Contact-Based Analysis of Aggregation of Intrinsically Disordered Proteins.

We review the contact-based description of aggregation of intrinsically disordered proteins in coarse-grained and all-atom models. We consider polyglutamines and polyalanines at various concentrations of the peptides. We also study associations of two chains of α-synuclein and up to 20 chains of a 12-residue-long segment of protein tau. We demonstrate that the total number of two-chain association events (in an aggregate that comprises at least two chains) provides a useful measure of the propensity to aggregate. This measure is consistent, for instance, with the previously reported mass spectroscopy data. The distribution of the number of association events is given essentially by a power law as a function of the duration of these events. The corresponding exponent depends on the protein and the temperature but not on the concentration of the proteins.

Final Remarks.

Aggregation of biomolecules is responsible for a number of neurodegenerative diseases, but it is also behind the formation of membraneless organelles that are vital to life. There are many novel experimental tools to investigate the phenomenon. There is also a rapid progress in its computational studies, as evidenced by the chapters in this volume.

The coexistence region in the Van der Waals fluid and the liquid-liquid phase transitions.

Cellular membraneless organelles are thought to be droplets formed within the two-phase region corresponding to proteinaceous systems endowed with the liquid-liquid transition. However, their metastability requires an additional constraint-they arise in a certain region of density and temperature between the spinodal and binodal lines. Here, we consider the well-studied van der Waals fluid as a test model to work out criteria to determine the location of the spinodal line for situations in which the equation of state is not known. Our molecular dynamics studies indicate that this task can be accomplished by considering the specific heat, the surface tension and characteristics of the molecular clusters, such as the number of component chains and radius of gyration.

Nascent Folding of Proteins Across the Three Domains of Life.

We study the nascent behavior of three model coarse-grained proteins in six rigid all-atom structures representing ribosomes that come from three domains of life. The synthesis of the proteins is implemented as a growth process. The geometry of the exit tunnel is quantified and shown to differ between the domains of life: both in volume and the size of constriction sites. This results in different characteristic times of capture within the tunnel and various probabilities of the escape. One of the proteins studied is the bacterial YibK which is knotted in its native state. A fraction of the trajectories results in knotting and the probability of doing so is largest for the bacterial ribosomes. Relaxing the condition of the rigidness of the ribosomes should result in a better avoidance of trapping and better proper folding.

Viscoelastic properties of wheat gluten in a molecular dynamics study.

Wheat (Triticum spp.) gluten consists mainly of intrinsincally disordered storage proteins (glutenins and gliadins) that can form megadalton-sized networks. These networks are responsible for the unique viscoelastic properties of wheat dough and affect the quality of bread. These properties have not yet been studied by molecular level simulations. Here, we use a newly developed α-C-based coarse-grained model to study ∼ 4000-residue systems. The corresponding time-dependent properties are studied through shear and axial deformations. We measure the response force to the deformation, the number of entanglements and cavities, the mobility of residues, the number of the inter-chain bonds, etc. Glutenins are shown to influence the mechanics of gluten much more than gliadins. Our simulations are consistent with the existing ideas about gluten elasticity and emphasize the role of entanglements and hydrogen bonding. We also demonstrate that the storage proteins in maize and rice lead to weaker elasticity which points to the unique properties of wheat gluten.

Cohesin-dockerin code in cellulosomal dual binding modes and its allosteric regulation by proline isomerization.

Cellulose is the most abundant organic molecule on Earth and represents a renewable and practically everlasting feedstock for the production of biofuels and chemicals. Self-assembled owing to the high-affinity cohesin-dockerin interaction, cellulosomes are huge multi-enzyme complexes with unmatched efficiency in the degradation of recalcitrant lignocellulosic substrates. The recruitment of diverse dockerin-borne enzymes into a multicohesin protein scaffold dictates the three-dimensional layout of the complex, and interestingly two alternative binding modes have been proposed. Using single-molecule fluorescence resonance energy transfer and molecular simulations on a range of cohesin-dockerin pairs, we directly detect varying distributions between these binding modes that follow a built-in cohesin-dockerin code. Surprisingly, we uncover a prolyl isomerase-modulated allosteric control mechanism, mediated by the isomerization state of a single proline residue, which regulates the distribution and kinetics of binding modes. Overall, our data provide a novel mechanistic understanding of the structural plasticity and dynamics of cellulosomes.

Properties of Cavities in Biological Structures-A Survey of the Protein Data Bank.

We performed a PDB-wide survey of proteins to assess their cavity content, using the SPACEBALL algorithm to calculate the cavity volumes. In addition, we determined the hydropathy character of the cavities. We demonstrate that the cavities of most proteins are hydrophilic, but smaller proteins tend to have cavities with hydrophobic walls. We propose criteria for distinguishing between cavities and pockets, and single out proteins with the largest cavities.

Mechanical Unfolding of Proteins-A Comparative Nonequilibrium Molecular Dynamics Study.

Mechanical signals regulate functions of mechanosensitive proteins by inducing structural changes that are determinant for force-dependent interactions. Talin is a focal adhesion protein that is known to extend under mechanical load, and it has been shown to unfold via intermediate states. Here, we compared different nonequilibrium molecular dynamics (MD) simulations to study unfolding of the talin rod. We combined boxed MD (BXD), steered MD, and umbrella sampling (US) techniques and provide free energy profiles for unfolding of talin rod subdomains. We conducted BXD, steered MD, and US simulations at different detail levels and demonstrate how these different techniques can be used to study protein unfolding under tension. Unfolding free energy profiles determined by BXD suggest that the intermediate states in talin rod subdomains are stabilized by force during unfolding, and US confirmed these results.

Transient knots in intrinsically disordered proteins and neurodegeneration.

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

Protein droplets in systems of disordered homopeptides and the amyloid glass phase.

In order to gain insight into the formation of proteinaceous liquid droplets, we study systems of many disordered homopeptide chains within our coarse-grained molecular dynamics model with conformation-dependent terms. We construct the phase diagrams for polyalanine of length 20 and polyglutamines of lengths 20, 40 and 60 based on the stationary-state cluster distribution. The phase diagrams are distinct but correspond to the same topology. We delineate the liquid-gas coexistence curve at around room temperature. We also identify a novel amyloid glass phase that is substantially cross linked forming amorphous and anisotropic spatial patterns. Generally, this phase is found at lower temperatures, but may also appear at room temperature for sufficiently long chains. We demonstrate the existence of fluid-like phenomena, like droplet fusion and fission. However, our available length scales have not yet shown the validity of the continuum physics description.

Proteins at curved fluid-fluid interfaces in a coarse-grained model.

We employ an empirical coarse-grained model with a proposed Gaussian-like interfacial potential to describe proteins at curved fluid-fluid interfaces such as occurring in bubbles and droplets. We consider the air-water and oil-water interfaces. We study the mass distributions and the geometry of the aqueous proteins as a function of the radius of curvature for protein G and two lipid transfer proteins. At curved interfaces the distortion of the proteins is different than at flat interfaces. We find that the proteins come closer to the surface of a bubble than to the surface of similarly curved droplet. In addition, the bubbles adsorb more proteins. We identify the pinning residues. We demonstrate the existence of the second layer in the density profile for sufficiently dense solutions.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins.

We present a new coarse-grained Cα-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Conformational Biases of α-Synuclein and Formation of Transient Knots.

We study local conformational biases in the dynamics of α-synuclein by using all-atom simulations with explicit and implicit solvents. The biases are related to the frequency of the specific contact formation. In both approaches, the protein is intrinsically disordered, and its strongest bias is to make bend and turn local structures. The explicit-solvent conformations can be substantially more extended which allows for formation of transient trefoil knots, both deep and shallow, that may last for up to 5 µs. The two-chain self-association events, both short- and long-lived, are dominated by formation of contacts in the central part of the sequence. This part tends to form helices when bound to a micelle.

Differentiating between Inactive and Active States of Rhodopsin by Atomic Force Microscopy in Native Membranes.

Membrane proteins, including G protein-coupled receptors (GPCRs), present a challenge in studying their structural properties under physiological conditions. Moreover, to better understand the activity of proteins requires examination of single molecule behaviors rather than ensemble averaged behaviors. Force-distance curve-based AFM (FD-AFM) was utilized to directly probe and localize the conformational states of a GPCR within the membrane at nanoscale resolution based on the mechanical properties of the receptor. FD-AFM was applied to rhodopsin, the light receptor and a prototypical GPCR, embedded in native rod outer segment disc membranes from photoreceptor cells of the retina in mice. Both FD-AFM and computational studies on coarse-grained models of rhodopsin revealed that the active state of the receptor has a higher Young's modulus compared to the inactive state of the receptor. Thus, the inactive and active states of rhodopsin could be differentiated based on the stiffness of the receptor. Differentiating the states based on the Young's modulus allowed for the mapping of the different states within the membrane. Quantifying the active states present in the membrane containing the constitutively active G90D rhodopsin mutant or apoprotein opsin revealed that most receptors adopt an active state. Traditionally, constitutive activity of GPCRs has been described in terms of two-state models where the receptor can achieve only a single active state. FD-AFM data are inconsistent with a two-state model but instead require models that incorporate multiple active states.

Steered molecular dynamics simulations reveal the role of Ca2+ in regulating mechanostability of cellulose-binding proteins.

The conversion of cellulosic biomass into biofuels requires degradation of the biomass into fermentable sugars. The most efficient natural cellulase system for carrying out this conversion is an extracellular multi-enzymatic complex named the cellulosome. In addition to temperature and pH stability, mechanical stability is important for functioning of cellulosome domains, and experimental techniques such as Single Molecule Force Spectroscopy (SMFS) have been used to measure the mechanical strength of several cellulosomal proteins. Molecular dynamics computer simulations provide complementary atomic-resolution quantitative maps of domain mechanical stability for identification of experimental leads for protein stabilization. In this study, we used multi-scale steered molecular dynamics computer simulations, benchmarked against new SMFS measurements, to measure the intermolecular contacts that confer high mechanical stability to a family 3 Carbohydrate Binding Module protein (CBM3) derived from the archetypal Clostridium thermocellum cellulosome. Our data predicts that electrostatic interactions in the calcium binding pocket modulate the mechanostability of the cellulose-binding module, which provides an additional design rule for the rational re-engineering of designer cellulosomes for biotechnology. Our data offers new molecular insights into the origins of mechanostability in cellulose binding domains and gives leads for synthesis of more robust cellulose-binding protein modules. On the other hand, simulations predict that insertion of a flexible strand can promote alternative unfolding pathways and dramatically reduce the mechanostability of the carbohydrate binding module, which gives routes to rational design of tailormade fingerprint complexes for force spectroscopy experiments.

Disordered peptide chains in an α-C-based coarse-grained model.

We construct a one-bead-per-residue coarse-grained dynamical model to describe intrinsically disordered proteins at significantly longer timescales than in the all-atom models. In this model, inter-residue contacts form and disappear during the course of the time evolution. The contacts may arise between the sidechains, the backbones or the sidechains and backbones of the interacting residues. The model yields results that are consistent with many all-atom and experimental data on these systems. We demonstrate that the geometrical properties of various homopeptides differ substantially in this model. In particular, the average radius of gyration scales with the sequence length in a residue-dependent manner.

Stability of structurally entangled protein dimers.

We studied stretching, folding and thermodynamic properties of structurally entangled protein dimers. The tests for entanglement involve four-terminal pulling. We study the dynamics of such pulling and contrast it with the standard two-terminal one. The two-chain entanglement is qualitatively characterized by its entangled core, which is defined as the minimal structure that is entangled. The existence of the entangled cores is found to be affecting both the mechanical and folding properties of the proteins. We also show that the folding pathways of the entangled proteins are not universal but the bottleneck is always the formation of the entangled conformation. We demonstrate that entanglement enhances thermodynamic stability.

Dual binding in cohesin-dockerin complexes: the energy landscape and the role of short, terminal segments of the dockerin module.

The assembly of the polysaccharide degradating cellulosome machinery is mediated by tight binding between cohesin and dockerin domains. We have used an empirical model known as FoldX as well as molecular mechanics methods to determine the free energy of binding between a cohesin and a dockerin from Clostridium thermocellum in two possible modes that differ by an approximately 180° rotation. Our studies suggest that the full-length wild-type complex exhibits dual binding at room temperature, i.e., the two modes of binding have comparable probabilities at equilibrium. The ability to bind in the two modes persists at elevated temperatures. However, single-point mutations or truncations of terminal segments in the dockerin result in shifting the equilibrium towards one of the binding modes. Our molecular dynamics simulations of mechanical stretching of the full-length wild-type cohesin-dockerin complex indicate that each mode of binding leads to two kinds of stretching pathways, which may be mistakenly taken as evidence of dual binding.