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.

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.

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.

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.

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.

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.

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.

Structural Changes in Barley Protein LTP1 Isoforms at Air-Water Interfaces.

We use a coarse-grained model to study the conformational changes in two barley proteins, LTP1 and its ligand adduct isoform LTP1b, that result from their adsorption to the air-water interface. The model introduces the interface through hydropathy indices. We justify the model by all-atom simulations. The choice of the proteins is motivated by making attempts to understand formation and stability of foam in beer. We demonstrate that both proteins flatten out at the interface and can make a continuous stabilizing and denser film. We show that the degree of the flattening depends on the protein (the layers of LTP1b should be denser than those of LTP1) and on the presence of glycation. It also depends on the number (≤4) of the disulfide bonds in the proteins. The geometry of the proteins is sensitive to the specificity of the absent bonds. We provide estimates of the volume of cavities of the proteins when away from the interface.

Proteins at air-water and oil-water interfaces in an all-atom model.

We study the behavior of five proteins at the air-water and oil-water interfaces by all-atom molecular dynamics. The proteins are found to get distorted when pinned to the interface. This behavior is consistent with the phenomenological way of introducing the interfaces in a coarse-grained model through a force that depends on the hydropathy indices of the residues. Proteins couple to the oil-water interface stronger than to the air-water one. They diffuse slower at the oil-water interface but do not depin from it, whereas depinning events are observed at the other interface. The reduction of the disulfide bonds slows the diffusion down.

Elastic moduli of biological fibers in a coarse-grained model: crystalline cellulose and ß-amyloids.

We study the mechanical response of cellulose and ß-amyloid microfibrils to three types of deformation: tensile, indentational, and shear. The cellulose microfibrils correspond to the allomorphs Iα or Iß whereas the ß-amyloid microfibrils correspond to the polymorphs of either two- or three-fold symmetry. This response can be characterized by three elastic moduli, namely, YL, YT, and S. We use a structure-based coarse-grained model to analyze the deformations in a unified manner. We find that each of the moduli is almost the same for the two allomorphs of cellulose but YL is about 20 times larger than YT (140 GPa vs. 7 GPa), indicating the existence of significant anisotropy. For cellulose we note that the anisotropy results from the involvement of covalent bonds in stretching. For ß-amyloid, the sense of anisotropy is opposite to that of cellulose. In the three-fold symmetry case, YL is about half of YT (3 vs. 7) whereas for two-fold symmetry the anisotropy is much larger (1.6 vs. 21 GPa). The S modulus is derived to be 1.2 GPa for three-fold symmetry and one half of it for the other symmetry and 3.0 GPa for cellulose. The values of the moduli reflect deformations in the hydrogen-bond network. Unlike in our theoretical approach, no experiment can measure all three elastic moduli with the same apparatus. However, our theoretical results are consistent with various measured values: typical YL for cellulose Iß ranges from 133 to 155 GPa, YT from 2 to 25 GPa, and S from 1.8 to 3.8 GPa. For ß-amyloid, the experimental values of S and YT are about 0.3 GPa and 3.3 GPa respectively, while the value of YL has not been reported.

The length but not the sequence of peptide linker modules exerts the primary influence on the conformations of protein domains in cellulosome multi-enzyme complexes.

Cellulosomes are large multi-protein catalysts produced by various anaerobic microorganisms to efficiently degrade plant cell-wall polysaccharides down into simple sugars. X-ray and physicochemical structural characterisations show that cellulosomes are composed of numerous protein domains that are connected by unstructured polypeptide segments, yet the properties and possible roles of these 'linker' peptides are largely unknown. We have performed coarse-grained and all-atom molecular dynamics computer simulations of a number of cellulosomal linkers of different lengths and compositions. Our data demonstrates that the effective stiffness of the linker peptides, as quantified by the equilibrium fluctuations in the end-to-end distances, depends primarily on the length of the linker and less so on the specific amino acid sequence. The presence of excluded volume - provided by the domains that are connected - dampens the motion of the linker residues and reduces the effective stiffness of the linkers. Simultaneously, the presence of the linkers alters the conformations of the protein domains that are connected. We demonstrate that short, stiff linkers induce significant rearrangements in the folded domains of the mini-cellulosome composed of endoglucanase Cel8A in complex with scaffoldin ScafT (Cel8A-ScafT) of Clostridium thermocellum as well as in a two-cohesin system derived from the scaffoldin ScaB of Acetivibrio cellulolyticus. We give experimentally testable predictions on structural changes in protein domains that depend on the length of linkers.

Structural entanglements in protein complexes.

We consider multi-chain protein native structures and propose a criterion that determines whether two chains in the system are entangled or not. The criterion is based on the behavior observed by pulling at both termini of each chain simultaneously in the two chains. We have identified about 900 entangled systems in the Protein Data Bank and provided a more detailed analysis for several of them. We argue that entanglement enhances the thermodynamic stability of the system but it may have other functions: burying the hydrophobic residues at the interface and increasing the DNA or RNA binding area. We also study the folding and stretching properties of the knotted dimeric proteins MJ0366, YibK, and bacteriophytochrome. These proteins have been studied theoretically in their monomeric versions so far. The dimers are seen to separate on stretching through the tensile mechanism and the characteristic unraveling force depends on the pulling direction.

Non-local effects of point mutations on the stability of a protein module.

We combine experimental and theoretical methods to assess the effect of a set of point mutations on c7A, a highly mechanostable type I cohesin module from scaffoldin CipA from Clostridium thermocellum. We propose a novel robust and computationally expedient theoretical method to determine the effects of point mutations on protein structure and stability. We use all-atom simulations to predict structural shifts with respect to the native protein and then analyze the mutants using a coarse-grained model. We examine transitions in contacts between residues and find that changes in the contact map usually involve a non-local component that can extend up to 50 Å. We have identified mutations that may lead to a substantial increase in mechanical and thermodynamic stabilities by making systematic substitutions into alanine and phenylalanine in c7A. Experimental measurements of the mechanical stability and circular dichroism data agree qualitatively with the predictions provided the thermal stability is calculated using only the contacts within the secondary structures.

The volume of cavities in proteins and virus capsids.

An improved algorithm for the calculation of the volume of internal cavities within protein structures and virus capsids as well as the volumes occupied by single amino acid residues were presented. The geometrical approach was based on atomic van der Waals radii. The results obtained with two sets of the radii, those proposed by Pauling and those determined by Tsai et al were compared. The main improvement compared with our previous approach is a more elaborate treatment of the regions at the very boundary of the cavities, which yields a more accurate volume estimate. The cavity volume of a number of Plant Pathogenesis-Related proteins of class 10 (PR-10) were reevaluated and the volumes and other geometrical parameters for about 400 capsids of icosahedral viruses were reported. Using the same approach the volumes of amino acid residues in polypeptides as mean values averaged over multiple conformations of the side chain were also estimated. Proteins 2016; 84:1275-1286. © 2016 Wiley Periodicals, Inc.

Structural fluctuations and thermal stability of proteins in crowded environments: effects of the excluded volume.

We perform molecular dynamics simulations for a simple coarse-grained model of a protein placed inside of a softly repulsive sphere of radius R. The protein is surrounded either by a number of same molecules or a number of spherical crowding particles that immitate other biomolecules such as the osmolytes. The two descriptions are shown to lead to distinct results when testing thermal stability as assessed by studying the unfolding times as a function of temperature. We consider three examples of proteins and show that crowding increases the thermal stability provided the inter-protein or protein-crowder interactions are repulsive. On the other hand, an introduction of attraction between the proteins is found to destabilize the proteins. Crowding by repulsive crowder particles is seen to enhance the RMSF in certain exposed regions. The effect grows on decreasing the size of the crowding particles. In the absence of crowding the RMSF anticorrelates with the coordination number related to the residue-residue interaction.

An Exploration of the Universe of Polyglutamine Structures.

Deposits of misfolded proteins in the human brain are associated with the development of many neurodegenerative diseases. Recent studies show that these proteins have common traits even at the monomer level. Among them, a polyglutamine region that is present in huntingtin is known to exhibit a correlation between the length of the chain and the severity as well as the earliness of the onset of Huntington disease. Here, we apply bias exchange molecular dynamics to generate structures of polyglutamine expansions of several lengths and characterize the resulting independent conformations. We compare the properties of these conformations to those of the standard proteins, as well as to other homopolymeric tracts. We find that, similar to the previously studied polyvaline chains, the set of possible transient folds is much broader than the set of known-to-date folds, although the conformations have different structures. We show that the mechanical stability is not related to any simple geometrical characteristics of the structures. We demonstrate that long polyglutamine expansions result in higher mechanical stability than the shorter ones. They also have a longer life span and are substantially more prone to form knotted structures. The knotted region has an average length of 35 residues, similar to the typical threshold for most polyglutamine-related diseases. Similarly, changes in shape and mechanical stability appear once the total length of the peptide exceeds this threshold of 35 glutamine residues. We suggest that knotted conformers may also harm the cellular machinery and thus lead to disease.

Criteria for folding in structure-based models of proteins.

In structure-based models of proteins, one often assumes that folding is accomplished when all contacts are established. This assumption may frequently lead to a conceptual problem that folding takes place in a temperature region of very low thermodynamic stability, especially when the contact map used is too sparse. We consider six different structure-based models and show that allowing for a small, but model-dependent, percentage of the native contacts not being established boosts the folding temperature substantially while affecting the time scales of folding only in a minor way. We also compare other properties of the six models. We show that the choice of the description of the backbone stiffness has a substantial effect on the values of characteristic temperatures that relate both to equilibrium and kinetic properties. Models without any backbone stiffness (like the self-organized polymer) are found to perform similar to those with the stiffness, including in the studies of stretching.

Dual binding mode in cohesin-dockerin complexes as assessed through stretching studies.

A recent experimental study by Jobst et al. of stretching of a wild-type (WT) cohesin-dockerin complex has identified two kinds of the force-displacement patterns, with a single or double-peaked final rupture, which are termed "short" and "long" here. This duality has been interpreted as arising from the existence of two kinds of binding. Here, we analyze the separation of two cohesin-dockerin complexes of C. thermocellum theoretically. We use a coarse-grained structure-based model and the values of the pulling speeds are nearly experimental. In their native states, the two systems differ in the mutual binding orientations of the molecules in the complex. We demonstrate that the WT complex (PDB:1OHZ) unravels along two possible pathways that are qualitatively consistent with the presence of the short and long patterns observed experimentally. On the other hand, the mutated complex (PDB:2CCL) leads only to short trajectories. The short and long stretching pathways also appear in the cohesin-dockerin-Xmodule complex (PDB:4IU3, WT) of R. flavefaciens. Thus the duality in the stretching patterns need not be necessarily due to the duality in binding.

Large conformational fluctuations of the multi-domain xylanase Z of Clostridium thermocellum.

The cellulosome is a multi-enzyme machinery which efficiently degrades plant cell-wall polysaccharides. The multiple domains of the cellulosome complexes are often tethered to one another by intrinsically disordered regions. The properties and functions of these disordered linkers are unknown to a large extent. In this work, we study the conformational variability of one component of the cellulosome - the multi-domain xylanase Z (XynZ) of Clostridium thermocellum. We use a coarse-grained protein model to efficiently simulate conformations of the enzyme. Our simulation results are in excellent agreement with data from small angle X-ray scattering experiments, which validates the simulation outcome. Both in the presence and absence of the cohesin domain, the XynZ enzyme appears to be flexible in the sense that it takes various compact and extended conformations. The physical interactions between the individual domains are rather weak and transient, and the XynZ enzyme is held together mainly by the flexible linkers connecting the domains. The end-to-end distance distributions for the flexible linkers can be rationalized by the excluded volume effect. Taken together, our results provide a detailed picture of the conformational ensemble of the XynZ enzyme in solution.

Statistical radii associated with amino acids to determine the contact map: fixing the structure of a type I cohesin domain in the Clostridium thermocellum cellulosome.

We propose to improve and simplify protein refinement procedures through consideration of which pairs of amino acid residues should form native contacts. We first consider 11 330 proteins from the CATH database to determine statistical distributions of contacts associated with a given type of amino acid. The distributions are set across the distances between the α-C atoms that are in contact. Based on this data, we determine typical radii of effective spheres that can be placed on the α-C atoms in order to reconstruct the distribution of the contact lengths. This is done by checking for overlaps with enlarged van der Waals spheres associated with heavy atoms on other amino acids.The resulting contacts can be used to identify non-native contacts that may arise during the time evolution of structure-based models. Here, the radii are used to guide reconstruction of nine missing side chains in a type I cohesin domain with the Protein Data Bank code 1AOH. We first identify the likely missing contacts and then sculpt the corresponding side chains by standard refinement tools to achieve consistency with the expected contact map. One ambiguity in refinement is resolved by determining all-atom conformational energies.