Conformations of a polyelectrolyte chain

Ha, Bae‐Yeun; Thirumalai, D.

doi:10.1103/physreva.46.r3012

Cited by 59 publications

(70 citation statements)

References 15 publications

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“…4,9 In accord with physical intuition, unfolded polypeptide chains have been shown to expand with increasing net charge. 4,14,30,31,33,53 Based on these results, an increase in net charge, |Z|, of unfolded CspTm from 3.8 at pH 7 to 10.2 at pH 2.9 would therefore be expected to lead to an expansion of the chain, in contrast to our experimental observation. In the past, the effect of charges on the dimensions of polymers has often been treated as an additional contribution to the effective excluded volume of the chain, and several theories have been developed based on this concept to describe the behavior of polyelectrolytes and polyampholytes 30,31,54 (all of which are conceptually similar).…”

Section: Treating Charge-charge Interactions In Unfolded Csptm With Pcontrasting

confidence: 55%

“…4,14,30,31,33,53 Based on these results, an increase in net charge, |Z|, of unfolded CspTm from 3.8 at pH 7 to 10.2 at pH 2.9 would therefore be expected to lead to an expansion of the chain, in contrast to our experimental observation. In the past, the effect of charges on the dimensions of polymers has often been treated as an additional contribution to the effective excluded volume of the chain, and several theories have been developed based on this concept to describe the behavior of polyelectrolytes and polyampholytes 30,31,54 (all of which are conceptually similar). In order to estimate the effect of charge interactions on the radius of gyration of CspTm, we used the polyampholyte theory developed by Higgs and Joanny, 30 which includes repulsive electrostatic interactions and a second-order correction to account for attractive electrostatic interactions of charges with opposite sign.…”

Section: Treating Charge-charge Interactions In Unfolded Csptm With Pcontrasting

confidence: 55%

“…This extensive data set allowed us to use polyelectrolyte theory in combination with an empirical denaturant binding model to separate long-range interactions resulting from the electrostatics from short-ranged intra-chain interactions. In contrast to the chemical heterogeneity of proteins, the effect of charges on the size of polymers can be treated in a self-consistent manner, [30][31][32][33] i.e., without additional parameters, and thus serves as a starting point for a more elaborate experimental investigation of the subtle balance of forces that determine the size of unfolded proteins and charged IDPs. 34 …”

Section: Introductionmentioning

confidence: 99%

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Single-molecule spectroscopy of the unexpected collapse of an unfolded protein at low pH

Hofmann

Nettels

Schuler

2013

The Journal of Chemical Physics

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The dimensions of intrinsically disordered and unfolded proteins critically depend on the solution conditions, such as temperature, pH, ionic strength, and osmolyte or denarurant concentration. However, a quantitative understanding of how the complex combination of chain-chain and chain-solvent interactions is affected by the solvent is still missing. Here, we take a step towards this goal by investigating the combined effect of pH and denaturants on the dimensions of an unfolded protein. We use single-molecule fluorescence spectroscopy to extract the dimensions of unfolded cold shock protein (CspTm) in mixtures of the denaturants urea and guanidinium chloride (GdmCl) at neutral and acidic pH. Surprisingly, even though a change in pH from 7 to 2.9 increases the net charge of CspTm from -3.8 to +10.2, the radius of gyration of the chain is very similar under both conditions, indicating that protonation of acidic side chains at low pH results in additional hydrophobic interactions. We use a simple shared binding site model that describes the joint effect of urea and GdmCl, together with polyampholyte theory and an ion cloud model that includes the chemical free energy of counterion interactions and side chain protonation, to quantify this effect. The dimensions of intrinsically disordered and unfolded proteins critically depend on the solution conditions, such as temperature, pH, ionic strength, and osmolyte or denarurant concentration. However, a quantitative understanding of how the complex combination of chain-chain and chain-solvent interactions is affected by the solvent is still missing. Here, we take a step towards this goal by investigating the combined effect of pH and denaturants on the dimensions of an unfolded protein. We use single-molecule fluorescence spectroscopy to extract the dimensions of unfolded cold shock protein (CspTm) in mixtures of the denaturants urea and guanidinium chloride (GdmCl) at neutral and acidic pH. Surprisingly, even though a change in pH from 7 to 2.9 increases the net charge of CspTm from −3.8 to +10.2, the radius of gyration of the chain is very similar under both conditions, indicating that protonation of acidic side chains at low pH results in additional hydrophobic interactions. We use a simple shared binding site model that describes the joint effect of urea and GdmCl, together with polyampholyte theory and an ion cloud model that includes the chemical free energy of counterion interactions and side chain protonation, to quantify this effect. © 2013 AIP Publishing LLC.

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Section: Treating Charge-charge Interactions In Unfolded Csptm With Pcontrasting

confidence: 55%

Section: Treating Charge-charge Interactions In Unfolded Csptm With Pcontrasting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

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Single-molecule spectroscopy of the unexpected collapse of an unfolded protein at low pH

Hofmann

Nettels

Schuler

2013

The Journal of Chemical Physics

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“…A considerable body of experimental and theoretical work suggests that the dimensions of unfolded proteins depend on parameters such as amino acid composition (4), temperature (18), and solvent quality (3,10,15,19). The continuous collapse of polymers has been treated exhaustively by a number of theories (20)(21)(22)(23)(24) based on general principles that relate the dimensions and the length of a chain to its free energy. However, a prerequisite for the quantitative application of these theories and their comparison to experimental results is that the dimensions of the Θ-state are known, which serves as an essential reference state.…”

mentioning

confidence: 99%

Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy

Hofmann

Soranno

Borgia

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

436

599

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The dimensions of unfolded and intrinsically disordered proteins are highly dependent on their amino acid composition and solution conditions, especially salt and denaturant concentration. However, the quantitative implications of this behavior have remained unclear, largely because the effective theta-state, the central reference point for the underlying polymer collapse transition, has eluded experimental determination. Here, we used single-molecule fluorescence spectroscopy and two-focus correlation spectroscopy to determine the theta points for six different proteins. While the scaling exponents of all proteins converge to 0.62 AE 0.03 at high denaturant concentrations, as expected for a polymer in good solvent, the scaling regime in water strongly depends on sequence composition. The resulting average scaling exponent of 0.46 AE 0.05 for the four foldable protein sequences in our study suggests that the aqueous cellular milieu is close to effective theta conditions for unfolded proteins. In contrast, two intrinsically disordered proteins do not reach the Θ-point under any of our solvent conditions, which may reflect the optimization of their expanded state for the interactions with cellular partners. Sequence analyses based on our results imply that foldable sequences with more compact unfolded states are a more recent result of protein evolution.protein folding | single-molecule FRET | coil-globule transition | polymer theory I t has become increasingly clear that the structure and dynamics of unfolded proteins are essential for understanding protein folding (1-3) and the functional properties of intrinsically disordered proteins (IDPs) (4-6). Theoretical concepts from polymer physics (7-9) have frequently been used to describe the properties of unfolded polypeptide chains (4, 10, 11) with the goal to establish the link between protein folding and collapse (12-15). However, the methodology to test many of these concepts experimentally has only become available rather recently (2,16,17). A considerable body of experimental and theoretical work suggests that the dimensions of unfolded proteins depend on parameters such as amino acid composition (4), temperature (18), and solvent quality (3,10,15,19). The continuous collapse of polymers has been treated exhaustively by a number of theories (20-24) based on general principles that relate the dimensions and the length of a chain to its free energy. However, a prerequisite for the quantitative application of these theories and their comparison to experimental results is that the dimensions of the Θ-state are known, which serves as an essential reference state. At the Θ-point*, chain-chain and chain-solvent interactions balance such that the polymer is at a critical point, at which the thermodynamic phase boundaries disappear. As a result, the polypeptide chain obeys the same length scaling as an ideal chain without excluded volume and intrachain interactions. However, the Θ-conditions for protein chains are unknown. Besides its importance for obtaining the corre...

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“…(1B)) suggests a first-order coil-globule transition in Mg 2+ . While less common in neutral homopolymers, a discontinuous coil-globule transition has been predicted to occur in strongly charged polyelectrolytes [17].…”

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confidence: 99%

Persistence Length Changes Dramatically as RNA Folds

et al. 2005

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We determine the persistence length, lp, for a bacterial group I ribozyme as a function of concentration of monovalent and divalent cations by fitting the distance distribution functions P (r) obtained from small angle X-ray scattering intensity data to the asymptotic form of the calculated PW LC (r) for a worm-like chain (WLC). The lp values change dramatically over a narrow range of Mg 2+ concentration from ∼21Å in the unfolded state (U) to ∼10Å in the compact (IC) and native states. Variations in lp with increasing Na + concentration are more gradual. In accord with the predictions of polyelectrolyte theory we find lp ∝ 1/κ 2 where κ is the inverse Debye-screening length.Elucidating the mechanisms by which RNA molecules self-assemble to form three dimensional structures is a challenging problem [1,2,3,4]. Because the native state (N) cannot form without significantly neutralizing the negative charge on [5,6] the phosphate group, RNA folding is sensitive to the valence, size, and shape of the counterions. At low counterion concentrations (C) RNA is unfolded (U) in the sense that it contains isolated stretches of base-paired stem loops that have large dynamical fluctuations. When C > C m , the midpoint of the transition from U to the N, RNA becomes compact as a result of formation of tertiary contacts. For many RNA molecules, such as the Tetrahymena ribozyme and RNase P, folding to the native state is preceded by the formation of multiple metastable kinetic intermediates (I) [1,2,7].The large dynamic conformational fluctuations in the U and I states make it difficult to characterize their structures. However, small angle scattering experiments can be used to determine the shape of RNA as it folds. The conformation of RNA in the U, N, and the I states is characterized by R g , the radius of gyration, and l p , the persistence length. Small Angle X-ray Scattering (SAXS) [2,8,9,10,11] and Small Angle Neutron Scattering (SANS) [12] experiments have been used to obtain R g as a function of counterions for a number of RNA molecules. In contrast, l p , which is a function of C and valence and shape of counterions, is more difficult to obtain.In this letter, we use SAXS data and theoretical results for the worm-like chain (WLC) to obtain l p for a 195 nucleotide group I ribozyme from pre-tRNA(Ile) of the Azoarcus bacterium as a function of C for monovalent and divalent counterions. The major conclusions of the present study are: (i) The experimentally determined distance distribution functions P (r) can be accurately fit using the theoretical results for wormlike chains for r/R g > 1 where R g is the radius of gyration of RNA. The l p values, which were calculated by fitting P (r) to P W LC (r) for r > R g , change dramatically from l p ≃ 21Å in the U state to l p ≃ 10 A in the compact conformation. (ii) The large reduction in l p occurs abruptly over a narrow concentration range in Mg 2+ whereas the decrease of l p in Na + is gradual. This result suggests that the compaction of RNA resembles a first order transition i...

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Conformations of a polyelectrolyte chain

Cited by 59 publications

References 15 publications

Single-molecule spectroscopy of the unexpected collapse of an unfolded protein at low pH

Single-molecule spectroscopy of the unexpected collapse of an unfolded protein at low pH

Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy

Persistence Length Changes Dramatically as RNA Folds

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