation of osteogenesis in embryonic stem cells.

The early gene regulatory networks (GRNs) that mediate stem cell differentiation are complex, and the underlying regulatory associations can be difficult to map accurately. In this study, the expression profiles of the genes Dlx5, Msx2 and Runx2 in mouse embryonic stem cells were monitored over a 48 hour period after exposure to the growth factors BMP2 and TGFß1. Candidate GRNs of early osteogenesis were constructed based on published experimental findings and simulation results of Boolean and ordinary differential equation models were compared with our experimental data in order to test the validity of these models. Three gene regulatory networks were found to be consistent with the data, one of these networks exhibited sustained oscillation, a behaviour which is consistent with the general view of embryonic stem cell plasticity. The work cycle presented in this paper illustrates how mathematical modelling can be used to elucidate from gene expression profiles GRNs that are consistent with experimental data.

Intracellular flow in optic nerve axons: a mechanism for cell death in glaucoma.

PURPOSE: In glaucoma, elevated intraocular pressure causes a progressive loss of retinal ganglion cells and results in optic neuropathy. The authors propose a potential mechanism for cell death, whereby elevated intraocular pressure causes fluid to permeate axonal membranes, creating a passive intracellular fluid flow within the axons. It is hypothesized that this intracellular flow locally depletes the adenosine triphosphate (ATP) concentration, disrupting axonal transport and leading to cell death. METHODS: A mathematical model was developed that takes into account the biomechanical principles underpinning the proposed hypothesis, and was solved to determine the implications of the mechanism. RESULTS: The model suggests that the raised intraocular pressures present in glaucoma are adequate to produce significant intracellular fluid flow. In the periphery of the optic nerve head, this flow may be sufficient to disrupt the diffusion of ATP and hence interrupt active axonal transport. CONCLUSIONS: The mathematical model demonstrates that it is physically plausible that a passive intracellular fluid flow could significantly contribute to the pathophysiology of the retinal ganglion cell axon in glaucoma.

Elucidating the interactions between the adhesive and transcriptional functions of beta-catenin in normal and cancerous cells.

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential role in cadherin-mediated adhesion. Two main hypotheses have been proposed concerning the balance between beta-catenin's adhesive and transcriptional functions: either beta-catenin's fate is determined by competition between its binding partners, or Wnt induces folding of beta-catenin into a conformation allocated preferentially to transcription. The experimental data supporting each hypotheses remain inconclusive. In this paper we present a new mathematical model of the Wnt pathway that incorporates beta-catenin's dual function. We use this model to carry out a series of in silico experiments and compare the behaviour of systems governed by each hypothesis. Our analytical results and model simulations provide further insight into the current understanding of Wnt signalling and, in particular, reveal differences in the response of the two modes of interaction between adhesion and signalling in certain in silico settings. We also exploit our model to investigate the impact of the mutations most commonly observed in human colorectal cancer. Simulations show that the amount of functional APC required to maintain a normal phenotype increases with increasing strength of the Wnt signal, a result which illustrates that the environment can substantially influence both tumour initiation and phenotype.

Epithelial cell deformation during surfactant-mediated airway reopening: a theoretical model.

A theoretical model is presented describing the reopening by an advancing air bubble of an initially liquid-filled collapsed airway lined with deformable epithelial cells. The model integrates descriptions of flow-structure interaction (accounting for nonlinear deformation of the airway wall and viscous resistance of the airway liquid flow), surfactant transport around the bubble tip (incorporating physicochemical parameters appropriate for Infasurf), and cell deformation (due to stretching of the airway wall and airway liquid flows). It is shown how the pressure required to drive a bubble into a flooded airway, peeling apart the wet airway walls, can be reduced substantially by surfactant, although the effectiveness of Infasurf is limited by slow adsorption at high concentrations. The model demonstrates how the addition of surfactant can lead to the spontaneous reopening of a collapsed airway, depending on the degree of initial airway collapse. The effective elastic modulus of the epithelial layer is shown to be a key determinant of the relative magnitude of strains generated by flow-induced shear stresses and by airway wall stretch. The model also shows how epithelial-layer compressibility can mediate strains arising from flow-induced normal stresses and stress gradients.