Learning Protein-Ligand Unbinding Pathways via Single-Parameter Community Detection.

Understanding the dynamics of biomolecular complexes, e.g., of protein-ligand (un)binding, requires the comprehension of paths such systems take between metastable states. In MD simulations, paths are usually not observable per se, but they need to be inferred from simulation trajectories. Here, we present a novel approach to cluster trajectories based on a community detection algorithm that necessitates only the definition of a single parameter. The unbinding of the streptavidin-biotin complex is used as a benchmark system and the A2a adenosine receptor in complex with the inhibitor ZM241385 as an elaborate application. We demonstrate how such clusters of trajectories correspond to pathways and how the approach helps in the identification of reaction coordinates for a considered (un)binding process.

Nonadiabatic dynamics of molecules interacting with metal surfaces: A quantum-classical approach based on Langevin dynamics and the hierarchical equations of motion.

A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees of freedom with Langevin dynamics for the classical degrees of freedom, namely, low-frequency vibrational modes within the molecule. The approach extends previous mixed quantum-classical methods based on Langevin equations to models containing strong electron-electron or quantum electronic-vibrational interactions, while maintaining a nonperturbative and non-Markovian treatment of the molecule-metal coupling. To demonstrate the approach, nonequilibrium transport observables are calculated for a molecular nanojunction containing strong interactions.

Basal delamination during mouse gastrulation primes pluripotent cells for differentiation.

The blueprint of the mammalian body plan is laid out during gastrulation, when a trilaminar embryo is formed. This process entails a burst of proliferation, the ingression of embryonic epiblast cells at the primitive streak, and their priming toward primitive streak fates. How these different events are coordinated remains unknown. Here, we developed and characterized a 3D culture of self-renewing mouse embryonic cells that captures the main transcriptional and architectural features of the early gastrulating mouse epiblast. Using this system in combination with microfabrication and in vivo experiments, we found that proliferation-induced crowding triggers delamination of cells that express high levels of the apical polarity protein aPKC. Upon delamination, cells become more sensitive to Wnt signaling and upregulate the expression of primitive streak markers such as Brachyury. This mechanistic coupling between ingression and differentiation ensures that the right cell types become specified at the right place during embryonic development.

Investigation of Rare Protein Conformational Transitions via Dissipation-Corrected Targeted Molecular Dynamics.

To sample rare events, dissipation-corrected targeted molecular dynamics (dcTMD) applies a constant velocity constraint along a one-dimensional reaction coordinate s, which drives an atomistic system from an initial state into a target state. Employing a cumulant approximation of Jarzynski's identity, the free energy ΔG(s) is calculated from the mean external work and dissipated work of the process. By calculating the friction coefficient Γ(s) from the dissipated work, in a second step, the equilibrium dynamics of the process can be studied by propagating a Langevin equation. While so far dcTMD has been mostly applied to study the unbinding of protein-ligand complexes, here its applicability to rare conformational transitions within a protein and the prediction of their kinetics are investigated. As this typically requires the introduction of multiple collective variables {xj} = x, a theoretical framework is outlined to calculate the associated free energy ΔG(x) and friction Γ(x) from dcTMD simulations along coordinate s. Adopting the α-ß transition of alanine dipeptide as well as the open-closed transition of T4 lysozyme as representative examples, the virtues and shortcomings of dcTMD to predict protein conformational transitions and the related kinetics are studied.

The Onset of Molecule-Spanning Dynamics in Heat Shock Protein Hsp90.

Protein dynamics have been investigated on a wide range of time scales. Nano- and picosecond dynamics have been assigned to local fluctuations, while slower dynamics have been attributed to larger conformational changes. However, it is largely unknown how fast (local) fluctuations can lead to slow global (allosteric) changes. Here, fast molecule-spanning dynamics on the 100 to 200 ns time scale in the heat shock protein 90 (Hsp90) are shown. Global real-space movements are assigned to dynamic modes on this time scale, which is possible by a combination of single-molecule fluorescence, quasi-elastic neutron scattering and all-atom molecular dynamics (MD) simulations. The time scale of these dynamic modes depends on the conformational state of the Hsp90 dimer. In addition, the dynamic modes are affected to various degrees by Sba1, a co-chaperone of Hsp90, depending on the location within Hsp90, which is in very good agreement with MD simulations. Altogether, this data is best described by fast molecule-spanning dynamics, which precede larger conformational changes in Hsp90 and might be the molecular basis for allostery. This integrative approach provides comprehensive insights into molecule-spanning dynamics on the nanosecond time scale for a multi-domain protein.

Predicting Protein-Ligand Binding and Unbinding Kinetics with Biased MD Simulations and Coarse-Graining of Dynamics: Current State and Challenges.

The prediction of drug-target binding and unbinding kinetics that occur on time scales between milliseconds and several hours is a prime challenge for biased molecular dynamics simulation approaches. This Perspective gives a concise summary of the theory and the current state-of-the-art of such predictions via biased simulations, of insights into the molecular mechanisms defining binding and unbinding kinetics as well as of the extraordinary challenges predictions of ligand kinetics pose in comparison to binding free energy predictions.

Path separation of dissipation-corrected targeted molecular dynamics simulations of protein-ligand unbinding.

Protein-ligand (un)binding simulations are a recent focus of biased molecular dynamics simulations. Such binding and unbinding can occur via different pathways in and out of a binding site. Here, we present a theoretical framework on how to compute kinetics along separate paths and on how to combine the path-specific rates into global binding and unbinding rates for comparison with experimental results. Using dissipation-corrected targeted molecular dynamics in combination with temperature-boosted Langevin equation simulations [S. Wolf et al., Nat. Commun. 11, 2918 (2020)] applied to a two-dimensional model and the trypsin-benzamidine complex as test systems, we assess the robustness of the procedure and discuss the aspects of its practical applicability to predict multisecond kinetics of complex biomolecular systems.

Anisotropic Friction in a Ligand-Protein Complex.

The effect of an externally applied directional force on molecular friction is so far poorly understood. Here, we study the force-driven dissociation of the ligand-protein complex biotin-streptavidin and identify anisotropic friction as a not yet described type of molecular friction. Using AFM-based stereographic single molecule force spectroscopy and targeted molecular dynamics simulations, we find that the rupture force and friction for biotin-streptavidin vary with the pulling angle. This observation holds true for friction extracted from Kramers' rate expression and by dissipation-corrected targeted molecular dynamics simulations based on Jarzynski's identity. We rule out ligand solvation and protein-internal friction as sources of the angle-dependent friction. Instead, we observe a heterogeneity in free energy barriers along an experimentally uncontrolled orientation parameter, which increases the rupture force variance and therefore the overall friction. We anticipate that anisotropic friction needs to be accounted for in a complete understanding of friction in biomolecular dynamics and anisotropic mechanical environments.

Nonequilibrium Modeling of the Elementary Step in PDZ3 Allosteric Communication.

While allostery is of paramount importance for protein signaling and regulation, the underlying dynamical process of allosteric communication is not well understood. The PDZ3 domain represents a prime example of an allosteric single-domain protein, as it features a well-established long-range coupling between the C-terminal α3-helix and ligand binding. In an intriguing experiment, Hamm and co-workers employed photoswitching of the α3-helix to initiate a conformational change of PDZ3 that propagates from the C-terminus to the bound ligand within 200 ns. Performing extensive nonequilibrium molecular dynamics simulations, the modeling of the experiment reproduces the measured time scales and reveals a detailed picture of the allosteric communication in PDZ3. In particular, a correlation analysis identifies a network of contacts connecting the α3-helix and the core of the protein, which move in a concerted manner. Representing a one-step process and involving direct α3-ligand contacts, this cooperative transition is considered as the elementary step in the propagation of conformational change.

Energy Transport and Its Function in Heptahelical Transmembrane Proteins.

Photoproteins such as bacteriorhodopsin (bR) and rhodopsin (Rho) need to effectively dissipate photoinduced excess energy to prevent themselves from damage. Another well-studied seven transmembrane (TM) helices protein is the ß2 adrenergic receptor (ß2AR), a G protein-coupled receptor for which energy dissipation paths have been linked with allosteric communication. To study the vibrational energy transport in the active and inactive states of these proteins, a master equation approach [J. Chem. Phys.2020, 152, 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure. Despite their overall structural similarity, the three 7TM proteins reveal quite different strategies to redistribute excess energy. While bR quickly removes the energy using the TM7 helix as a "lightning rod", Rho exhibits a rather poor energy dissipation, which might eventually require the hydrolysis of the Schiff base between the protein and the retinal chromophore to prevent overheating. Heating the ligand adrenaline of ß2AR, the resulting energy transport network of the protein is found to change significantly upon switching from the active state to the inactive state. While the energy flow may highlight aspects of the inter-residue couplings of ß2AR, it seems not particularly suited to explain allosteric phenomena.

Ligand Unbinding Pathway and Mechanism Analysis Assisted by Machine Learning and Graph Methods.

We present two methods to reveal protein-ligand unbinding mechanisms in biased unbinding simulations by clustering trajectories into ensembles representing unbinding paths. The first approach is based on a contact principal component analysis for reducing the dimensionality of the input data, followed by identification of unbinding paths and training a machine learning model for trajectory clustering. The second approach clusters trajectories according to their pairwise mean Euclidean distance employing the neighbor-net algorithm, which takes into account input data bias in the distances set and is superior to dendrogram construction. Finally, we describe a more complex case where the reaction coordinate relevant for path identification is a single intraligand hydrogen bond, highlighting the challenges involved in unbinding path reaction coordinate detection.

Cooperative Protein Allosteric Transition Mediated by a Fluctuating Transmission Network.

Allosteric communication between distant protein sites represents a key mechanism of biomolecular regulation and signal transduction. Compared to other processes such as protein folding, however, the dynamical evolution of allosteric transitions is still not well understood. As an example of allosteric coupling between distant protein regions, we consider the global open-closed motion of the two domains of T4 lysozyme, which is triggered by local motion in the hinge region. Combining extensive molecular dynamics simulations with a correlation analysis of interresidue contacts, we identify a network of interresidue distances that move in a concerted manner. The cooperative process originates from a cogwheel-like motion of the hydrophobic core in the hinge region, which constitutes an evolutionary conserved and flexible transmission network. Through rigid contacts and the protein backbone, the small local changes of the hydrophobic core are passed on to the distant terminal domains and lead to the emergence of a rare global conformational transition. As in an Ising-type model, the cooperativity of the allosteric transition can be explained via the interaction of local fluctuations.

Molecular Origin of Driving-Dependent Friction in Fluids.

The friction coefficient of fluids may become a function of the velocity at increased external driving. This non-Newtonian behavior is of general theoretical interest and of great practical importance, for example, for the design of lubricants. Although the effect has been observed in large-scale atomistic simulations of bulk liquids, its theoretical formulation and microscopic origin are not well understood. Here, we use dissipation-corrected targeted molecular dynamics, which pulls apart two tagged liquid molecules in the presence of surrounding molecules, and analyze this nonequilibrium process via a generalized Langevin equation. The approach is based on a second-order cumulant expansion of Jarzynski's identity, which is shown to be valid for fluids and therefore allows for an exact computation of the friction profile as well of the underlying memory kernel. We show that velocity-dependent friction in fluids results from an intricate interplay of near-order structural effects and the non-Markovian behavior of the friction memory kernel. For complex fluids such as the model lubricant C40H82, the memory kernel exhibits a stretched-exponential long-time decay, which reflects the multitude of timescales of the system.

Temporal control of the integrated stress response by a stochastic molecular switch.

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

Predicting Ion Channel Conductance via Dissipation-Corrected Targeted Molecular Dynamics and Langevin Equation Simulations.

Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, here we applied dissipation-corrected targeted molecular dynamics in combination with Langevin equation simulations to potassium diffusion through the gramicidin A channel as a test system. Performing a nonequilibrium principal component analysis on backbone dihedral angles, we find coupled protein-ion dynamics to occur during ion transfer. The dissipation-corrected free energy profiles correspond well to predictions from other biased simulation methods. The incorporation of an external electric field in Langevin simulations enables the prediction of macroscopic observables in the form of I-V characteristics.

finDr: A web server for in silico D-peptide ligand identification.

In the rapidly expanding field of peptide therapeutics, the short in vivo half-life of peptides represents a considerable limitation for drug action. D-peptides, consisting entirely of the dextrorotatory enantiomers of naturally occurring levorotatory amino acids (AAs), do not suffer from these shortcomings as they are intrinsically resistant to proteolytic degradation, resulting in a favourable pharmacokinetic profile. To experimentally identify D-peptide binders to interesting therapeutic targets, so-called mirror-image phage display is typically performed, whereby the target is synthesized in D-form and L-peptide binders are screened as in conventional phage display. This technique is extremely powerful, but it requires the synthesis of the target in D-form, which is challenging for large proteins. Here we present finDr, a novel web server for the computational identification and optimization of D-peptide ligands to any protein structure (https://findr.biologie.uni-freiburg.de/). finDr performs molecular docking to virtually screen a library of helical 12-mer peptides extracted from the RCSB Protein Data Bank (PDB) for their ability to bind to the target. In a separate, heuristic approach to search the chemical space of 12-mer peptides, finDr executes a customizable evolutionary algorithm (EA) for the de novo identification or optimization of D-peptide ligands. As a proof of principle, we demonstrate the validity of our approach to predict optimal binders to the pharmacologically relevant target phenol soluble modulin alpha 3 (PSMα3), a toxin of methicillin-resistant Staphylococcus aureus (MRSA). We validate the predictions using in vitro binding assays, supporting the success of this approach. Compared to conventional methods, finDr provides a low cost and easy-to-use alternative for the identification of D-peptide ligands against protein targets of choice without size limitation. We believe finDr will facilitate D-peptide discovery with implications in biotechnology and biomedicine.

Current approaches to fate mapping and lineage tracing using image data.

Visualizing, tracking and reconstructing cell lineages in developing embryos has been an ongoing effort for well over a century. Recent advances in light microscopy, labelling strategies and computational methods to analyse complex image datasets have enabled detailed investigations into the fates of cells. Combined with powerful new advances in genomics and single-cell transcriptomics, the field of developmental biology is able to describe the formation of the embryo like never before. In this Review, we discuss some of the different strategies and applications to lineage tracing in live-imaging data and outline software methodologies that can be applied to various cell-tracking challenges.

Data-Driven Langevin Modeling of Nonequilibrium Processes.

Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled, nonequilibrium processes can be associated with a biased energy landscape, which accounts for finite sampling effects and external driving. When the data-driven Langevin equation (dLE) approach [Phys. Rev. Lett. 2015, 115, 050602] is extended to the modeling of nonequilibrium processes, an efficient way to calculate multidimensional Langevin fields is outlined. The dLE is shown to correctly account for various nonequilibrium processes, including the enforced dissociation of sodium chloride in water, the pressure-jump induced nucleation of a liquid of hard spheres, and the conformational dynamics of a helical peptide sampled from nonstationary short trajectories.

Hierarchical dynamics in allostery following ATP hydrolysis monitored by single molecule FRET measurements and MD simulations.

We report on a study that combines advanced fluorescence methods with molecular dynamics (MD) simulations to cover timescales from nanoseconds to milliseconds for a large protein. This allows us to delineate how ATP hydrolysis in a protein causes allosteric changes at a distant protein binding site, using the chaperone Hsp90 as test system. The allosteric process occurs via hierarchical dynamics involving timescales from nano- to milliseconds and length scales from Ångstroms to several nanometers. We find that hydrolysis of one ATP is coupled to a conformational change of Arg380, which in turn passes structural information via the large M-domain α-helix to the whole protein. The resulting structural asymmetry in Hsp90 leads to the collapse of a central folding substrate binding site, causing the formation of a novel collapsed state (closed state B) that we characterise structurally. We presume that similar hierarchical mechanisms are fundamental for information transfer induced by ATP hydrolysis through many other proteins.

Through bonds or contacts? Mapping protein vibrational energy transfer using non-canonical amino acids.

Vibrational energy transfer (VET) is essential for protein function. It is responsible for efficient energy dissipation in reaction sites, and has been linked to pathways of allosteric communication. While it is understood that VET occurs via backbone as well as via non-covalent contacts, little is known about the competition of these two transport channels, which determines the VET pathways. To tackle this problem, we equipped the ß-hairpin fold of a tryptophan zipper with pairs of non-canonical amino acids, one serving as a VET injector and one as a VET sensor in a femtosecond pump probe experiment. Accompanying extensive non-equilibrium molecular dynamics simulations combined with a master equation analysis unravel the VET pathways. Our joint experimental/computational endeavor reveals the efficiency of backbone vs. contact transport, showing that even if cutting short backbone stretches of only 3 to 4 amino acids in a protein, hydrogen bonds are the dominant VET pathway.