Scaling of Folding Times with Protein Size

Naganathan, Athi N.; Muñoz, Víctor

doi:10.1021/ja044449u

Cited by 152 publications

(185 citation statements)

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“…equation (2) where ΔH(T) is the equilibrium unfolding enthalpy at a given temperature and ΔC p the change in heat capacity upon unfolding (61). n σ represents the frequency at which the excess enthalpy fluctuations in the unfolded state reach enthalpy values characteristic of the native state.…”

Section: Free Energy Barriers To Foldingmentioning

confidence: 99%

“…The barriers obtained with this method are consistent with the estimates from equation 1. In fact, a plot of the barrier heights calculated from equation 2 at 333 K versus the logarithm of experimental folding rates (in energy units) crosses the zero barrier at ~ 1/(1 microsecond), providing an independent estimate of the average diffusion coefficient for folding (61). Another interesting aspect of this analysis is that it is entirely based on thermodynamic properties.…”

Section: Free Energy Barriers To Foldingmentioning

confidence: 99%

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Dynamics, Energetics, and Structure in Protein Folding

et al. 2006

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For many decades, protein folding experimentalists have worked with no information about the timescales of relevant protein folding motions and without methods for estimating the height of folding barriers. Experiments in protein folding have been interpreted using chemical models in which the folding process is characterized as a series of equilibria between two or more distinct states that interconvert with activated kinetics. Accordingly, the information to be extracted from experiment was circumscribed to apparent equilibrium constants and relative folding rates. Recent developments are changing this situation dramatically. The combination of fast-folding experiments with the development of analytical methods more closely connected to physical theory reveals that folding barriers in native conditions range from minimally high (~14 RT for the very slow folder AcP) to nonexisting. While slow-folding (i.e. 1 millisecond or longer) single domain proteins are expected to fold in a two-state fashion, microsecond-folding proteins should exhibit complex behavior arising from crossing marginal or negligible folding barriers. This realization opens a realm of exciting opportunities for experimentalists. The free energy surface of a protein with marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic from structural factors in folding. Kinetic experiments on these proteins provide the unique opportunity to measure folding dynamics directly. Furthermore, the complex distributions of time-dependent folding behaviors expected for these proteins might be accessible to single molecule measurements. Here, we discuss some of these recent developments in protein folding, emphasizing aspects that can serve as a guide for experimentalists interested in exploiting this new avenue of research.In folding to their biologically active 3D structures, proteins must coordinate the vast number of degrees of freedom of their polypeptide chains by forming complex networks of noncovalent interactions. Therefore, understanding protein folding involves determining the relations between the energetics of weak interactions and protein conformation, and the collective chain dynamics that govern the search in conformational space. In modern rate theory, these issues are resolved by mapping the potential energy of the molecule as a function of the relevant coordinates. The dynamics are then represented as diffusion on such an energy surface(1,2). For folding reactions, however, even the solvent-averaged free energy surface is hyper-dimensional due to the large number of relevant coordinates (i.e. thousands of atomic coordinates for a small protein)(3). Folding hypersurfaces should also be topographically complex due to frustration between the myriads of possible interactions (3,4). Moreover, molecular simulations(5-8) and NMR dynamics experiments(9) indicate that protein conformational motions span a wide range of timescales (i.e. from picoseconds to milliseconds). The implication is that measuri...

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Section: Free Energy Barriers To Foldingmentioning

confidence: 99%

Section: Free Energy Barriers To Foldingmentioning

confidence: 99%

Dynamics, Energetics, and Structure in Protein Folding

et al. 2006

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“…Sometime ago it was shown theoretically that the folding time ,τ F , should depend on N [7,8,9] but only recently has experimental data confirmed this prediction [4,6,10,11,12]. It has been…”

Section: Introductionmentioning

confidence: 99%

Effect of Finite Size on Cooperativity and Rates of Protein Folding

Kouza

O’Brien

et al. 2005

J. Phys. Chem. A

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We analyze the dependence of cooperativity of the thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N , using lattice models with side chains, off-lattice Go models and the available experimental data. A dimensionless measure of cooperativity,The results of simulations and the analysis of experimental data further confirm the earlier prediction that ζ is universal with ζ = 1 + γ, where exponent γ characterizes the susceptibility of a self-avoiding walk. This finding suggests that the structural characteristics in the denaturated state are manifested in the folding cooperativity at the transition temperature. The folding rates k F for the Go models and a dataset of 69 proteins can be fit using k F = k 0 F exp(−cN β ). Both β = 1/2 and 2/3 provide a good fit of the data. We find that k F = k 0 F exp(−cN 1 2 ), with the average (over the dataset of proteins) k 0 F ≈ (0.2µs) −1 and c ≈ 1.1, can be used to estimate folding rates to within an order of magnitude in most cases. The minimal models give identical N dependence with c ≈ 1. The prefactor for off-lattice Go models is nearly four orders of magnitude larger than the experimental value.

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“…We now know that folding barriers increase with protein size, and that proteins Ͻ55 residues are likely to have marginal folding barriers (15). The role of protein structure (or topology) on the determination of folding rates, and thus folding barriers, was originally established by the observation of good correlations between folding rates and empirical structural parameters [i.e., the relative contact order (16)], and then further corroborated by the application of simple statistical mechanical models to the prediction of folding rates (17).…”

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confidence: 99%

Large-scale modulation of thermodynamic protein folding barriers linked to electrostatics

Halskau

Pérez-Jiménez

Ibarra‐Molero

et al. 2008

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

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natural selection ͉ homologous proteins ͉ structural pK shifts ͉ conformational ensembles ͉ differential scanning calorimetry C onventionally, the folding and function of single-domain proteins are described as two-state processes in analogy to elementary chemical reactions. The protein molecule is assumed to reside in either of two states: folded or active and unfolded or inactive, which interconvert by crossing a high free-energy barrier with transition-state-like kinetics. However, proteins can in principle exist in many different conformations or microstates because of their thousands of degrees of freedom. Such inherent complexity is best described by using low-dimensional freeenergy surfaces, which are obtained by projecting the solventaveraged energy as a function of atomic coordinates onto a few order parameters [the energy landscape approach (1)]. A freeenergy surface description includes the two-state folding model as a particular scenario, but is more general. In this approach barriers, basins of attraction, and even finer topographical details of the surface (i.e., roughness) emerge from detailed balancing between conformational entropy and the energy from stabilizing interactions (see refs. 2 and 3 for some specific examples). Therefore, surfaces that exhibit marginal barriers or are even completely barrierless appear as interesting alternatives to the two-state folding picture (1). These predictions have been confirmed experimentally in recent years (4-6).If the folding barriers are comparable to the thermal energy (RT), ensembles of conformations with an intermediate degree of structure become significantly populated and interconvert with diffusive dynamics. This realization opens a realm of possibilities for the experimental study of protein folding reactions and mechanisms (recently reviewed in ref. 7). Moreover, it also has important implications for protein function because the conformational fluctuations associated with marginal folding barriers could be exploited to modulate activity and/or synchronize the action of enzymes in sequential reactions (8). Examples of how this could be achieved have been recently explored for protein binding with the fly-cast model (9, 10) and related analyses (11), as well as for the optimization of allosteric coupling (12).Another important consequence of shallow free-energy surfaces is that their shape can be resolved in equilibrium experiments sensitive to the energy fluctuations associated with protein conformation, such as differential scanning calorimetry (DSC). Building on this idea, Muñoz and Sanchez-Ruiz have recently developed a phenomenological variable-barrier model for the analysis of DSC data (13). In this analysis, the DSC thermogram is fitted to an idealized (i.e., a Landau quartic polynomial) one-dimensional free-energy surface from which it is possible to estimate the barrier height and the population of conformational ensembles with an intermediate degree of structure (13). Although these folding barriers are intrinsically ''thermodynamic,'' ...

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Scaling of Folding Times with Protein Size

Cited by 152 publications

References 14 publications

Dynamics, Energetics, and Structure in Protein Folding

Dynamics, Energetics, and Structure in Protein Folding

Effect of Finite Size on Cooperativity and Rates of Protein Folding

Large-scale modulation of thermodynamic protein folding barriers linked to electrostatics

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