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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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Folding energy landscape of repeat-proteins.(A) A 5-element repeat-protein folding landscape is shown. Each macrostate is depicted as function of the number of folded elements, their internal energy, and added entropy. The population of each possible macrostate is shown colored according to its free energy. Some of the macrostates are labeled according to the location of the folded elements from N to C termini (00000 fully unfolded, 11111 fully folded). (B) Change in the relative population of each configuration as the temperature changes.
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pcbi-1000070-g008: Folding energy landscape of repeat-proteins.(A) A 5-element repeat-protein folding landscape is shown. Each macrostate is depicted as function of the number of folded elements, their internal energy, and added entropy. The population of each possible macrostate is shown colored according to its free energy. Some of the macrostates are labeled according to the location of the folded elements from N to C termini (00000 fully unfolded, 11111 fully folded). (B) Change in the relative population of each configuration as the temperature changes.

Mentions: Since the presented method recovers the values for all the parameters of the analytical model, we can compute the overall energy and entropy of every possible macro-state. The resulting repeat-protein folding free energy landscape is presented in Figure 8. We use for illustration the example of the shortest three TPR-repeat protein. The fully unfolded state is at the top of the funnel, a state that has the highest entropy and the lowest energy (Figure 8A). At the bottom, the fully folded state has the opposite contributions. In between there exist several discrete possibilities corresponding to the folding of different numbers of elements. Each of these ‘steps’ has a characteristic energy/added entropy balance, reflecting the fact that the protein is finite and inhomogeneous. The added entropy is a result of the underlying degrees of freedom, which we describe within the coarse grained model. The population of each of the states depends on this precise balance at any given temperature. At low temperatures, the fully folded states and states with 4 elements folded (or 1 ‘crack’ introduced) are mostly populated, while at high temperatures the fully unfolded and the states with one-element folded are populated (Figure 8B). Right at the folding temperature several intermediate species become populated, and this distribution need not be homogeneous (Figure 8B). Each of these intermediate states will contribute to the overall cooperativity and stability of the repeat-protein domain, and the spontaneous population of them might be functionally relevant, as discussed below.


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)

Folding energy landscape of repeat-proteins.(A) A 5-element repeat-protein folding landscape is shown. Each macrostate is depicted as function of the number of folded elements, their internal energy, and added entropy. The population of each possible macrostate is shown colored according to its free energy. Some of the macrostates are labeled according to the location of the folded elements from N to C termini (00000 fully unfolded, 11111 fully folded). (B) Change in the relative population of each configuration as the temperature changes.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000070-g008: Folding energy landscape of repeat-proteins.(A) A 5-element repeat-protein folding landscape is shown. Each macrostate is depicted as function of the number of folded elements, their internal energy, and added entropy. The population of each possible macrostate is shown colored according to its free energy. Some of the macrostates are labeled according to the location of the folded elements from N to C termini (00000 fully unfolded, 11111 fully folded). (B) Change in the relative population of each configuration as the temperature changes.
Mentions: Since the presented method recovers the values for all the parameters of the analytical model, we can compute the overall energy and entropy of every possible macro-state. The resulting repeat-protein folding free energy landscape is presented in Figure 8. We use for illustration the example of the shortest three TPR-repeat protein. The fully unfolded state is at the top of the funnel, a state that has the highest entropy and the lowest energy (Figure 8A). At the bottom, the fully folded state has the opposite contributions. In between there exist several discrete possibilities corresponding to the folding of different numbers of elements. Each of these ‘steps’ has a characteristic energy/added entropy balance, reflecting the fact that the protein is finite and inhomogeneous. The added entropy is a result of the underlying degrees of freedom, which we describe within the coarse grained model. The population of each of the states depends on this precise balance at any given temperature. At low temperatures, the fully folded states and states with 4 elements folded (or 1 ‘crack’ introduced) are mostly populated, while at high temperatures the fully unfolded and the states with one-element folded are populated (Figure 8B). Right at the folding temperature several intermediate species become populated, and this distribution need not be homogeneous (Figure 8B). Each of these intermediate states will contribute to the overall cooperativity and stability of the repeat-protein domain, and the spontaneous population of them might be functionally relevant, as discussed below.

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