Morphogenesis is one of the grand challenges in biology. Shape arises because cells change in number, size, shape, and movement; understanding how this actually happens and how it is controlled is a natural goal. Our work forms a small rivulet off the main stream that aims to quantifies the ideas espoused by the early pioneers of developmental biology such as Roux, His, and D’Arcy Thompson (read an essay from Development on the centenary of  “On growth and form”) and has led to a deeper appreciation of the role of physics in organogenesis in the context of how we should describe it, how we may predict it, and finally, how we may control it.

To correctly quantify the geometry of tissue morphogenesis, we have developed  approaches to tissue tectonics using invariants that respect translational and rotational motions to characterize and compare dynamic fate maps of multi-cellular tissues, borrowing ideas from hydrodynamics. This approach allows one to distinguish the change in tissue shape because of the relative magnitudes of cell shape changes and cell movements, with many experimental implications for robustness in developing tissues (e.g. in convergent extension, etc.). More recently, we have used ideas from nonlinear dynamics and continuum mechanics to characterize properly invariant measures of deformation that describe the dynamic morphoskeletons – the organizers of large scale cell movements in multicellular tissues. This has led to a framework for uncovering the basis for epithelial morphogenesis modeled by active nematodynamics, complex fluid flows in three dimensions, and gastrulation movements in a variety of contexts.  A recent outcome has been to complement this with direct measurements of the forces associated with morphing tissues.

Moving towards a predictive theory for how genes link to geometry, we have taken an evo-devo approach linking a mathematical approach to natural history (by quantifying shapes using  collections drawn from the Natural History Museum (London) – to study the beaks of Darwin’s finches, the Smithsonian (Washington) – to study beak shapes across avian radiations, and university collections such as those at UC Berkeley and Harvard – to study egg shapes across more than 1500 bird species) to a biophysical approach to explore the physical basis of morphogenesis in plants and animals. Current work in this area includes quantifying the statistical geometry and topology of deer antlers, mammalian brains across multiple species, and gut morphology in birds and their link to diets.

For example, inspired by observations, we provided a theoretical basis for the evolution of multicellular tissue organization in choanoflagellates, likely the closest eukaryotic relatives of metazoans using simple, testable geometrical and biophysical principles. Separately, we showed how it is necessary to incorporate neuromuscular dynamics to explain the morphological transitions between the larval and polyp stages in the sea-anemone, in what is likely a conserved mechanism across cnidarians.

We have also worked on understanding the form of plant organs, such as leaves and flowers, treated as mathematical problems of how to embed non-Euclidean surface metrics in three-dimensional space – in such contexts as the shape of a leaf, the blooming of a flower and the elongation of Columbine petal spurs using cell shape change- and understanding the recent evolutionary radiation of this species.  We have also shown how slow movements of water can lead to morphological changes in such instances as the opening and closing of a pine cone or the coiling and overwinding of tendrils, explaining observations going back to Darwin’s work on the power of movement in plants.

In the study of morphogenesis in animals,  we showed that hydraulics could play an important role in guiding and informing the dynamics of cystic organoids. We then showed that the basic theoretical principles in our study allowed us to explain embryo size and cell fate control during the early developmental stages of  mammalian embryos, and also explained size control of the inner ear in fishes. We have recently come back to basis for lumenization in other developmental contexts from the perspective of morphogenetic control.

By quantifying the concept of differential growth, first elucidated by Wilhelm His and popularized by DW Thompson, we explained the growth and form of the coiled vertebrate gut  with scaling ideas, results corroborated using our own biophysical experiments and those done in collaboration with colleagues, across multiple species and across developmental time. This idea also allowed us to explain villification, the formation of protrusions responsible for nutrient absorption in the intestine, and our study linking experiments and computations explains the process in a growing organism and across species.  We have also studied the geometrical and physical basis for differential gene expression during villi formation, the genetic underpinnings of gut coiling and more recently, the active mechanics of gut elongation. Most recently, we have shown how the regional specification of gut morphology is intimately linked to variations in gene expression patterns, which we can control and transform using retroviral techniques, suggestive of evolutionary pathways for the developmental plasticity of this most flexible of organs.

When combined with our study of sulcification, whereby sharp creases form on the surface of soft solids,  we have been able to explain the gyrification of the mammalian brain that has a cortex that grows but is constrained by the underlying white matter. Our experiments using a humble swelling gel along with a computational model shows that we can recapitulate the basic folding patterns in the human fetal brain, and also construct a  gyrification morphospace for the patterns seen across species in terms of two geometric parameters that correspond to the relative thickness of the cortex and the relative growth of the cortex. We are currently studying morphologies and dysmorphologies in mammalian brains using the ferret as a model system, correlating specific mutations that are known to change overall brain size, cortical expansion rates, and cortical thickness  to specific changes in folding patterns along with their functional consequences.

As the scientist Wolpert noted, “It is not birth, marriage or death but gastrulation that is the most important part of a life.”  Recently, in a collaboration with experimental colleagues who had shown that varying the signaling pathways controlling critical cell behaviors in the chick embryo can generate gastrulation modes seen in amphibians, reptiles and teleost fish, we have shown how a theoretical model that couples actomyosin activity to tissue flow, provides a basis for the dynamics of gastrulation morphologies  as a spontaneous instability, and has led to a gastrulation phase diagram! We are currently exploring the mathematical properties of the governing equations and have recently generalized them to low-dimensional settings to explain the transition from ingression and thickening to folding.

In other collaborations, we have been working to see how these principles associated with differential activity in the presomitic mesoderm can lead to body elongation dynamics common across vertebrates, and excitability can be the precursor of the patterning processing associated with somitogenesis.

Differential growth and motion are but two of many principles associated with patterning in living systems; other examples include differential diffusion (first elucidated by Turing), differential adhesion, differential motility etc. We have also explored the role of differential activity and differential contractility from a theoretical perspective to explain prior experimental observations of phenomena that range from cytoskeletal dynamics and super-precipitation patterns to cartilage condensation in multicellular tissues.