Branching patterns emerge in a mathematical model of the dynamics of lung development.

Recent experimental work has described an elegant pattern of branching in the development of the lung. Multiple forms of branching have been identified, including side branching and tip bifurcation. A particularly interesting feature is the phenomenon of 'orthogonal rotation of the branching plane'. The lung must fill 3D space with the essentially 2D phenomenon of branching. It accomplishes this by rotating the branching plane by 90° with each generation. The mechanisms underlying this rotation are not understood. In general, the programmes that underlie branching have been hypothetically attributed to genetic 'subroutines' under the control of a 'global master routine' to invoke particular subroutines at the proper time and location, but the mechanisms of these routines are not known. Here, we demonstrate that fundamental mechanisms, the reaction and diffusion of biochemical morphogens, can create these patterns. We used a partial differential equation model that postulates three morphogens, which we identify with specific molecules in lung development. We found that cascades of branching events, including side branching, tip splitting and orthogonal rotation of the branching plane, all emerge immediately from the model, without further assumptions. In addition, we found that one branching mode can be easily switched to another, by increasing or decreasing the values of key parameters. This shows how a 'global master routine' could work by the alteration of a single parameter. Being able to simulate cascades of branching events is necessary to understand the critical features of branching, such as orthogonal rotation of the branching plane between successive generations, and branching mode switch during lung development. Thus, our model provides a paradigm for how genes could possibly act to produce these spatial structures. Our low-dimensional model gives a qualitative understanding of how generic physiological mechanisms can produce branching phenomena, and how the system can switch from one branching pattern to another using low-dimensional 'control knobs'. The model provides a number of testable predictions, some of which have already been observed (though not explained) in experimental work.

Preferred mitotic orientation in pattern formation by vascular mesenchymal cells.

Cellular self-organization is essential to physiological tissue and organ development. We previously observed that vascular mesenchymal cells, a multipotent subpopulation of aortic smooth muscle cells, self-organize into macroscopic, periodic patterns in culture. The patterns are produced by cells gathering into raised aggregates in the shape of nodules or ridges. To determine whether these patterns are accounted for by an oriented pattern of cell divisions or postmitotic relocation of cells, we acquired time-lapse, videomicrographic phase-contrast, and fluorescence images during self-organization. Cell division events were analyzed for orientation of daughter cells in mitoses during separation and their angle relative to local cell alignment, and frequency distribution of the mitotic angles was analyzed by both histographic and bin-free statistical methods. Results showed a statistically significant preferential orientation of daughter cells along the axis of local cell alignment as early as day 8, just before aggregate formation. This alignment of mitotic axes was also statistically significant at the time of aggregate development (day 11) and after aggregate formation was complete (day 15). Treatment with the nonmuscle myosin II inhibitor, blebbistatin, attenuated alignment of mitotic orientation, whereas Rho kinase inhibition eliminated local cell alignment, suggesting a role for stress fiber orientation in this self-organization. Inhibition of cell division using mitomycin C reduced the macroscopic pattern formation. Time-lapse monitoring of individual cells expressing green fluorescent protein showed postmitotic movement of cells into neighboring aggregates. These findings suggest that polarization of mitoses and postmitotic migration of cells both contribute to self-organization into periodic, macroscopic patterns in vascular stem cells.

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework.

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation.

Directing tissue morphogenesis via self-assembly of vascular mesenchymal cells.

Rebuilding injured tissue for regenerative medicine requires technologies to reproduce tissue/biomaterials mimicking the natural morphology. To reconstitute the tissue pattern, current approaches include using scaffolds with specific structure to plate cells, guiding cell spreading, or directly moving cells to desired locations. However, the structural complexity is limited. Also, the artificially-defined patterns are usually disorganized by cellular self-organization in the subsequent tissue development, such as cell migration and cell-cell communication. Here, by working in concert with cellular self-organization rather than against it, we experimentally and mathematically demonstrate a method which directs self-organizing vascular mesenchymal cells (VMCs) to assemble into desired multicellular patterns. Incorporating the inherent chirality of VMCs revealed by interfacing with microengineered substrates and VMCs' spontaneous aggregation, differences in distribution of initial cell plating can be amplified into the formation of striking radial structures or concentric rings, mimicking the cross-sectional structure of liver lobules or osteons, respectively. Furthermore, when co-cultured with VMCs, non-pattern-forming endothelial cells (ECs) tracked along the VMCs and formed a coherent radial or ring pattern in a coordinated manner, indicating that this method is applicable to heterotypical cell organization.