Publications

This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand -- whose precise form derives directly from the theory of perfect plasticity -- behaves quadratically close to the origin and grows linearly once a specific threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector field -- the Cauchy stress in the terminology of perfect plasticity -- which allows us to define characteristic lines, and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study BF, we show that this vector field is actually continuous, save for possibly two points. The different behaviors of the energy density at zero and at infinity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data devoid of any regularity properties, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data. We also show a partial regularity result for the minimizer.

Surface tension at cavity walls can play havoc with the mechanical properties of perforated soft solids when the cavities are filled with a fluid. This study is an investigation of the macroscopic elastic properties of elastomers embedding spherical cavities filled with a pressurized liquid in the presence of surface tension, starting with the linearization of the fully nonlinear model and ending with the enhancement properties of the linearized model when many such liquid filled cavities are present.

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed in nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, such as asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by the local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.

Learning in living organisms is typically associated with networks of neurons. The use of large numbers of adjustable units has also been a crucial factor in the continued success of artificial neural networks. In light of the complexity of both living and artificial neural networks, it is surprising to see that very simple organisms -- even unicellular organisms that do not possess a nervous system -- are capable of certain forms of learning. Since in these cases learning may be implemented with much simpler structures than neural networks, it is natural to ask how simple the building blocks required for basic forms of learning may be. The purpose of this study is to discuss the simplest dynamical systems that model a fundamental form of non-associative learning, habituation, and to elucidate technical implementations of such systems, which may be used to implement non-associative learning in neuromorphic computing and related applications.

Gametes in many species develop in cysts—clusters of germ cells formed by incomplete cytokinesis—that remain connected through intercellular bridges (ICBs). These connections enable sharing of cytoplasmic components between germ cells and, in the female germ line, enrich select cells in the cyst to become the oocyte(s). In mice, germline cysts of variable sizes are generated during embryonic development, thought to result from cyst fractures. Studies of fixed samples failed to capture fracture events, and thus, the mechanism remained elusive. Here, we use high-resolution live imaging of germ cells within their native tissue environment to visualize germline cyst dynamics. With this novel approach, we reveal a striking motile phenotype of gonad-resident germ cells and show that this randomly oriented cell-autonomous motile behavior during cyst formation underlies fracture events. Conversely, we show that stabilized ICBs help resist excessive fracturing. Additionally, we find that motility and thus fracture rates gradually decrease during development in a sex-dependent manner, completely ceasing by the end of cyst-forming divisions. These results lead to a model where the opposing activities of developmentally regulated cell motility and stable ICBs give rise to cysts of variable sizes. We corroborate these results by developing a model that uses experimentally measured fracture rates to simulate cyst formation and fracture and show that it can reproduce experimentally measured cyst sizes in both male and female. Understanding how variable cysts form will enable further studies of mammalian oocyte selection and establishment of the ovarian reserve.

This paper briefly reprises, with added commentary, a talk I gave on transport and flows within living cells at an APS-DFD meeting. Directed transport is especially important in large cells, such as eggs where developmental factors need to be properly localized, and early embryos whose organelles and genetic material must be properly positioned before cell division. I discuss two cases—a nematode single-cell embryo and a fruit fly egg cell—where advances in mathematical modeling and large-scale simulation of fluid-structure interactions have helped us understand fundamental mechanisms of force transduction and self-organization within the cell.

Cells modified outside of the body and then reintroduced provide an advantage over most small-molecule therapeutics in that cells can be designed to recognize target molecules in specific tissues and then act locally. Two studies now demonstrate advances in cell engineering for treating human disease (see the Perspective by Davila and Brentjens). Reddy et al. engineered human T cells to make a synthetic receptor that recognized overactive T cells such as those causing autoimmune disease and organ rejection. The most effective modified cells tested were ones in which the synthetic receptor initiated a program causing the production of both an anti-inflammatory cytokine and a receptor that acted as sink for a locally produced proinflammatory cytokine. In mouse models, such cells could be designed with logic programs that protect the desired tissues without detrimental systemic immunosuppression. Simic et al. modified T cells to produce a synthetic receptor that recognized an antigen localized to the extracellular matrix of the brain. The synthetic receptor activated a circuit stimulating the production of chimeric antigen receptors that targeted and killed cancer cells in the brain but not those implanted elsewhere in the mouse. A mouse model of neuroinflammatory brain disease could be treated with cells engineered to locally produce an anti-inflammatory cytokine.

Extracellular-signal-regulated kinase (ERK) signaling controls development and homeostasis and is genetically deregulated in human diseases, including neurocognitive disorders and cancers. Although the list of ERK functions is vast and steadily growing, the full spectrum of processes controlled by any specific ERK activation event remains unknown. Here, we show how ERK functions can be systematically identified using targeted perturbations and global readouts of ERK activation. Our experimental model is the Drosophila embryo, where ERK signaling at the embryonic poles has thus far only been associated with the transcriptional patterning of the future larva. Through a combination of live imaging and phosphoproteomics, we demonstrated that ERK activation at the poles is also critical for maintaining the speed and synchrony of embryonic cleavages. The presented approach to interrogating phosphorylation networks identifies a hidden function of a well-studied signaling event and sets the stage for similar studies in other organisms.

Studies in Drosophila were essential in delineating the highly conserved RAS signaling pathway. Indeed, some pathway components, such as Son of sevenless or Corkscrew, were named after mutant phenotypes in flies. Here, we discuss how Drosophila, with its ever-expanding arsenal of precise genetic manipulations and quantitative phenotypic assays, can be harnessed for investigating how RAS signaling is genetically deregulated in human diseases. The general approach is based on analyzing how disease mutations affect well-studied RAS-dependent developmental processes. Focusing on our work in the fly embryo and larval trachea, we illustrate this approach for missense mutations in MEK, a central kinase in the RAS cascade, which is deregulated in developmental abnormalities and cancers. The established approach provides clear insights into genotype/phenotype associations and can be extended to other signaling systems.