To flexibly navigate, many animals rely on internal spatial representations that persist when the animal is standing still in darkness, and update accurately by integrating the animal's movements in the absence of localizing sensory cues. Theories of mammalian head direction cells have proposed that these dynamics can be realized in a special class of networks that maintain a localized bump of activity via structured recurrent connectivity, and that shift this bump of activity via angular velocity input. Although there are many different variants of these so-called ring attractor networks, they all rely on large numbers of neurons to generate representations that persist in the absence of input and accurately integrate angular velocity input. Surprisingly, in the fly, Drosophila melanogaster, a head direction representation is maintained by a much smaller number of neurons whose dynamics and connectivity resemble those of a ring attractor network. These findings challenge our understanding of ring attractors and their putative implementation in neural circuits. Here, we analyzed failures of angular velocity integration that emerge in small attractor networks with only a few computational units. Motivated by the peak performance of the fly head direction system in darkness, we mathematically derived conditions under which small networks, even with as few as 4 neurons, achieve the performance of much larger networks. The resulting description reveals that by appropriately tuning the network connectivity, the network can maintain persistent representations over the continuum of head directions, and it can accurately integrate angular velocity inputs. We then analytically determined how performance degrades as the connectivity deviates from this optimally-tuned setting, and we find a trade-off between network size and the tuning precision needed to achieve persistence and accurate integration. This work shows how even small networks can accurately track an animal's movements to guide navigation, and it informs our understanding of the functional capabilities of discrete systems more broadly.

The self-assembly of proteins into highly ordered nanoscale architectures is a hallmark of biological systems. The sophisticated functions of these molecular machines have inspired the development of methods to engineer self-assembling protein nanostructures; however, the design of multi-component protein nanomaterials with high accuracy remains an outstanding challenge. Here we report a computational method for designing protein nanomaterials in which multiple copies of two distinct subunits co-assemble into a specific architecture. We use the method to design five 24-subunit cage-like protein nanomaterials in two distinct symmetric architectures and experimentally demonstrate that their structures are in close agreement with the computational design models. The accuracy of the method and the number and variety of two-component materials that it makes accessible suggest a route to the construction of functional protein nanomaterials tailored to specific applications.

Nature provides many examples of self- and co-assembling protein-based molecular machines, including icosahedral protein cages that serve as scaffolds, enzymes, and compartments for essential biochemical reactions and icosahedral virus capsids, which encapsidate and protect viral genomes and mediate entry into host cells. Inspired by these natural materials, we report the computational design and experimental characterization of co-assembling, two-component, 120-subunit icosahedral protein nanostructures with molecular weights (1.8 to 2.8 megadaltons) and dimensions (24 to 40 nanometers in diameter) comparable to those of small viral capsids. Electron microscopy, small-angle x-ray scattering, and x-ray crystallography show that 10 designs spanning three distinct icosahedral architectures form materials closely matching the design models. In vitro assembly of icosahedral complexes from independently purified components occurs rapidly, at rates comparable to those of viral capsids, and enables controlled packaging of molecular cargo through charge complementarity. The ability to design megadalton-scale materials with atomic-level accuracy and controllable assembly opens the door to a new generation of genetically programmable protein-based molecular machines.

The fast turnover of membrane components through endocytosis and recycling allows precise control of the composition of the plasma membrane. Endocytic recycling can be rapid with some molecules returning to the plasma membrane with a <5 minutes. Existing methods to study these trafficking pathways utilize chemical, radioactive, or fluorescent labeling of cell surface receptors in pulse-chase experiments, which require tedious washing steps and manual collection of samples. Here, we introduce a live-cell endocytic recycling assay, based on a newly designed cell-impermeable, fluorogenic ligand for HaloTag: 'Janelia Fluor 635i' (JFi; i=impermeant) which allows real-time detection of membrane receptor recycling at steady state. We used this method to study the effect of iron depletion on transferrin receptor (TfR) recycling using the chelator desferrioxamine. We found this perturbation significantly increases the TfR recycling rate. The high temporal resolution and simplicity of this assay provides a clear advantage over extant methods and makes it ideal for large scale cellular imaging studies. This assay can be adapted to examine other cellular kinetic parameters such as protein turnover and biosynthetic trafficking.

To study the complex synaptic interactions underpinning dendritic information processing in single neurons, experimenters require methods to mimic presynaptic neurotransmitter release at multiple sites with no physiological damage. We show that laser scanning systems built around large-aperture acousto-optic deflectors and high numerical aperture objective lenses provide the sub-millisecond, sub-micron precision necessary to achieve physiological, exogenous synaptic stimulation. Our laser scanning systems can produce the sophisticated spatio-temporal patterns of synaptic input that are necessary to investigate single-neuron dendritic physiology.

Symmetric cell division requires the even partitioning of genetic information and cytoplasmic contents between daughter cells. Whereas the mechanisms coordinating the segregation of the genome are well known, the processes that ensure organelle segregation between daughter cells remain less well understood. Here we identify multiple actin assemblies with distinct but complementary roles in mitochondrial organization and inheritance in mitosis. First, we find a dense meshwork of subcortical actin cables assembled throughout the mitotic cytoplasm. This network scaffolds the endoplasmic reticulum and organizes three-dimensional mitochondrial positioning to ensure the equal segregation of mitochondrial mass at cytokinesis. Second, we identify a dynamic wave of actin filaments reversibly assembling on the surface of mitochondria during mitosis. Mitochondria sampled by this wave are enveloped within actin clouds that can spontaneously break symmetry to form elongated comet tails. Mitochondrial comet tails promote randomly directed bursts of movement that shuffle mitochondrial position within the mother cell to randomize inheritance of healthy and damaged mitochondria between daughter cells. Thus, parallel mechanisms mediated by the actin cytoskeleton ensure both equal and random inheritance of mitochondria in symmetrically dividing cells.

The actin cytoskeleton plays multiple critical roles in cells, from cell migration to organelle dynamics. The small and transient actin structures regulating organelle dynamics are challenging to detect with fluorescence microscopy, making it difficult to determine whether actin filaments are directly associated with specific membranes. To address these limitations, we developed fluorescent-protein-tagged actin nanobodies, termed 'actin chromobodies' (ACs), targeted to organelle membranes to enable high-resolution imaging of sub-organellar actin dynamics.

Cytotoxic T lymphocytes (CTLs) use polarized secretion to rapidly destroy virally infected and tumor cells. To understand the temporal relationships between key events leading to secretion, we used high-resolution 4D imaging. CTLs approached targets with actin-rich projections at the leading edge, creating an initially actin-enriched contact with rearward-flowing actin. Within 1 min, cortical actin reduced across the synapse, T cell receptors (TCRs) clustered centrally to form the central supramolecular activation cluster (cSMAC), and centrosome polarization began. Granules clustered around the moving centrosome within 2.5 min and reached the synapse after 6 min. TCR-bearing intracellular vesicles were delivered to the cSMAC as the centrosome docked. We found that the centrosome and granules were delivered to an area of membrane with reduced cortical actin density and phospholipid PIP2. These data resolve the temporal order of events during synapse maturation in 4D and reveal a critical role for actin depletion in regulating secretion.

The cellular mechanisms governing non-muscle myosin II (NM2) filament assembly are largely unknown. Using EGFP-NM2A knock-in fibroblasts and multiple super-resolution imaging modalities, we characterized and quantified the sequential amplification of NM2 filaments within lamellae, wherein filaments emanating from single nucleation events continuously partition, forming filament clusters that populate large-scale actomyosin structures deeper in the cell. Individual partitioning events coincide spatially and temporally with the movements of diverging actin fibres, suppression of which inhibits partitioning. These and other data indicate that NM2A filaments are partitioned by the dynamic movements of actin fibres to which they are bound. Finally, we showed that partition frequency and filament growth rate in the lamella depend on MLCK, and that MLCK is competing with centrally active ROCK for a limiting pool of monomer with which to drive lamellar filament assembly. Together, our results provide new insights into the mechanism and spatio-temporal regulation of NM2 filament assembly in cells.