A hierarchical polar coordinate model for epimorphic regeneration

Top-down models in biology: explanation and control of complex living systems above the molecular level

It is widely assumed in developmental biology and bioengineering that optimal understanding and control of complex living systems follows from models of molecular events. The success of reductionism has overshadowed attempts at top-down models and control policies in biological systems. However, other fields, including physics, engineering and neuroscience, have successfully used the explanations and models at higher levels of organization, including least-action principles in physics and control-theoretic models in computational neuroscience. Exploiting the dynamic regulation of pattern formation in embryogenesis and regeneration requires new approaches to understand how cells cooperate towards large-scale anatomical goal states. Here, we argue that top-down models of pattern homeostasis serve as proof of principle for extending the current paradigm beyond emergence and molecule-level rules. We define top-down control in a biological context, discuss the examples of how cognitive neuroscience and physics exploit these strategies, and illustrate areas in which they may offer significant advantages as complements to the mainstream paradigm. By targeting system controls at multiple levels of organization and demystifying goal-directed (cybernetic) processes, top-down strategies represent a roadmap for using the deep insights of other fields for transformative advances in regenerative medicine and systems bioengineering.

Morphogenetic fields in embryogenesis, regeneration, and cancer: non-local control of complex patterning

Establishment of shape during embryonic development, and the maintenance of shape against injury or tumorigenesis, requires constant coordination of cell behaviors toward the patterning needs of the host organism. Molecular cell biology and genetics have made great strides in understanding the mechanisms that regulate cell function. However, generalized rational control of shape is still largely beyond our current capabilities. Significant instructive signals function at long range to provide positional information and other cues to regulate organism-wide systems properties like anatomical polarity and size control. Is complex morphogenesis best understood as the emergent property of local cell interactions, or as the outcome of a computational process that is guided by a physically encoded map or template of the final goal state? Here I review recent data and molecular mechanisms relevant to morphogenetic fields: large-scale systems of physical properties that have been proposed to store patterning information during embryogenesis, regenerative repair, and cancer suppression that ultimately controls anatomy. Placing special emphasis on the role of endogenous bioelectric signals as an important component of the morphogenetic field, I speculate on novel approaches for the computational modeling and control of these fields with applications to synthetic biology, regenerative medicine, and evolutionary developmental biology.

Types of supernumerary outgrowths produced after inverting the dorsoventral limb axis of the anuranBufo bufo

Contralateral grafts were performed on the larval limb buds of the anuranBufo bufo. The dorsoventral axis of 80 buds at stages IV or V was inverted. Ten tadpoles were used as controls. Fifty-two supernumerary structures developed, all of them in dorsal or ventral locations on the host stump. The majority (32 out of the 44 outgrowths with more than 3 toes) were normal limbs of stump handedness. However, the following abnormal structures were also observed: 2 double-posterior, 3 mixed-symmetric, and 7 undetermined cases. These results are in agreement with the predictions of a hierarchical polar coordinate model for epimorphic regeneration.

Diverse supernumerary structures develop after inverting the anteroposterior limb axis of the anuran

Contralateral limb bud graftings were performed on tadpoles of the anuran Bufo bufo. The anteroposterior axis was inverted while the larvae were at stage IV or V (e.g., between 22-30 days after fertilization). Eighty-four tadpoles were operated on, 10 of which were used as controls. At anterior or posterior location 104 supernumerary structures developed in toto. They were collected and whole-mount examined after being stained with Alcian blue. They were further prepared for serial sectioning, mounting, and staining with hematoxylin and eosin. The majority of these supernumerary structures were found to be normal limbs of the stump handedness in agreement with all models and experiments on the urodeles axolotl and newt. However, some of the structures were clearly abnormal: double symmetric or of mixed handedness. This result is consistent with a prediction of a hierarchical polar coordinate model. The fact that no such structures have been found in the experiments on the urodeles may be due to the expected low probability for their appearance and the fact that only few such limbs have been sectioned and analyzed as yet.

A two vector field model of limb regeneration and transplant phenomena

We propose a new field description of limb regeneration in developmental biology. Central to our approach is the recognition of the importance of vector fields as descriptors in problems involving polarities or a sense of direction. In limb regeneration these vector fields represent the organisms sense of the distal direction, and its sense of the circumferential ordering of structures. Essentially all experimental results obtained to date are consistent with or explained by the model.