Equilibrium simulation of trp-cage in the presence of protein crowders

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.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

GB1 Dimerization in Crowders: A Multiple Resolution Approach

In-cell protein-protein association, which is crucial in enzyme catalysis and polymerization, occurs in an environment that is highly heterogeneous and crowded. The crowder molecules exclude the reactant molecules from occupying certain regions of the cell, resulting in changes in the reaction thermodynamics and kinetics. Recent studies, both experiment and simulations, revealed that the nature of the interaction between crowder and protein species, in particular the soft interactions, plays an important role in crowder induced effects on protein association. To this end, from a simulation perspective, it is important to decipher the level of structural resolution in a protein-crowder model that can faithfully capture the influence of crowding on protein association. Here, we investigate the dimerization of model system GB1 in the presence of lysozyme crowders at two structural resolutions. The lower resolution model assumes both protein and crowder species as spherical beads, similar to the analytical scaled particle theory model, whereas the higher resolution model retains residue specific structural details for protein and crowder species. From the higher resolution model, it is found that GB1 dimer formation is destabilized in the presence of lysozyme crowders, and the destabilization is more for the side-by-side dimer compared to the domain-swapped dimer, in qualitative agreement with experimental findings. However, the low resolution CG model predicts stabilization of the dimers in the presence of the lysozyme crowder, similar to the SPT model. Our results indicate a nontrivial role of the choice of model resolution in computer simulation studies investigating crowder induced effects.

Crowding revisited: Open questions and future perspectives

Although biophysical studies have traditionally been performed in diluted solutions, it was pointed out in the late 1990s that the cellular milieu contains several other macromolecules, creating a condition of molecular crowding. How crowding affects protein stability is an important question heatedly discussed over the past 20 years. Theoretical estimations have suggested a 5-20°C effect of fold stabilisation. This estimate, however, is at variance with what has been verified experimentally that proposes only a limited increase of stability, opening the question whether some of the assumptions taken for granted should be reconsidered. The present review critically analyses the causes of this discrepancy and discusses the limitations and implications of the current concept of crowding.

On the Effects of Disordered Tails, Supertertiary Structure and Quinary Interactions on the Folding and Function of Protein Domains

The vast majority of our current knowledge about the biochemical and biophysical properties of proteins derives from in vitro studies conducted on isolated globular domains. However, a very large fraction of the proteins expressed in the eukaryotic cell are structurally more complex. In particular, the discovery that up to 40% of the eukaryotic proteins are intrinsically disordered, or possess intrinsically disordered regions, and are highly dynamic entities lacking a well-defined three-dimensional structure, revolutionized the structure–function paradigm and our understanding of proteins. Moreover, proteins are mostly characterized by the presence of multiple domains, influencing each other by intramolecular interactions. Furthermore, proteins exert their function in a crowded intracellular milieu, transiently interacting with a myriad of other macromolecules. In this review we summarize the literature tackling these themes from both the theoretical and experimental perspectives, highlighting the effects on protein folding and function that are played by (i) flanking disordered tails; (ii) contiguous protein domains; (iii) interactions with the cellular environment, defined as quinary structures. We show that, in many cases, both the folding and function of protein domains is remarkably perturbed by the presence of these interactions, pinpointing the importance to increase the level of complexity of the experimental work and to extend the efforts to characterize protein domains in more complex contexts.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Crowding affects structural dynamics and contributes to membrane association of the NS3/4A complex

Using molecular dynamics simulations, we describe how crowded environments affect the internal dynamics and diffusion of the hepatitis C virus proteases NS3/4A. This protease plays a key role in viral replication and is successfully used as a target for antiviral treatment. The NS3 enzyme requires a peptide cofactor, called NS4A, with its central part interacting with the NS3 β-sheet, and flexible, protruding terminal tails that are unstructured in water solution. The simulations describe the enzyme and water molecules at atomistic resolution, whereas crowders are modeled via either all-atom or coarse-grained models to emphasize different aspects of crowding. Crowders reflect the polyethylene glycol (PEG) molecules used in the experiments to mimic the crowded surrounding. A bead-shell model of folded coarse-grained PEG molecules considers mainly the excluded volume effect, whereas all-atom PEG models afford more protein-like crowder interactions. Circular dichroism spectroscopy experiments of the NS4A N-terminal tail show that a helical structure is formed in the presence of PEG crowders. The simulations suggest that crowding may assist in the formation of an NS4A helical fragment, positioned exactly where a transmembrane helix would fold upon the NS4A contact with the membrane. In addition, partially interactive PEGs help the NS4A N-tail to detach from the protease surface, thus enabling the process of helix insertion and potentially helping the virus establish a replication machinery needed to produce new viruses. Results point to an active role of crowding in assisting structural changes in disordered protein fragments that are necessary for their biological function.

Stabilizing or Destabilizing: Simulations of Chymotrypsin Inhibitor 2 under Crowding Reveal Existence of a Crossover Temperature

The effect of macromolecular crowding on the stability of proteins can change with temperature. This dependence might reveal a delicate balance between two factors: the entropic excluded volume and the stability-modulating quinary interactions. Here we computationally investigate the thermal stability of the native state of chymotrypsin inhibitor 2 (CI2), which was previously shown by experiments to be destabilized by protein crowders at room temperature. Mimicking experimental conditions, our enhanced-sampling atomistic simulations of CI2 surrounded by lysozyme and bovine serum albumin reproduce this destabilization but also provide evidence of a crossover temperature above which lysozyme is found to become stabilizing, as previously predicted by analysis of thermodynamic data. We relate this crossover to the different CI2-crowder interactions and the local packing experienced by CI2. In fact, we clearly show that the pronounced stabilization induced by lysozyme at high temperatures stems from the tight local packing created around CI2 by this smaller crowder.

Protein thermal stability

Proteins, in general, fold to a well-organized three-dimensional structure in order to function. The stability of this functional shape can be perturbed by external environmental conditions, such as temperature. Understanding the molecular factors underlying the resistance of proteins to the thermal stress has important consequences. First of all, it can aid the design of thermostable enzymes able to perform efficient catalysis in the high-temperature regime. Second, it is an essential brick of knowledge required to decipher the evolutionary pathways of life adaptation on Earth. Thanks to the development of atomistic simulations and ad hoc enhanced sampling techniques, it is now possible to investigate this problem in silico, and therefore provide support to experiments. After having described the methodological aspects, the chapter proposes an extended discussion on two problems. First, we focus on thermophilic proteins, a perfect model to address the issue of thermal stability and molecular evolution. Second, we discuss the issue of how protein thermal stability is affected by crowded in vivo-like conditions.

Modeling Crowded Environment in Molecular Simulations

Biomolecules perform their various functions in living cells, namely in an environment that is crowded by many macromolecules. Thus, simulating the dynamics and interactions of biomolecules should take into account not only water and ions but also other binding partners, metabolites, lipids and macromolecules found in cells. In the last decade, research on how to model macromolecular crowders around proteins in order to simulate their dynamics in models of cellular environments has gained a lot of attention. In this mini-review we focus on the models of crowding agents that have been used in computer modeling studies of proteins and peptides, especially via molecular dynamics simulations.

Stability and Local Unfolding of SOD1 in the Presence of Protein Crowders

Using NMR and Monte Carlo (MC) methods, we investigate the stability and dynamics of superoxide dismutase 1 (SOD1) in homogeneous crowding environments, where either bovine pancreatic trypsin inhibitor (BPTI) or the B1 domain of streptococcal protein G (PGB1) serves as a crowding agent. By NMR, we show that both crowders, and especially BPTI, cause a drastic loss in the overall stability of SOD1 in its apo monomeric form. Additionally, we determine chemical shift perturbations indicating that SOD1 interacts with the crowder proteins in a residue-specific manner that further depends on the identity of the crowding protein. Furthermore, the specificity of SOD1-crowder interactions is reciprocal: chemical shift perturbations on BPTI and PGB1 identify regions that interact preferentially with SOD1. By MC simulations, we investigate the local unfolding of SOD1 in the absence and presence of the crowders. We find that the crowders primarily interact with the long flexible loops of the folded SOD1 monomer. The basic mechanisms by which the SOD1 β-barrel core unfolds remain unchanged when adding the crowders. In particular, both with and without the crowders, the second β-sheet of the barrel is more dynamic and unfolding-prone than the first. Notably, the MC simulations (exploring the early stages of SOD1 unfolding) and the NMR experiments (under equilibrium conditions) identify largely the same set of PGB1 and BPTI residues as prone to form SOD1 contacts. Thus, contacts stabilizing the unfolded state of SOD1 in many cases appear to form early in the unfolding reaction.

Towards capturing cellular complexity: combining encapsulation and macromolecular crowding in a reverse micelle

This paper studies the orientational structure and dynamics of multi-protein systems under confinement and discusses the implications on biological cells.

Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations

Replica-exchange molecular dynamics (REMD) and their variants have been widely used in simulations of the biomolecular structure and dynamics. Replica exchange with solute tempering (REST) is one of the methods where temperature of a pre-defined solute molecule is exchanged between replicas, while solvent temperatures in all the replicas are kept constant. REST greatly reduces the number of replicas compared to the temperature REMD, while replicas at low temperatures are often trapped under their conditions, interfering with the conformational sampling. Here, we introduce a new scheme of REST, referred to as generalized REST (gREST), where the solute region is defined as a part of a molecule or a part of the potential energy terms, such as the dihedral-angle energy term or Lennard-Jones energy term. We applied this new method to folding simulations of a β-hairpin (16 residues) and a Trp-cage (20 residues) in explicit water. The protein dihedral-angle energy term is chosen as the solute region in the simulations. gREST reduces the number of replicas necessary for good random walks in the solute-temperature space and covers a wider conformational space compared to the conventional REST2. Considering the general applicability, gREST should become a promising tool for the simulations of protein folding, conformational dynamics, and an in silico drug design.

Markov modeling of peptide folding in the presence of protein crowders

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

Role of Macromolecular Crowding on the Intracellular Diffusion of DNA Binding Proteins

Recent experiments suggest that cellular crowding facilitates the target search dynamics of proteins on DNA, the mechanism of which is not yet known. By using large scale computer simulations, we show that two competing factors, namely the width of the depletion layer that separates the crowder cloud from the DNA molecule and the degree of protein-crowder crosstalk, act in harmony to affect the target search dynamics of proteins. The impacts vary from nonspecific to specific target search regime. During a nonspecific search, dynamics of a protein is only minimally affected, whereas, a significantly different behaviour is observed when the protein starts forming a specific protein-DNA complex. We also find that the severity of impacts largely depends upon physiological crowder concentration and deviation from it leads to attenuation in the binding kinetics. Based on extensive kinetic study and binding energy landscape analysis, we further present a comprehensive molecular description of the search process that allows us to interpret the experimental findings.

Macromolecular crowding and the importance of proper hydration for the structure and dynamics of protein solutions

Extensive computational studies of ubiquitin crowding with a special focus on protein hydration directly visible in dielectric spectra.

Crowding in Cellular Environments at an Atomistic Level from Computer Simulations

The effects of crowding in biological environments on biomolecular structure, dynamics, and function remain not well understood. Computer simulations of atomistic models of concentrated peptide and protein systems at different levels of complexity are beginning to provide new insights. Crowding, weak interactions with other macromolecules and metabolites, and altered solvent properties within cellular environments appear to remodel the energy landscape of peptides and proteins in significant ways including the possibility of native state destabilization. Crowding is also seen to affect dynamic properties, both conformational dynamics and diffusional properties of macromolecules. Recent simulations that address these questions are reviewed here and discussed in the context of relevant experiments.

Protein States as Symmetry Transitions in the Correlation Matrices

Over the last few years, there has been significant progress in the knowledge on protein folding. However, some aspects of protein folding still need further attention. One of these is the exact relationship between the folded and unfolded states and the differences between them. Whereas the folded state is well known, at least from a structural point of view (just think of the thousands of structures in online databases), the unfolded state is more elusive. Also, these are dynamic states of matter, and this aspect cannot be overlooked. Molecular dynamics-derived correlation matrices are an invaluable source of information on the protein dynamics. Here, bulk eigenvalue spectra of the correlation matrices obtained from the Trp-cage dynamics in the folded and unfolded states have been analyzed. The associated modes represent localized vibrations and are significantly affected by the fine details of the structure and interactions. Therefore, these bulk modes can be used as probes of the protein local dynamics in different states. The results of these analyses show that the correlation matrices describing the folded and unfolded dynamics belong to different symmetry classes. This finding provides new support to the phase-transition models of protein folding.

Protein Aggregation and Molecular Crowding: Perspectives From Multiscale Simulations

Cells are extremely crowded environments, thus the use of diluted salted aqueous solutions containing a single protein is too simplistic to mimic the real situation. Macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, interactions with cognate biomolecules, and pathological aggregation. The latter phenomenon typically leads to the formation of amyloid fibrils that are linked to several lethal neurodegenerative diseases, but that can also play a functional role in certain organisms. The majority of molecular simulations performed before the last few years were conducted in diluted solutions and were restricted both in the timescales and in the system dimensions by the available computational resources. In recent years, several computational solutions were developed to get close to physiological conditions. In this review we summarize the main computational techniques used to tackle the issue of protein aggregation both in a diluted and in a crowded environment.

Protein folding, binding, and droplet formation in cell-like conditions

The many bystander macromolecules in the crowded cellular environments present both steric repulsion and weak attraction to proteins undergoing folding or binding and hence impact the thermodynamic and kinetic properties of these processes. The weak but nonrandom binding with bystander macromolecules may facilitate subcellular localization and biological function. Weak binding also leads to the emergence of a protein-rich droplet phase, which has been implicated in regulating a variety of cellular functions. All these important problems can now be addressed by realistic modeling of intermolecular interactions. Configurational sampling of concentrated protein solutions is an ongoing challenge.

Peptide folding in the presence of interacting protein crowders

Using Monte Carlo methods, we explore and compare the effects of two protein crowders, BPTI and GB1, on the folding thermodynamics of two peptides, the compact helical trp-cage and the β-hairpin-forming GB1m3. The thermally highly stable crowder proteins are modeled using a fixed backbone and rotatable side-chains, whereas the peptides are free to fold and unfold. In the simulations, the crowder proteins tend to distort the trp-cage fold, while having a stabilizing effect on GB1m3. The extent of the effects on a given peptide depends on the crowder type. Due to a sticky patch on its surface, BPTI causes larger changes than GB1 in the melting properties of the peptides. The observed effects on the peptides stem largely from attractive and specific interactions with the crowder surfaces, and differ from those seen in reference simulations with purely steric crowder particles.

Correlation Analysis of Trp-Cage Dynamics in Folded and Unfolded States

A fundamental and still debated problem is how folded structures of proteins are related to their unfolded state. Besides the classical view, in which a large number of conformations characterize the unfolded state while the folded one is dominated by a single structure, recently a reassessment of the denatured state has been suggested. A growing amount of evidence indicates that not only the folded but also the unfolded state is at least partially organized. Here, we try to answer the question of how different protein dynamics is in folded and unfolded states by performing all-atom molecular dynamics simulations on the model protein Trp-cage. Random matrix theory inspired analysis of the correlation matrices has been carried out. The spectra of these correlation matrices show that the low rank modes of Trp-cage dynamics are outside of the limit expected for a random system both in folded and in unfolded conditions. These findings shed light on the nature of the unfolded state of the proteins, suggesting that it is much less random than previously thought.