Branching Dynamics In A Model Of Lung Development Based On Reaction-diffusion Mechanisms

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 splitting. In the lung, these occur in sequence:first side branching creates the primary stalks; then, there is a change of mode to tip splitting. The programs 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. However, the actual mechanisms underlying these routines are not understood. Being able to understand the mechanisms of branching, not only is an essential in the developmental field, but also plays a key role in tissue engineering and medicine field.Here, we demonstrate that the reaction and diffusion of biochemical morphogens can create these patterns. We used a Partial Differential Equation model that postulates3morphogens, which we identify with specific molecules in lung development. We found that side branching, tip splitting and orthogonal rotation of the branching plane all emerge immediately from the model. 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 the "global master routine" could work by the alteration of a single parameter.Further, we attempt to explain the phenomena above, and others, as growing out of two fundamental instabilities that determine branching dynamics in this system, one in the longitudinal (growth) direction and the other in the transverse direction. We used a decoupling method of the original branching process into the two semi-independent dynamics, activator/inhibitor subsystem and the growth process, to assist our understanding, and to design numerical experiment to prove our hypothesis.We found that, in this model,1) side branching results from a pattern-formation instability of the activator/inhibitor subsystem in the longitudinal direction, far from equilibrium. This instability is fundamentally different compared to the popular "temporal-to-spatial" conversion concept;2) tip splitting is due to a Turing-style instability, along the transversal direction, that creates the splitting of the activator peak at the growing tip, the occurrence of which requires the widening of the growing stalk. Tip splitting is abolished when transversal stalk widening is prevented;3) when both instabilities are satisfied simultaneously, we see tip bifurcation together with side branching.Thus, our model provides a paradigm for how genes could possibly act to produce 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.