Symmetry and frustration in protein energy landscapes: a near degeneracy resolves the Rop dimer-folding mystery

The Curious Case of A31P, a Topology-Switching Mutant of the Repressor of Primer Protein: A Molecular Dynamics Study of Its Folding and Misfolding

The effect of mutations on protein structures is usually rather localized and minor. Finding a mutation that can single-handedly change the fold and/or topology of a protein structure is a rare exception. The A31P mutant of the homodimeric Repressor of primer (Rop) protein is one such exception: This single mutation ─and as demonstrated by two independent crystal structure determinations─ can convert the canonical (left-handed/all-antiparallel) 4-α-helical bundle of Rop to a new form (right-handed/mixed parallel and antiparallel bundle) displaying a previously unobserved "bisecting U" topology. The main problem with understanding the dramatic effect of this mutation on the folding of Rop is to understand its very existence: Most computational methods appear to agree that the mutation should have had no appreciable effect, with the majority of energy minimization methods and protein structure prediction protocols indicating that this mutation is fully consistent with the native Rop structure, requiring only a local and minor change at the mutation site. Here we use two long (10 μs each) molecular dynamics simulations to compare the stability and dynamics of the native Rop versus a hypothetical structure that is identical with the native Rop but is carrying this single Alanine31 to Proline mutation. Comparative analysis of the two trajectories convincingly shows that, in contrast to the indications from energy minimization ─but in agreement with the experimental data─, this hypothetical native-like A31P structure is unstable, with its turn regions almost completely unfolding, even under the relatively mild 320 K NpT simulations that we have used for this study. We discuss the implication of these findings for the folding of the A31P mutant, especially with respect to the proposed model of a double-funneled energy landscape.

The role of cryptic ancestral symmetry in histone folding mechanisms across Eukarya and Archaea

Histones compact and store DNA in both Eukarya and Archaea, forming heterodimers in Eukarya and homodimers in Archaea. Despite this, the folding mechanism of histones across species remains unclear. Our study addresses this gap by investigating 11 types of histone and histone-like proteins across humans, Drosophila, and Archaea through multiscale molecular dynamics (MD) simulations, complemented by NMR and circular dichroism experiments. We confirm and elaborate on the widely applied "folding upon binding" mechanism of histone dimeric proteins and report a new alternative conformation, namely, the inverted non-native dimer, which may be a thermodynamically metastable configuration. Protein sequence analysis indicated that the inverted conformation arises from the hidden ancestral head-tail sequence symmetry underlying all histone proteins, which is congruent with the previously proposed histone evolution hypotheses. Finally, to explore the potential formations of homodimers in Eukarya, we utilized MD-based AWSEM and AI-based AlphaFold-Multimer models to predict their structures and conducted extensive all-atom MD simulations to examine their respective structural stabilities. Our results suggest that eukaryotic histones may also form stable homodimers, whereas their disordered tails bring significant structural asymmetry and tip the balance towards the formation of commonly observed heterotypic dimers.

Evolution avoids a pathological stabilizing interaction in the immune protein S100A9

Stability constrains evolution. While much is known about constraints on destabilizing mutations, less is known about the constraints on stabilizing mutations. We recently identified a mutation in the innate immune protein S100A9 that provides insight into such constraints. When introduced into human S100A9, M63F simultaneously increases the stability of the protein and disrupts its natural ability to activate Toll-like receptor 4. Using chemical denaturation, we found that M63F stabilizes a calcium-bound conformation of hS100A9. We then used NMR to solve the structure of the mutant protein, revealing that the mutation distorts the hydrophobic binding surface of hS100A9, explaining its deleterious effect on function. Hydrogen-deuterium exchange (HDX) experiments revealed stabilization of the region around M63F in the structure, notably Phe37. In the structure of the M63F mutant, the Phe37 and Phe63 sidechains are in contact, plausibly forming an edge-face π-stack. Mutating Phe37 to Leu abolished the stabilizing effect of M63F as probed by both chemical denaturation and HDX. It also restored the biological activity of S100A9 disrupted by M63F. These findings reveal that Phe63 creates a molecular staple with Phe37 that stabilizes a nonfunctional conformation of the protein, thus disrupting function. Using a bioinformatic analysis, we found that S100A9 proteins from different organisms rarely have Phe at both positions 37 and 63, suggesting that avoiding a pathological stabilizing interaction indeed constrains S100A9 evolution. This work highlights an important evolutionary constraint on stabilizing mutations, namely, that they must avoid inappropriately stabilizing nonfunctional protein conformations.

Side chain flexibility and the symmetry of protein homodimers

A comprehensive analysis of crystallographic data of 565 high-resolution protein homodimers comprised of over 250,000 residues suggests that amino acids form two groups that differ in their tendency to distort or symmetrize the structure of protein homodimers. Residues of the first group tend to distort the protein homodimer and generally have long or polar side chains. These include: Lys, Gln, Glu, Arg, Asn, Met, Ser, Thr and Asp. Residues of the second group contribute to protein symmetry and are generally characterized by short or aromatic side chains. These include: Ile, Pro, His, Val, Cys, Leu, Trp, Tyr, Phe, Ala and Gly. The distributions of the continuous symmetry measures of the proteins and the continuous chirality measures of their building blocks highlight the role of side chain geometry and the interplay between entropy and symmetry in dictating the conformational flexibility of proteins.

Experimentally-driven protein structure modeling

Revolutions in natural and exact sciences started at the dawn of last century have led to the explosion of theoretical, experimental, and computational approaches to determine structures of molecules, complexes, as well as their rich conformational dynamics. Since different experimental methods produce information that is attributed to specific time and length scales, corresponding computational methods have to be tailored to these scales and experiments. These methods can be then combined and integrated in scales, hence producing a fuller picture of molecular structure and motion from the "puzzle pieces" offered by various experiments. Here, we describe a number of computational approaches to utilize experimental data to glance into structure of proteins and understand their dynamics. We will also discuss the limitations and the resolution of the constraints-based modeling approaches. SIGNIFICANCE: Experimentally-driven computational structure modeling and determination is a rapidly evolving alternative to traditional approaches for molecular structure determination. These new hybrid experimental-computational approaches are proving to be a powerful microscope to glance into the structural features of intrinsically or partially disordered proteins, dynamics of molecules and complexes. In this review, we describe various approaches in the field of experimentally-driven computational structure modeling.

The near-symmetry of protein oligomers: NMR-derived structures

The majority of oligomeric proteins form clusters which have rotational or dihedral symmetry. Despite the many advantages of symmetric packing, protein oligomers are only nearly symmetric, and the origin of this phenomenon is still in need to be fully explored. Here we apply near-symmetry analyses by the Continuous Symmetry Measures methodology of protein homomers to their natural state, namely their structures in solution. NMR-derived structural data serves us for that purpose. We find that symmetry deviations of proteins are by far higher in solution, compared to the crystalline state; that much of the symmetry distortion is due to amino acids along the interface between the subunits; that the distortions are mainly due to hydrophilic amino acids; and that distortive oligomerization processes such as the swap-domain mechanism can be identified by the symmetry analysis. Most of the analyses were carried out on distorted C2-symmetry dimers, but C3 and D2 cases were analyzed as well. Our NMR analysis supports the idea that the crystallographic B-factor represents non-classical crystals, in which different conformers pack in the crystal, perhaps from the conformers which the NMR analysis provides.

A multifunnel energy landscape encodes the competing α-helix and β-hairpin conformations for a designed peptide

Depending on the amino acid sequence, as well as the local environment, some peptides have the capability to fold into multiple secondary structures. Conformational switching between such structures is a key element of protein folding and aggregation. Specifically, understanding the molecular mechanism underlying the transition from an α-helix to a β-hairpin is critical because it is thought to be a harbinger of amyloid assembly. In this study, we explore the energy landscape for an 18-residue peptide (DP5), designed by Araki and Tamura to exhibit equal propensities for the α-helical and β-hairpin forms. We find that the degeneracy is encoded in the multifunnel nature of the underlying free energy landscape. In agreement with experiment, we also observe that mutation of tyrosine at position 12 to serine shifts the equilibrium in favor of the α-helix conformation, by altering the landscape topography. The transition from the α-helix to the β-hairpin is a complex stepwise process, and occurs via collapsed coil-like intermediates. Our findings suggest that even a single mutation can tune the emergent features of the landscape, providing an efficient route to protein design. Interestingly, the transition pathways for the conformational switch seem to be minimally perturbed upon mutation, suggesting that there could be universal microscopic features that are conserved among different switch-competent protein sequences.

Improved algorithms for quantifying the near symmetry of proteins: complete side chains analysis

Symmetry of proteins, an important source of their elegant structure and unique functions, is not as perfect as it may seem. In the framework of continuous symmetry, in which symmetry is no longer a binary yes/no property, such imperfections can be quantified and used as a global descriptor of the three-dimensional structure. We present an improved algorithm for calculating the continuous symmetry measure for proteins that takes into account their complete set of atoms including all side chains. Our method takes advantage of the protein sequence and the division into peptides in order to improve the accuracy and efficiency of the calculation over previous methods. The Hungarian algorithm is applied to solve the assignment problem and find the permutation that defines the symmetry operation. Analysis of the symmetry of several sets of protein homomers, with various degrees of rotational symmetry is presented. The new methodology lays the foundations for accurate, efficient and reliable large scale symmetry analysis of protein structure and can be used as a collective variable that describes changes of the protein geometry along various processes, both at the backbone level and for the complete protein structure.

Sliding Mechanism at a Coiled-Coil Interface

The α-helical coiled coil (CC) is a common protein motif that because of the simplicity of its sequence/structure relationship, it has been studied extensively to address fundamental questions in protein science as well as to develop strategies for designing protein with novel architectures. Nevertheless, a complete understanding of CC structures and their dynamics is still far from achieved. Particularly, spontaneous sliding at interfaces of CC proteins was observed for some systems, but its mechanism and usage as an intrinsic conformational change at CCs in protein-protein interfaces is unclear. Using coarse-grained and atomistic simulations, we study various sequences of homodimeric CC, in both parallel and antiparallel configurations. Both the strength of the hydrophobic core and the existence of salt bridges at the periphery of the interface affect sliding dynamics at the CC interface. Although the energy landscape for sliding along a CC interface is different for parallel and antiparallel configurations, both are characterized by a free energy of 1-1.5 kcal/mol, depending on the residues that constitute the CC interface. These barrier heights suggest that sliding kinetics is relatively slow in CC systems and are not expected to be of long length scale, yet they can be involved in functional motions. Our study explains the sliding that has been experimentally observed for the antiparallel CC of the dynein stalk region and the nuclear pore complex and suggests that this one-dimensional motion is an intrinsic feature in CC systems that can be involved in other CC systems.

Effect of ethanol on insulin dimer dissociation

Insulin-dimer dissociation is an essential biochemical process required for the activity of the hormone. We investigate this dissociation process at the molecular level in water and at the same time, in 5% and 10% water-ethanol mixtures. We compute the free energy surface of the protein dissociation processes by employing biased molecular dynamics simulation. In the presence of ethanol (EtOH), we observe a marked lowering in the free energy barrier of activation of dimer dissociation from that in the neat water, by as much as ∼50%, even in the 5% water-ethanol solution. In addition, ethanol is found to induce significant changes in the dissociation pathway. We extract the most probable conformations of the intermediate states along the minimum energy pathway in the case of all the three concentrations (EtOH mole fractions 0, 5, and 10). We explore the change in microscopic structures that occur in the presence of ethanol. Interestingly, we discover a stable intermediate state in the water-ethanol binary mixture where the centers of the monomers are separated by about 3 nm and the contact order parameter is close to zero. This intermediate is stabilized by the wetting of the interface between the two monomers by the preferential distribution of ethanol and water molecules. This wetting serves to reduce the free energy barrier significantly and thus results in an increase in the rate of dimer dissociation. We also analyze the solvation of the two monomers during the dissociation and both the proteins' departure from the native state configuration to obtain valuable insights into the dimer dissociation processes.

Atomistic simulations indicate the functional loop-to-coiled-coil transition in influenza hemagglutinin is not downhill

Influenza hemagglutinin (HA) mediates viral entry into host cells through a large-scale conformational rearrangement at low pH that leads to fusion of the viral and endosomal membranes. Crystallographic and biochemical data suggest that a loop-to-coiled-coil transition of the B-loop region of HA is important for driving this structural rearrangement. However, the microscopic picture for this proposed "spring-loaded" movement is missing. In this study, we focus on understanding the transition of the B loop and perform a set of all-atom molecular dynamics simulations of the full B-loop trimeric structure with the CHARMM36 force field. The free-energy profile constructed from our simulations describes a B loop that stably folds half of the postfusion coiled coil in tens of microseconds, but the full coiled coil is unfavorable. A buried hydrophilic residue, Thr59, is implicated in destabilizing the coiled coil. Interestingly, this conserved threonine is the only residue in the B loop that strictly differentiates between the group 1 and 2 HA molecules. Microsecond-scale constant temperature simulations revealed that kinetic traps in the structural switch of the B loop can be caused by nonnative, intramonomer, or intermonomer β-sheets. The addition of the A helix stabilized the postfusion state of the B loop, but introduced the possibility for further β-sheet structures. Overall, our results do not support a description of the B loop in group 2 HAs as a stiff spring, but, rather, it allows for more structural heterogeneity in the placement of the fusion peptides during the fusion process.

Evolved Minimal Frustration in Multifunctional Biomolecules

Protein folding is often viewed in terms of a funneled potential or free energy landscape. A variety of experiments now indicate the existence of multifunnel landscapes, associated with multifunctional biomolecules. Here, we present evidence that these systems have evolved to exhibit the minimal number of funnels required to fulfill their cellular functions, suggesting an extension to the principle of minimum frustration. We find that minimal disruptive mutations result in additional funnels, and the associated structural ensembles become more diverse. The same trends are observed in an atomic cluster. These observations suggest guidelines for rational design of engineered multifunctional biomolecules.

On the folding of a structurally complex protein to its metastable active state

For successful protease inhibition, the reactive center loop (RCL) of the two-domain serine protease inhibitor, α1-antitrypsin (α1-AT), needs to remain exposed in a metastable active conformation. The α1-AT RCL is sequestered in a β-sheet in the stable latent conformation. Thus, to be functional, α1-AT must always fold to a metastable conformation while avoiding folding to a stable conformation. We explore the structural basis of this choice using folding simulations of coarse-grained structure-based models of the two α1-AT conformations. Our simulations capture the key features of folding experiments performed on both conformations. The simulations also show that the free energy barrier to fold to the latent conformation is much larger than the barrier to fold to the active conformation. An entropically stabilized on-pathway intermediate lowers the barrier for folding to the active conformation. In this intermediate, the RCL is in an exposed configuration, and only one of the two α1-AT domains is folded. In contrast, early conversion of the RCL into a β-strand increases the coupling between the two α1-AT domains in the transition state and creates a larger barrier for folding to the latent conformation. Thus, unlike what happens in several proteins, where separate regions promote folding and function, the structure of the RCL, formed early during folding, determines both the conformational and the functional fate of α1-AT. Further, the short 12-residue RCL modulates the free energy barrier and the folding cooperativity of the large 370-residue α1-AT. Finally, we suggest experiments to test the predicted folding mechanism for the latent state.

The enigma of the near-symmetry of proteins: Domain swapping

The majority of proteins form oligomers which have rotational symmetry. Literature has suggested many functional advantages that the symmetric packing offers. Yet, despite these advantages, the vast majority of protein oligomers are only nearly symmetric. A key question in the field of proteins structure is therefore, if symmetry is so advantageous, why do oligomers settle for aggregates that do not maximize that structural property? The answer to that question is apparently multi-parametric, and involves distortions at the interaction zones of the monomer units of the oligomer in order to minimize the free energy, the dynamics of the protein, the effects of surroundings parameters, and the mechanism of oligomerization. The study of this problem is in its infancy: Only the first parameter has been explored so far. Here we focus on the last parameter-the mechanism of formation. To test this effect we have selected to focus on the domain swapping mechanism of oligomerization, by which oligomers form in a mechanism that swaps identical portions of monomeric units, resulting in an interwoven oligomer. We are using continuous symmetry measures to analyze in detail the oligomer formed by this mechanism, and found, that without exception, in all analyzed cases, perfect symmetry is given away, and we are able to identify that the main burden of distortion lies in the hinge regions that connect the swapped portions. We show that the continuous symmetry analysis method clearly identifies the hinge region of swapped domain proteins-considered to be a non-trivial task. We corroborate our conclusion about the central role of the hinge region in affecting the symmetry of the oligomers, by a special probability analysis developed particularly for that purpose.

Impact of Turn Propensity on the Folding Rates of Z34C Protein: Implications for the Folding of Helix-Turn-Helix Motif

The rate-limiting step for the folding of the helix-turn-helix (HTH) protein, Z34C, involves β-turn region ²⁰DPNL²³. This reverse turn has been observed to be part of the transition state in the folding process for Z34C, influencing its folding rates. Molecular dynamics simulations were performed on this turn peptide and its two mutants, D20A and P21A, to study turn formation using GROMOS54A7 force field. We find that this region has a turn propensity of its own, and the highest turn propensity is observed for the wild-type, which correlates well with available experimental results. We also find that a slight unfavorable change in ΔG _{turn folding} causes a drastic change in the folding rates of HTH motif and a mechanistic interpretation is given. Implications of these observations for the folding of the HTH protein Z34C are discussed.

Highly Coarse-Grained Representations of Transmembrane Proteins

Numerous biomolecules and biomolecular complexes, including transmembrane proteins (TMPs), are symmetric or at least have approximate symmetries. Highly coarse-grained models of such biomolecules, aiming at capturing the essential structural and dynamical properties on resolution levels coarser than the residue scale, must preserve the underlying symmetry. However, making these models obey the correct physics is in general not straightforward, especially at the highly coarse-grained resolution where multiple (∼3-30 in the current study) amino acid residues are represented by a single coarse-grained site. In this paper, we propose a simple and fast method of coarse-graining TMPs obeying this condition. The procedure involves partitioning transmembrane domains into contiguous segments of equal length along the primary sequence. For the coarsest (lowest-resolution) mappings, it turns out to be most important to satisfy the symmetry in a coarse-grained model. As the resolution is increased to capture more detail, however, it becomes gradually more important to match modular repeats in the secondary structure (such as helix-loop repeats) instead. A set of eight TMPs of various complexity, functionality, structural topology, and internal symmetry, representing different classes of TMPs (ion channels, transporters, receptors, adhesion, and invasion proteins), has been examined. The present approach can be generalized to other systems possessing exact or approximate symmetry, allowing for reliable and fast creation of multiscale, highly coarse-grained mappings of large biomolecular assemblies.

The thermodynamics of protein aggregation reactions may underpin the enhanced metabolic efficiency associated with heterosis, some balancing selection, and the evolution of ploidy levels

Identifying the physical basis of heterosis (or "hybrid vigor") has remained elusive despite over a hundred years of research on the subject. The three main theories of heterosis are dominance theory, overdominance theory, and epistasis theory. Kacser and Burns (1981) identified the molecular basis of dominance, which has greatly enhanced our understanding of its importance to heterosis. This paper aims to explain how overdominance, and some features of epistasis, can similarly emerge from the molecular dynamics of proteins. Possessing multiple alleles at a gene locus results in the synthesis of different allozymes at reduced concentrations. This in turn reduces the rate at which each allozyme forms soluble oligomers, which are toxic and must be degraded, because allozymes co-aggregate at low efficiencies. The model developed in this paper can explain how heterozygosity impacts the metabolic efficiency of an organism. It can also explain why the viabilities of some inbred lines seem to decline rapidly at high inbreeding coefficients (F > 0.5), which may provide a physical basis for truncation selection for heterozygosity. Finally, the model has implications for the ploidy level of organisms. It can explain why polyploids are frequently found in environments where severe physical stresses promote the formation of soluble oligomers. The model can also explain why complex organisms, which need to synthesize aggregation-prone proteins that contain intrinsically unstructured regions (IURs) and multiple domains because they facilitate complex protein interaction networks (PINs), tend to be diploid while haploidy tends to be restricted to relatively simple organisms.

Interdomain Contacts Control Native State Switching of RfaH on a Dual-Funneled Landscape

RfaH is a virulence factor from Escherichia coli whose C-terminal domain (CTD) undergoes a dramatic α-to-β conformational transformation. The CTD in its α-helical fold is stabilized by interactions with the N-terminal domain (NTD), masking an RNA polymerase binding site until a specific recruitment site is encountered. Domain dissociation is triggered upon binding to DNA, allowing the NTD to interact with RNA polymerase to facilitate transcription while the CTD refolds into the β-barrel conformation that interacts with the ribosome to activate translation. However, structural details of this transformation process in the context of the full protein remain to be elucidated. Here, we explore the mechanism of the α-to-β conformational transition of RfaH in the full-length protein using a dual-basin structure-based model. Our simulations capture several features described experimentally, such as the requirement of disruption of interdomain contacts to trigger the α-to-β transformation, confirms the roles of previously indicated residues E48 and R138, and suggests a new important role for F130, in the stability of the interdomain interaction. These native basins are connected through an intermediate state that builds up upon binding to the NTD and shares features from both folds, in agreement with previous in silico studies of the isolated CTD. We also examine the effect of RNA polymerase binding on the stabilization of the β fold. Our study shows that native-biased models are appropriate for interrogating the detailed mechanisms of structural rearrangements during the dramatic transformation process of RfaH.

To carry out their biological functions, proteins must fold into defined three-dimensional structures. In most proteins, a single fold determined by the amino acid sequence, and sometimes influenced by environmental conditions, is believed to be suited for each protein’s dedicated task. However, some proteins challenge this broadly accepted paradigm, adopting different structures that can enable diverse roles or trigger pathological responses, such as prion diseases. Escherichia coli RfaH constitutes a dramatic example of this atypical behavior. RfaH C-terminal domain folds into either a helical bundle that binds to the N-terminal domain and inhibits unregulated recruitment to the transcription complex or, in the presence of a specific DNA target, into a stand-alone β-barrel structure that binds to the ribosome and couples transcription and translation of RfaH-dependent genes. To understand the mechanism of this structural rearrangement, we performed molecular dynamics using a model where the stabilizing interactions from both folds are integrated. Our results argue that this transformation requires destabilization of the domain interface, is favored by interactions between the N-terminal domain of RfaH and RNA polymerase, and proceeds via a bound intermediate state that connects both folds.

EsxB, a secreted protein from Bacillus anthracis forms two distinct helical bundles

The EsxB protein from Bacillus anthracis belongs to the WXG100 family, a group of proteins secreted by a specialized secretion system. We have determined the crystal structures of recombinant EsxB and discovered that the small protein (∼10 kDa), comprised of a helix-loop-helix (HLH) hairpin, is capable of associating into two different helical bundles. The two basic quaternary assemblies of EsxB are an antiparallel (AP) dimer and a rarely observed bisecting U (BU) dimer. This structural duality of EsxB is believed to originate from the heptad repeat sequence diversity of the first helix of its HLH hairpin, which allows for two alternative helix packing. The flexibility of EsxB and the ability to form alternative helical bundles underscore the possibility that this protein can serve as an adaptor in secretion and can form hetero-oligomeric helix bundle(s) with other secreted members of the WXG100 family, such as EsxW. The highly conserved WXG motif is located within the loop of the HLH hairpin and is mostly buried within the helix bundle suggesting that its role is mainly structural. The exact functions of the motif, including a proposed role as a secretion signal, remain unknown.

The near-symmetry of proteins

The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.

Evolution, energy landscapes and the paradoxes of protein folding

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Predictive energy landscapes for folding α-helical transmembrane proteins

We explore the hypothesis that the folding landscapes of membrane proteins are funneled once the proteins' topology within the membrane is established. We extend a protein folding model, the associative memory, water-mediated, structure, and energy model (AWSEM) by adding an implicit membrane potential and reoptimizing the force field to account for the differing nature of the interactions that stabilize proteins within lipid membranes, yielding a model that we call AWSEM-membrane. Once the protein topology is set in the membrane, hydrophobic attractions play a lesser role in finding the native structure, whereas polar-polar attractions are more important than for globular proteins. We examine both the quality of predictions made with AWSEM-membrane when accurate knowledge of the topology and secondary structure is available and the quality of predictions made without such knowledge, instead using bioinformatically inferred topology and secondary structure based on sequence alone. When no major errors are made by the bioinformatic methods used to assign the topology of the transmembrane helices, these two types of structure predictions yield roughly equivalent quality structures. Although the predictive energy landscape is transferable and not structure based, within the correct topological sector we find the landscape is indeed very funneled: Thermodynamic landscape analysis indicates that both the total potential energy and the contact energy decrease as native contacts are formed. Nevertheless the near symmetry of different helical packings with respect to native contact formation can result in multiple packings with nearly equal thermodynamic occupancy, especially at temperatures just below collapse.

Structural plasticity of 4-α-helical bundles exemplified by the puzzle-like molecular assembly of the Rop protein

The dimeric Repressor of Primer (Rop) protein, a widely used model system for the study of coiled-coil 4-α-helical bundles, is characterized by a remarkable structural plasticity. Loop region mutations lead to a wide range of topologies, folding states, and altered physicochemical properties. A protein-folding study of Rop and several loop variants has identified specific residues and sequences that are linked to the observed structural plasticity. Apart from the native state, native-like and molten-globule states have been identified; these states are sensitive to reducing agents due to the formation of nonnative disulfide bridges. Pro residues in the loop are critical for the establishment of new topologies and molten globule states; their effects, however, can be in part compensated by Gly residues. The extreme plasticity in the assembly of 4-α-helical bundles reflects the capacity of the Rop sequence to combine a specific set of hydrophobic residues into strikingly different hydrophobic cores. These cores include highly hydrated ones that are consistent with the formation of interchain, nonnative disulfide bridges and the establishment of molten globules. Potential applications of this structural plasticity are among others in the engineering of bio-inspired materials.

From structure to function: the convergence of structure based models and co-evolutionary information

Understanding protein folding and function is one of the most important problems in biological research. Energy landscape theory and the folding funnel concept have provided a framework to investigate the mechanisms associated to these processes. Since protein energy landscapes are in most cases minimally frustrated, structure based models (SMBs) have successfully determined the geometrical features associated with folding and functional transitions. However, structural information is limited, particularly with respect to different functional configurations. This is a major limitation for SBMs. Alternatively, statistical methods to study amino acid co-evolution provide information on residue-residue interactions useful for the study of structure and function. Here, we show how the combination of these two methods gives rise to a novel way to investigate the mechanisms associated with folding and function. We use this methodology to explore the mechanistic aspects of protein translocation in the integral membrane protease FtsH. Dual basin-SBM simulations using the open and closed state of this hexameric motor reveals a functionally important paddling motion in the catalytic cycle. We also find that Direct Coupling Analysis (DCA) predicts physical contacts between AAA and peptidase domains of the motor, which are crucial for the open to close transition. Our combined method, which uses structural information from the open state experimental structure and co-evolutionary couplings, suggests that this methodology can be used to explore the functional landscape of complex biological macromolecules previously inaccessible to methods dependent on experimental structural information. This efficient way to sample the conformational space of large systems creates a theoretical/computational framework capable of better characterizing the functional landscape in large biomolecular assemblies.

Symmetric protein architecture in protein design: top-down symmetric deconstruction

Top-down symmetric deconstruction (TDSD) is a joint experimental and computational approach to generate a highly stable, functionally benign protein scaffold for intended application in subsequent functional design studies. By focusing on symmetric protein folds, TDSD can leverage the dramatic reduction in sequence space achieved by applying a primary structure symmetric constraint to the design process. Fundamentally, TDSD is an iterative symmetrization process, in which the goal is to maintain or improve properties of thermodynamic stability and folding cooperativity inherent to a starting sequence (the "proxy"). As such, TDSD does not attempt to solve the inverse protein folding problem directly, which is computationally intractable. The present chapter will take the reader through all of the primary steps of TDSD-selecting a proxy, identifying potential mutations, establishing a stability/folding cooperativity screen-relying heavily on a successful TDSD solution for the common β-trefoil fold.

Localized frustration and binding-induced conformational change in recognition of 5S RNA by TFIIIA zinc finger

Protein TFIIIA is composed of nine tandemly arranged Cys2His2 zinc fingers. It can bind either to the 5S RNA gene as a transcription factor or to the 5S RNA transcript as a chaperone. Although structural and biochemical data provided valuable information on the recognition between the TFIIIIA and the 5S DNA/RNA, the involved conformational motions and energetic factors contributing to the binding affinity and specificity remain unclear. In this work, we conducted MD simulations and MM/GBSA calculations to investigate the binding-induced conformational changes in the recognition of the 5S RNA by the central three zinc fingers of TFIIIA and the energetic factors that influence the binding affinity and specificity at an atomistic level. Our results revealed drastic interdomain conformational changes between these three zinc fingers, involving the exposure/burial of several crucial DNA/RNA binding residues, which can be related to the competition between DNA and RNA for the binding of TFIIIA. We also showed that the specific recognition between finger 4/finger 6 and the 5S RNA introduces frustrations to the nonspecific interactions between finger 5 and the 5S RNA, which may be important to achieve optimal binding affinity and specificity.

Detecting repetitions and periodicities in proteins by tiling the structural space

The notion of energy landscapes provides conceptual tools for understanding the complexities of protein folding and function. Energy landscape theory indicates that it is much easier to find sequences that satisfy the “Principle of Minimal Frustration” when the folded structure is symmetric (Wolynes, P. G. Symmetry and the Energy Landscapes of Biomolecules. Proc. Natl. Acad. Sci. U.S.A.1996, 93, 14249–14255). Similarly, repeats and structural mosaics may be fundamentally related to landscapes with multiple embedded funnels. Here we present analytical tools to detect and compare structural repetitions in protein molecules. By an exhaustive analysis of the distribution of structural repeats using a robust metric, we define those portions of a protein molecule that best describe the overall structure as a tessellation of basic units. The patterns produced by such tessellations provide intuitive representations of the repeating regions and their association toward higher order arrangements. We find that some protein architectures can be described as nearly periodic, while in others clear separations between repetitions exist. Since the method is independent of amino acid sequence information, we can identify structural units that can be encoded by a variety of distinct amino acid sequences.

Evolutionary pressure on the topology of protein interface interaction networks

The densely connected structure of protein-protein interaction (PPI) networks reflects the functional need of proteins to cooperate in cellular processes. However, PPI networks do not adequately capture the competition in protein binding. By contrast, the interface interaction network (IIN) studied here resolves the modular character of protein-protein binding and distinguishes between simultaneous and exclusive interactions that underlie both cooperation and competition. We show that the topology of the IIN is under evolutionary pressure, and we connect topological features of the IIN to specific biological functions. To reveal the forces shaping the network topology, we use a sequence-based computational model of interface binding along with network analysis. We find that the more fragmented structure of IINs, in contrast to the dense PPI networks, arises in large part from the competition between specific and nonspecific binding. The need to minimize nonspecific binding favors specific network motifs, including a minimal number of cliques (i.e., fully connected subgraphs) and many disconnected fragments. Validating the model, we find that these network characteristics are closely mirrored in the IIN of clathrin-mediated endocytosis. Features unexpected on the basis of our motif analysis are found to indicate either exceptional binding selectivity or important regulatory functions.

Weak frustration regulates sliding and binding kinetics on rugged protein-DNA landscapes

A fundamental step in gene-regulatory activities, such as repression, transcription, and recombination, is the binding of regulatory DNA-binding proteins (DBPs) to specific targets in the genome. To rapidly localize their regulatory genomic sites, DBPs reduce the dimensionality of the search space by combining three-dimensional (3D) diffusion in solution with one-dimensional (1D) sliding along DNA. However, the requirement to form a thermodynamically stable protein-DNA complex at the cognate genomic target sequence imposes a challenge on the protein because, as it navigates one-dimensionally along the genome, it may come in close contact with sites that share partial or even complete sequence similarity with the functional DNA sequence. This puzzling issue creates a conflict between two basic requirements: finding the cognate site quickly and stably binding it. Here, we structurally assessed the interface adopted by a variety of DBPs to bind DNA specifically and nonspecifically, and found that many DBPs utilize one interface to specifically recognize a DNA sequence and another to assist in propagating along the DNA through nonspecific associations. While these two interfaces overlap each other in some proteins, they present partial overlap in others and frustrate the protein-DNA interface. Using coarse-grained molecular dynamics simulations, we demonstrate that the existence of frustration in DBPs is a compromise between rapid 1D diffusion along other regions in the genome (high frustration smoothens the landscape for sliding) and rapid formation of a stable and essentially active protein-DNA complex (low frustration reduces the free energy barrier for switching between the two binding modes).

Molecular machines

Molecular machines (MM) are essential components of living cells. They conduct mechanical work, transport materials into and out of cells, assist in processing enzymatic reactions, and more. Their operations are frequently combined with significant conformational transitions. Computational studies of these conformational transitions and their coupling to molecular functions are discussed. It is argued that coarse descriptions of these molecules which are based on mass density and shape provide useful information on directions of action. It is further argued that MM are likely to have well focused and narrow reaction pathways. The proposal for such pathways is supported by evolutionary analyses of homologous machines. Finally, these observations are used to build atomically detailed models of these systems that are making the link from structure to functions (kinetics and thermodynamics). For that purpose enhanced sampling techniques are required.

The role of loop closure propensity in the refolding of Rop protein probed by molecular dynamics simulations

Rop protein is a homo-dimer of helix-turn-helix and has relatively slow folding and unfolding rates compared to other dimeric proteins of similar size. Fluorescence studies cited in literature suggest that mutation of turn residues D30-A31 to G30-G31 (Gly₂) increases its folding and unfolding rates considerably. A further increase in number of glycines in the turn region results in decrease of folding rates compared to Gly₂ mutant. To understand the effect of glycine mutation on folding/unfolding rates of Rop and the conformational nature of turn region involved in formation of early folding species, we performed molecular dynamics simulations of turn peptides, ²⁵KLNELDADEQ³⁴ (DA peptide), ²⁵KLNELGGDEQ³⁴ (G₂ peptide), ²⁵KLNELGGGDEQ³⁵ (G₃ peptide) and ²⁵KLNELGGGEQ³⁴ (G₃(') peptide) from Rop at 300 K. Further Wt-Rop and mutant G₂-Rop monomers and dimers were also studied separately by molecular dynamics simulations. Our results show that glycine based peptides (G(n) peptides) have a higher loop closure propensity compared to DA. Comparison of monomeric and dimeric Rop simulations suggests that dimeric Rop necessarily requires α(L) conformation to be sampled at D30/G30 position in the turn region. Since glycine (at position 30) can readily adopt α(L) conformation, G(n) loop plays a dual role in both facilitating loop closure as well as facilitating reorganization/packing of helices required for structural adjustment during dimer formation in the folding of Rop. Based on our simulation results and available literature, we suggest a tentative kinetic model for Rop folding which allows us to estimate the contribution of loop closure propensity to the overall folding rates.

Energetics of oligomeric protein folding and association

In nature, proteins most often exist as complexes, with many of these consisting of identical subunits. Understanding of the energetics governing the folding and misfolding of such homooligomeric proteins is central to understanding their function and misfunction, in disease or biotechnology. Much progress has been made in defining the mechanisms and thermodynamics of homooligomeric protein folding. In this review, we outline models as well as calorimetric and spectroscopic methods for characterizing oligomer folding, and describe extensive results obtained for diverse proteins, ranging from dimers to octamers and higher order aggregates. To our knowledge, this area has not been reviewed comprehensively in years, and the collective progress is impressive. The results provide evolutionary insights into the development of subunit interfaces, mechanisms of oligomer folding, and contributions of oligomerization to protein stability, function and regulation. Thermodynamic analyses have also proven valuable for understanding protein misfolding and aggregation mechanisms, suggesting new therapeutic avenues. Successful recent designs of novel, functional proteins demonstrate increased understanding of oligomer folding. Further rigorous analyses using multiple experimental and computational approaches are still required, however, to achieve consistent and accurate prediction of oligomer folding energetics. Modeling the energetics remains challenging but is a promising avenue for future advances.

An adaptive weighted ensemble procedure for efficient computation of free energies and first passage rates

We introduce an adaptive weighted-ensemble procedure (aWEP) for efficient and accurate evaluation of first-passage rates between states for two-state systems. The basic idea that distinguishes aWEP from conventional weighted-ensemble (WE) methodology is the division of the configuration space into smaller regions and equilibration of the trajectories within each region upon adaptive partitioning of the regions themselves into small grids. The equilibrated conditional∕transition probabilities between each pair of regions lead to the determination of populations of the regions and the first-passage times between regions, which in turn are combined to evaluate the first passage times for the forward and backward transitions between the two states. The application of the procedure to a non-trivial coarse-grained model of a 70-residue calcium binding domain of calmodulin is shown to efficiently yield information on the equilibrium probabilities of the two states as well as their first passage times. Notably, the new procedure is significantly more efficient than the canonical implementation of the WE procedure, and this improvement becomes even more significant at low temperatures.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Folding helical proteins in explicit solvent using dihedral-biased tempering

Using a single-trajectory-based tempering method with a high-temperature dihedral bias, we repeatedly folded four helical proteins [α(3)D (PDB ID: 2A3D, 73 residues), α(3)W (1LQ7, 67 residues), Fap1-NR(α) (2KUB, 81 residues) and S-836 (2JUA, 102 residues)] and some of the mutants in explicit solvent within several microseconds. The lowest root-mean-square deviations of backbone atoms from the experimentally determined structures were 1.9, 1.4, 1.0, and 2.1 Å, respectively. Cluster analyses of folding trajectories showed the native conformation usually occupied the most populated cluster. The simulation protocol can be applied to large-scale simulations of other helical proteins on commonly accessible computing platforms.

Mirror images as naturally competing conformations in protein folding

Evolution has selected a protein's sequence to be consistent with the native state geometry, as this configuration must be both thermodynamically stable and kinetically accessible to prevent misfolding and loss of function. In simple protein geometries, such as coiled-coil helical bundles, symmetry produces a competing, globally different, near mirror image with identical secondary structure and similar native contact interactions. Experimental techniques such as circular dichroism, which rely on probing secondary structure content, cannot readily distinguish these folds. Here, we want to clarify whether the native fold and mirror image are energetically competitive by investigating the free energy landscape of three-helix bundles. To prevent a bias from a specific computational approach, the present study employs the structure prediction forcefield PFF01/02, explicit solvent replica exchange molecular dynamics (REMD) with the Amber94 forcefield, and structure-based simulations based on energy landscape theory. We observe that the native fold and its mirror image have a similar enthalpic stability and are thermodynamically competitive. There is evidence that the mirror fold has faster folding kinetics and could function as a kinetic trap. All together, our simulations suggest that mirror images might not just be a computational annoyance but are competing folds that might switch depending on environmental conditions or functional considerations.

Configuration-dependent diffusion dynamics of downhill and two-state protein folding

Configuration-dependent diffusion (CDD) is important for protein folding kinetics with small thermodynamic barriers. CDD can be even more crucial in downhill folding without thermodynamic barriers. We explored the CDD of a downhill protein (BBL), and a two-state protein (CI2). The hidden kinetic barriers due to CDD were revealed. The increased ~1 k(B)T kinetic barrier is in line with experimental value based on other fast folding proteins. Compared to that of CI2, the effective free-energy profile of BBL is found to be significantly influenced by CDD, and the kinetics are totally determined by diffusion. These findings are consistent with both earlier bulk and single-molecule fluorescence measurements. In addition, we found the temperature dependence of CDD. We also found that the ratio of folding transition temperature against optimal kinetic folding temperature can provide both a quantitative measure for the underlying landscape topography and an indicator for the possible appearance of downhill folding. Our study can help for a better understanding of the role of diffusion in protein folding dynamics.

Strand swapping regulates the iron-sulfur cluster in the diabetes drug target mitoNEET

MitoNEET is a recently identified diabetes drug target that coordinates a transferable 2Fe-2S cluster, and additionally contains an unusual strand swap. In this manuscript, we use a dual basin structure-based model to predict and characterize the folding and functionality of strand swapping in mitoNEET. We demonstrate that a strand unswapped conformation is kinetically accessible and that multiple levels of control are employed to regulate the conformational dynamics of the system. Environmental factors such as temperature can shift route preference toward the unswapped pathway. Additionally we see that a region recently identified as contributing to frustration in folding acts as a regulatory hinge loop that modulates conformational balance. Interestingly, strand unswapping transfers strain specifically to cluster-coordinating residues, opening the cluster-coordinating pocket. Strengthening contacts within the cluster-coordinating pocket opens a new pathway between the swapped and unswapped conformation that utilizes cracking to bypass the unfolded basin. These results suggest that local control within distinct regions affect motions important in regulating mitoNEET's 2Fe-2S clusters.

Prediction of native-state hydrogen exchange from perfectly funneled energy landscapes

Simulations based on perfectly funneled energy landscapes often capture many of the kinetic features of protein folding. We examined whether simulations based on funneled energy functions can also describe fluctuations in native-state protein ensembles. We quantitatively compared the site-specific local stability determined from structure-based folding simulations, with hydrogen exchange protection factors measured experimentally for ubiquitin, chymotrypsin inhibitor 2, and staphylococcal nuclease. Different structural definitions for the open and closed states based on the number of native contacts for each residue, as well as the hydrogen-bonding state, or a combination of both criteria were evaluated. The predicted exchange patterns agree with the experiments under native conditions, indicating that protein topology indeed has a dominant effect on the exchange kinetics. Insights into the simplest mechanistic interpretation of the amide exchange process were thus obtained.

Heterogeneous path ensembles for conformational transitions in semi-atomistic models of adenylate kinase

We performed "weighted ensemble" path-sampling simulations of adenylate kinase, using several semi-atomistic protein models. The models have an all-atom backbone with various levels of residue interactions. The primary result is that full statistically rigorous path sampling required only a few weeks of single-processor computing time with these models, indicating the addition of further chemical detail should be readily feasible. Our semi-atomistic path ensembles are consistent with previous biophysical findings: the presence of two distinct pathways, identification of intermediates, and symmetry of forward and reverse pathways.