In classical mechanics we typically study systems that can be represented by point-like particles and are subject to external forcing. In contrast, in living systems we encounter extended objects which undergo internal forcing to generate cyclic changes in shape or configuration. Such dynamics occur across scales, from proteins undergoing conformational changes to cells crawling on surfaces to centipedes wiggling through soil and debris. The physics of such “self-deforming” systems is remarkably rich, especially when coupled to non-trivial environments. In this talk I will narrate a few examples of surprising emergent dynamics in living and nonliving (robot) systems arising from the interplay of traveling waves of body bending and environmental heterogeneities. I will describe how undulatory limbless robophysical models that mix wave and particle-like properties can mechanically “diffract” in regular arrays of obstacles and exponentially localize in disordered environments. Such insights have proven useful in highlighting the importance of mechanics in living systems, e.g. the role of passive dynamics in the locomotion of snakes and nematode worms in heterogeneous environments. Discovery of principles of self-deforming systems is informing and guiding the commercialization of elongate robots (e.g. in a startup company I co-founded) that can self-propel effectively in dirty, dull, and dangerous situations.

Biology provides numerous examples of phase-separated protein and nucleic acid condensates, which establish distinct compartments for spatially organizing biomolecules within living cells. This mechanism of spatial organization relies on the ability of biomolecular systems to navigate high-dimensional phase diagrams by tuning the interactions among proteins and nucleic acids in a multicomponent mixture. In this talk, I will discuss optimization and machine learning approaches that can be used to design the compositions of multicomponent biomolecular condensates. These approaches reveal how compositional specificity is encoded in complex mixtures and how intrinsically disordered protein sequences can be designed to stabilize coexisting multicomponent condensates. These results shed light on the physicochemical limits of phase-separation-mediated spatial organization in biological systems and establish practical strategies for engineering fully programmable biomolecular condensates.