POLARIS: Path of Least Action Analysis on Energy Landscapes

CLEAPA: a framework for exploring the conformational landscape of cryo-EM using energy-aware pathfinding algorithm

MOTIVATION

Cryo-electron microscopy (cryo-EM) is a powerful technique for studying macromolecules and holds the potential for identifying kinetically preferred transition sequences between conformational states. Typically, these sequences are explored within two-dimensional energy landscapes. However, due to the complexity of biomolecules, representing conformational changes in two dimensions can be challenging. Recent advancements in reconstruction models have successfully extracted structural heterogeneity from cryo-EM images using higher-dimension latent space. Nonetheless, creating high-dimensional conformational landscapes in the latent space and then searching for preferred paths continues to be a formidable task.

RESULTS

This study introduces an innovative framework for identifying preferred trajectories within high-dimensional conformational landscapes. Our method encompasses the search for the minimum energy path in the graph, where edge weights are determined based on the energy estimation at each node using local density. The effectiveness of this approach is demonstrated by identifying accurate transition states in both synthetic and real-world datasets featuring continuous conformational changes.

AVAILABILITY AND IMPLEMENTATION

The CLEAPA package is available at https://github.com/tengyulin/energy_aware_pathfinding/.

Structural basis of closed groove scrambling by a TMEM16 protein

Activation of Ca2+-dependent TMEM16 scramblases induces phosphatidylserine externalization, a key step in multiple signaling processes. Current models suggest that the TMEM16s scramble lipids by deforming the membrane near a hydrophilic groove and that Ca2+ dependence arises from the different association of lipids with an open or closed groove. However, the molecular rearrangements underlying groove opening and how lipids reorganize outside the closed groove remain unknown. Here we directly visualize how lipids associate at the closed groove of Ca2+-bound fungal nhTMEM16 in nanodiscs using cryo-EM. Functional experiments pinpoint lipid-protein interaction sites critical for closed groove scrambling. Structural and functional analyses suggest groove opening entails the sequential appearance of two π-helical turns in the groove-lining TM6 helix and identify critical rearrangements. Finally, we show that the choice of scaffold protein and lipids affects the conformations of nhTMEM16 and their distribution, highlighting a key role of these factors in cryo-EM structure determination.

Structural basis of closed groove scrambling by a TMEM16 protein

Activation of Ca2+-dependent TMEM16 scramblases induces the externalization of phosphatidylserine, a key molecule in multiple signaling processes. Current models suggest that the TMEM16s scramble lipids by deforming the membrane near a hydrophilic groove, and that Ca2+ dependence arises from the different association of lipids with an open or closed groove. However, the molecular rearrangements involved in groove opening and of how lipids reorganize outside the closed groove remain unknown. Using cryogenic electron microscopy, we directly visualize how lipids associate at the closed groove of Ca2+-bound nhTMEM16 in nanodiscs. Functional experiments pinpoint the lipid-protein interaction sites critical for closed groove scrambling. Structural and functional analyses suggest groove opening entails the sequential appearance of two π-helical turns in the groove-lining TM6 helix and identify critical rearrangements. Finally, we show that the choice of scaffold protein and lipids affects the conformations of nhTMEM16 and their distribution, highlighting a key role of these factors in cryoEM structure determination.

Structural basis of closed groove scrambling by a TMEM16 protein

Activation of Ca2+-dependent TMEM16 scramblases induces the externalization of phosphatidylserine, a key molecule in multiple signaling processes. Current models suggest that the TMEM16s scramble lipids by deforming the membrane near a hydrophilic groove, and that Ca2+ dependence arises from the different association of lipids with an open or closed groove. However, the molecular rearrangements involved in groove opening and of how lipids reorganize outside the closed groove remain unknown. Using cryogenic electron microscopy, we directly visualize how lipids associate at the closed groove of Ca2+-bound nhTMEM16 in nanodiscs. Functional experiments pinpoint the lipid-protein interaction sites critical for closed groove scrambling. Structural and functional analyses suggest groove opening entails the sequential appearance of two π-helical turns in the groove-lining TM6 helix and identify critical rearrangements. Finally, we show that the choice of scaffold protein and lipids affects the conformations of nhTMEM16 and their distribution, highlighting a key role of these factors in cryoEM structure determination.

Beyond ManifoldEM: geometric relationships between manifold embeddings of a continuum of 3D molecular structures and their 2D projections

ManifoldEM is an established method of geometric machine learning developed to extract information on conformational motions of molecules from their projections obtained by cryogenic electron microscopy (cryo-EM). In a previous work, in-depth analysis of the properties of manifolds obtained for simulated ground-truth data from molecules exhibiting domain motions has led to improvements of this method, as demonstrated in selected applications of single-particle cryo-EM. In the present work this analysis has been extended to investigate the properties of manifolds constructed by embedding data from synthetic models represented by atomic coordinates in motion, or three-dimensional density maps from biophysical experiments other than single-particle cryo-EM, with extensions to cryo-electron tomography and single-particle imaging with a X-ray free-electron laser. Our theoretical analysis revealed interesting relationships between all these manifolds, which can be exploited in future work.

Frozen in time: analyzing molecular dynamics with time-resolved cryo-EM

Molecular machines, such as polymerases, ribosomes, or proteasomes, fulfill complex tasks requiring the thermal energy of their environment. They achieve this by restricting random motion along a path of possible conformational changes. These changes are often directed through engagement with different cofactors, which can best be compared to a Brownian ratchet. Many molecular machines undergo three major steps throughout their functional cycles, including initialization, repetitive processing, and termination. Several of these major states have been elucidated by cryogenic electron microscopy (cryo-EM). However, the individual steps for these machines are unique and multistep processes themselves, and their coordination in time is still elusive. To measure these short-lived intermediate events by cryo-EM, the total reaction time needs to be shortened to enrich for the respective pre-equilibrium states. This approach is termed time-resolved cryo-EM (trEM). In this review, we sum up the methodological development of trEM and its application to a range of biological questions.

Recovery of Conformational Continuum From Single-Particle Cryo-EM Images: Optimization of ManifoldEM Informed by Ground Truth

This work is based on the manifold-embedding approach to study biological molecules exhibiting continuous conformational changes. Previous work established a method-now termed ManifoldEM-capable of reconstructing 3D movies and accompanying free-energy landscapes from single-particle cryo-EM images of macromolecules exercising multiple conformational degrees of freedom. While ManifoldEM has proven its viability in several experimental studies, critical limitations and uncertainties have been found throughout its extended development and use. Guided by insights from studies with cryo-EM ground-truth data, simulated from atomic structures undergoing conformational changes, we have built a novel framework, ESPER, able to retrieve the free-energy landscape and respective 3D Coulomb potential maps for all states simulated. As shown by a direct comparison of ground truth vs. recovered maps, and analysis of experimental data from the 80S ribosome and ryanodine receptor, ESPER offers substantial improvements relative to the previous work.

Assembly mechanism of surface-functionalized nanocubes

Faceted nanoparticles can be used as building blocks to assemble nanomaterials with exceptional optical and catalytic properties. Recent studies have shown that surface functionalization of such nanoparticles with organic molecules, polymer chains, or DNA can be used to control the separation distance and orientation of particles within their assemblies. In this study, we computationally investigate the mechanism of assembly of nanocubes grafted with short-chain molecules. Our approach involves computing the interaction free energy landscape of a pair of such nanocubes via Monte Carlo simulations and using the Dijkstra algorithm to determine the minimum free energy pathway connecting key states in the landscape. We find that the assembly pathway of nanocubes is very rugged involving multiple energy barriers and metastable states. Analysis of nanocube configurations along the pathway reveals that the assembly mechanism is dominated by sliding motion of nanocubes relative to each other punctuated by their local dissociation at grafting points involving lineal separation and rolling motions. The height of energy barriers between metastable states depends on factors such as the interaction strength and surface roughness of the nanocubes and the steric repulsion from the grafts. These results imply that the observed assembly configuration of nanocubes depends not only on their globally stable minimum free energy state but also on the assembly pathway leading to this state. The free energy landscapes and assembly pathways presented in this study along with the proposed guidelines for engineering such pathways should be useful to researchers aiming to achieve uniform nanostructures from self-assembly of faceted nanoparticles.

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature it has the potential to provide information about a biomolecule's conformational variability and underlying free-energy landscape. However, treating cryo-EM as a single-molecule technique is challenging because of the low signal-to-noise ratio (SNR) in individual particles. In this work, we propose the cryo-BIFE method (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. We test the framework on several synthetic systems where the imaging parameters and conditions were controlled. We found that for realistic cryo-EM environments and relevant biomolecular systems, it is possible to recover the underlying free energy, with the pose accuracy and SNR as crucial determinants. We then use the method to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of [Formula: see text]. We expect our tool for extracting free-energy profiles from cryo-EM images to enable more complete characterization of the thermodynamic ensemble of biomolecules.