Treatment of flexibility of protein backbone in simulations of protein-ligand interactions using steered molecular dynamics.

To ensure that an external force can break the interaction between a protein and a ligand, the steered molecular dynamics simulation requires a harmonic restrained potential applied to the protein backbone. A usual practice is that all or a certain number of protein's heavy atoms or Cα atoms are fixed, being restrained by a small force. This present study reveals that while fixing both either all heavy atoms and or all Cα atoms is not a good approach, while fixing a too small number of few atoms sometimes cannot prevent the protein from rotating under the influence of the bulk water layer, and the pulled molecule may smack into the wall of the active site. We found that restraining the Cα atoms under certain conditions is more relevant. Thus, we would propose an alternative solution in which only the Cα atoms of the protein at a distance larger than 1.2 nm from the ligand are restrained. A more flexible, but not too flexible, protein will be expected to lead to a more natural release of the ligand.

Rhizobium etli has two L-asparaginases with low sequence identity but similar structure and catalytic center.

The genome of Rhizobium etli, a nitrogen-fixing bacterial symbiont of legume plants, encodes two L-asparaginases, ReAIV and ReAV, that have no similarity to the well characterized enzymes of class 1 (bacterial type) and class 2 (plant type). It has been hypothesized that ReAIV and ReAV might belong to the same structural class 3 despite their low level of sequence identity. When the crystal structure of the inducible and thermolabile protein ReAV was solved, this hypothesis gained a stronger footing because the key residues of ReAV are also present in the sequence of the constitutive and thermostable ReAIV protein. High-resolution crystal structures of ReAIV now confirm that it is a class 3 L-asparaginase that is structurally similar to ReAV but with important differences. The most striking differences concern the peculiar hydration patterns of the two proteins, the presence of three internal cavities in ReAIV and the behavior of the zinc-binding site. ReAIV has a high pH optimum (9-11) and a substrate affinity of ∼1.3 mM at pH 9.0. These parameters are not suitable for the direct application of ReAIV as an antileukemic drug, although its thermal stability and lack of glutaminase activity would be of considerable advantage. The five crystal structures of ReAIV presented in this work allow a possible enzymatic scenario to be postulated in which the zinc ion coordinated in the active site is a dispensable element. The catalytic nucleophile seems to be Ser47, which is part of two Ser-Lys tandems in the active site. The structures of ReAIV presented here may provide a basis for future enzyme-engineering experiments to improve the kinetic parameters for medicinal applications.

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.

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.

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.

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).

Quantitative determination of mechanical stability in the novel coronavirus spike protein.

We report on the novel observation about the gain in nanomechanical stability of the SARS-CoV-2 (CoV2) spike (S) protein in comparison with SARS-CoV from 2002 (CoV1). Our findings have several biological implications in the subfamily of coronaviruses, as they suggest that the receptor binding domain (RBD) (∼200 amino acids) plays a fundamental role as a damping element of the massive viral particle's motion prior to cell-recognition, while also facilitating viral attachment, fusion and entry. The mechanical stability via pulling of the RBD is 250 pN and 200 pN for CoV2 and CoV1 respectively, and the additional stability observed for CoV2 (∼50 pN) might play a role in the increasing spread of COVID-19.

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.

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 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.

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.

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.

Topological transformations in proteins: effects of heating and proximity of an interface.

Using a structure-based coarse-grained model of proteins, we study the mechanism of unfolding of knotted proteins through heating. We find that the dominant mechanisms of unfolding depend on the temperature applied and are generally distinct from those identified for folding at its optimal temperature. In particular, for shallowly knotted proteins, folding usually involves formation of two loops whereas unfolding through high-temperature heating is dominated by untying of single loops. Untying the knots is found to generally precede unfolding unless the protein is deeply knotted and the heating temperature exceeds a threshold value. We then use a phenomenological model of the air-water interface to show that such an interface can untie shallow knots, but it can also make knots in proteins that are natively unknotted.

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.

Multiple folding pathways of proteins with shallow knots and co-translational folding.

We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.

Polysaccharide-Protein Complexes in a Coarse-Grained Model.

We construct two variants of coarse-grained models of three hexaoses: one based on the centers of mass of the monomers and the other associated with the C4 atoms. The latter is found to be better defined and more suitable for studying interactions with proteins described within α-C based models. We determine the corresponding effective stiffness constants through all-atom simulations and two statistical methods. One method is the Boltzmann inversion (BI) and the other, named energy-based (EB), involves direct monitoring of energies as a function of the variables that define the stiffness potentials. The two methods are generally consistent in their account of the stiffness. We find that the elastic constants differ between the hexaoses and are noticeably different from those determined for the crystalline cellulose Iß. The nonbonded couplings through hydrogen bonds between different sugar molecules are modeled by the Lennard-Jones potentials and are found to be stronger than the hydrogen bonds in proteins. We observe that the EB method agrees with other theoretical and experimental determinations of the nonbonded parameters much better than BI. We then consider the hexaose-Man5B catalytic complexes and determine the contact energies between their the C4-α-C atoms. These interactions are found to be stronger than the proteinic hydrogen bonds: about four times as strong for cellohexaose and two times for mannohexaose. The fluctuational dynamics of the coarse-grained complexes are found to be compatible with previous all-atom studies by Bernardi et al.

Cotranslational folding of deeply knotted proteins.

Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot.

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.

Structure-based analysis of thermodynamic and mechanical properties of cavity-containing proteins--case study of plant pathogenesis-related proteins of class 10.

We provide theoretical comparisons of the physical properties of eighteen proteins with the pathogenesis-related proteins of class 10 (PR-10) fold, which is characterized by a large hydrophobic cavity enclosed between a curved ß-sheet and a variable α-helix. Our novel algorithm to calculate the volume of internal cavities within protein structures is used to demonstrate that, although the sizes of the cavities of the investigated PR-10 proteins vary significantly, their other physical properties, such as thermodynamic and mechanical parameters or parameters related to folding, are very close. The largest variations (in the order of 20%) are predicted for the optimal folding times. We show that, on squeezing, the PR-10 proteins behave differently from typical virus capsids.