RESEARCH

Over the last couple of decades, structural biologists have delivered a treasure-trove of data on the shapes and sizes of large biomacromolecules and their assemblies. When this information is combined with the biochemistry and genetics to understand aspects of the kinetics and manipulate them, we can begin to ask questions about how structure impacts function dynamically at both the level of the individual molecule and in large aggregates of molecules such as polymeric filaments and membranes.

We are particularly interested in the statistical and continuum mechanics of macromolecular assemblies such as disordered cytoskeletal-like networks of actin and crosslinkers, ordered assemblies such as microtubules, actin bundles, DNA-loops etc. in the context of questions such as the linear and nonlinear rheology of these "living" materials", and the mechanochemistry of active biological engines driven by growth, shrinkage and spring-like behavior.

Abstract: Networks of cross-linked and bundled actin filaments are ubiquitous in the cellular cytoskeleton, but their elasticity remains poorly understood. We show that these networks exhibit exceptional elastic behavior that reflects the mechanical properties of individual filaments. There are two distinct regimes of elasticity, one reflecting bending of single filaments and a second reflecting stretching of entropic fluctuations of filament length. The mechanical stiffness can vary by several decades with small changes in cross- link concentration, and can increase markedly upon application of external stress. We parameterize the full range of behavior in a state diagram and elucidate its origin with a robust model.

Some other representative publications:

Stored elastic energy powers the 60-micron extension of the Limulus polyphemus sperm actin bundle,
Shin, J., L. Mahadevan, G. Waller, K. Langsmo and P. Matsudaira, Journal of Cell Biology, 162(7), 1183-88, 2003.  

Multiscale methods for modeling protein-DNA complexes,
Villa, E. , Balaeff, A., L. Mahadevan and K. Schulten, SIAM Multiscale Modeling and Simulation, 2, 527-553 (2004).

Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcements
C. Brangwynne, F. Mackintosh, S. Kumar, N. Geisse, J. Talbot, L. Mahadevan, K. Parker, D. Ingber and D. Weitz, Journal of Cell Biology , 173, 733, 2006.

Nonlinear mechanics of soft fibrous networks
A. Kabla and L. Mahadevan, Journal of the Royal Society - Interface, 4, 99, 2007.

A quantitative analysis of contractility in active cytoskeletal protein networks
P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008.

Moving up in scale from macromolecular assemblies, the cell is the minimal self-contained unit in biology; its whole is clearly more than a sum of its parts as it is by itself able to survive, reproduce and evolve. We are still quite far away from any comprehensive understanding of how the cell is able to achieve all that it does, but glimpses of the workings are becoming more frequent than in the past.

Some of the questions that interest us are : how is cell shape determined ? how does a cell move ? how does it stick ? Can one think about the cell as a material with evolving properties ? Can one reconstitute aspects of the behavior of a cell using its parts ? How do tissues form ? change ? What is the role of force in regulating the growth and shape of organs and organisms ? We have few answers, but are working on sharpening our questions using a combination of experiments and theory.

Non-equilibration of hydrostatic pressure in blebbing cells,
G. Charras, J. Yarrow, M. Horton, L. Mahadevan and T. Mitchison, Nature, 435, 365-69. 2005.

Abstract: Current models for protrusive motility in animal cells focus on cytoskeleton-based mechanisms, where localized protrusion is driven by local regulation of actin biochemistry. In plants and fungi, protrusion is driven primarily by hydrostatic pressure. For hydrostatic pressure to drive localized protrusion in animal cells, it would have to be locally regulated, but current models treating cytoplasm as an incompressible viscoelastic continuum or viscous liquid require that hydrostatic pressure equilibrates essentially instantaneously over the whole cell. Here, we use cell blebs as reporters of local pressure in the cytoplasm. When we locally perfuse blebbing cells with cortex-relaxing drugs to dissipate pressure on one side, blebbing continues on the untreated side, implying non-equilibration of pressure on scales of approximately 10 microns in 10 ms. We can account for localization of pressure by considering the cytoplasm as a contractile, elastic network infiltrated by cytosol. Motion of the fluid relative to the network generates spatially heterogeneous transients in the pressure field, and can be described in the framework of poroelasticity.

Some other representative publications:

A dynamic fate map of the forebrain shows how vertebrate eyes form and explains two causes of cyclopia.
S. England, G. Blanchard, L. Mahadevan, and R. Adams, Development, 133, 4613-4617, 2006.

Universal dynamics of cell spreading,
D. Cuvelier, Y-S Chu, M Thery, S Dufour, J-P Thiery, M Bornens, P. Nassoy and L. Mahadevan, Current Biology , 17, 694, 2007.

Force of an actin spring
J.H. Shin, B.K. Tam, R.R. Brau, M.J. Lang, L. Mahadevan, and Paul Matsudaira, Biophysical Journal, 92, 3729, 2007.

Signal processing by the HOG MAP kinase pathway
P. Hersen, M. McClean, L. Mahadevan, and S. Ramanathan, Proceedings of the National Academy of Sciences (USA), 105, 7165, 2008.

Life and times of a cellular bleb
G. Charras, M. Coughlin, T. Mitchison and L. Mahadevan, Biophysical Journal, 94, 1836, 2008.

Given the enormous diversity of plant and fungal life on our planet, it is perhaps surprising that there are so few people studying them. But then again, perhaps it is not, given our myopic anthropocentric view. The adaptations that plants and fungi have engineering through evolution are truly exquisite, from the ability to silently haul water to the top of a giant Sequoia to the myriad mechanisms for seed and spore dispersal, pollination, drought resistance etc.

The adaptive designs seen raise a host of physical and physico-chemical questions, few of which seem to have been studied quantitatively either from an experimental or a theoretical perspective. Our preliminary studies are currently focused on aspects of movements in plants and fungi, using the specific to illustrate the general, and revolve around understanding passive and active mechanisms of water movements in these hydraulic engineering marvels.

Physical limits and design principles for plant and fungal movements,
J. Skotheim and L. Mahadevan, Science, 308, 1308-10, 2005.

Abstract: The typical scales for plant and fungal movements vary over many orders of magnitude in time and length, but they are ultimately based on hydraulics and mechanics. We show that quantification of the length and time scales involved in plant and fungal motions leads to a natural classification, whose physical basis can be understood through an analysis of the mechanics of water transport through an elastic tissue. Our study also suggests a design principle for nonmuscular hydraulically actuated structures: Rapid actuation requires either small size or the enhancement of motion on large scales via elastic instabilities.

Some other representative publications:

How the Venus Flytrap snaps,
Forterre, Y., J. Skotheim, J. Dumais and L. Mahadevan, Nature, 433, 421-25, 2005.  

Self-organized origami,
L. Mahadevan and S. Rica, Science, 307, 1740, 2005.  

Optimal vein density in artificial and real leaves,
X. Noblin, L. Mahadevan, I. Coomaraswamy, D. Weitz, N. Holbrook and M. Zwieniecki, Proceedings of the National Academy of Sciences (USA), 105, 9140, 2008.

How kelp produce blade shapes suited to different flow regimes: a new wrinkle
M. Koehl, W. Silk, H. Liang and L. Mahadevan, Integrative and Comparative Biology, in press.

Botanical ratchets
I. Kulic, M. Mani, H. Murbach, R. Thoakar and L. Mahadevan, submitted.

Biology is almost synonymous with autonomous movement, although plants might seem to be an exception (but read on for exceptions to this ! ). Movement requires force production, and its spatiotemporal coordination and control in light of sensory feedback from the environment. The questions any study of coordinated movement raises thus impinge on molecular, cellular and tissue dynamics and neuroscience, and from a mathematical perspective involves ideas from continuum dynamics, control theory, optimization etc. and impinge on questions of sensory physiology, behavior, ecology etc.

Our current focus involves aspects of biological and biomimetic locomotion, and thus involves both trying to understand gait and speed selection and transition in different modes of locomotion such as crawling, inch-worming, reptation, swimming and in building simple physical models to study these. An outstanding question in this regard is a theory of locomotion that couples the internal and external dynamics to sensory feedback.

Biomimetic ratcheting motion of lubricated hydrogel filaments,
Mahadevan, L., S. Daniel and M. Chaudhury, Proceedings of the National Academy of Sciences (USA), 101, 23-26, 2004.  

Abstract: Inspired by the locomotion of terrestrial limbless animals, we study the motion of a lubricated rod of a hydrogel on a soft substrate. We show that it is possible to mimic observed biological gaits by vibrating the substrate and by using a variety of mechanisms to break longitudinal and lateral symmetry. Our simple theory and experiments provide a unified view of the creeping, undulating, and inchworming gaits observed in limbless locomotion on land, all of which originate as symmetry-breaking bifurcations of a simple base state associated with periodic longitudinal oscillations of a slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on substrates.

Some other representative publications:

Sensorimotor control during isothermal tracking in Caenorhabditis elegans
Linjiao Luo, Damon A. Clark, David Biron, L. Mahadevan, and Aravinthan D.T.Samuel, The Journal of Experimental Biology 209, 4652-4662, 2006.

Power-limited contraction dynamics of Vorticella convallaria: an ultrafast biological spring
A. Upadhyaya, M. Baraban, J. Wong, P. Matsudaira, A. van Oudenaarden and L. Mahadevan, Biophysical Journal, 94, 265, 2008.

Mechanosensation and mechanical load modulate the locomotory gait in Caenorhabditis elegans
J. Korta, D. Clark, C. Gabel, L. Mahadevan, and A. Samuel, The Journal of Experimental Biology, 210, 2383, 2007.

Settling and swimming of flexible fluid lubricated foils
M. Argentina, J. Skotheim and L. Mahadevan, Physical Review Letters, 99, 224053, 2007.

Limbless undulatory propulsion on land
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008.