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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins.

We present a new coarse-grained C-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.

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.

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.

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.

Steered molecular dynamics simulations reveal the role of Ca 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.

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.

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.

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.

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.

Self-assembly of model proteins into virus capsids.

We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions.

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

We study the mechanical response of cellulose and β-amyloid microfibrils to three types of deformation: tensile, indentational, and shear. The cellulose microfibrils correspond to the allomorphs Iα or Iβ whereas the β-amyloid microfibrils correspond to the polymorphs of either two- or three-fold symmetry. This response can be characterized by three elastic moduli, namely, Y, Y, and S.

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.

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.