Physics of proteins

A geometrical framework for thinking about proteins

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.

Reframing the Protein Folding Problem: Entropy as Organizer

It has been a long-standing conviction that a protein's native fold is selected from a vast number of conformers by the optimal constellation of enthalpically favorable interactions. In marked contrast, this Perspective introduces a different mechanism, one that emphasizes conformational entropy as the principal organizer in protein folding while proposing that the conventional view is incomplete. This mechanism stems from the realization that hydrogen bond satisfaction is a thermodynamic necessity. In particular, a backbone hydrogen bond may add little to the stability of the native state, but a completely unsatisfied backbone hydrogen bond would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization, typically between -5 and -15 kcal/mol under physiological conditions. Consequently, upon folding, buried backbone polar groups must form hydrogen bonds, and they do so by assembling scaffolds of α-helices and/or strands of β-sheet, the only conformers in which, with rare exception, hydrogen bond donors and acceptors are exactly balanced. In addition, only a few thousand viable scaffold topologies are possible for a typical protein domain. This thermodynamic imperative winnows the folding population by culling conformers with unsatisfied hydrogen bonds, thereby reducing the entropy cost of folding. Importantly, conformational restrictions imposed by backbone···backbone hydrogen bonding in the scaffold are sequence-independent, enabling mutation─and thus evolution─without sacrificing the structure.

Protein folding - seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of β-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

Atomically Precise Preorganization of Open Metal Sites on Gold Nanoclusters with High Catalytic Performance

Gold nanoclusters with surface open sites are crucial for practical applications in catalysis. We have developed a surface geometric mismatch strategy by using mixed ligands of different type of hindrance. When bulky phosphine Ph₃ P and planar dipyridyl amine (Hdpa) are simultaneously used, steric repulsion between the ligands will reduce the ligand coverage of gold clusters. A well-defined access granted gold nanocluster [Au₂₃ (Ph₃ P)₁₀ (dpa)₂ Cl](SO₃ CF₃ )₂ (Au₂₃ , dpa=dipyridylamido) has been successfully synthesized. Single crystal structural determination reveals that Au₂₃ has eight uncoordinated gold atoms in the shape of a distorted bicapped triangular prism. The accessibility of the exposed Au atoms has been confirmed quantitatively by luminescent titration with 2-naphthalenethiol. This cluster has excellent performance toward selective oxidation of benzyl alcohol to benzaldehyde and demonstrates excellent stability due to the protection of negatively charged multidentate ligand dpa.

Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis

Proteins in cellular environments are highly susceptible. Local perturbations to any residue can be sensed by other spatially distal residues in the protein molecule, showing long-range correlations in the native dynamics of proteins. The long-range correlations of proteins contribute to many biological processes such as allostery, catalysis, and transportation. Revealing the structural origin of such long-range correlations is of great significance in understanding the design principle of biologically functional proteins. In this work, based on a large set of globular proteins determined by X-ray crystallography, by conducting normal mode analysis with the elastic network models, we demonstrate that such long-range correlations are encoded in the native topology of the proteins. To understand how native topology defines the structure and the dynamics of the proteins, we conduct scaling analysis on the size dependence of the slowest vibration mode, average path length, and modularity. Our results quantitatively describe how native proteins balance between order and disorder, showing both dense packing and fractal topology. It is suggested that the balance between stability and flexibility acts as an evolutionary constraint for proteins at different sizes. Overall, our result not only gives a new perspective bridging the protein structure and its dynamics but also reveals a universal principle in the evolution of proteins at all different sizes.

The long-range correlated fluctuations are closely related to many biological processes of the proteins, such as catalysis, ligand binding, biomolecular recognition, and transportation. In this paper, we elucidate the structural origin of the long-range correlation and describe how native contact topology defines the slow-mode dynamics of the native proteins. Our result suggests an evolutionary constraint for proteins at different sizes, which may shed light on solving many biophysical problems such as structure prediction, multi-scale molecular simulations, and the design of molecular machines. Moreover, in statistical physics, as the long-range correlations are notable signs of the critical point, unveiling the origin of such criticality can extend our understanding of the organizing principle of a large variety of complex systems.

Chain stiffness bridges conventional polymer and bio-molecular phases

Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses-one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.

A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model

Coarse-grained (CG) protein models in the structural biology literature have improved over the years from being simple tools to understand general folding and aggregation driving forces to capturing detailed structures achieved by actual folding sequences. Here, we ask whether such models can be developed systematically from recent advances in bottom-up coarse-graining methods without relying on bioinformatic data (e.g., protein data bank statistics). We use relative entropy coarse-graining to develop a hybrid CG but Go¯-like CG peptide model, hypothesizing that the landscape of proteinlike folds is encoded by the backbone interactions, while the sidechain interactions define which of these structures globally minimizes the free energy in a unique native fold. To construct a model capable of capturing varied secondary structures, we use a new extended ensemble relative entropy method to coarse-grain based on multiple reference atomistic simulations of short polypeptides with varied α and β character. Subsequently, we assess the CG model as a putative protein backbone forcefield by combining it with sidechain interactions based on native contacts but not incorporating native distances explicitly, unlike standard Go¯ models. We test the model's ability to fold a range of proteins and find that it achieves high accuracy (∼2 Å root mean square deviation resolution for both short sequences and large globular proteins), suggesting the strong role that backbone conformational preferences play in defining the fold landscape. This model can be systematically extended to non-natural amino acids and nonprotein polymers and sets the stage for extensions to non-Go¯ models with sequence-specific sidechain interactions.

The elixir phase of chain molecules

A phase of matter is a familiar notion for inanimate physical matter. The nature of a phase of matter transcends the microscopic material properties. For example, materials in the liquid phase have certain common properties independent of the chemistry of the constituents: liquids take the shape of the container; they flow; and they can be poured-alcohol, oil, and water as well as a Lennard-Jones computer model exhibit similar behavior when poised in the liquid phase. Here, we identify a hitherto unstudied "phase" of matter, the elixir phase, in a simple model of a polymeric chain whose backbone has the correct local cylindrical symmetry induced by the tangent to the chain. The elixir phase appears on breaking the cylindrical symmetry by adding side spheres along the negative normal direction, as in proteins. This phase, nestled between other phases, has multiple ground states made up of building blocks of helices and almost planar sheets akin to protein native folds. We discuss the similarities of this "phase" of a finite size system to the liquid crystal and spin glass phases. Our findings are relevant for understanding proteins; the creation of novel bioinspired nanomachines; and also may have implications for life elsewhere in the cosmos.

Collapse Transitions of Proteins and the Interplay Among Backbone, Sidechain, and Solvent Interactions

Proteins can collapse into compact globules or form expanded, solvent-accessible, coil-like conformations. Additionally, they can fold into well-defined three-dimensional structures or remain partially or entirely disordered. Recent discoveries have shown that the tendency for proteins to collapse or remain expanded is not intrinsically coupled to their ability to fold. These observations suggest that proteins do not have to form compact globules in aqueous solutions. They can be intrinsically disordered, collapsed, or expanded, and even form well-folded, elongated structures. This ability to decouple collapse from folding is determined by the sequence details of proteins. In this review, we highlight insights gleaned from studies over the past decade. Using a polymer physics framework, we explain how the interplay among sidechains, backbone units, and solvent determines the driving forces for collapsed versus expanded states in aqueous solvents.

Polymers and biopolymers at interfaces

This review updates recent progress in the understanding of the behaviour of polymers at surfaces and interfaces, highlighting examples in the areas of wetting, dewetting, crystallization, and 'smart' materials. Recent developments in analysis tools have yielded a large increase in the study of biological systems, and some of these will also be discussed, focussing on areas where surfaces are important. These areas include molecular binding events and protein adsorption as well as the mapping of the surfaces of cells. Important techniques commonly used for the analysis of surfaces and interfaces are discussed separately to aid the understanding of their application.

Protein folding, misfolding and aggregation: The importance of two-electron stabilizing interactions

Proteins associated with neurodegenerative diseases are highly pleiomorphic and may adopt an all-α-helical fold in one environment, assemble into all-β-sheet or collapse into a coil in another, and rapidly polymerize in yet another one via divergent aggregation pathways that yield broad diversity of aggregates’ morphology. A thorough understanding of this behaviour may be necessary to develop a treatment for Alzheimer’s and related disorders. Unfortunately, our present comprehension of folding and misfolding is limited for want of a physicochemical theory of protein secondary and tertiary structure. Here we demonstrate that electronic configuration and hyperconjugation of the peptide amide bonds ought to be taken into account to advance such a theory. To capture the effect of polarization of peptide linkages on conformational and H-bonding propensity of the polypeptide backbone, we introduce a function of shielding tensors of the C^α atoms. Carrying no information about side chain-side chain interactions, this function nonetheless identifies basic features of the secondary and tertiary structure, establishes sequence correlates of the metamorphic and pH-driven equilibria, relates binding affinities and folding rate constants to secondary structure preferences, and manifests common patterns of backbone density distribution in amyloidogenic regions of Alzheimer’s amyloid β and tau, Parkinson’s α-synuclein and prions. Based on those findings, a split-intein like mechanism of molecular recognition is proposed to underlie dimerization of Aβ, tau, αS and PrP^C, and divergent pathways for subsequent association of dimers are outlined; a related mechanism is proposed to underlie formation of PrP^Sc fibrils. The model does account for: (i) structural features of paranuclei, off-pathway oligomers, non-fibrillar aggregates and fibrils; (ii) effects of incubation conditions, point mutations, isoform lengths, small-molecule assembly modulators and chirality of solid-liquid interface on the rate and morphology of aggregation; (iii) fibril-surface catalysis of secondary nucleation; and (iv) self-propagation of infectious strains of mammalian prions.

Computational protein design: a review

Proteins are one of the most versatile modular assembling systems in nature. Experimentally, more than 110 000 protein structures have been identified and more are deposited every day in the Protein Data Bank. Such an enormous structural variety is to a first approximation controlled by the sequence of amino acids along the peptide chain of each protein. Understanding how the structural and functional properties of the target can be encoded in this sequence is the main objective of protein design. Unfortunately, rational protein design remains one of the major challenges across the disciplines of biology, physics and chemistry. The implications of solving this problem are enormous and branch into materials science, drug design, evolution and even cryptography. For instance, in the field of drug design an effective computational method to design protein-based ligands for biological targets such as viruses, bacteria or tumour cells, could give a significant boost to the development of new therapies with reduced side effects. In materials science, self-assembly is a highly desired property and soon artificial proteins could represent a new class of designable self-assembling materials. The scope of this review is to describe the state of the art in computational protein design methods and give the reader an outline of what developments could be expected in the near future.

Critical Fluctuations in the Native State of Proteins

Based on protein structural ensembles determined by nuclear magnetic resonance, we study the position fluctuations of residues by calculating distance-dependent correlations and conducting finite-size scaling analysis. The fluctuations exhibit high susceptibility and long-range correlations up to the protein sizes. The scaling relations between the correlations or susceptibility and protein sizes resemble those in other physical and biological systems near their critical points. These results indicate that, at the native states, motions of each residue are felt by every other one in the protein. We also find that proteins with larger susceptibility are more frequently observed in nature. Overall, our results suggest that the protein's native state is critical.

Structural characterization of the interaction of α-synuclein nascent chains with the ribosomal surface and trigger factor

The ribosome is increasingly becoming recognized as a key hub for integrating quality control processes associated with protein biosynthesis and cotranslational folding (CTF). The molecular mechanisms by which these processes take place, however, remain largely unknown, in particular in the case of intrinsically disordered proteins (IDPs). To address this question, we studied at a residue-specific level the structure and dynamics of ribosome-nascent chain complexes (RNCs) of α-synuclein (αSyn), an IDP associated with Parkinson's disease (PD). Using solution-state nuclear magnetic resonance (NMR) spectroscopy and coarse-grained molecular dynamics (MD) simulations, we find that, although the nascent chain (NC) has a highly disordered conformation, its N-terminal region shows resonance broadening consistent with interactions involving specific regions of the ribosome surface. We also investigated the effects of the ribosome-associated molecular chaperone trigger factor (TF) on αSyn structure and dynamics using resonance broadening to define a footprint of the TF-RNC interactions. We have used these data to construct structural models that suggest specific ways by which emerging NCs can interact with the biosynthesis and quality control machinery.

Mapping the Protein Fold Universe Using the CamTube Force Field in Molecular Dynamics Simulations

It has been recently shown that the coarse-graining of the structures of polypeptide chains as self-avoiding tubes can provide an effective representation of the conformational space of proteins. In order to fully exploit the opportunities offered by such a ‘tube model’ approach, we present here a strategy to combine it with molecular dynamics simulations. This strategy is based on the incorporation of the ‘CamTube’ force field into the Gromacs molecular dynamics package. By considering the case of a 60-residue polyvaline chain, we show that CamTube molecular dynamics simulations can comprehensively explore the conformational space of proteins. We obtain this result by a 20 μs metadynamics simulation of the polyvaline chain that recapitulates the currently known protein fold universe. We further show that, if residue-specific interaction potentials are added to the CamTube force field, it is possible to fold a protein into a topology close to that of its native state. These results illustrate how the CamTube force field can be used to explore efficiently the universe of protein folds with good accuracy and very limited computational cost.

Modelling protein behaviour using computer simulations has progressively emerged in the last 50 years as a powerful strategy in structural and molecular biology. Over this period there has been a continuing interest in pushing the boundaries of this approach in terms of the size of the systems and the timescale of the processes that can be studied. Coarse-grained models offer in principle great opportunities in this context, but it has been extremely challenging to obtain force fields of accuracy comparable to that typical of fully atomistic models. We show here that the representation of protein molecules as self-avoiding tubes within the CamTube model enables the comprehensive, accurate and very fast exploration of the conformational space of proteins in molecular dynamics simulations. We illustrate in particular how the comprehensive mapping of the protein fold universe obtained using the CamTube model offers the possibility of analysing the behaviour of proteins in a wide range of non-native states.

Flexible xxx-asp/asn and gly-xxx residues of equine cytochrome C in matrix-assisted laser desorption/ionization in-source decay mass spectrometry

The backbone flexibility of a protein has been studied from the standpoint of the susceptibility of amino acid residues to in-source decay (ISD) in matrix-assisted laser desorption/ionization mass spectrometry (MALDI MS). Residues more susceptible to MALDI-ISD, namely Xxx-Asp/Asn and Gly-Xxx, were identified from the discontinuous intense peak of c'-ions originating from specific cleavage at N-Cα bonds of the backbone of equine cytochrome c. The identity of the residues susceptible to ISD was consistent with the known flexible backbone amides as estimated by hydrogen/deuterium exchange (HDX) experiments. The identity of these flexible amino acid residues (Asp, Asn, and Gly) is consistent with the fact that these residues are preferred in flexible secondary structure free from intramolecular hydrogen-bonded structures such as α-helix and β-sheet. The MALDI-ISD spectrum of equine cytochrome c gave not only intense N-terminal side c'-ions originating from N-Cα bond cleavage at Xxx-Asp/Asn and Gly-Xxx residues, but also C-terminal side complement z'-ions originating from the same cleavage sites. The present study implies that MALDI-ISD can give information about backbone flexibility of proteins, comparable with the protection factors estimated by HDX.

The phylogenomic roots of modern biochemistry: origins of proteins, cofactors and protein biosynthesis

The complexity of modern biochemistry developed gradually on early Earth as new molecules and structures populated the emerging cellular systems. Here, we generate a historical account of the gradual discovery of primordial proteins, cofactors, and molecular functions using phylogenomic information in the sequence of 420 genomes. We focus on structural and functional annotations of the 54 most ancient protein domains. We show how primordial functions are linked to folded structures and how their interaction with cofactors expanded the functional repertoire. We also reveal protocell membranes played a crucial role in early protein evolution and show translation started with RNA and thioester cofactor-mediated aminoacylation. Our findings allow elaboration of an evolutionary model of early biochemistry that is firmly grounded in phylogenomic information and biochemical, biophysical, and structural knowledge. The model describes how primordial α-helical bundles stabilized membranes, how these were decorated by layered arrangements of β-sheets and α-helices, and how these arrangements became globular. Ancient forms of aminoacyl-tRNA synthetase (aaRS) catalytic domains and ancient non-ribosomal protein synthetase (NRPS) modules gave rise to primordial protein synthesis and the ability to generate a code for specificity in their active sites. These structures diversified producing cofactor-binding molecular switches and barrel structures. Accretion of domains and molecules gave rise to modern aaRSs, NRPS, and ribosomal ensembles, first organized around novel emerging cofactors (tRNA and carrier proteins) and then more complex cofactor structures (rRNA). The model explains how the generation of protein structures acted as scaffold for nucleic acids and resulted in crystallization of modern translation.

The native conformation of plasmepsin II is kinetically trapped at neutral pH

Plasmepsin II (PMII), an aspartic protease from the malarial parasite Plasmodium falciparum, represents a model for understanding protease structure/function relationships due to its unique structure and properties. The present study undertook a thermodynamic and kinetic analysis of the PMII folding mechanism and a pH stability profile. Differential scanning calorimetry revealed that the native state of PMII (Np) was irreversibly unfolded, and in the pH range of 6.5-8.0, PMII refolds to a denatured state (Rp) with higher thermal stability than Np. Rp could also be formed upon partially unfolding PMII at pH 11.0 and 37 °C for 2h, followed by adjustment to a pH in the range of 6.5-8.0. While Rp could be folded/unfolded reversibly, Np was shown to exist as a kinetically trapped state. By examining the unfolding kinetics of Np and the kinetics of Rp folding to Np at 25 °C, it was found that Np is kinetically trapped by an unfolding barrier of 25.5 kcal/mol, and yet once unfolded, is prevented from folding by a comparable folding barrier. The folding mechanism of PMII is similar to that reported for pepsin. It is hypothesized that the PMII zymogen also utilizes a prosegment-catalyzed folding mechanism.

Monte Carlo simulations of the HP model (the "Ising model" of protein folding)

Using Wang-Landau sampling with suitable Monte Carlo trial moves (pull moves and bond-rebridging moves combined) we have determined the density of states and thermodynamic properties for a short sequence of the HP protein model. For free chains these proteins are known to first undergo a collapse "transition" to a globule state followed by a second "transition" into a native state. When placed in the proximity of an attractive surface, there is a competition between surface adsorption and folding that leads to an intriguing sequence of "transitions". These transitions depend upon the relative interaction strengths and are largely inaccessible to "standard" Monte Carlo methods.

Cholera- and anthrax-like toxins are among several new ADP-ribosyltransferases

Chelt, a cholera-like toxin from Vibrio cholerae, and Certhrax, an anthrax-like toxin from Bacillus cereus, are among six new bacterial protein toxins we identified and characterized using in silico and cell-based techniques. We also uncovered medically relevant toxins from Mycobacterium avium and Enterococcus faecalis. We found agriculturally relevant toxins in Photorhabdus luminescens and Vibrio splendidus. These toxins belong to the ADP-ribosyltransferase family that has conserved structure despite low sequence identity. Therefore, our search for new toxins combined fold recognition with rules for filtering sequences--including a primary sequence pattern--to reduce reliance on sequence identity and identify toxins using structure. We used computers to build models and analyzed each new toxin to understand features including: structure, secretion, cell entry, activation, NAD+ substrate binding, intracellular target binding and the reaction mechanism. We confirmed activity using a yeast growth test. In this era where an expanding protein structure library complements abundant protein sequence data--and we need high-throughput validation--our approach provides insight into the newest toxin ADP-ribosyltransferases.

Exploring the universe of protein structures beyond the Protein Data Bank

It is currently believed that the atlas of existing protein structures is faithfully represented in the Protein Data Bank. However, whether this atlas covers the full universe of all possible protein structures is still a highly debated issue. By using a sophisticated numerical approach, we performed an exhaustive exploration of the conformational space of a 60 amino acid polypeptide chain described with an accurate all-atom interaction potential. We generated a database of around 30,000 compact folds with at least of secondary structure corresponding to local minima of the potential energy. This ensemble plausibly represents the universe of protein folds of similar length; indeed, all the known folds are represented in the set with good accuracy. However, we discover that the known folds form a rather small subset, which cannot be reproduced by choosing random structures in the database. Rather, natural and possible folds differ by the contact order, on average significantly smaller in the former. This suggests the presence of an evolutionary bias, possibly related to kinetic accessibility, towards structures with shorter loops between contacting residues. Beside their conceptual relevance, the new structures open a range of practical applications such as the development of accurate structure prediction strategies, the optimization of force fields, and the identification and design of novel folds.

Amino acid interaction preferences in proteins

Understanding the key factors that influence the interaction preferences of amino acids in the folding of proteins have remained a challenge. Here we present a knowledge-based approach for determining the effective interactions between amino acids based on amino acid type, their secondary structure, and the contact based environment that they find themselves in the native state structure as measured by their number of neighbors. We find that the optimal information is approximately encoded in a 60 x 60 matrix describing the 20 types of amino acids in three distinct secondary structures (helix, beta strand, and loop). We carry out a clustering scheme to understand the similarity between these interactions and to elucidate a nonredundant set. We demonstrate that the inferred energy parameters can be used for assessing the fit of a given sequence into a putative native state structure.

The role of secondary structure in protein structure selection

The presence of highly regular secondary structure motifs in protein structure is a fascinating area of study. The secondary structures play important roles in protein structure and protein folding. We investigate the folding properties of protein by introducing the effect of secondary structure elements. We observed the emergence of several structures with both large average energy gap and high designability. The dynamic study indicates that these structures are more foldable than those without the effect of secondary structures.

Protein structures, folds and fold spaces

There has been considerable progress towards the goal of understanding the space of possible tertiary structures adopted by proteins. Despite a greatly increased rate of structure determination and a deliberate strategy of sequencing proteins expected to be very different from those already known, it is now rare to see a genuinely new fold, leading to the conclusion that we have seen the majority of natural structural types. The increase in knowledge has also led to a critical examination of traditional fold-based classifications and their meaning for evolution and protein structures. We review these issues and discuss possible solutions.

Understanding protein structure from a percolation perspective

Underlying the unique structures and diverse functions of proteins are a vast range of amino-acid sequences and a highly limited number of folds taken up by the polypeptide backbone. By investigating the role of noncovalent connections at the backbone level and at the detailed side-chain level, we show that these unique structures emerge from interplay between random and selected features. Primarily, the protein structure network formed by these connections shows simple (bond) and higher order (clique) percolation behavior distinctly reminiscent of random network models. However, the clique percolation specific to the side-chain interaction network bears signatures unique to proteins characterized by a larger degree of connectivity than in random networks. These studies reflect some salient features of the manner in which amino acid sequences select the unique structure of proteins from the pool of a limited number of available folds.

A condensation-ordering mechanism in nanoparticle-catalyzed peptide aggregation

Nanoparticles introduced in living cells are capable of strongly promoting the aggregation of peptides and proteins. We use here molecular dynamics simulations to characterise in detail the process by which nanoparticle surfaces catalyse the self-assembly of peptides into fibrillar structures. The simulation of a system of hundreds of peptides over the millisecond timescale enables us to show that the mechanism of aggregation involves a first phase in which small structurally disordered oligomers assemble onto the nanoparticle and a second phase in which they evolve into highly ordered as their size increases.

Protein misfolding and aggregation are associated with a wide variety of human disorders, which include Alzheimer's and Parkinson's diseases and late onset diabetes. It has been recently realised that the process of aggregation may be triggered by the presence of nanoparticles. We use here molecular dynamics simulations to characterise the molecular mechanism by which such nanoparticles are capable of enhancing the rate of formation of peptide aggregates. Our findings indicate that nanoparticle surfaces act as a catalyst that increases the local concentration of peptides, thus facilitating their subsequent assembly into stable fibrillar structures. The approach that we present, in addition to providing a description of the process of aggregation of peptides in the presence of nanoparticles, will enable the study of the mechanism of action of a variety of other potential aggregation-promoting agents present in living organisms, including lipid membranes and other cellular components.

Inter-helical interactions in membrane proteins: analysis based on the local backbone geometry and the side chain interactions

The availability of a significant number of the structures of helical membrane proteins has prompted us to investigate the mode of helix-helix packing. In the present study, we have considered a dataset of alpha-helical membrane proteins representing structures solved from all the known superfamilies. We have described the geometry of all the helical residues in terms of local coordinate axis at the backbone level. Significant inter-helical interactions have been considered as contacts by weighing the number of atom-atom contacts, including all the side-chain atoms. Such a definition of local axis and the contact criterion has allowed us to investigate the inter-helical interaction in a systematic and quantitative manner. We show that a single parameter (designated as alpha), which is derived from the parameters representing the mutual orientation of local axes, is able to accurately capture the details of helix-helix interaction. The analysis has been carried out by dividing the dataset into parallel, anti-parallel, and perpendicular orientation of helices. The study indicates that a specific range of alpha value is preferred for interactions among the anti-parallel helices. Such a preference is also seen among interacting residues of parallel helices, however to a lesser extent. No such preference is seen in the case of perpendicular helices, the contacts that arise mainly due to the interaction of surface helices with the end of the trans-membrane helices. The study supports the prevailing view that the anti-parallel helices are well packed. However, the interactions between helices of parallel orientation are non-trivial. The packing in alpha-helical membrane proteins, which is systematically and rigorously investigated in this study, may prove to be useful in modeling of helical membrane proteins.

Thermodynamics of tubelike flexible polymers

In this work, we discuss the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among nonbonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness influences the thermodynamic behavior of simple tubelike polymers significantly, i.e., for a given temperature, the formation of secondary structures strongly depends on the tube thickness.

First-principles design of nanomachines

Learning from nature's amazing molecular machines, globular proteins, we present a framework for the predictive design of nanomachines. We show that the crucial ingredients for a chain molecule to behave as a machine are its inherent anisotropy and the coupling between the local Frenet coordinate reference frames of nearby monomers. We demonstrate that, even in the absence of heterogeneity, protein-like behavior is obtained for a simple chain molecule made up of just 30 hard spheres. This chain spontaneously switches between 2 distinct geometries, a single helix and a dual helix, merely because of thermal fluctuations.

Universal features in the genome-level evolution of protein domains

Novel protein domain stochastic duplication/innovation models that are independent of genome-specific features are used to interpret global trends of genome evolution.

Background

Protein domains can be used to study proteome evolution at a coarse scale. In particular, they are found on genomes with notable statistical distributions. It is known that the distribution of domains with a given topology follows a power law. We focus on a further aspect: these distributions, and the number of distinct topologies, follow collective trends, or scaling laws, depending on the total number of domains only, and not on genome-specific features.

Results

We present a stochastic duplication/innovation model, in the class of the so-called 'Chinese restaurant processes', that explains this observation with two universal parameters, representing a minimal number of domains and the relative weight of innovation to duplication. Furthermore, we study a model variant where new topologies are related to occurrence in genomic data, accounting for fold specificity.

Conclusions

Both models have general quantitative agreement with data from hundreds of genomes, which indicates that the domains of a genome are built with a combination of specificity and robust self-organizing phenomena. The latter are related to the basic evolutionary 'moves' of duplication and innovation, and give rise to the observed scaling laws, a priori of the specific evolutionary history of a genome. We interpret this as the concurrent effect of neutral and selective drives, which increase duplication and decrease innovation in larger and more complex genomes. The validity of our model would imply that the empirical observation of a small number of folds in nature may be a consequence of their evolution.

Self-templated nucleation in peptide and protein aggregation

Peptides and proteins exhibit a common tendency to assemble into highly ordered fibrillar aggregates, whose formation proceeds in a nucleation-dependent manner that is often preceded by the formation of oligomeric assemblies. This process has received much attention because disordered oligomeric aggregates have been associated with neurodegenerative disorders such as Alzheimer's and Parkinson's disease. Here we describe a self-templated nucleation mechanism that determines the transition between the initial condensation of polypeptide chains into disordered assemblies and their reordering into fibrillar structures. The results that we present show that at the molecular level this transition is due to the ability of polypeptide chains to reorder within oligomers into fibrillar assemblies whose surfaces act as templates that stabilize the disordered assemblies.

A generic mechanism of emergence of amyloid protofilaments from disordered oligomeric aggregates

The presence of oligomeric aggregates, which is often observed during the process of amyloid formation, has recently attracted much attention because it has been associated with a range of neurodegenerative conditions including Alzheimer's and Parkinson's diseases. We provide a description of a sequence-indepedent mechanism by which polypeptide chains aggregate by forming metastable oligomeric intermediate states prior to converting into fibrillar structures. Our results illustrate that the formation of ordered arrays of hydrogen bonds drives the formation of beta-sheets within the disordered oligomeric aggregates that form early under the effect of hydrophobic forces. Individual beta-sheets initially form with random orientations and subsequently tend to align into protofilaments as their lengths increase. Our results suggest that amyloid aggregation represents an example of the Ostwald step rule of first-order phase transitions by showing that ordered cross-beta structures emerge preferentially from disordered compact dynamical intermediate assemblies.

Variations in clique and community patterns in protein structures during allosteric communication: investigation of dynamically equilibrated structures of methionyl tRNA synthetase complexes

The allosteric concept has played a key role in understanding the biological functions of proteins. The rigidity or plasticity and the conformational population are the two important ideas invoked in explaining the allosteric effect. Although molecular insights have been gained from a large number of structures, a precise assessment of the ligand-induced conformational changes in proteins at different levels, ranging from gross topology to intricate details, remains a challenge. In this study, we have explored the conformational changes in the complexes of methionyl tRNA synthetase (MetRS) through novel network parameters such as cliques and communities, which identify the rigid regions in the protein structure networks (PSNs) constructed from the noncovalent interactions of amino acid side chains. MetRS belongs to the aminoacyl tRNA synthetase (aaRS) family that plays a crucial role in the translation of genetic code. These enzymes are modular with distinct domains from which extensive genetic, kinetic, and structural data are available, highlighting the role of interdomain communication. The network parameters evaluated here on the conformational ensembles of MetRS complexes, generated from molecular dynamics simulations, have enabled us to understand the interdomain communication in detail. Additionally, the characterization of conformational changes in terms of cliques and communities has also become possible, which had eluded conventional analyses. Furthermore, we find that most of the residues participating in cliques and communities are strikingly different from those that take part in long-range communication. The cliques and communities evaluated here for the first time on PSNs have beautifully captured the local geometries in detail within the framework of global topology. Here the allosteric effect is revealed at the residue level via identification of the important residues specific for structural rigidity and functional flexibility in MetRS. This ought to enhance our understanding of the functioning of aaRS in general.