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The energy landscapes of repeat-containing proteins: topology, cooperativity, and the folding funnels of one-dimensional architectures.

Ferreiro DU, Walczak AM, Komives EA, Wolynes PG - PLoS Comput. Biol. (2008)

Bottom Line: The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (DeltaG(water)) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.

ABSTRACT
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 (DeltaG(water)) 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.

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Application of the coarse-grained model to predict the chemical denaturant induced unfolding.(A) The computed free energy in water and m-value for the coarse grain model with the elementary parameters from Figure 6, and T = 0.9147 Tf, α = 1.7 (closed circles), and the experimentally determined values (open circles). (B) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 0.9 Tf. (C) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 1.1 Tf.
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pcbi-1000070-g007: Application of the coarse-grained model to predict the chemical denaturant induced unfolding.(A) The computed free energy in water and m-value for the coarse grain model with the elementary parameters from Figure 6, and T = 0.9147 Tf, α = 1.7 (closed circles), and the experimentally determined values (open circles). (B) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 0.9 Tf. (C) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 1.1 Tf.

Mentions: The value of the parameters for elementary interactions in the analytical model were determined from temperature denaturations of the topologically based model, but the values should be applicable to analyze any denaturation method. We further applied the analytical model to analyze the chemical denaturation behavior of the TPR-repeat protein family, and quantitatively compare the predicted parameters to the experimentally observed values. In making this mapping, there are two input parameters in the analytical treatment of chemical denaturations that need to be determined, the experimental folding temperature Tf, and the susceptibility to denaturant parameter αj. We first treat these as free parameters and fit their values to minimize the differences in both the m-value and the ΔGwater to the experimentally measured ones. Figure 7A shows the close quantitative agreement between the experiments and values obtained from the analytical model. For the free parameters, the values we recover are T = 0.91 Tf, and αj 1.7 kB [D]−1. We can crudely compare this with the apparent folding temperature of CTPR3 (∼355 K) (http://www.yale.edu/reganlab) and the temperature at which the denaturations were actually performed (∼298 K), then T = 0.84 Tf. In principle, the susceptibility can be estimated from the difference in solvent accessible surface area (SASA) between the fully folded and the fully unfolded states [35]. The m-value estimated from the crystallographic structure of CTPR3 is 1.5 kcal mol−1 [GuHCl]−1. With this value, αj is estimated to be 0.7 (eq. 6), for an homogeneous repeat-protein, a 2.5 fold difference from the value recovered from the analytical model. This difference is likely to arise from the non-additivity of the natural interaction energetics, that are not explicitly treated in the topological model from which the parameters for the analytical model were derived (Figure 6). This parallels the behavior of activation free energies which are underestimated in purely additive models [36].


The energy landscapes of repeat-containing proteins: topology, cooperativity, and the folding funnels of one-dimensional architectures.

Ferreiro DU, Walczak AM, Komives EA, Wolynes PG - PLoS Comput. Biol. (2008)

Application of the coarse-grained model to predict the chemical denaturant induced unfolding.(A) The computed free energy in water and m-value for the coarse grain model with the elementary parameters from Figure 6, and T = 0.9147 Tf, α = 1.7 (closed circles), and the experimentally determined values (open circles). (B) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 0.9 Tf. (C) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 1.1 Tf.
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2366061&req=5

pcbi-1000070-g007: Application of the coarse-grained model to predict the chemical denaturant induced unfolding.(A) The computed free energy in water and m-value for the coarse grain model with the elementary parameters from Figure 6, and T = 0.9147 Tf, α = 1.7 (closed circles), and the experimentally determined values (open circles). (B) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 0.9 Tf. (C) Folding curves predicted for TPR proteins of different lengths (from 5 to 30), at T = 1.1 Tf.
Mentions: The value of the parameters for elementary interactions in the analytical model were determined from temperature denaturations of the topologically based model, but the values should be applicable to analyze any denaturation method. We further applied the analytical model to analyze the chemical denaturation behavior of the TPR-repeat protein family, and quantitatively compare the predicted parameters to the experimentally observed values. In making this mapping, there are two input parameters in the analytical treatment of chemical denaturations that need to be determined, the experimental folding temperature Tf, and the susceptibility to denaturant parameter αj. We first treat these as free parameters and fit their values to minimize the differences in both the m-value and the ΔGwater to the experimentally measured ones. Figure 7A shows the close quantitative agreement between the experiments and values obtained from the analytical model. For the free parameters, the values we recover are T = 0.91 Tf, and αj 1.7 kB [D]−1. We can crudely compare this with the apparent folding temperature of CTPR3 (∼355 K) (http://www.yale.edu/reganlab) and the temperature at which the denaturations were actually performed (∼298 K), then T = 0.84 Tf. In principle, the susceptibility can be estimated from the difference in solvent accessible surface area (SASA) between the fully folded and the fully unfolded states [35]. The m-value estimated from the crystallographic structure of CTPR3 is 1.5 kcal mol−1 [GuHCl]−1. With this value, αj is estimated to be 0.7 (eq. 6), for an homogeneous repeat-protein, a 2.5 fold difference from the value recovered from the analytical model. This difference is likely to arise from the non-additivity of the natural interaction energetics, that are not explicitly treated in the topological model from which the parameters for the analytical model were derived (Figure 6). This parallels the behavior of activation free energies which are underestimated in purely additive models [36].

Bottom Line: The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (DeltaG(water)) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.

ABSTRACT
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 (DeltaG(water)) 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.

Show MeSH
Related in: MedlinePlus