Virtual-tissue computer simulations define the roles of cell adhesion and proliferation in the onset of kidney cystic disease

In autosomal dominant polycystic kidney disease (ADPKD), cysts accumulate and progressively impair renal function. Mutations in PKD1 and PKD2 genes are causally linked to ADPKD, but how these mutations drive cell behaviors that underlie ADPKD pathogenesis is unknown. Human ADPKD cysts frequently express cadherin-8 (cad8), and expression of cad8 ectopically in vitro suffices to initiate cystogenesis. To explore cell behavioral mechanisms of cad8-driven cyst initiation, we developed a virtual-tissue computer model. Our simulations predicted that either reduced cell-cell adhesion or reduced contact inhibition of proliferation triggers cyst induction. To reproduce the full range of cyst morphologies observed in vivo, changes in both cell adhesion and proliferation are required. However, only loss-of-adhesion simulations produced morphologies matching in vitro cad8-induced cysts. Conversely, the saccular cysts described by others arise predominantly by decreased contact inhibition, that is, increased proliferation. In vitro experiments confirmed that cell-cell adhesion was reduced and proliferation was increased by ectopic cad8 expression. We conclude that adhesion loss due to cadherin type switching in ADPKD suffices to drive cystogenesis. Thus, control of cadherin type switching provides a new target for therapeutic intervention

Computer Simulation of Cellular Patterning Within the Drosophila Pupal Eye

We present a computer simulation and associated experimental validation of assembly of glial-like support cells into the interweaving hexagonal lattice that spans the Drosophila pupal eye. This process of cell movements organizes the ommatidial array into a functional pattern. Unlike earlier simulations that focused on the arrangements of cells within individual ommatidia, here we examine the local movements that lead to large-scale organization of the emerging eye field. Simulations based on our experimental observations of cell adhesion, cell death, and cell movement successfully patterned a tracing of an emerging wild-type pupal eye. Surprisingly, altering cell adhesion had only a mild effect on patterning, contradicting our previous hypothesis that the patterning was primarily the result of preferential adhesion between IRM-class surface proteins. Instead, our simulations highlighted the importance of programmed cell death (PCD) as well as a previously unappreciated variable: the expansion of cells' apical surface areas, which promoted rearrangement of neighboring cells. We tested this prediction experimentally by preventing expansion in the apical area of individual cells: patterning was disrupted in a manner predicted by our simulations. Our work demonstrates the value of combining computer simulation with in vivo experiments to uncover novel mechanisms that are perpetuated throughout the eye field. It also demonstrates the utility of the Glazier–Graner–Hogeweg model (GGH) for modeling the links between local cellular interactions and emergent properties of developing epithelia as well as predicting unanticipated results in vivo

3D Multi-Cell Simulation of Tumor Growth and Angiogenesis

We present a 3D multi-cell simulation of a generic simplification of vascular tumor growth which can be easily extended and adapted to describe more specific vascular tumor types and host tissues. Initially, tumor cells proliferate as they take up the oxygen which the pre-existing vasculature supplies. The tumor grows exponentially. When the oxygen level drops below a threshold, the tumor cells become hypoxic and start secreting pro-angiogenic factors. At this stage, the tumor reaches a maximum diameter characteristic of an avascular tumor spheroid. The endothelial cells in the pre-existing vasculature respond to the pro-angiogenic factors both by chemotaxing towards higher concentrations of pro-angiogenic factors and by forming new blood vessels via angiogenesis. The tumor-induced vasculature increases the growth rate of the resulting vascularized solid tumor compared to an avascular tumor, allowing the tumor to grow beyond the spheroid in these linear-growth phases. First, in the linear-spherical phase of growth, the tumor remains spherical while its volume increases. Second, in the linear-cylindrical phase of growth the tumor elongates into a cylinder. Finally, in the linear-sheet phase of growth, tumor growth accelerates as the tumor changes from cylindrical to paddle-shaped. Substantial periods during which the tumor grows slowly or not at all separate the exponential from the linear-spherical and the linear-spherical from the linear-cylindrical growth phases. In contrast to other simulations in which avascular tumors remain spherical, our simulated avascular tumors form cylinders following the blood vessels, leading to a different distribution of hypoxic cells within the tumor. Our simulations cover time periods which are long enough to produce a range of biologically reasonable complex morphologies, allowing us to study how tumor-induced angiogenesis affects the growth rate, size and morphology of simulated tumors

Adhesion Failures Determine the Pattern of Choroidal Neovascularization in the Eye: A Computer Simulation Study

Choroidal neovascularization (CNV) of the macular area of the retina is the major cause of severe vision loss in adults. In CNV, after choriocapillaries initially penetrate Bruch's membrane (BrM), invading vessels may regress or expand (CNV initiation). Next, during Early and Late CNV, the expanding vasculature usually spreads in one of three distinct patterns: in a layer between BrM and the retinal pigment epithelium (sub-RPE or Type 1 CNV), in a layer between the RPE and the photoreceptors (sub-retinal or Type 2 CNV) or in both loci simultaneously (combined pattern or Type 3 CNV). While most studies hypothesize that CNV primarily results from growth-factor effects or holes in BrM, our three-dimensional simulations of multi-cell model of the normal and pathological maculae recapitulate the three growth patterns, under the hypothesis that CNV results from combinations of impairment of: 1) RPE-RPE epithelial junctional adhesion, 2) Adhesion of the RPE basement membrane complex to BrM (RPE-BrM adhesion), and 3) Adhesion of the RPE to the photoreceptor outer segments (RPE-POS adhesion). Our key findings are that when an endothelial tip cell penetrates BrM: 1) RPE with normal epithelial junctions, basal attachment to BrM and apical attachment to POS resists CNV. 2) Small holes in BrM do not, by themselves, initiate CNV. 3) RPE with normal epithelial junctions and normal apical RPE-POS adhesion, but weak adhesion to BrM (e.g. due to lipid accumulation in BrM) results in Early sub-RPE CNV. 4) Normal adhesion of RBaM to BrM, but reduced apical RPE-POS or epithelial RPE-RPE adhesion (e.g. due to inflammation) results in Early sub-retinal CNV. 5) Simultaneous reduction in RPE-RPE epithelial binding and RPE-BrM adhesion results in either sub-RPE or sub-retinal CNV which often progresses to combined pattern CNV. These findings suggest that defects in adhesion dominate CNV initiation and progression

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution

Filopodial-Tension Model of Convergent-Extension of Tissues.

In convergent-extension (CE), a planar-polarized epithelial tissue elongates (extends) in-plane in one direction while shortening (converging) in the perpendicular in-plane direction, with the cells both elongating and intercalating along the converging axis. CE occurs during the development of most multicellular organisms. Current CE models assume cell or tissue asymmetry, but neglect the preferential filopodial activity along the convergent axis observed in many tissues. We propose a cell-based CE model based on asymmetric filopodial tension forces between cells and investigate how cell-level filopodial interactions drive tissue-level CE. The final tissue geometry depends on the balance between external rounding forces and cell-intercalation traction. Filopodial-tension CE is robust to relatively high levels of planar cell polarity misalignment and to the presence of non-active cells. Addition of a simple mechanical feedback between cells fully rescues and even improves CE of tissues with high levels of polarity misalignments. Our model extends easily to three dimensions, with either one converging and two extending axes, or two converging and one extending axes, producing distinct tissue morphologies, as observed in vivo

3D filopodial tension model versions.

<p>(<b>A</b>) Rotation around the polarization vector produces the 3D equatorial model. (<b>B</b>) Rotation around the convergence line results in the 3D bipolar model. (<b>A’-A”</b>) Initial and final states of a simulation of the equatorial model with all <b>cells’</b> polarization vectors pointing up. (<b>B’-B”</b>) Initial and final states of a simulation of the bipolar model with all <b>cells’</b> convergence axis lying vertically.</p

List of reference parameters values used in the simulations.

<p>Parameter sweeps vary one of the first 7 parameters, while keeping all the others constant. Key: λ_force, pulling strength; t_interval, time interval between link formation/breakage (MCS); r_max, maximum distance between <b>cells</b> (<b>cell</b> diameters); n_max, maximum number of links per <b>cell</b>; ϑ_max, maximum angle (radians); N, number of <b>cells</b>; cd, <b>cell</b> diameter (lattice sites); T, temperature or level of noise in the simulations; λ_volume, <b>cell</b> stiffness; n_orders, neighboring orders for lattice site flip and contact energy; J_c,M, adhesion energy between <b>cells</b> and <b>medium</b>; J_c,c, adhesion energy between <b>cells</b>.</p

Simulation snapshots and metrics.

<p>(<b>A</b>) Snapshots of a 2D simulation with reference parameter values, showing the initial configuration (left) and the configuration when the length of the major axis (L₊, red lines) increases to twice the length of the minor axis (L_-, blue lines), i.e., κ = 0.5. The simulation contains N = 109 <b>cells</b> (in green) with the tension forces shown by the white segments connecting their centers-of-mass. (<b>B</b>) Graph of L_-/L₊ versus time for the reference 2D simulation. For all simulations we measured the final value of the ratio between the length of minor and major axes of the tissue κ (shown in red), and the time τ (shown in blue) when the length of the major axis doubles the length of the minor axis (L_-/L₊ = 0.5).</p