In the broadest terms, we are interested in understanding what makes living matter different from dead matter:  What is special about the interactions between biological molecules or cells that allows living systems to achieve their exquisite degree of self-organization in space and time?  To answer this question, we build models that try to capture the interactions and feedbacks that are at the root of biological order and function in particular systems, and we work closely with experimental groups to design and analyze experiments to test these models. Under this general umbrella, we are pursuing several distinct lines of research, with a particular focus on pattern formation and morphogenesis in animal development and on the physics of biological clocks and oscillators.  A few examples of current and recent projects are described below.  For more details and a fuller overview of the sorts of problems we work on, see this research statement (from 2018) or browse our publications.

Morphogenesis and Development

One of the most dramatic examples of self-organization in biology is animal development--the process by which a fertilized egg transforms itself into an adult animal.  We are interested in how the interactions between cells encode the final size, shape, and pattern of the animal and its constituent organs and tissues.

Growth, Size, and Fluctuating Asymmetry
How do tissues and organs "know" what size to grow to, and how accurately can that size be specified? We are investigating how various feedback processes can stop tissue growth at the correct size and how the sizes of contralateral (i.e. matching left and right) organs can be specified with high precision.  In particular, we are working with the experimental lab of Pierre Léopold to quantitatively understand the origins of size asymmetry in wildtype and mutant fruit fly wings.  In order to address questions of growth control, we have also developed a formalism for modeling noisy growth (figure, left) and applied this formalism to models of growth regulation by mechanical feedback.

The Response of Cells and Tissues to Mechanical Stress
As tissues are physically pushed and pulled into place during development, they are often subject to large mechanical stresses.  Together with the lab of Yohanns Bellaïche, we are exploring how epithelial tissues and their constituent cells respond to these stresses and, in particular, how they regulate their cytoskeleton to limit their deformation.  We have found that a novel class of apical stress fibers plays an important role in this mechanical response; these fibers have the unexpected property that their number per cell scales with cell area, providing insight into how a cell's mechanical properties adjust to its size.

Pattern Formation
Animal tissues can exhibit strikingly regular and reproducible patterns of cell fate.  For example, the cone photoreceptors in the zebrafish retina come in four different spectral subtypes (or "colors") that are arranged in an almost perfectly crystalline lattice (figure, right; collaboration with Pamela Raymond).  We want to know how such patterns are created de novo.  In addition to the zebrafish cone mosaic, systems of interest include Drosophila imaginal disks and, most recently, colonies of human pluripotent stem cells (together with the lab of Jianping Fu).

Oscillators and Circadian Clocks

Almost all plants and animals and many unicellular organisms possess a circadian clock--an autonomous oscillator with a period of around 24 hours that helps the organism to keep track of daily cycles in its environment.  One of the most remarkable examples of such a clock is found in the cyanobacterium (i.e. photosynthetic bacterium) S. elongatus, which builds its oscillator from only three core proteins, one of whose phosphorylation state reads out the time of day.  Together with Pieter Rein ten Wolde, members of the Lubensky group are responsible for several models that clarify how such a simple biophysical system can oscillate and, especially, how energy from ATP is used to sustain a regular rhythm (figure below, left).  We have also explored how the clock is able to maintain its high precision in the complicated, noisy environment of a living cell (figure below, center).  Most recently, inspired by our work on the S. elongatus clock, we have become interested in a more general question:  What is a circadian clock good for, anyway?  Or, more specifically, why is it better to have a clock than just to sense the current environmental conditions and respond to them.  Two leading hypotheses are that clocks allow organisms to filter out noise in their environment (you don't want to think the sun has gone down when it has only passed behind a cloud) and to anticipate and prepare for upcoming changes in conditions.  We have developed theoretical models that quantify when each of these mechanisms allow the clock to confer an adaptive advantage in a simple, unicellular organism and how large this advantage is (figure below, right).