Developmental biology. Fishing for morphogens

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.

Matrix GLA protein, an inhibitory morphogen in pulmonary vascular development

Deficiency of matrix GLA protein (MGP), an inhibitor of bone morphogenetic protein (BMP)-2/4, is known to cause arterial calcification and peripheral pulmonary artery stenosis. Yet the vascular role of MGP remains poorly understood. To further investigate MGP, we created a new MGP transgenic mouse model with high expression of the transgene in the lungs. The excess MGP led to a disruption of the pulmonary pattern of BMP-4, and resulted in significant morphological defects in the pulmonary artery tree. Specifically, the vascular branching pattern lacked characteristic side branching, whereas control lungs had extensive side branching accounting for as much as 40% of the vascular endothelium. The vascular changes could be explained by a dramatic reduction of phosphorylated SMAD1/5/8 in the alveolar epithelium, and in epithelial expression of the activin-like kinase receptor 1 and vascular endothelial growth factor, both critical in vascular formation. Abnormalities were also found in the terminal airways and in lung cell differentiation; high levels of surfactant protein-B were distributed in an abnormal pattern suggesting lost coordination between vasculature and airways. Ex vivo, lung cells from MGP transgenic mice showed higher proliferation, in particular surfactant protein B-expressing cells, and conditioned medium from these cells poorly supported in vitro angiogenesis compared with normal lung cells. The vascular branching defect can be mechanistically explained by a computational model based on activator/inhibitor reaction-diffusion dynamics, where BMP-4 and MGP are considered as an activating and inhibitory morphogen, respectively, suggesting that morphogen interactions are important for vascular branching.

Pattern formation by vascular mesenchymal cells

In embryogenesis, immature mesenchymal cells aggregate and organize into patterned tissues. Later in life, a pathological recapitulation of this process takes place in atherosclerotic lesions, when vascular mesenchymal cells organize into trabecular bone tissue within the artery wall. Here we show that multipotential adult vascular mesenchymal cells self-organize in vitro into patterns that are predicted by a mathematical model based on molecular morphogens interacting in a reaction-diffusion process. We identify activator and inhibitor morphogens for stripe, spot, and labyrinthine patterns and confirm the model predictions in vitro. Thus, reaction-diffusion principles may play a significant role in morphogenetic processes in adult mesenchymal cells.

Understanding biological complexity: lessons from the past

Advances in molecular biology now permit complex biological systems to be tracked at an exquisite level of detail. The information flow is so great, however, that using intuition alone to draw connections is unrealistic. Thus, the need to integrate mathematical biology with experimental biology is greater than ever. To achieve this integration, obstacles that have traditionally prevented effective communication between theoreticians and experimentalists must be overcome, so that experimentalists learn the language of mathematics and dynamical modeling and theorists learn the language of biology. Fifty years ago Alan Hodgkin and Andrew Huxley published their quantitative model of the nerve action potential; in the same year, Alan Turing published his work on pattern formation in activator-inhibitor systems. These classic studies illustrate two ends of the spectrum in mathematical biology: the detailed model approach and the minimal model approach. When combined, they are highly synergistic in analyzing the mechanisms underlying the behavior of complex biological systems. Their effective integration will be essential for unraveling the physical basis of the mysteries of life.