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Frustration in Biomolecules
Diego U. Ferreiro, Elizabeth A. Komives, Peter G. Wolynes
TL;DR
Protein folding and biomolecular function must be understood despite conflicting interactions encoded by sequence. This review develops energy landscape theory and tests frustration concepts in polymers, simulations, and proteins. It concludes that global frustration is generally small in real proteins, while local frustration can be functionally important, although experiments and current force fields do not yet quantify ruggedness precisely.
Problem
Biomolecules must decode sequences into functional structures and dynamics, but conflicting interactions make folding and protein design difficult to understand and predict.
Method
The review combines logic and condensed-matter examples with energy landscape theory, heteropolymer simulations, bioinformatic energy-function inference, and analyses of natural and designed proteins.
Results
The paper finds that minimal frustration explains rapid, cooperative folding in lattice models, while most real proteins show small overall frustration and functionally relevant local frustration.
Takeaways & Limitations
Frustration provides a framework for relating biomolecular architecture to folding, binding, catalysis, allostery, and structure prediction.
Takeaways & Limitations
Direct experiments cannot easily quantify the ruggedness of most real protein landscapes, and even the most successful all-atom force field remains less cooperative than laboratory calorimetry.
Abstract
from arXiv · showhide
Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their 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 a 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 how structure connects to function. 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, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.
1 Perspectives on Frustration
Frustration arises when conflicting interactions prevent all local goals from being satisfied, producing degeneracy, barriers, and slow dynamics. In biomolecular heteropolymers, sequence complexity can reshape rugged landscapes into funnels, enabling specific and faster folding while preserving functional roles for localized frustration.
- Motivation: Biomolecules decode one-dimensional sequences into three-dimensional structures and four-dimensional dynamics, making folding a demanding information-processing task.The paper frames biomolecules as molecular information processors whose structures and motions support cellular functions.
- Frustration, Logic and Magnets: Frustration occurs when conflicting goals or interactions prevent simultaneous optimization, a problem shared by logic, computer science, magnets, and biomolecules.In triangular antiferromagnets, at least one interaction remains high-energy because no spin arrangement minimizes every interaction.
- Frustration, Logic and Magnets: Widespread frustration creates degenerate or metastable states and slow dynamics, making equilibrium or the global ground state difficult to reach.Spin glasses can remain out of equilibrium, with outcomes depending on system history and cooling conditions.
- Frustration, Logic and Magnets: Associative-memory magnets store globally encoded patterns, but excessive pattern loading causes spin-glass behavior and makes robust recollection impossible.The models have a finite storage capacity that scales linearly with system size.
- Frustration in Heteropolymers: Increasing sequence complexity transforms polymer landscapes from rugged and degenerate toward funneled landscapes with reduced trapping and more specific folding.Homopolymers have many near-equivalent states, while evolved sequences can make one structure dominate as the ground state.
- Frustration in Heteropolymers: Lower frustration in lattice heteropolymers supports faster folding and cooperative transitions, whereas higher frustration produces near-degenerate intermediates, trapping, and broadened transitions.Highly frustrated polymers resemble glass-forming liquids thermodynamically, while unfrustrated ones exhibit crystal-like first-order transitions.
- Frustration in Heteropolymers: Energy landscape theory quantifies frustration by comparing the folded-state energy with the random-landscape ground-state estimate using energy distributions sampled across configurations.The approach uses the configuration-space size, mean energy, variance, and chain entropy to estimate landscape properties without exhaustive enumeration.
2 Frustration and the energy landscape of real proteins
Energy landscape theory links protein folding thermodynamics and kinetics to the degree of frustration, while structure-based and learned energy functions provide ways to assess and reduce landscape ruggedness. Real proteins are globally near-minimally frustrated, but local frustration, incomplete models, and experimental limits constrain precise quantification.
- 2.1 The energy landscape of real proteins: Minimal frustration predicts a correlation between protein folding rates and thermodynamic stability because smooth funnel-like landscapes contain few significant barriers.This relationship is imperfect in real proteins but contrasts with the often-unpredictable rate–equilibrium relations of small-molecule chemistry.
- 2.1 The energy landscape of real proteins: φ-value analysis identifies the protein regions most critical to rate-limiting folding steps and supports the minimal frustration principle.Its success, together with controlled lattice-model behavior, provides global support for applying landscape theory to natural proteins.
- 2.1 The energy landscape of real proteins: Direct kinetic experiments cannot precisely determine residual energetic frustration in most real proteins, although indirect studies of molten globules can constrain ruggedness through Tg and Eg.The limitation arises because glassy effects are too weak to provide an accurate Tg from folding kinetics alone.
- 2.2 A license to learn via bioinformatics: Structure prediction and energy functions: Reliable folding across small proteins requires further tuning, and better-tuned models are more cooperative, indicating that current atomistic force fields retain excess frustration.Even the most successful reported model remains less cooperative than laboratory calorimetry, leaving room for improvement.
- 2.2 A license to learn via bioinformatics: Structure prediction and energy functions: Energy functions learned by optimizing funnel-like landscapes can produce transferable models whose free-energy profiles funnel near-native structures and recognize correct twilight-zone alignments.The learned coefficients are trained on known structures, then applied to proteins outside the training set.
- 2.3 Localizing and Visualizing Frustration in Natural Proteins: Pairwise local frustration is quantified by comparing native interactions with decoys generated either by residue-identity changes or by alternative compact structures.The two approaches distinguish mutational and configurational frustration and probe different competing interaction sets.
3 Frustration in the evolution of natural proteins and in protein design
Protein design and sequence simplification reveal how frustration constrains foldability while guiding the engineering of stable structures. Reduced alphabets can preserve folding for some topologies, but competing interactions and topological traps limit generality.
- Frustration and the complexity of Nature’s amino acid code: Simplifying BPTI by replacing 29 of 58 residues with alanine still allowed folding, although most mutants were thermodynamically destabilized.The effects depended on mutation position, and cumulative destabilization appeared additive when targeted sites contributed little to the cooperative folding core.
- Frustration and the complexity of Nature’s amino acid code: An 8-alanine substitution in a protease binding site preserved stability while stabilizing alternative conformations, linking engineered strain to frustration.The effect could not be attributed to structural deviations, so the authors relate such conflicts to frustration in folding.
- Frustration and the complexity of Nature’s amino acid code: Landscape theory predicts that larger alphabets can reduce ruggedness while maintaining a stability gap, making specific folds more robustly encodable.Once a topology is specified and the starting sequence has low overall frustration, competing structures are destabilized by the landscape topography.
- Frustration and the complexity of Nature’s amino acid code: Reduced-alphabet proteins can adopt native-like conformations and retain folding dynamics, but SH3 proteins could not be made functional with the three-letter IKE code.As alphabet complexity decreased, minimally frustrated interactions diminished and highly frustrated interactions appeared; tertiary conflicts limited coding reduction for this β-sheet-rich topology.
- Frustration in artificially designed proteins: Designing sequences against native and misfolded decoy structures aims to create a globally funneled landscape, but exhaustive protein-sequence search remains impractical.A 100-residue chain using 20 amino acids has about 1.2 x 10^130 possible sequences, while randomly generated sequences rarely fold.
- Frustration in artificially designed proteins: Top7 is unusually unfrustrated yet exhibits nonnative competing structures and β-swapping, illustrating topological frustration in designed proteins.Simulations found kinetic topological traps with polarized folding and several energetically competitive nonnative structures.
4 Folding kinetics and frustration
Folding kinetics reflect both topological and energetic frustration: conflicting interactions, traps, and repeat coupling reshape pathways, rates, and the interpretation of kinetic measurements. The review also connects frustration to symmetry, functional mechanisms, and anomalous folding behavior.
- Topological frustration: Sequence-distant contacts lose more entropy, requiring more compensating interactions and contributing to the correlation between folding rate and contact order.Contact order serves as a rough proxy for loop entropy.
- Topological frustration: Topological frustration can redirect folding routes and function: deleting IL-1β’s frustrated β-bulge preserves receptor affinity but abolishes signaling.The β-bulge lies between β-strands 4 and 5, where contacts direct folding-route selection.
- Symmetry effects: Symmetry reuses interactions, broadens the energy distribution, and increases the occurrence of low-energy structures despite fewer independent energetic bets.The energetic threshold for folding is the ground-state energy floor of random heteropolymers, Eg/N.
- Frustration in repeat proteins: Repeat-protein folding is shaped by local energetics: interface strength changes stability, folding rate, and cooperativity, while terminal repeats can shift transition states and reroute folding.Repeat symmetry also permits parallel initiation from either terminus, depending on the stability of nucleating repeats.
- Anomalous φ values: Nearly 1000 mutation measurements found most φ-values between 0 and 1, clustering around φ = 0.36±0.11 under isostability, while topology roughly predicts site-specific variation.This behavior is reported for natural proteins with simple kinetic behavior and is consistent with fractional local-native-structure occupancy.
- Anomalous φ values: On rugged landscapes, traps slow folding and can make φ-values difficult to interpret because transition-state reorganization depends on unknown non-native contacts.The φ-value analysis assumes that mutation leaves the transmission coefficient, related to configurational diffusion and internal friction, unchanged.
5 Functional consequences of Frustration
Local frustration helps explain how proteins bind, switch conformations, undergo metastable rearrangements, catalyze reactions, and aggregate. Across these functions, frustrated regions often mark structurally dynamic or interaction-sensitive parts of biomolecules.
- Binding sites are often frustrated: Binding interfaces usually form minimally frustrated contacts, while approximately 25% of pre-existing monomer contacts become less frustrated upon association and about 7% become more frustrated.The decrease largely reflects changed solvent accessibility and contact type upon binding.
- Frustration in allostery and local conformational changes: Highly frustrated regions are enriched at sites that reconfigure during allosteric transitions, whereas rigid conserved cores are connected by minimally frustrated interactions.Frustrated clusters often localize near pivot points, shifted local environments, or allosteric effector-binding sites.
- Frustration in allostery and local conformational changes: Allosteric switching involves a balanced exchange of local frustration between substates rather than completely minimally frustrated displaced regions.Some regions relieve frustration in one conformation; others retain frustration while exchanging interactions.
- Frustration in metastable and multistable proteins: In hemagglutinin, highly frustrated regions at neutral pH correspond to sites that rearrange and become less frustrated after acid-triggered conformational change.The fusion peptide is highly frustrated before triggering and is poised to interact with the endosomal membrane.
- Frustration in metastable and multistable proteins: Metastable proteins use frustrated regions to accommodate large rearrangements, including serpin strand insertion, domain swapping, and latent or polymeric states.In serpins, the swapped strand and the helix that must dislodge are highly frustrated, and domain swapping can initiate aggregation.
- Frustration, dynamics, and catalysis: Catalytic sites are expected to be locally frustrated because precise chemistry brings together residues that would otherwise favor different interactions, producing stability-function trade-offs.Mutations that stabilize folds can reduce catalytic power, whereas destabilizing mutations are often associated with increased catalytic activity.
- Frustration, dynamics, and catalysis: High frustration in thrombin surface loops corresponds more closely to microsecond-to-millisecond dynamics than to nanosecond motions, supporting a role in large-amplitude catalytic motions.Energetically unfavorable loop interactions facilitate conversion between ensembles needed for catalysis.
- Frustration and the initiation of aggregation: Frustration also helps explain selective association and cellular robustness by favoring correct partners, while domain-swapping symmetry can promote aggregation.The review links minimal frustration to reliable refolding and identifies domain swapping as an aggregation-initiation mechanism.
6 Frustration is a fundamental aspect of biochemistry
Frustration connects biomolecular architecture, dynamics, and function by producing degeneracy, metastability, and locally specialized interactions. The review links these effects to folding, specificity, self-assembly, and organization across cellular length scales.
- Frustration and emergent behavior: Imperfectly satisfiable constraints create state degeneracy, enabling emergent responses to subtle local energetic changes but potentially causing glass-like freezing.The balance between limited and excessive frustration distinguishes adaptable behavior from dynamics too slow for meaningful state exploration.
- Protein folding: Minimal frustration explains broad features of protein folding while deviations from its expectations identify situations where further discoveries may arise.The principle has generated testable hypotheses, interpreted diverse experiments, and supported computational tools.
- Folding and function: Frustration averaged across proteins helps infer energy functions for structure prediction, while local frustration contributes to folding kinetics and protein functions.Deviations from perfectly funneled landscapes can reflect previously unrecognized functional constraints.
- Interaction specificity: Protein sequences coevolve to preserve interaction specificity and limit inappropriate contacts despite the large number of proteins in cells.This constraint helps prevent cellular matter from becoming dominated by nonspecific interactions.
- Metastable dynamics: Low-free-energy excited states can arise from large-scale harmonic motions, local folding or unfolding, frustrated interactions, sequence symmetry, or combinations of these mechanisms.Frustrated local interactions can produce energetically degenerate structures and alternate conformations.
- Self-organization: For large nanoscale assemblies, the central challenge is reaching stable structures kinetically, with frustrated systems facing larger barriers and very large proteins sometimes requiring chaperones.Chaperone-assisted refolding may function as kinetic proofreading by dismantling misfolded molecules and allowing another folding attempt.
- Cellular organization: Cellular-scale organization involves nonequilibrium chemical-energy flows and motor activity that may help overcome large barriers and high glass-transition temperatures.An effective cytoskeletal temperature of 10,000 K was measured for only a minute fraction of degrees of freedom, and new tools are needed at this scale.