Allosteric Communication Mediated by Protein Contact Clusters: A Dynamical Model.

Describing the puzzling phenomenon of long-range communication between distant protein sites, allostery is of paramount importance in biomolecular regulation and signal transduction. It is commonly assumed to arise from a conformational rearrangement of the protein, although the underlying dynamical process has remained largely elusive. This study introduces a dynamical model of allosteric communication based on "contact clusters"─localized groups of highly correlated contacts that facilitate interactions between secondary structures.

Accurate estimation of the normalized mutual information of multidimensional data.

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the inter-relation of two stochastic variables X and Y, it fails for multidimensional variables, such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information I(X, Y) does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound (I ∈ [0, ∞)), i.

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.

Log-periodic oscillations as real-time signatures of hierarchical dynamics in proteins.

The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys.

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 , which drives an atomistic system from an initial state into a target state. Employing a cumulant approximation of Jarzynski's identity, the free energy Δ() is calculated from the mean external work and dissipated work of the process. By calculating the friction coefficient Γ() from the dissipated work, in a second step, the equilibrium dynamics of the process can be studied by propagating a Langevin equation.

Toward a Benchmark for Markov State Models: The Folding of HP35.

Adopting a 300 μs long MD trajectory of the folding of villin headpiece (HP35) by D. E. Shaw Research, we recently constructed a Markov state model (MSM) based on inter-residue contacts.

Selecting Features for Markov Modeling: A Case Study on HP35.

Markov state models represent a popular means to interpret molecular dynamics trajectories in terms of memoryless transitions between metastable conformational states. To provide a mechanistic understanding of the considered biomolecular process, these states should reflect structurally distinct conformations and ensure a time scale separation between fast intrastate and slow interstate dynamics. Adopting the folding of villin headpiece (HP35) as a well-established model problem, here we discuss the selection of suitable input coordinates or "features", such as backbone dihedral angles and interresidue distances.

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.

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 β adrenergic receptor (βAR), 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 [, , 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure.

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 α-helix and ligand binding. In an intriguing experiment, Hamm and co-workers employed photoswitching of the α-helix to initiate a conformational change of PDZ3 that propagates from the C-terminus to the bound ligand within 200 ns.

Correlation-Based Feature Selection to Identify Functional Dynamics in Proteins.

To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component analysis (TICA), which aim to maximize the variance and the time scale of the first components, respectively. A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances.

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.

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.

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 [.

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 hierarchical dynamics involving timescales from nano- to milliseconds and length scales from Ångstroms to several nanometers.

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.

Modeling non-Markovian data using Markov state and Langevin models.

Markov processes provide a popular approach to construct low-dimensional dynamical models of a complex biomolecular system. By partitioning the conformational space into metastable states, protein dynamics can be approximated in terms of memory-less jumps between these states, resulting in a Markov state model (MSM). Alternatively, suitable low-dimensional collective variables may be identified to construct a data-driven Langevin equation (dLE).

MSMPathfinder: Identification of Pathways in Markov State Models.

Markov state models represent a popular means to interpret biomolecular processes in terms of memoryless transitions between metastable conformational states. To gain insight into the underlying mechanism, it is instructive to determine all relevant pathways between initial and final states of the process. Currently available methods, such as Markov chain Monte Carlo and transition path theory, are convenient for identifying the most frequented pathways.

Real-time observation of ligand-induced allosteric transitions in a PDZ domain.

While allostery is of paramount importance for protein regulation, the underlying dynamical process of ligand (un)binding at one site, resulting time evolution of the protein structure, and change of the binding affinity at a remote site are not well understood. Here the ligand-induced conformational transition in a widely studied model system of allostery, the PDZ2 domain, is investigated by transient infrared spectroscopy accompanied by molecular dynamics simulations. To this end, an azobenzene-derived photoswitch is linked to a peptide ligand in a way that its binding affinity to the PDZ2 domain changes upon switching, thus initiating an allosteric transition in the PDZ2 domain protein.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation.

Multisecond ligand dissociation dynamics from atomistic simulations.

Coarse-graining of fully atomistic molecular dynamics simulations is a long-standing goal in order to allow the description of processes occurring on biologically relevant timescales. For example, the prediction of pathways, rates and rate-limiting steps in protein-ligand unbinding is crucial for modern drug discovery. To achieve the enhanced sampling, we perform dissipation-corrected targeted molecular dynamics simulations, which yield free energy and friction profiles of molecular processes under consideration.

Master equation model to predict energy transport pathways in proteins.

Recent time-resolved experiments and accompanying molecular dynamics simulations allow us to monitor the flow of vibrational energy in biomolecules. As a simple means to describe these experimental and simulated data, Buchenberg et al. [J.

Energy Transport Pathways in Proteins: A Non-equilibrium Molecular Dynamics Simulation Study.

To facilitate the observation of biomolecular energy transport in real time and with single-residue resolution, recent experiments by Baumann et al. ( 2019 , 58 , 2899 , DOI: 10.1002/anie.

Photocontrolling Protein-Peptide Interactions: From Minimal Perturbation to Complete Unbinding.

An azobenzene-derived photoswitch has been covalently cross-linked to two sites of the S-peptide in the RNase S complex in a manner that the α-helical content of the S-peptide reduces upon -to- isomerization of the photoswitch. Three complementary experimental techniques have been employed, isothermal titration calorimetry, circular dichroism spectroscopy and intrinsic tyrosine fluorescence quenching, to determine the binding affinity of the S-peptide to the S-protein in the two states of the photoswitch. Five mutants with the photoswitch attached to different sites of the S-peptide have been explored, with the goal to maximize the change in binding affinity upon photoswitching, and to identify the mechanisms that determine the binding affinity.