Publications

Simulating 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.

The flagellum is the most complex macromolecular structure known in bacteria and is composed of around two dozen distinct proteins. The main building block of the long, external flagellar filament, flagellin, is secreted through the flagellar type-III secretion system at a remarkable rate of several tens of thousands of amino acids per second, significantly surpassing the rates achieved by other pore-based protein secretion systems. The evolutionary implications and potential benefits of this high secretion rate for flagellum assembly and function, however, have remained elusive. In this study, we provide both experimental and theoretical evidence that the flagellar secretion rate has been evolutionarily optimized to facilitate rapid and efficient construction of a functional flagellum. By synchronizing flagellar assembly, we found that a minimal filament length of 2.5 μm was required for swimming motility. Biophysical modeling revealed that this minimal filament length threshold resulted from an elasto-hydrodynamic instability of the whole swimming cell, dependent on the filament length. Furthermore, we developed a stepwise filament labeling method combined with electron microscopy visualization to validate predicted flagellin secretion rates of up to 10,000 amino acids per second. A biophysical model of flagellum growth demonstrates that the observed high flagellin secretion rate efficiently balances filament elongation and energy consumption, thereby enabling motility in the shortest amount of time. Taken together, these insights underscore the evolutionary pressures that have shaped the development and optimization of the flagellum and type-III secretion system, illuminating the intricate interplay and cost-benefit tradeoff between functionality and efficiency in assembly of large macromolecular structures.

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.

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.

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.

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.

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

Macrocycles are a promising therapeutic class. The incorporation of heterochiral and non-natural chemical building-blocks presents challenges for rational design, however. With no existing machine learning methods tailored for heterochiral macrocycle design, we developed a novel convolutional autoencoder model to rapidly generate energetically favorable macrocycle backbones for heterochiral design and structure prediction. Our approach surpasses the current state-of-the-art method, Generalized Kinematic loop closure (GenKIC) in the Rosetta software suite. Given the absence of large, available macrocycle datasets, we created a custom dataset in-house and in silico. Our model, CyclicCAE, produces energetically stable backbones and designable structures more rapidly than GenKIC. It enables users to perform energy minimization, generate structurally similar or diverse inputs via MCMC, and conduct inpainting with fixed anchors or motifs. We propose that this novel method will accelerate the development of stable macrocycles, speeding up macrocycle drug design pipelines.

Granular flows in small-outlet hoppers exhibit several characteristic but poorly understood behaviors: temporary clogs (pauses) where flow stops before later spontaneously restarting, permanent clogs that last indefinitely, and non-Gaussian, nonmonotonic flow-rate statistics. These aspects have been studied independently, but a model of hopper flow that explains all three has not been formulated. Here, we introduce a phenomenological model that provides a unifying dynamical mechanism for all three behaviors: coupling between the flow rate and a hidden mode that controls the stability of clogs. In the theory, flow rate evolves according to Langevin dynamics with multiplicative noise and an absorbing state at zero flow, conditional on the hidden mode. The model fully reproduces the statistics of pause and clog events of a large (>40000 flows) experimental dataset, including nonexponentially distributed clogging times and non-Gaussian flow rate distribution, and explains the stretched-exponential growth of the average clogging time with outlet size. Further, we identify the physical nature of the hidden mode in microscopic configurational features, including size and smoothness of the static arch structure formed during pauses and clogs. Our work provides a unifying framework for several poorly understood clogging phenomena, and suggests numerous new paths toward further understanding of this complex system.

Cell populations must adjust their phenotypic composition to adapt to changing environments. One adaptation strategy is to maintain distinct phenotypic subsets within the population and to modulate their relative abundances via gene regulation. Another strategy involves genetic mutations, which can be augmented by stress-response pathways. Here, we studied how a migrating bacterial population regulates its phenotypic distribution to traverse diverse environments. We generated isogenic Escherichia coli populations with varying distributions of swimming behaviors and observed their phenotype distributions during migration in liquid and porous environments. We found that the migrating populations became enriched with high-performing swimming phenotypes in each environment, allowing the populations to adapt without requiring mutations or gene regulation. This adaptation is dynamic and rapid, reversing in a few doubling times when migration ceases. By measuring the chemoreceptor abundance distributions during migration toward different attractants, we demonstrated that adaptation acts on multiple chemotaxis-related traits simultaneously. These measurements are consistent with a general mechanism in which adaptation results from a balance between cell growth generating diversity and collective migration eliminating underperforming phenotypes. Thus, collective migration enables cell populations with continuous, multidimensional phenotypes to flexibly and rapidly adapt their phenotypic composition to diverse environmental conditions.