Publications

How thousands of microtubules and molecular motors self-organize into spindles remains poorly understood. By combining static, nanometer-resolution, large-scale electron tomography reconstructions and dynamic, optical-resolution, polarized light microscopy, we test an active liquid crystal continuum model of mitotic spindles in human tissue culture cells. The predictions of this coarse-grained theory quantitatively agree with the experimentally measured spindle morphology and fluctuation spectra. These findings argue that local interactions and polymerization produce collective alignment, diffusive-like motion, and polar transport which govern the behaviors of the spindle's microtubule network, and provide a means to measure the spindle's material properties. This work demonstrates that a coarse-grained theory featuring measurable, physically-interpretable parameters can quantitatively describe the mechanical behavior and self-organization of human mitotic spindles.

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and cell nucleus.

Discrimination thresholds reveal the limits of human perception; scientists have studied them since the time of Fechner in the 1800s. Forced-choice psychophysical methods combined with the method of constant stimuli or parametric adaptive trial-placement procedures are well-suited for measuring one-dimensional psychometric functions. However, extending these methods to characterize psychometric fields in higher-dimensional stimulus spaces, such as three-dimensional color space, poses a significant challenge. Here, we introduce a novel Wishart Process Psychophysical Model (WPPM) that leverages the smooth variation of threshold across stimulus space. We demonstrate the use of the WPPM in conjunction with a non-parametric adaptive trial-placement procedure by characterizing the full psychophysical field for color discrimination in the isoluminant plane. Each participant (N = 8) completed between 6,000 and 6,466 three-alternative forced-choice (3AFC) oddity color discrimination trials. The WPPM was fit to these trials. Importantly, once fit, the WPPM allows readout of discrimination performance between any pair of stimuli, providing a comprehensive characterization of the psychometric field. In addition, the WPPM readouts were validated for each participant by comparison with 25 probe psychometric functions. These were measured with an additional 6,000 trials per participant that were held out from the WPPM fit. The dataset offers a foundational resource for developing perceptual color metrics and for benchmarking mechanistic models of color processing. This approach is broadly generalizable to other perceptual domains …

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Increasing experimental evidence showed that neural representations for a specific stimulus can change over time in a phenomenon called “representational drift” (RD). However, the underlying mechanisms for this widespread phenomenon remain poorly understood. Here, we study RD in the piriform cortex of the olfactory system with a realistic neural network model that incorporates two general mechanisms for synaptic weight dynamics operating at two well-separated timescales: spontaneous multiplicative fluctuations on a scale of days and spike-timing-dependent plasticity (STDP) effects on a scale of seconds. We show that the slow multiplicative fluctuations in synaptic sizes, which lead to a steady-state distribution of synaptic weights consistent with experiments, can induce RD effects that are in quantitative agreement with recent empirical evidence. Furthermore, our model reveals that the fast STDP learning dynamics during presentation of a given odor drives the system toward a low-dimensional representational manifold, which effectively reduces the dimensionality of synaptic weight fluctuations and thus suppresses RD. Specifically, our model explains why representations of already “learned” odors drift slower than unfamiliar ones, as well as the dependence of the drift rate with the frequency of stimulus presentation—both of which align with recent experimental data. The proposed model not only offers a simple explanation for the emergence of RD and its relation to learning in the piriform cortex, but also provides a general theoretical framework for studying representation dynamics in other neural systems.

Our visual capabilities depend on neural response properties in visual areas of our brains. Neurons exhibit a wide variety of selective response properties, but the reasons for this diversity are unknown. Here, we related the distribution of neuronal tuning properties to the information capacity of the population. Our results from theory, simulations, and analysis of recordings from macaque primary visual cortex (V1) reveal that diversity of amplitude and bandwidth drive complementary changes to the representational geometry of a population. Amplitude diversity pushes the centers of the representations further apart, whereas bandwidth heterogeneity decorrelates the center locations. These geometric changes separate out representations for distinct stimuli, creating more efficient encoding. We study how both types of diversity affect the population code for two different perceptual tasks: discrimination and identification. While both types of diversity improve encoding for both tasks, their distinct impacts on geometry make each more beneficial for one of the two tasks. Amplitude diversity impacts coding efficiency more for discrimination than it does for identification, while bandwidth diversity has a stronger impact on identification. These complementary effects indicate the importance of both types of diversity for perception. Finally, because tuning diversity exists across species and brain areas, our results suggest a fundamental neural coding strategy that may be applicable to a wide range of behavior.

Learning probability models from data is at the heart of many machine learning endeavors, but is notoriously difficult due to the curse of dimensionality. We introduce a new framework for learning normalized energy (log probability) models that is inspired from diffusion generative models, which rely on networks optimized to estimate the score. We modify a score network architecture to compute an energy while preserving its inductive biases. The gradient of this energy network with respect to its input image is the score of the learned density, which can be optimized using a denoising objective. Importantly, the gradient with respect to the noise level provides an additional score that can be optimized with a novel secondary objective, ensuring consistent and normalized energies across noise levels. We train an energy network with this dual score matching objective on the ImageNet64 dataset, and obtain a cross-entropy (negative log likelihood) value comparable to the state of the art. We further validate our approach by showing that our energy model strongly generalizes: estimated log probabilities are nearly independent of the specific images in the training set. Finally, we demonstrate that both image probability and dimensionality of local neighborhoods vary significantly with image content, in contrast with traditional assumptions such as concentration of measure or support on a low-dimensional manifold.

Computational psychiatry studies suggest that individuals with autism spectrum disorder (ASD) inflexibly update their expectations. Here we leveraged high-yield rodent psychophysics, extensive behavioral modeling and brain-wide single-cell extracellular recordings to assess whether mice with different genetic perturbations associated with ASD show this same computational anomaly, and if so, what neurophysiological features are shared across genotypes. Mice harboring mutations in Fmr1, Cntnap2 or Shank3B show a blunted update of priors during decision-making. Compared with mice that flexibly updated their priors, inflexible updating of priors was associated with a shift in the weighting of prior encoding from sensory to frontal cortices. Furthermore, frontal areas in mouse models of ASD showed more units encoding deviations from the animals’ long-run prior, and sensory responses did not differentiate between expected and unexpected observations. These findings suggest that distinct genetic instantiations of ASD may yield common neurophysiological and behavioral phenotypes.

Generative diffusion models learn probability densities over diverse image datasets by estimating the score with a neural network trained to remove noise. Despite their remarkable success in generating high-quality images, the internal mechanisms of the underlying score networks are not well understood. Here, we examine a UNet trained for denoising on the ImageNet dataset, to better understand its internal representation and computation of the score. We show that the middle block of the UNet decomposes individual images into sparse subsets of active channels, and that the vector of spatial averages of these channels can provide a nonlinear representation of the underlying clean images. We develop a novel algorithm for stochastic reconstruction of images from this representation and demonstrate that it recovers a sample from a set of images defined by a target image representation. We then study the properties of the representation and demonstrate that Euclidean distances in the latent space correspond to distances between conditional densities induced by representations as well as semantic similarities in the image space. Applying a clustering algorithm in the representation space yields groups of images that share both fine details (e.g., specialized features, textured regions, small objects), as well as global structure, but are only partially aligned with object identities. Thus, we show for the first time that a network trained solely on denoising contains a rich and accessible sparse representation of images.

We present a new implementation of the driven similarity renormalization group (DSRG) based on a density matrix renormalization group (DMRG) reference. The explicit build of high-order reduced density matrices is avoided by forming matrix-product-state compressed intermediates. This algorithm facilitates the application of DSRG second- and third-order perturbation theories to dodecacene with an active space of 50 electrons in 50 orbitals. This active space appears the largest employed to date within the framework of internally contracted multireference formalism. The DMRG-DSRG approach is applied to several challenging systems, including the singlet-triplet gaps ($\Delta_{\rm ST}$) of oligoacenes ranging from naphthalene to dodecacene, the vertical excitation energies of zeaxanthin, and the ground-state potential energy curve (PEC) of Cr$_2$ molecule. Our best estimate for the vertical $\Delta_{\rm ST}$ of dodecacene is 0.22 eV, showing an excellent agreement with that of the linearized adiabatic connection method (0.24 eV). For zeaxanthin, all DSRG schemes suggest the order of $\rm 2\, ^1 A_g^- < 1\, ^1 B_u^+ < 1\, ^1 B_u^-$ for excited states. Both the equilibrium and the shoulder regions of the Cr$_2$ PEC are reasonably reproduced by the linearized DSRG with one- and two-body operators.