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 geometrical approaches to tissue tectonics using invariants based on velocity gradients 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 to characterize properly invariant measures of deformation that describe the dynamic morphoskeletons – the organizers of large scale cell movements in multicellular tissues.  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 explored the physical basis of morphogenesis in plants and animals in a variety of examples – from fungi to flowers, from the vertebrate gut to the mammalian brain. For example, inspired by observations from our experimental colleagues, 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.

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.

morphogenesis in animalsIn the study of morphogenesis in animals,  we suggested that hydraulics could play an important role in guiding and informing the dynamics of cystic organoids, and followed this with studies of embryo size and cell fate control during the early developmental stages of  mammalian embryos, and in the size control of the inner ear in fishes. By quantifying the concept of differential growth, first elucidated by D’Arcy Thompson, we have explained the growth and form of the coiled vertebrate gut  with scaling ideas, results corroborated using our own biophysical experiments and those done by our collaborators across multiple species. 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.

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.

Differential growth is but one of many principles associated with patterning in living systems. We have also explored the role of differential motility and contractility from a theoretical perspective, and are currently working to see how these principles might also be relevant to understanding the elongation of the body and the patterning processing associated with somitogenesis.

Linking evolution and development, we have explored the form, morphogenesis, and function of avian egg shape, the statistical geometry of insect wings, and that of mammalian brains.


Related Publications

Dynamic morphoskeletons in development. M. Serra, S. Streichan, M. Chuai, C. J. Weijer, and L. Mahadevan, Proc. Natl. Acad. Sci.,  117, 11444–11449, 2020. [DOI] [View PDF] [Download PDF]
On the growth and form of the gut T. Savin, N.A. Kurpios, A.E. Shyer, P. Florescu, H. Liang, L. Mahadevan & C.J. Tabin,  Nature  476:57-62, 2011. [View PDF] [Download PDF]
Villification: how the gut gets its villi A. Shyer, T. Tallinen, N. Nerurkar, Z. Wei, E. Kim, D. Kaplan, C. Tabin and L. Mahadevan  Science,  342, 212-218, 2013. [View PDF] [Download PDF]
Bending gradients: how the intestinal stem cell gets its home  A. Shyer, T. Huycke, C-H Lee, L. Mahadevan, and C. Tabin,  Cell  , 161, 569-80, 201, 2015. [View PDF] [Download PDF]
BMP signaling controls buckling forces to modulate looping morphogenesis of the gut N. L. Nerurkar, L. Mahadevan, and C.J. Tabin,  Proceedings of the National Academy of Sciences  (USA), 114, 2277-82, 2017. [View PDF] [Download PDF]
Molecular control of macroscopic forces drives formation of the vertebrate hindgut N.L. Nerurkar, CH Lee, L. Mahadevan & C.J. Tabin, Nature 565, 2019. [DOI] [View PDF] [Download PDF]
Unfolding the sulcus E. Hohlfeld and L. Mahadevan,  Physical Review Letters , 106, 105702, 2011. [View PDF] [Download PDF]
Surface sulci in squeezed soft solids T. Tallinen, J.S. Biggins, and L. Mahadevan,  Physical Review Letters , 110, 024302, 2013. [View PDF] [Download PDF]
Gyrification from constrained cortical expansion T. Tallinen, J.Y. Chung, J.S. Biggins, and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) , 111, 35:12667-12672, 2014. [View PDF] [Download PDF]
On the growth and form of cortical convolutions T. Tallinen, J.Y. Chung, F. Rousseau, N. Girard, J. Lefèvre, and L. Mahadevan,  Nature Physics , 12, 588-93, 2016. [DOI] [View PDF] [Download PDF]
Excitable dynamics and yap-dependent mechanical cues drive the segmentation clock A. Hubaud, I. Regev, L. Mahadevan, O. Pourquié,  Cell  171, 1-15, 2017. [View PDF] [Download PDF]
Mechanical coupling coordinates the co-elongation of axial and paraxial tissues in avian embryos F. Xiong, W. Ma, B. Benazaref, L. Mahadevan, O. Pourquie, BioRxiv [ONLINE ARTICLE] [DOI]
The shape of a long leaf H. Liang and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) ,106, 22049, 2009. [View PDF] [Download PDF]
Growth, geometry and mechanics of the blooming lily H-Y. Liang and L. Mahadevan,  Proceedings of the National Academy of Sciences , 108, 5516-21, 2011. [View PDF] [Download PDF]
The Foppl-von Karman equations for plates with incompatible strains M. Lewicka, L. Mahadevan, and M. Pakzad,  Proceedings of the Royal Society, Lond. (A) , 467, 402-426, 2011. [View PDF] [Download PDF]
Models for elastic shells with incompatible strains M. Lewicka, L. Mahadevan and M.R. Pakzad,  Proceedings of the Royal Society (A) , 470, 20130604, 2014. [View PDF] [Download PDF]
The Monge–Ampère constraint: Matching of isometries, density and regularity, and elastic theories of shallow shells
M. Lewicka, L. Mahadevan, M. R. Pakzad,  Ann. I. H. Poincare - AN , 2015.  [View PDF] [Download PDF]
Size control of the inner ear via hydraulic feedback. K.R. Mosaliganti, I. A. Swinburne, C.U. Chan, N.D. Obholzer, A. A. Green, S. Tanksale, L Mahadevan, and S.G. Megason, eLife 2019;8:e39596. 2019. [DOI] [View PDF] [Download PDF]
Organ size control via hydraulically gated oscillations Teresa Ruiz-Herrero, Kévin Alessandri, Basile V. Gurchenkov, Pierre Nassoy and L. Mahadevan,  Development  144, 4422-4427, 2017. [View PDF] [Download PDF]
Hydraulic control of mammalian embryo size and cell fate
C.J. Chan, M. Costanzo, T. Ruiz-Herrero, G. Monke, R. Petrie, L. Mahadevan, T. Hiiragi, Nature 571, 112–116, 2019. [DOI] [View PDF] [Download PDF]
Differential activity-driven instabilities in biphasic active matter C. A. Weber, C. H. Rycroft, and L. Mahadevan,  Physical Review Letters  120, 248003, 2018. [DOI] [View PDF] [Download PDF]
Biophysical principles of choanoflagellate self-organization. B. T. Larson, T. Ruiz-Herrero , S. Lee , S. Kumar, and L. Mahadevan, and N. King, Proc. Natl. Acad. Sci.,  [DOI] [View PDF] [Download PDF]
Mechanical coupling coordinates the co-elongation of axial and paraxial tissues in avian embryos. F. Xiong, W. Ma, B. Benazeraf,  L. Mahadevan, and O. Pourquie.  Dev. Cell. 55,  354–366, 2020. [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Shape-shifting structured lattices via multimaterial 4D printing. J.W. Boley, W.M. van Rees, C. Lissandrello, M.N. Horenstein, R.L. Truby, A. Kotikian, J.A. Lewis, and L. MahadevanProc. Natl. Acad.  Sci.116 (42) 20856-20862, 2019. [ONLINE ARTICLE] [View PDF] [Download PDF]
Balancing efficiency and homogeneity of biomaterial transport in networks. S. Liese, L. Mahadevan and A. Carlson. Europhysics Letters, Vol. 135 | No. 5 [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]