Publications

imulating membrane proteins accurately combines two challenges into one: properly capturing the structure and dynamics of proteins as well as correctly representing the membrane environment in which they are usually embedded. Beginning with pioneering efforts in the 1980s and 1990s,1−7 both challenges have been met with increasing success over the years. Simulations of membrane proteins in realistic cellular contexts over many microseconds are now common.Concomitant advances in the determination of membrane protein structures, with over 50 unique structures determined 8 annually have further expanded the reach of simulations in this area. This Special Issue highlights a number of recent molecular dynamics (MD) simulations of membrane proteins and covers a wide range of applications and specialized techniques.

Hamiltonian Monte Carlo (HMC) is the mainstay of applied Bayesian inference for differentiable models. However, HMC still struggles to sample from hierarchical models that induce densities with multiscale geometry: a large step size is needed to efficiently explore low curvature regions while a small step size is needed to accurately explore high curvature regions. We introduce the delayed rejection generalized HMC (DR-G-HMC) sampler that overcomes this challenge by employing dynamic step size selection, inspired by differential equation solvers. In generalized HMC, each iteration does a single leapfrog step. DR-G-HMC sequentially makes proposals with geometrically decreasing step sizes upon rejection of earlier proposals. This simulates Hamiltonian dynamics that can adjust its step size along a (stochastic) Hamiltonian trajectory to deal with regions of high curvature. DR-G-HMC makes generalized HMC competitive by decreasing the number of rejections which otherwise cause inefficient backtracking and prevents directed movement. We present experiments to demonstrate that DR-G-HMC (1) correctly samples from multiscale densities, (2) makes generalized HMC methods competitive with the state of the art No-U-Turn sampler, and (3) is robust to tuning parameters.

In computational physics, chemistry, and biology, the implementation of new techniques in shared and open-source software lowers barriers to entry and promotes rapid scientific progress. However, effectively training new software users presents several challenges. Common methods like direct knowledge transfer and in-person workshops are limited in reach and comprehensiveness. Furthermore, while the COVID-19 pandemic highlighted the benefits of online training, traditional online tutorials can quickly become outdated and may not cover all the software’s functionalities. To address these issues, here we introduce “PLUMED Tutorials,” a collaborative model for developing, sharing, and updating online tutorials. This initiative utilizes repository management and continuous integration to ensure compatibility with software updates. Moreover, the tutorials are interconnected to form a structured learning path and are enriched with automatic annotations to provide broader context. This paper illustrates the development, features, and advantages of PLUMED Tutorials, aiming to foster an open community for creating and sharing educational resources.

Neurons in the hippocampus are correlated with different variables, including space, time, sensory cues, rewards and actions, in which the extent of tuning depends on ongoing task demands1,2,3,4,5,6,7,8. However, it remains uncertain whether such diverse tuning corresponds to distinct functions within the hippocampal network or whether a more generic computation can account for these observations9. Here, to disentangle the contribution of externally driven cues versus internal computation, we developed a task in mice in which space, auditory tones, rewards and context were juxtaposed with changing relevance. High-density electrophysiological recordings revealed that neurons were tuned to each of these modalities. By comparing movement paths and action sequences, we observed that external variables had limited direct influence on hippocampal firing. Instead, spiking was influenced by online action plans and modulated by goal uncertainty. Our results suggest that internally generated cell assembly sequences are selected and updated by action plans towards deliberate goals. The apparent tuning of hippocampal neuronal spiking to different sensory modalities might emerge due to alignment to the afforded action progression within a task rather than representation of external cues.

We study level set teleportation, an optimization routine which tries to accelerate gradient descent (GD) by maximizing the gradient norm over a level set of the objective. While teleportation intuitively speeds-up GD via bigger steps, current work lacks convergence theory for convex functions, guarantees for solving the teleportation operator, and even clear empirical evidence showing this acceleration. We resolve these open questions. For convex functions satisfying Hessian stability, we prove that GD with teleportation obtains a combined sub-linear/linear convergence rate which is strictly faster than GD when the optimality gap is small. This is in sharp contrast to the standard (strongly) convex setting, where teleportation neither improves nor worsens convergence. To evaluate teleportation in practice, we develop a projected-gradient method requiring only Hessian-vector products. We use this to show that gradient methods with access to a teleportation oracle out-perform their standard versions on a variety of problems. We also find that GD with teleportation is faster than truncated Newton methods, particularly for non-convex optimization.

Tissue deformations during morphogenesis can be active, driven by internal processes, or passive, resulting from stresses applied at their boundaries. Here, we introduce the Drosophila hindgut primordium as a model for studying boundary-driven tissue morphogenesis. We characterize its deformations and show that its complex shape changes can be a passive consequence of the deformations of the active regions of the embryo that surround it. First, we find an intermediate characteristic triangular shape in the 3D deformations of the hindgut. We construct a minimal model of the hindgut primordium as an elastic ring deformed by active midgut invagination and germ band extension on an ellipsoidal surface, which robustly captures the symmetry-breaking into this triangular shape. We then quantify the 3D kinematics of the tissue by a set of contours and discover that the hindgut deforms in two stages: an initial translation on the curved embryo surface followed by a rapid breaking of shape symmetry. We extend our model to show that the contour kinematics in both stages are consistent with our passive picture. Our results suggest that the role of in-plane deformations during hindgut morphogenesis is to translate the tissue to a region with anisotropic embryonic curvature and show that uniform boundary conditions are sufficient to generate the observed nonuniform shape change. Our work thus provides a possible explanation for the various characteristic shapes of blastopore-equivalents in different organisms and a framework for the mechanical emergence of global morphologies in complex developmental systems.

We study emergent dynamics in a viscous drop subject to interfacial nematic activity. Using hydrodynamic simulations, we show how the interplay of nematodynamics, activity-driven flows in the fluid bulk, and surface deformations gives rise to a sequence of self-organized behaviors of increasing complexity, from periodic braiding motions of topological defects to chaotic defect dynamics and active turbulence, along with spontaneous shape changes and translation. Our findings recapitulate qualitative features of experiments and shed light on the mechanisms underpinning morphological dynamics in active interfaces.

Using a state-of-the-art numerical scheme, we show that the Higgs mode under excitation exhibits chirped oscillations and exponential decay when fluctuations are included. This is in stark contrast to conventional BCS collisionless dynamics which predict power-law decay and the absence of chirping. The chirped amplitude mode enables us to determine the local modification of the effective potential even when the system is in a long-lived prethermal state. We then show that this chirped amplitude mode is an experimentally observable quantity since the photoinduced (super)current in pump-probe experiments serves as an efficient proxy for the order parameter dynamics, including the chirped dynamics. Our result is based on the attractive Hubbard model using dynamical mean-field theory within the symmetry-broken state after a excitation across the superconducting gap. Since the collective response involves long timescales, we extend the hierarchical low-rank compression method for nonequilibrium Green's functions to symmetry-broken states and show that it serves as an efficient representation despite long-lived memory kernels.

Humans and monkeys can rapidly recognize objects in everyday scenes. While it is known that this ability relies on neural computations in the ventral stream of visual cortex, it is not well understood where this computation first arises. Previous work suggests selectivity for object shape first emerges in area V4. To explore the mechanisms of this selectivity, we generated a continuum of images between “scrambled” textures and photographic images of both natural and man-made environments, using techniques that preserve the local statistics of the original image while discarding information about scene and shape. We measured image responses from single units in area V4 from two awake macaque monkeys. Neuronal populations in V4 could reliably distinguish photographic from scrambled images, could more reliably discriminate between photographic images than between scrambled images, and responded with greater dynamic range to photographic images than scrambled images. Responses to partially scrambled images were more similar to fully scrambled responses than photographic responses, even for perceptually subtle changes. This same pattern emerged when these images were analyzed with an image-computable similarity metric that predicts human judgements of image degradation (DISTS - Deep Image Structure and Texture Similarity). Finally, analysis of response dynamics showed that sensitivity to differences between photographic and scrambled responses grew slowly, peaked 190 ms after response onset, and persisted for hundreds of milliseconds following response offset, suggesting that this signal may arise from recurrent mechanisms.

Accurately placing macromolecular assemblies in the cellular context is important in understanding their mechanistic role inside the cell. Previously, we developed a 2D template-matching (2DTM) approach (Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]; Lucas et al., 2021[Lucas, B. A., Himes, B. A., Xue, L., Grant, T., Mahamid, J. & Grigorieff, N. (2021). eLife, 10, e68946.]) in cisTEM (Grant et al., 2018[Grant, T., Rohou, A. & Grigorieff, N. (2018). eLife, 7, e35383.]) to detect targets in cellular cryo-EM images with high positional and orientational accuracy. 2DTM not only detects targets such as ribosomes in cryo-EM images but also provides data that enable the in situ classification and high-resolution reconstruction of these targets (Lucas et al., 2022[Lucas, B. A., Zhang, K., Loerch, S. & Grigorieff, N. (2022). eLife, 11, e79272.], 2023[Lucas, B. A., Himes, B. A. & Grigorieff, N. (2023). eLife, 12, 12RP90486.]; Elferich et al., 2022[Elferich, J., Schiroli, G., Scadden, D. T. & Grigorieff, N. (2022). eLife, 11, e80980.]). Building on these successes, this work aims to improve the 2DTM framework to detect more challenging targets in various environments.

A 2DTM search yields a signal-to-noise ratio (SNR) for every location in the cryo-EM image that depends on the cross-correlation between the template and the image (Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]). A target is detected when the SNR value exceeds a statistically defined threshold that limits the average false positives to one per image, based on the assumption that the cryo-EM image is dominated by noise and cellular background and that the cross-correlation values observed across the image after whitening the noise/background follow a Gaussian distribution. The 2DTM SNR can be further normalized by subtracting the mean and dividing by the standard deviation of cross-correlations calculated across all sampled orientations at each location in the image (Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]). This step is often referred to as `z-score' normalization (Spiegel & Stephens, 1999[Spiegel, M. R. & Stephens, L. J. (1999). Schaum's Outline of Theory and Problems of Statistics, 3rd ed. New York: McGraw-Hill.]). Using the z-score instead of the SNR improves the detection of capsomers in rotavirus double-layered particles (DLPs; Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]) and ribosomes in a crowded cellular environment (Lucas et al., 2022[Lucas, B. A., Zhang, K., Loerch, S. & Grigorieff, N. (2022). eLife, 11, e79272.]). In the following, we will refer to the outputs of 2DTM as the 2DTM SNR and 2DTM z-score, respectively.

Previous applications of 2DTM have shown that the 2DTM SNR and z-score function differently depending on the characteristics of the sample and target. For example, when low-resolution features were suppressed by using a near-focus image setting (70 nm), the 2DTM SNR map showed a flat background with sharp peaks indicating the locations of apoferritins, even in a dense protein (bovine serum albumin) background (Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]). On the other hand, low-resolution features from the target itself when strongly defocused (>2000 nm), or from the background structural noise, can result in broader peaks or an uneven background in the SNR map, complicating target detection (Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]; Lucas et al., 2022[Lucas, B. A., Zhang, K., Loerch, S. & Grigorieff, N. (2022). eLife, 11, e79272.]). The misleading low-resolution background can be suppressed by calculating the 2DTM z-score (Rickgauer et al., 2017[Rickgauer, J. P., Grigorieff, N. & Denk, W. (2017). eLife, 6, e25648.]), which removes spurious correlations between the template and the structural noise in the image, thereby flattening the background and improving the detectability of targets in cellular environments (Rickgauer et al., 2020[Rickgauer, J. P., Choi, H., Lippincott-Schwartz, J. & Denk, W. (2020). bioRxiv, 2020.04.22.053868.]; Lucas et al., 2022[Lucas, B. A., Zhang, K., Loerch, S. & Grigorieff, N. (2022). eLife, 11, e79272.]). In Fig. 1[link](a), a segment of a previously published micrograph of a yeast lamella near the nucleus is presented (Lucas et al., 2022[Lucas, B. A., Zhang, K., Loerch, S. & Grigorieff, N. (2022). eLife, 11, e79272.]). This image section contains various cellular compartments located from left to right, including the vacuole, cytoplasm and nucleus. Using the mature 60S as a search template, 2DTM outputs a 2DTM SNR map and a 2DTM z-score map [Figs. 1[link](b) and 1[link](c)]. The bright spots in the 2DTM SNR map are locations with high correlation values, indicating 60S ribosomes. However, the peaks are surrounded by halos of increased SNR values extending to other low-resolution features in the image, such as membranes. The z-score map removes these halos and spurious matches of high-contrast features, thereby reducing the number of false detections (membranes or partial overlap with ribosomes) while preserving locations with high-resolution matches from the riboso