Frustration in Biomolecules

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.Comment: 97 pages, 30 figure

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 towards 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

Amino acid metabolism conflicts with protein diversity

The twenty protein coding amino acids are found in proteomes with different relative abundances. The most abundant amino acid, leucine, is nearly an order of magnitude more prevalent than the least abundant amino acid, cysteine. Amino acid metabolic costs differ similarly, constraining their incorporation into proteins. On the other hand, sequence diversity is necessary for protein folding, function and evolution. Here we present a simple model for a cost-diversity trade-off postulating that natural proteomes minimize amino acid metabolic flux while maximizing sequence entropy. The model explains the relative abundances of amino acids across a diverse set of proteomes. We found that the data is remarkably well explained when the cost function accounts for amino acid chemical decay. More than one hundred proteomes reach comparable solutions to the trade-off by different combinations of cost and diversity. Quantifying the interplay between proteome size and entropy shows that proteomes can get optimally large and diverse

Resolving the fine structure in the energy landscapes of repeat proteins

Ankyrin (ANK) repeat proteins are coded by tandem occurrences of patterns with around 33 amino acids. They often mediate protein–protein interactions in a diversity of biological systems. These proteins have an elongated non-globular shape and often display complex folding mechanisms. This work investigates the energy landscape of representative proteins of this class made up of 3, 4 and 6 ANK repeats using the energy-landscape visualisation method (ELViM). By combining biased and unbiased coarse-grained molecular dynamics AWSEM simulations that sample conformations along the folding trajectories with the ELViM structure-based phase space, one finds a three-dimensional representation of the globally funnelled energy surface. In this representation, it is possible to delineate distinct folding pathways. We show that ELViMs can project, in a natural way, the intricacies of the highly dimensional energy landscapes encoded by the highly symmetric ankyrin repeat proteins into useful low-dimensional representations. These projections can discriminate between multiplicities of specific parallel folding mechanisms that otherwise can be hidden in oversimplified depictions.M.N.S. was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq; Grant 130147/2020-6). This research was supported by the Center for Theoretical Biological Physics sponsored by the NSF (Grant PHY-2019745). A.B.O. acknowledges the Robert A. Welch Postdoctoral Fellow program. P.G.W. is also supported by the D.R. Bullard-Welch Chair at Rice University (Grant C-0016). V.B.P.L. was supported by CNPq (Grant 310017/2020-3) and FAPESP (Grants 2019/22540-3 and 2018/18668-1). D.U.F. is a CONICET researcher and is supported by Grant PICT2016/1467, UBACYT, and NASA Astrobiology Institute-Enigma (Grant 80NSSC18M0093).Peer ReviewedPostprint (published version

Protein stability and dynamics modulation: the case of human frataxin

Frataxin (FXN) is an α/β protein that plays an essential role in iron homeostasis. Apparently, the function of human FXN (hFXN) depends on the cooperative formation of crucial interactions between helix α1, helix α2, and the C-terminal region (CTR) of the protein. In this work we quantitatively explore these relationships using a purified recombinant fragment hFXN90-195. This variant shows the hydrodynamic behavior expected for a monomeric globular domain. Circular dichroism, fluorescence, and NMR spectroscopies show that hFXN90-195 presents native-like secondary and tertiary structure. However, chemical and temperature induced denaturation show that CTR truncation significantly destabilizes the overall hFXN fold. Accordingly, limited proteolysis experiments suggest that the native-state dynamics of hFXN90-195 and hFXN90-210 are indeed different, being the former form much more sensitive to the protease at specific sites. The overall folding dynamics of hFXN fold was further explored with structure-based protein folding simulations. These suggest that the native ensemble of hFXN can be decomposed in at least two substates, one with consolidation of the CTR and the other without consolidation of the CTR. Explicit-solvent all atom simulations identify some of the proteolytic target sites as flexible regions of the protein. We propose that the local unfolding of CTR may be a critical step for the global unfolding of hFXN, and that modulation of the CTR interactions may strongly affect hFXN physiological function.Facultad de Ciencias Exacta

The Energy Landscapes of Repeat-Containing Proteins: Topology, Cooperativity, and the Folding Funnels of One-Dimensional Architectures

Repeat-proteins are made up of near repetitions of 20– to 40–amino acid stretches. These polypeptides usually fold up into non-globular, elongated architectures that are stabilized by the interactions within each repeat and those between adjacent repeats, but that lack contacts between residues distant in sequence. The inherent symmetries both in primary sequence and three-dimensional structure are reflected in a folding landscape that may be analyzed as a quasi–one-dimensional problem. We present a general description of repeat-protein energy landscapes based on a formal Ising-like treatment of the elementary interaction energetics in and between foldons, whose collective ensemble are treated as spin variables. The overall folding properties of a complete “domain” (the stability and cooperativity of the repeating array) can be derived from this microscopic description. The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (ΔGwater) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins. We show how the parameters for the “coarse-grained” description in terms of foldon spin variables can be extracted from more detailed folding simulations on perfectly funneled landscapes. To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions. Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are “poised” at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions

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.Fil: Craig, Patricio Oliver. Fundación Instituto Leloir; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. University of California San Diego. Department of Chemistry and Biochemistry; Estados UnidosFil: Lätzer, Joachim. Rutgers University. BioMaPS Institute; Estados UnidosFil: Weinkam, Patrick. University of California at San Francisco. Department of Bioengineering and Therapeutic Sciences; Estados UnidosFil: Hoffman, Ryan M. B.. University Of California At San Diego; Estados UnidosFil: Ferreiro, Diego. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Komives, Elizabeth A.. University Of California At San Diego; Estados UnidosFil: Wolynes, Peter G.. University Of California At San Diego; Estados Unido