Docking-based long timescale simulation of cell-size protein systems at atomic resolution

Anisotropic coarse-grain Monte Carlo simulations of lysozyme, lactoferrin, and NISTmAb by precomputing atomistic models

We develop a multiscale coarse-grain model of the NIST Monoclonal Antibody Reference Material 8671 (NISTmAb) to enable systematic computational investigations of high-concentration physical instabilities such as phase separation, clustering, and aggregation. Our multiscale coarse-graining strategy captures atomic-resolution interactions with a computational approach that is orders of magnitude more efficient than atomistic models, assuming the biomolecule can be decomposed into one or more rigid bodies with known, fixed structures. This method reduces interactions between tens of thousands of atoms to a single anisotropic interaction site. The anisotropic interaction between unique pairs of rigid bodies is precomputed over a discrete set of relative orientations and stored, allowing interactions between arbitrarily oriented rigid bodies to be interpolated from the precomputed table during coarse-grained Monte Carlo simulations. We present this approach for lysozyme and lactoferrin as a single rigid body and for the NISTmAb as three rigid bodies bound by a flexible hinge with an implicit solvent model. This coarse-graining strategy predicts experimentally measured radius of gyration and second osmotic virial coefficient data, enabling routine Monte Carlo simulation of medically relevant concentrations of interacting proteins while retaining atomistic detail. All methodologies used in this work are available in the open-source software Free Energy and Advanced Sampling Simulation Toolkit.

Diffusion of proteins in crowded solutions studied by docking-based modeling

The diffusion of proteins is significantly affected by macromolecular crowding. Molecular simulations accounting for protein interactions at atomic resolution are useful for characterizing the diffusion patterns in crowded environments. We present a comprehensive analysis of protein diffusion under different crowding conditions based on our recent docking-based approach simulating an intracellular crowded environment by sampling the intermolecular energy landscape using the Markov Chain Monte Carlo protocol. The procedure was extensively benchmarked, and the results are in very good agreement with the available experimental and theoretical data. The translational and rotational diffusion rates were determined for different types of proteins under crowding conditions in a broad range of concentrations. A protein system representing most abundant protein types in the E. coli cytoplasm was simulated, as well as large systems of other proteins of varying sizes in heterogeneous and self-crowding solutions. Dynamics of individual proteins was analyzed as a function of concentration and different diffusion rates in homogeneous and heterogeneous crowding. Smaller proteins diffused faster in heterogeneous crowding of larger molecules, compared to their diffusion in the self-crowded solution. Larger proteins displayed the opposite behavior, diffusing faster in the self-crowded solution. The results show the predictive power of our structure-based simulation approach for long timescales of cell-size systems at atomic resolution.

Modeling reveals the strength of weak interactions in stacked-ring assembly

Cells employ many large macromolecular machines for the execution and regulation of processes that are vital for cell and organismal viability. Interestingly, cells cannot synthesize these machines as functioning units. Instead, cells synthesize the molecular parts that must then assemble into the functional complex. Many important machines, including chaperones such as GroEL and proteases such as the proteasome, comprise protein rings that are stacked on top of one another. While there is some experimental data regarding how stacked-ring complexes such as the proteasome self-assemble, a comprehensive understanding of the dynamics of stacked-ring assembly is currently lacking. Here, we developed a mathematical model of stacked-trimer assembly and performed an analysis of the assembly of the stacked homomeric trimer, which is the simplest stacked-ring architecture. We found that stacked rings are particularly susceptible to a form of kinetic trapping that we term "deadlock," in which the system gets stuck in a state where there are many large intermediates that are not the fully assembled structure but that cannot productively react. When interaction affinities are uniformly strong, deadlock severely limits assembly yield. We thus predicted that stacked rings would avoid situations where all interfaces in the structure have high affinity. Analysis of available crystal structures indicated that indeed the majority-if not all-of stacked trimers do not contain uniformly strong interactions. Finally, to better understand the origins of deadlock, we developed a formal pathway analysis and showed that, when all the binding affinities are strong, many of the possible pathways are utilized. In contrast, optimal assembly strategies utilize only a small number of pathways. Our work suggests that deadlock is a critical factor influencing the evolution of macromolecular machines and provides general principles for understanding the self-assembly efficiency of existing machines.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Assembly of Protein Complexes in and on the Membrane with Predicted Spatial Arrangement Constraints

Membrane proteins play crucial roles in various cellular processes, and their interactions with other proteins in and on the membrane are essential for their proper functioning. While an increasing number of structures of more membrane proteins are being determined, the available structure data is still sparse. To gain insights into the mechanisms of membrane protein complexes, computational docking methods are necessary due to the challenge of experimental determination. Here, we introduce Mem-LZerD, a rigid-body membrane docking algorithm designed to take advantage of modern membrane modeling and protein docking techniques to facilitate the docking of membrane protein complexes. Mem-LZerD is based on the LZerD protein docking algorithm, which has been constantly among the top servers in many rounds of CAPRI protein docking assessment. By employing a combination of geometric hashing, newly constrained by the predicted membrane height and tilt angle, and model scoring accounting for the energy of membrane insertion, we demonstrate the capability of Mem-LZerD to model diverse membrane protein-protein complexes. Mem-LZerD successfully performed unbound docking on 13 of 21 (61.9%) transmembrane complexes in an established benchmark, more than shown by previous approaches. It was additionally tested on new datasets of 44 transmembrane complexes and 92 peripheral membrane protein complexes, of which it successfully modeled 35 (79.5%) and 15 (16.3%) complexes respectively. When non-blind orientations of peripheral targets were included, the number of successes increased to 54 (58.7%). We further demonstrate that Mem-LZerD produces complex models which are suitable for molecular dynamics simulation. Mem-LZerD is made available at https://lzerd.kiharalab.org.

GRAMM Web Server for Protein Docking

Prediction of the structure of protein complexes by docking methods is a well-established research field. The intermolecular energy landscapes in protein-protein interactions can be used to refine docking predictions and to detect macro-characteristics, such as the binding funnel. A new GRAMM web server for protein docking predicts a spectrum of docking poses that characterize the intermolecular energy landscape in protein interaction. A user-friendly interface provides options to choose free or template-based docking, as well as other advanced features, such as clustering of the docking poses, and interactive visualization of the docked models.

Prediction of protein interactions is essential for studying biomolecular mechanisms

Structural characterization of protein interactions is essential for our ability to understand and modulate physiological processes. Computational approaches to modeling of protein complexes provide structural information that far exceeds capabilities of the existing experimental techniques. Protein structure prediction in general, and prediction of protein interactions in particular, has been revolutionized by the rapid progress in Deep Learning techniques. The work of Schweke et al. (Proteomics 2023, 23, 2200323) presents a community-wide study of an important problem of distinguishing physiological protein-protein complexes/interfaces (experimentally determined or modeled) from non-physiological ones. The authors designed and generated a large benchmark set of physiological and non-physiological homodimeric complexes, and evaluated a large set of scoring functions, as well as AlphaFold predictions, on their ability to discriminate the non-physiological interfaces. The problem of separating physiological interfaces from non-physiological ones is very difficult, largely due to the lack of a clear distinction between the two categories in a crowded environment inside a living cell. Still, the ability to identify key physiologically significant interfaces in the variety of possible configurations of a protein-protein complex is important. The study presents a major data resource and methodological development in this important direction for molecular and cellular biology.

Single-molecule tracking to determine the abundances and stoichiometries of freely-diffusing protein complexes in living cells: Past applications and future prospects

Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein participates in homo- and hetero-oligomeric complexes of different size and subunit composition are therefore critical to advance our understanding of how cellular physiology is governed by these molecular interactions. Biomolecular complex formation changes the diffusion coefficient of constituent proteins, and these changes can be measured using fluorescence microscopy-based approaches, such as single-molecule tracking, fluorescence correlation spectroscopy, and fluorescence recovery after photobleaching. In this review, we focus on the use of single-molecule tracking to identify, resolve, and quantify the presence of freely-diffusing proteins and protein complexes in living cells. We compare and contrast different data analysis methods that are currently employed in the field and discuss experimental designs that can aid the interpretation of the obtained results. Comparisons of diffusion rates for different proteins and protein complexes in intracellular aqueous environments reported in the recent literature reveal a clear and systematic deviation from the Stokes-Einstein diffusion theory. While a complete and quantitative theoretical explanation of why such deviations manifest is missing, the available data suggest the possibility of weighing freely-diffusing proteins and protein complexes in living cells by measuring their diffusion coefficients. Mapping individual diffusive states to protein complexes of defined molecular weight, subunit stoichiometry, and structure promises to provide key new insights into how protein-protein interactions regulate protein conformational, translational, and rotational dynamics, and ultimately protein function.

Understanding How Cells Probe the World: A Preliminary Step towards Modeling Cell Behavior?

Cell biologists have long aimed at quantitatively modeling cell function. Recently, the outstanding progress of high-throughput measurement methods and data processing tools has made this a realistic goal. The aim of this paper is twofold: First, to suggest that, while much progress has been done in modeling cell states and transitions, current accounts of environmental cues driving these transitions remain insufficient. There is a need to provide an integrated view of the biochemical, topographical and mechanical information processed by cells to take decisions. It might be rewarding in the near future to try to connect cell environmental cues to physiologically relevant outcomes rather than modeling relationships between these cues and internal signaling networks. The second aim of this paper is to review exogenous signals that are sensed by living cells and significantly influence fate decisions. Indeed, in addition to the composition of the surrounding medium, cells are highly sensitive to the properties of neighboring surfaces, including the spatial organization of anchored molecules and substrate mechanical and topographical properties. These properties should thus be included in models of cell behavior. It is also suggested that attempts at cell modeling could strongly benefit from two research lines: (i) trying to decipher the way cells encode the information they retrieve from environment analysis, and (ii) developing more standardized means of assessing the quality of proposed models, as was done in other research domains such as protein structure prediction.

Size of the protein-protein energy funnel in crowded environment

Association of proteins to a significant extent is determined by their geometric complementarity. Large-scale recognition factors, which directly relate to the funnel-like intermolecular energy landscape, provide important insights into the basic rules of protein recognition. Previously, we showed that simple energy functions and coarse-grained models reveal major characteristics of the energy landscape. As new computational approaches increasingly address structural modeling of a whole cell at the molecular level, it becomes important to account for the crowded environment inside the cell. The crowded environment drastically changes protein recognition properties, and thus significantly alters the underlying energy landscape. In this study, we addressed the effect of crowding on the protein binding funnel, focusing on the size of the funnel. As crowders occupy the funnel volume, they make it less accessible to the ligands. Thus, the funnel size, which can be defined by ligand occupancy, is generally reduced with the increase of the crowders concentration. This study quantifies this reduction for different concentration of crowders and correlates this dependence with the structural details of the interacting proteins. The results provide a better understanding of the rules of protein association in the crowded environment.