Dynamics, Energetics, and Structure in Protein Folding

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106

The small helical protein BBL has been shown to fold and unfold in the absence of a free energy barrier according to a battery of quantitative criteria in equilibrium experiments, including probedependent equilibrium unfolding, complex coupling between denaturing agents, characteristic DSC thermogram, gradual melting of secondary structure, and heterogeneous atom-by-atom unfolding behaviors spanning the entire unfolding process. Here, we present the results of nanosecond T-jump experiments probing backbone structure by IR and end-to-end distance by FRET. The folding dynamics observed with these two probes are both exponential with common relaxation times but have large differences in amplitude following their probe-dependent equilibrium unfolding. The quantitative analysis of amplitude and relaxation time data for both probes shows that BBL folding dynamics are fully consistent with the one-state folding scenario and incompatible with alternative models involving one or several barrier crossing events. At 333 K, the relaxation time for BBL is 1.3 s, in agreement with previous folding speed limit estimates. However, late folding events at room temperature are an order of magnitude slower (20 s), indicating a relatively rough underlying energy landscape. Our results in BBL expose the dynamic features of one-state folding and chart the intrinsic time-scales for conformational motions along the folding process. Interestingly, the simple self-averaging folding dynamics of BBL are the exact dynamic properties required in molecular rheostats, thus supporting a biological role for one-state folding.downhill folding ͉ folding landscape ͉ landscape topography ͉ protein dynamics T heory asserts that protein folding kinetics can be described as diffusion on a low dimensional free energy surface obtained by projecting the hyperdimensional energy landscapes of proteins into one or a few suitable order parameters (1, 2). The overall topography of such free energy surface and the conformational motions guiding folding are not resolvable by classical folding kinetics, but could be probed by time-resolved experiments of downhill folding (3). The difficulty resides in identifying examples of downhill folding relaxations. Stretched exponential decays and kinetic memory effects are not reliable signatures because they require the downhill free energy landscape to be rugged (4), and can also originate from other sources (5). Recently, downhill folding has been pursued by reengineering the fast-folding -repressor to accelerate folding with either mutations (6, 7) or stabilizing cosolvents (8). Approach to the barrierless regime was correlated with the emergence of an additional faster kinetic relaxation interpreted as the downhill decay from a vanishing barrier top (7). From these experiments, a folding speed limit of Ϸ2.5 s at 340 K was proposed for -repressor. This time-scale is close to the recent upper limit estimate of N/100 s (9) for -repressor [N ϭ 80] residues.A powerful alternative would be to measure conformational dynamics ...

Section: Discussionsupporting

confidence: 61%

mentioning

confidence: 99%

Dynamics of one-state downhill protein folding

Oliva¹,

Naganathan²,

Muñoz³

2009

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106

“…Recent work by Henry and Eaton (28) also suggests the prefactor is relatively uniform across two-state folding proteins based on analysis of folding rates from a different set of analytic models. The value for the average prefactor k 0 ϳ 10 5 s Ϫ1 agrees within an order of magnitude with estimates based on semiempirical and theoretical models (5, 51, 52) as well as analysis of thermodynamic data from differential scanning calorimetry (53). This value also is consistent with the fastest measured rates, ϳ1 s, if the time scale for downhill folding is approximated by the Arrhenius rate with a vanishing barrier (26,34).…”

Section: Resultssupporting

confidence: 85%

Excluded volume, local structural cooperativity, and the polymer physics of protein folding rates

Portman

2007

A coarse-grained variational model is used to investigate the polymer dynamics of barrier crossing for a diverse set of two-state folding proteins. The model gives reliable folding rate predictions provided excluded volume terms that induce minor structural cooperativity are included in the interaction potential. In general, the cooperative folding routes have sharper interfaces between folded and unfolded regions of the folding nucleus and higher free energy barriers. The calculated free energy barriers are strongly correlated with native topology as characterized by contact order. Increasing the rigidity of the folding nucleus changes the local structure of the transition state ensemble nonuniformly across the set of proteins studied. Nevertheless, the calculated prefactors k0 are found to be relatively uniform across the protein set, with variation in 1/k0 less than a factor of 5. This direct calculation justifies the common assumption that the prefactor is roughly the same for all small two-state folding proteins. Using the barrier heights obtained from the model and the best-fit monomer relaxation time 30 ns, we find that 1/k0 ϳ 1-5 s (with average 1/k0 ϳ 4 s). This model can be extended to study subtle aspects of folding such as the variation of the folding rate with stability or solvent viscosity and the onset of downhill folding.nucleation ͉ prefactor ͉ topology F olding in small proteins is often well characterized as a cooperative transition between two well defined structural populations: an unstructured globule ensemble and a structured folded ensemble. The transition rate between free energy minima is controlled by the dynamics of passing through an unstable transition region determined by saddlepoints in the free energy surface. Accordingly, the rate is expected to follow Arrhenius formwhere ␤ ϭ 1/k B T is the inverse temperature and ⌬F † is the free energy difference between the unfolded and transition-state ensembles. The exponential factor in Eq. 1 reflects the equilibrium population of the transition-state ensemble relative to unfolded ensemble and the prefactor, k 0 , is the time scale associated with the dynamics of crossing the free energy barrier. Successful identification of specific residues structured in the transition-state ensemble by several different theoretical models (1-8) and numerous simulation studies (see, e.g., refs. 9-11 and references therein) has established that the topology of the native structure determines the folding mechanism of these proteins. In addition, two-state folding rates are well correlated with very simple measures of the native state topology such as contact order (12-15). While additive potentials often produce reasonable structural characterization of the transition state ensemble, the range of simulated folding rates and their relationship with contact order does not agree with experiment (10). In this paper we present direct folding rate calculations that capture the trends noted earlier in lattice models (16, 17) and very recently in continuum models ...

“…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).…”

mentioning

confidence: 99%

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

Halskau

Pérez-Jiménez

Ibarra‐Molero

et al. 2008

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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,'' ...