Funneling and frustration in the energy landscapes of some designed and simplified proteins

Coordinate-Dependent Drift-Diffusion Reveals the Kinetic Intermediate Traps of Top7-Based Proteins

The computer-designed Top7 served as a scaffold to produce immunoreactive proteins by grafting of the 2F5 HIV-1 antibody epitope (Top7-2F5) followed by biotinylation (Top7-2F5-biotin). The resulting nonimmunoglobulin affinity proteins were effective in inducing and detecting the HIV-1 antibody. However, the grafted Top7-2F5 design led to protein aggregation, as opposed to the soluble biotinylated Top7-2F5-biotin. The structure-based model predicted that the thermodynamic cooperativity of Top7 increases after grafting and biotin-labeling, reducing their intermediate state populations. In this work, the folding kinetic traps that might contribute to the aggregation propensity are investigated by the diffusion theory. Since the engineered proteins have similar sequence and structural homology, they served as protein models to study the kinetic intermediate traps that were uncovered by characterizing the position-dependent drift-velocity (v(Q)) and the diffusion (D(Q)) coefficients. These coordinate-dependent coefficients were taken into account to obtain the folding and transition path times over the free energy transition states containing the intermediate kinetic traps. This analysis may be useful to predict the aggregated kinetic traps of scaffold-epitope proteins that might compose novel diagnostic and therapeutic platforms.

Biotinylation Eliminates the Intermediate State of Top7 Designed with an HIV-1 Epitope

Broadly neutralizing antibodies against HIV-1 are rare with the 2F5 antibody being one of the most protective. Insertion of an antibody epitope into a stable and small protein scaffold overcomes many of the obstacles found to produce antibodies. However, the design leads to grafting of epitopes that may cause protein aggregation. Here, I investigated the 2F5 epitope grafted into the Top7 as the scaffold in which the resulting immunoreactive protein precipitates along the storage time, as opposed to its completely soluble biotinylated version. Molecular dynamics showed that biotinylation eliminates the intermediate state of the scaffold-epitope Top7-2F5 by switching a noncooperative to a cooperative folding. The aggregation propensity of the Top7-designed proteins is examined in light of thermodynamic cooperativity and kinetic traps along the decreasing depth of the intermediate ensemble in the free energy landscape. This protocol may predict stable and soluble scaffold-epitopes with the purpose of composing novel therapeutic and diagnostic platforms.

Fundamental Challenges and Outlook in Simulating Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) populate an ensemble of dynamic conformations, making their structural characterization by experiments challenging. Many IDPs undergo liquid-liquid phase separation into dense membraneless organelles with myriad cellular functions. Multivalent interactions in low-complexity IDPs promote the formation of these subcellular coacervates. While solution NMR, Förster resonance energy transfer (FRET), and small-angle X-ray scattering (SAXS) studies on IDPs have their own challenges, recent computational methods draw a rational trade-off to characterize the driving forces underlying phase separation. In this Perspective, we critically evaluate the scope of approximation-free field theoretic simulations, well-tempered ensemble methods, enhanced sampling techniques, coarse-grained force fields, and slab simulation approaches to offer an improved understanding of phase separation. A synergy between simulation length scale and model resolution would reduce the existing caveats and enable theories of polymer physics to elucidate finer details of liquid-liquid phase separation (LLPS). These computational advances offer promise for rigorous characterization of the IDP proteome and designing peptides with tunable material and self-assembly properties.

Maximum Entropy Optimized Force Field for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) constitute a significant fraction of eukaryotic proteomes. High-resolution characterization of IDP conformational ensembles can help elucidate their roles in a wide range of biological processes but remains challenging both experimentally and computationally. Here, we present a generic algorithm to improve the accuracy of coarse-grained IDP models using a diverse set of experimental measurements. It combines maximum entropy optimization and least-squares regression to systematically adjust model parameters and improve the agreement between simulation and experiment. We successfully applied the algorithm to derive a transferable force field, which we term the maximum entropy optimized force field (MOFF), for de novo prediction of IDP structures. Statistical analysis of force field parameters reveals features of amino acid interactions not captured by potentials designed to work well for folded proteins. We anticipate its combination of efficiency and accuracy will make MOFF useful for studying the phase separation of IDPs, which drives the formation of various biological compartments.

Competition of individual domain folding with inter-domain interaction in WW domain engineered repeat proteins

Engineered repeat proteins have proven to be a fertile ground for studying the competition between folding, misfolding and transient aggregation of tethered protein domains. We examine the interplay between folding and inter-domain interactions of engineered FiP35 WW domain repeat proteins with n = 1 through 5 repeats. We characterize protein expression, thermal and guanidium melts, as well as laser T-jump kinetics. All experimental data is fitted by a global fitting model with two states per domain (U, N), plus a third state M to account for non-native states due to domain interactions present in all but the monomer. A detailed structural model is provided by coarse-grained simulated annealing using the AWSEM Hamiltonian. Tethered FiP35 WW domains with n = 2 and 3 domains are just slightly less stable than the monomer. The n = 4 oligomer is yet less stable, its expression yield is much lower than the monomer's, and depends on the purification tag used. The n = 5 plasmid did not express at all, indicating the sudden onset of aggregation past n = 4. Thus, tethered FiP35 has a critical nucleus size for inter-domain aggregation of n ≈ 4. According to our simulations, misfolded structures become increasingly prevalent as one proceeds from monomer to pentamer, with extended inter-domain beta sheets appearing first, then multi-sheet 'intramolecular amyloid' structures, and finally novel motifs containing alpha helices. We discuss the implications of our results for oligomeric aggregate formation and structure, transient aggregation of proteins whilst folding, as well as for protein evolution that starts with repeat proteins.

Localizing Frustration in Proteins Using All-Atom Energy Functions

The problems of protein folding and protein design are two sides of the same coin. Protein folding involves exploring a protein's configuration space given a fixed sequence, whereas protein design involves searching in sequence space given a particular target structure. For a protein to fold quickly and reliably, its energy landscape must be biased toward the folded ensemble throughout its configuration space and must lack deep kinetic traps that would otherwise frustrate folding. Evolution has "designed" the sequences of many naturally occurring proteins, through an eons-long process of random mutation and selection, to yield landscapes with a minimal degree of frustration. The task facing humans hoping to design protein sequences that fold into particular structures is to use the available approximate energy functions to sculpt funneled landscapes that work in the laboratory. In this work, we demonstrate how to calculate several localized frustration measures using an all-atom energy function. Specifically, we employ the Rosetta energy function, which has been used successfully to design proteins and which has a natural pairwise decomposition that is suitably solvent-averaged. We calculate these newly developed frustration measures for both a mutated WW domain, FiP35, and a three-helix bundle that was designed completely by humans, Alpha3D. The structure of FiP35 exhibits less localized frustration than that of Alpha3D. A mutation toward the consensus sequence for WW domains in FiP35, which has been shown unexpectedly in experiment to disrupt folding, induces localized frustration by disrupting the hydrophobic core. By performing a limited redesign on the sequence of Alpha3D, we show that some, but not all, mutations that lower the energy also result in decreased frustration. The results suggest that, in addition to being useful for detecting residual frustration in protein structures, optimizing the localized frustration measures presented here may be a useful and automatic means of balancing positive and negative design in protein design tasks.

Nonnative Energetic Frustrations in Protein Folding at Residual Level: A Simulation Study of Homologous Immunoglobulin-like β-Sandwich Proteins

Nonnative interactions cause energetic frustrations in protein folding and were found to dominate key events in folding intermediates. However, systematically characterizing energetic frustrations that are caused by nonnative intra-residue interactions at residual resolution is still lacking. Recently, we studied the folding of a set of homologous all-α proteins and found that nonnative-contact-based energetic frustrations are highly correlated to topology of the protein native-contact network. Here, we studied the folding of nine homologous immunoglobulin-like (Ig-like) β-sandwich proteins, and examined nonnative-contact-based energetic frustrations Gō-like model. Our calculations showed that nonnative-interaction-based energetic frustrations in β-sandwich proteins are much more complicated than those in all-α proteins, and they exhibit highly heterogeneous effects on the folding of secondary structures. Further, the nonnative interactions introduced distinct correlations in the folding of different folding-patches of β-sandwich proteins. Taken together, a strong interplay might exist between nonnative-interaction energetic frustrations and the protein native-contact networks, which ensures that β-sandwich domains adopt a common folding mechanism.

Effects of thymic selection on T cell recognition of foreign and tumor antigenic peptides

The advent of cancer immunotherapy has generated renewed hope for the treatment of many malignancies by introducing a number of novel strategies that exploit various properties of the immune system. These therapies are based on the idea that cytotoxic T lymphocytes (CTLs) directly recognize and respond to tumor-associated neoantigens (TANs) in much the same way as they would to foreign peptides presented on cell surfaces. To date, however, nearly all attempts to optimize immunotherapeutic strategies have been empirical. Here, we develop a model of T cell selection based on the assumption of random interaction strengths between a self-peptide and the various T cell receptors. The model enables the analytical study of the effects of selection on the CTL recognition of TANs and completely foreign peptides and can estimate the number of CTLs that can detect donor-matched transplants. We show that negative selection thresholds chosen to reflect experimentally observed thymic survival rates result in near-optimal production of T cells that are capable of surviving selection and recognizing foreign antigen. These analytical results are confirmed by simulation.

Protein Folding and Structure Prediction from the Ground Up II: AAWSEM for α/β Proteins

The atomistic associative memory, water mediated, structure and energy model (AAWSEM) is an efficient coarse-grained force field with transferable tertiary interactions that incorporates local in sequence energetic biases using structural information derived from all-atom simulations of long segments of the protein. For α helical proteins, the accuracy of structure prediction using AAWSEM has been established previously. In this article, we examine the capability of AAWSEM to predict the structure of α/β proteins. We also elaborate on an iterative approach that uses the structures from a first round of AAWSEM simulation as fragment memories. This iterative scheme improves the quality of the structure prediction and makes the free energy profile more funneled toward native configurations. We explore the use of clustering analyses as a way of evaluating the confidence in various structure prediction models. Clustering using a local relative order parameter (mutual Q) of the predicted structural ensemble turns out to be optimal. The tightest cluster according to mutual Q generally has the most correctly folded structure. Since there is no bioinformatic input, AAWSEM amounts to an ab initio protein structure prediction method that combines the efficiency of coarse-grained simulations with the local structural accuracy that can be achieved from all-atom simulations.

Using natural sequences and modularity to design common and novel protein topologies

Protein design is still a challenging undertaking, often requiring multiple attempts or iterations for success. Typically, the source of failure is unclear, and scoring metrics appear similar between successful and failed cases. Nevertheless, the use of sequence statistics, modularity and symmetry from natural proteins, combined with computational design both at the coarse-grained and atomistic levels is propelling a new wave of design efforts to success. Here we highlight recent examples of design, showing how the wealth of natural protein sequence and topology data may be leveraged to reduce the search space and increase the likelihood of achieving desired outcomes.

Protein Frustratometer 2: a tool to localize energetic frustration in protein molecules, now with electrostatics

The protein frustratometer is an energy landscape theory-inspired algorithm that aims at localizing and quantifying the energetic frustration present in protein molecules. Frustration is a useful concept for analyzing proteins’ biological behavior. It compares the energy distributions of the native state with respect to structural decoys. The network of minimally frustrated interactions encompasses the folding core of the molecule. Sites of high local frustration often correlate with functional regions such as binding sites and regions involved in allosteric transitions. We present here an upgraded version of a webserver that measures local frustration. The new implementation that allows the inclusion of electrostatic energy terms, important to the interactions with nucleic acids, is significantly faster than the previous version enabling the analysis of large macromolecular complexes within a user-friendly interface. The webserver is freely available at URL: http://frustratometer.qb.fcen.uba.ar.

Human Frataxin Folds Via an Intermediate State. Role of the C-Terminal Region

The aim of this study is to investigate the folding reaction of human frataxin, whose deficiency causes the neurodegenerative disease Friedreich's Ataxia (FRDA). The characterization of different conformational states would provide knowledge about how frataxin can be stabilized without altering its functionality. Wild-type human frataxin and a set of mutants, including two highly destabilized FRDA-associated variants were studied by urea-induced folding/unfolding in a rapid mixing device and followed by circular dichroism. The analysis clearly indicates the existence of an intermediate state (I) in the folding route with significant secondary structure content but relatively low compactness, compared with the native ensemble. However, at high NaCl concentrations I-state gains substantial compaction, and the unfolding barrier is strongly affected, revealing the importance of electrostatics in the folding mechanism. The role of the C-terminal region (CTR), the key determinant of frataxin stability, was also studied. Simulations consistently with experiments revealed that this stretch is essentially unstructured, in the most compact transition state ensemble (TSE2). The complete truncation of the CTR drastically destabilizes the native state without altering TSE2. Results presented here shed light on the folding mechanism of frataxin, opening the possibility of mutating it to generate hyperstable variants without altering their folding kinetics.

Protein misfolding occurs by slow diffusion across multiple barriers in a rough energy landscape

The timescale for the microscopic dynamics of proteins during conformational transitions is set by the intrachain diffusion coefficient, D. Despite the central role of protein misfolding and aggregation in many diseases, it has proven challenging to measure D for these processes because of their heterogeneity. We used single-molecule force spectroscopy to overcome these challenges and determine D for misfolding of the prion protein PrP. Observing directly the misfolding of individual dimers into minimal aggregates, we reconstructed the energy landscape governing nonnative structure formation. Remarkably, rather than displaying multiple pathways, as typically expected for aggregation, PrP dimers were funneled into a thermodynamically stable misfolded state along a single pathway containing several intermediates, one of which blocked native folding. Using Kramers' rate theory, D was found to be 1,000-fold slower for misfolding than for native folding, reflecting local roughening of the misfolding landscape, likely due to increased internal friction. The slow diffusion also led to much longer transit times for barrier crossing, allowing transition paths to be observed directly for the first time to our knowledge. These results open a new window onto the microscopic mechanisms governing protein misfolding.

Native contact density and nonnative hydrophobic effects in the folding of bacterial immunity proteins

The bacterial colicin-immunity proteins Im7 and Im9 fold by different mechanisms. Experimentally, at pH 7.0 and 10°C, Im7 folds in a three-state manner via an intermediate but Im9 folding is two-state-like. Accordingly, Im7 exhibits a chevron rollover, whereas the chevron arm for Im9 folding is linear. Here we address the biophysical basis of their different behaviors by using native-centric models with and without additional transferrable, sequence-dependent energies. The Im7 chevron rollover is not captured by either a pure native-centric model or a model augmented by nonnative hydrophobic interactions with a uniform strength irrespective of residue type. By contrast, a more realistic nonnative interaction scheme that accounts for the difference in hydrophobicity among residues leads simultaneously to a chevron rollover for Im7 and an essentially linear folding chevron arm for Im9. Hydrophobic residues identified by published experiments to be involved in nonnative interactions during Im7 folding are found to participate in the strongest nonnative contacts in this model. Thus our observations support the experimental perspective that the Im7 folding intermediate is largely underpinned by nonnative interactions involving large hydrophobics. Our simulation suggests further that nonnative effects in Im7 are facilitated by a lower local native contact density relative to that of Im9. In a one-dimensional diffusion picture of Im7 folding with a coordinate- and stability-dependent diffusion coefficient, a significant chevron rollover is consistent with a diffusion coefficient that depends strongly on native stability at the conformational position of the folding intermediate.

In order to fold correctly, a globular protein must avoid being trapped in wrong, i.e., nonnative conformations. Thus a biophysical account of how attractive nonnative interactions are bypassed by some amino acid sequences but not others is key to deciphering protein structure and function. We examine two closely related bacterial immunity proteins, Im7 and Im9, that are experimentally known to fold very differently: Whereas Im9 folds directly, Im7 folds through a mispacked conformational intermediate. A simple model we developed accounts for their intriguingly different folding kinetics in terms of a balance between the density of native-promoting contacts and the hydrophobicity of local amino acid sequences. This emergent principle is extensible to other biomolecular recognition processes.

Theoretical perspectives on nonnative interactions and intrinsic disorder in protein folding and binding

The diverse biological functions of intrinsically disordered proteins (IDPs) have markedly raised our appreciation of protein conformational versatility, whereas the existence of energetically favorable yet functional detrimental nonnative interactions underscores the physical limitations of evolutionary optimization. Here we survey recent advances in using biophysical modeling to gain insight into experimentally observed nonnative behaviors and IDP properties. Simulations of IDP interactions to date focus mostly on coupled folding-binding, which follows essentially the same organizing principle as the local-nonlocal coupling mechanism in cooperative folding of monomeric globular proteins. By contrast, more innovative theories of electrostatic and aromatic interactions are needed for the conceptually novel but less-explored 'fuzzy' complexes in which the functionally bound IDPs remain largely disordered.

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.

cgDNA: a software package for the prediction of sequence-dependent coarse-grain free energies of B-form DNA

cgDNA is a package for the prediction of sequence-dependent configuration-space free energies for B-form DNA at the coarse-grain level of rigid bases. For a fragment of any given length and sequence, cgDNA calculates the configuration of the associated free energy minimizer, i.e. the relative positions and orientations of each base, along with a stiffness matrix, which together govern differences in free energies. The model predicts non-local (i.e. beyond base-pair step) sequence dependence of the free energy minimizer. Configurations can be input or output in either the Curves+ definition of the usual helical DNA structural variables, or as a PDB file of coordinates of base atoms. We illustrate the cgDNA package by comparing predictions of free energy minimizers from (a) the cgDNA model, (b) time-averaged atomistic molecular dynamics (or MD) simulations, and (c) NMR or X-ray experimental observation, for (i) the Dickerson–Drew dodecamer and (ii) three oligomers containing A-tracts. The cgDNA predictions are rather close to those of the MD simulations, but many orders of magnitude faster to compute. Both the cgDNA and MD predictions are in reasonable agreement with the available experimental data. Our conclusion is that cgDNA can serve as a highly efficient tool for studying structural variations in B-form DNA over a wide range of sequences.

Learning To Fold Proteins Using Energy Landscape Theory

This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation.

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.

Sequence analysis on the information of folding initiation segments in ferredoxin-like fold proteins

BACKGROUND

While some studies have shown that the 3D protein structures are more conservative than their amino acid sequences, other experimental studies have shown that even if two proteins share the same topology, they may have different folding pathways. There are many studies investigating this issue with molecular dynamics or Go-like model simulations, however, one should be able to obtain the same information by analyzing the proteins' amino acid sequences, if the sequences contain all the information about the 3D structures. In this study, we use information about protein sequences to predict the location of their folding segments. We focus on proteins with a ferredoxin-like fold, which has a characteristic topology. Some of these proteins have different folding segments.

RESULTS

Despite the simplicity of our methods, we are able to correctly determine the experimentally identified folding segments by predicting the location of the compact regions considered to play an important role in structural formation. We also apply our sequence analyses to some homologues of each protein and confirm that there are highly conserved folding segments despite the homologues' sequence diversity. These homologues have similar folding segments even though the homology of two proteins' sequences is not so high.

CONCLUSION

Our analyses have proven useful for investigating the common or different folding features of the proteins studied.

Perspective: Reaches of chemical physics in biology

Chemical physics as a discipline contributes many experimental tools, algorithms, and fundamental theoretical models that can be applied to biological problems. This is especially true now as the molecular level and the systems level descriptions begin to connect, and multi-scale approaches are being developed to solve cutting edge problems in biology. In some cases, the concepts and tools got their start in non-biological fields, and migrated over, such as the idea of glassy landscapes, fluorescence spectroscopy, or master equation approaches. In other cases, the tools were specifically developed with biological physics applications in mind, such as modeling of single molecule trajectories or super-resolution laser techniques. In this introduction to the special topic section on chemical physics of biological systems, we consider a wide range of contributions, all the way from the molecular level, to molecular assemblies, chemical physics of the cell, and finally systems-level approaches, based on the contributions to this special issue. Chemical physicists can look forward to an exciting future where computational tools, analytical models, and new instrumentation will push the boundaries of biological inquiry.