Publications

Suspensions of swimming particles exhibit complex collective behaviors driven by hydrodynamic interactions, showing persistent large-scale flows and long-range correlations. While heavily studied, it remains unclear how such structures depend on the system size and swimmer concentration. To address these issues, we simulate very large systems of suspended swimmers across a range of system sizes and volume fractions. For this we use high-performance simulation tools that build on slender body theory and implicit resolution of steric interactions. At low volume fractions and long times, the particle simulations reveal dynamic flow structures and correlation functions that scale with the system size. These results are consistent with a mean-field limit and agree well with a corresponding kinetic theory. At higher concentrations, the system departs from mean-field behavior. Flow structures become cellular, and correlation lengths scale with the particle size. Here, translational motion is suppressed, while rotational dynamics dominate. These findings highlight the limitations of dilute mean-field models and reveal new behaviors in dense active suspensions.

We examine theoretically the flow interactions and forward flight dynamics of tandem or in-line flapping wings. Two wings are driven vertically with prescribed heaving-and-plunging motions, and the horizontal propulsion speeds and positions are dynamically selected through aero- or hydro-dynamic interactions. Our simulations employ an improved vortex sheet method to solve for the locomotion of the pair within the collective flow field, and we identify 'schooling states' in which the wings travel together with nearly constant separation. Multiple terminal configurations are achieved by varying the initial conditions, and the emergent separations are approximately integer multiples of the wavelength traced out by each wing. We explain the stability of these states by perturbing the follower and mapping out an effective potential for its position in the leader's wake. Each equilibrium position is stabilized since smaller separations are associated with in-phase follower-wake motions that constructively reinforce the flow but lead to decreased thrust on the follower; larger separations are associated with antagonistic follower-wake motions, increased thrust, and a weakened collective wake. The equilibria and their stability are also corroborated by a linearized theory for the motion of the leader, the wake it produces, and its effect on the follower. We also consider a weakly-flapping follower driven with lower heaving amplitude than the leader. We identify 'keep-up' conditions for which the wings may still 'school' together despite their dissimilar kinematics, with the 'freeloading' follower passively assuming a favorable position within the wake that permits it to travel significantly faster than it would in isolation.

As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints that self-motion imposes on retinal velocities. When an eye translates and rotates in a stationary 3D scene, the velocity at each retinal location is constrained to a line segment in the 2D space of retinal velocities. The slope and intercept of this segment is determined by the eye's translation and rotation, and the position along the segment is determined by the local scene depth. Since all possible velocities arising from a stationary scene must lie on this segment, velocities that are not must correspond to objects moving within the scene. We hypothesize that humans make use of these constraints by using deviations of local velocity from these constraint lines to detect moving objects. To test this, we used a virtual reality headset to present rich wide-field stimuli, simulating the visual experience of translating forward in several virtual environments with varied precision of depth information. Participants had to determine if a cued object moved relative to the scene. Consistent with the hypothesis, we found that performance depended on the deviation of the object velocity from the constraint segment, rather than a difference between retinal velocities of the object and its local surround. We also found that the endpoints of the constraint segment reflected the precision of depth information available in the different virtual environments.

s we move through the world, the pattern of light projected on our eyes is complex and dynamic. Even in a world that is completely stationary, our self-motion results in velocities on the retina. Added to this there exist independently moving objects, which also create evolving patterns of light on our eyes. Despite the fact that both induce retinal velocities, we are somehow able to accurately distinguish between stable parts of the environment and independently moving objects. One might hypothesize this is achieved by detecting discontinuities in the spatial pattern of velocities, however this computation is also sensitive to velocity discontinuities at the boundaries of stationary objects. We instead propose that humans make use of the specific constraints that self-motion imposes on retinal velocities. When an eye translates and rotates within a rigid 3D world, the velocity at each location on the retina is constrained to a line segment in the 2D space of retinal velocities (Longuet, Higgins, Prazdny 1980). The slope and intercept of this segment is determined by the eye's translation and rotation, and the position along the segment is determined by depth of the scene. Since all possible velocities arising from a rigid world must lie on this segment, velocities not on the segment must correspond to moving objects. We hypothesize that humans make use of these constraints, by partially inferring self-motion based on the global pattern of retinal velocities, and using deviations of local velocity from the resulting constraint lines to detect moving objects. We call this the depth constraint segment.
We first test if the depth constraint has an effect on 2D velocity discrimination using a simplified stimulus made with a collection of plaids that drifted according to a moving observer. Under these conditions, we failed to find convincing evidence that the constraint had on 2D velocity discrimination. We then tried to test the hypothesis with more naturalistic stimuli, viewed within a head-mounted virtual reality device, simulating a translation forward in different virtual environments. This time, consistent with the hypothesis, we found that performance depended on the deviation of the object velocity from the constraint segment, not on the difference between retinal velocities of the object and its surrounding velocities. Finally, we examine the effect of self-motion on detecting a specific kind of motion artifact (jitter) that occurs in an augmented reality display. We found that our ability to perceive the motion artifact depended on self-motion and the evoked eye movements.

Huntington's disease (HD) is an inherited neurodegenerative disorder associated with motor and cognitive decline, caused by a mutation in the poly-glutamine (polyQ) region near the N-terminus of the huntingtin (htt) protein. Expansion of the polyQ region results in the disease that is characterized by oligomeric and fibrillar aggregates of mutated protein. The first 17 amino acids (Nt17) of htt, which are adjacent to the polyQ tract, function as a lipid-binding domain, facilitated by the formation of an amphipathic α-helix. There is increasing evidence that lipid interactions may play a role in the toxic gain of function associated with the htt polyQ expansion, as membrane-related changes, including structural abnormalities of several organelles, are observed in HD. Given the uneven and curved shapes of organelles, it is important to examine the mechanistic preferences that drive the preferential partitioning of Nt17 to curved membranes. To better understand the role of the cell membrane environment in the interaction and aggregation of htt, circular dichroism, fluorescence microscopy, and coarse-grained molecular dynamics were employed to measure the association of Nt17 with phospholipid vesicles and subsequent effects throughout time. In zwitterionic curved membranes, sensing was driven by the bulky sidechains of phenylalanine residues, which are able to sense lipid packing defects in the curved regions of the membrane. However, in a mixture of zwitterionic and anionic lipids, curvature sensing is affected by the anionic lipid content, implying the surface charge of membranes affects the curvature sensing process. Salt screening experiments suggest a balance between the electrostatic and hydrophobic interactions that governs the extent to which Nt17 can sense physiologically relevant regions of curvature.

The structure of compound eyes in arthropods has been the subject of many studies, revealing important biological principles. Until recently, these studies were constrained by the two-dimensional nature of available ultrastructural data. By taking advantage of the novel three-dimensional ultrastructural dataset obtained using volume electron microscopy, we present the first cellular-level reconstruction of the whole compound eye of an insect, the miniaturized parasitoid wasp Megaphragma viggianii. The compound eye of the female M. viggianii consists of 29 ommatidia and contains 478 cells. Despite the almost anucleate brain, all cells of the compound eye contain nuclei. As in larger insects, the dorsal rim area of the eye in M. viggianii contains ommatidia that are believed to be specialized in polarized light detection as reflected in their corneal and retinal morphology. We report the presence of three ‘ectopic’ photoreceptors. Our results offer new insights into the miniaturization of compound eyes and scaling of sensory organs in general.

A direct solver is introduced for solving overdetermined linear systems involving nonuniform discrete Fourier transform matrices. Such matrices can be transformed into a Cauchy-like form that has hierarchical low rank structure. The rank structure of this matrix is explained, and it is shown that the ranks of the relevant submatrices grow only logarithmically with the number of columns of the matrix. A fast rank-structured hierarchical approximation method based on this analysis is developed, along with a hierarchical least-squares solver for these and related systems. This result is a direct method for inverting nonuniform discrete transforms with a complexity that is usually nearly linear with respect to the degrees of freedom in the problem. This solver is benchmarked against various iterative and direct solvers in the setting of inverting the one-dimensional type-II (or forward) transform, for a range of condition numbers and problem sizes (up to (4 10

Human perceptual sensitivity often improves with training, a phenomenon known as “perceptual learning.” Another important perceptual dimension is appearance, the subjective sense of stimulus magnitude. Are training-induced improvements in sensitivity accompanied by more accurate appearance? Here, we examined this question by measuring both discrimination (sensitivity) and estimation (appearance) responses to near-horizontal motion directions, which are known to be repulsed away from horizontal. Participants performed discrimination and estimation tasks before and after training in either the discrimination or the estimation task or none (control group). Human observers who trained in either discrimination or estimation exhibited improvements in discrimination accuracy, but estimation repulsion did not decrease; instead, it either persisted or increased. Hence, distortions in perception can be exacerbated after perceptual learning. We developed a computational observer model in which perceptual learning arises from increases in the precision of underlying neural representations, which explains this counterintuitive finding. For each observer, the fitted model accounted for discrimination performance, the distribution of estimates, and their changes with training. Our empirical findings and modeling suggest that learning enhances distinctions between categories, a potentially important aspect of real-world perception and perceptual learning.

Amphipathic helices (AHs) are secondary structures that can facilitate binding of proteins to the membrane by folding into a helix with hydrophobic and hydrophilic faces that interact with the same surfaces in the lipid membrane. Septins are cytoskeletal proteins that preferentially bind to domains of micron-scale curvature on the cell membrane. Studies have shown that AH domains in septin are essential for curvature sensing. We present the first computational study of septin AH interactions with lipid bilayers. Using all-atom simulations and metadynamics-enhanced sampling, we study the effect of charge distribution at the flanking ends of septin AH on the energy for helical folding and its consequences on the binding configuration and affinity to the membrane. This is relevant to septins, since the net positive charge on the flanking C-terminal amino acids is a conserved property across several organisms. Simulations revealed that the energy barrier for folding in the neutral-capped AH is much larger than the charge-capped AH, leading to a small fraction of AH folding and integration to the membrane compared to a significantly folded configuration in the bound charge-capped AH. These observations are consistent with the binding measurements of synthetic AH constructs with variable helicity to lipid vesicles. Additionally, we examined an extended AH sequence including eight amino acids upstream and downstream of the AH to mimic the native protein. Again, simulations and experiments show that the extended peptide, with a net positive charge at C-terminus, adopts a strong helical configuration in solution, giving rise to a higher membrane affinity. Altogether, these results identify the energy cost for folding of AHs as a regulator of AH binding configuration and affinity and provide a basic template for parameterizing AH-membrane interactions as a starting point for the future multiscale simulations for septin-membrane interactions.

Germline-soma segregation is crucial for fertility. Primordial germ cells (PGCs) arise early in development and are the very first cells to form in the Drosophila embryo. At the time of PGC formation, the embryo is a syncytium where nuclei divide within a common cytoplasm. Whereas invaginating plasma membrane furrows enclose nuclei to form somatic lineages during the 14th nuclear division cycle, PGCs emerge from the syncytium during the 9th division cycle in a mechanistically distinct process. PGC formation depends on maternally deposited germ granules localized at the embryo’s posterior pole. Germ granules trigger protrusion of membrane buds that enlarge to surround several nuclei that reach the posterior pole. Buds are remodeled to cells through mitotic division and constriction of the bud neck. Previous studies implicated F-actin,1 actin regulators,2,3 and contractile ring components4 in mitotic furrow formation, but what drives bud emergence and how germ granules provoke reshaping of the plasma membrane remain unknown. Here, we investigate the mechanism of germ-granule-induced bud formation. Treating the embryo as a pressurized elastic shell, we used mathematical modeling to examine possible mechanical mechanisms for local membrane protrusion. One mechanism, outward buckling produced by polymerization of a branched F-actin network, is supported by experimental data. Further, we show that germ granules modify membrane lipid composition, promoting local branched F-actin polymerization that initiates PGC formation. We propose that a mechanism for membrane lipid regulation of F-actin dynamics in migrating cells has been adapted for PGC formation in response to spatial cues provided by germ granules.