Spectral diffusion and the energy landscape of a protein

We present a novel type of spectral diffusion experiment in the millikelvin range to characterize the energy landscape of a protein as compared with that of a glass. We measure the time evolution of spectral holes for more than 300 hr after well-defined initial nonequilibrium conditions. We show that the model of noninteracting two-level systems can describe spectral diffusion in the glass, but fails for the protein. Our results further demonstrate that randomness in the energy landscape of a protein shows features of organization. There are “deep minimum” states separated by barriers, the heights of which we are able to estimate. The energy landscape of a glass is featureless by comparison.

The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin

The grail of protein science is the connection between structure and function. For myoglobin (Mb) this goal is close. Described as only a passive dioxygen storage protein in texts, we argue here that Mb is actually an allosteric enzyme that can catalyze reactions among small molecules. Studies of the structural, spectroscopic, and kinetic properties of Mb lead to a model that relates structure, energy landscape, dynamics, and function. Mb functions as a miniature chemical reactor, concentrating and orienting diatomic molecules such as NO, CO, O2, and H2O2 in highly conserved internal cavities. Reactions can be controlled because Mb exists in distinct taxonomic substates with different catalytic properties and connectivities of internal cavities.

Solvent effects on the energy landscapes and folding kinetics of polyalanine

The effect of a solvation on the thermodynamics and kinetics of polyalanine (Ala12) is explored on the basis of its energy landscapes in vacuum and in an aqueous solution. Both energy landscapes are characterized by two basins, one associated with α-helical structures and the other with coil and β-structures of the peptide. In both environments, the basin that corresponds to the α-helical structure is considerably narrower than the basin corresponding to the β-state, reflecting their different contributions to the entropy of the peptide. In vacuum, the α-helical state of Ala12 constitutes the native state, in agreement with common helical propensity scales, whereas in the aqueous medium, the α-helical state is destabilized, and the β-state becomes the native state. Thus solvation has a dramatic effect on the energy landscape of this peptide, resulting in an inverted stability of the two states. Different folding and unfolding time scales for Ala12 in hydrophilic and hydrophobic chemical environments are caused by the higher entropy of the native state in water relative to vacuum. The concept of a helical propensity has to be extended to incorporate environmental solvent effects.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.

Conformation, energy, and folding ability of selected amino acid sequences.

Evolutionary selection of sequences is studied with a knowledge-based Hamiltonian to find the design principle for folding to a model protein structure. With sequences selected by naive energy minimization, the model structure tends to be unstable and the folding ability is low. Sequences with high folding ability have only the low-lying energy minimum but also an energy landscape which is similar to that found for the native sequence over a wide region of the conformation space. Though there is a large fluctuation in foldable sequences, the hydrophobicity pattern and the glycine locations are preserved among them. Implications of the design principle for the molecular mechanism of folding are discussed.

Protein folding kinetics exhibit an Arrhenius temperature dependence when corrected for the temperature dependence of protein stability

The anomalous temperature dependence of protein folding has received considerable attention. Here we show that the temperature dependence of the folding of protein L becomes extremely simple when the effects of temperature on protein stability are corrected for; the logarithm of the folding rate is a linear function of 1/T on constant stability contours in the temperature–denaturant plane. This convincingly demonstrates that the anomalous temperature dependence of folding derives from the temperature dependence of the interactions that stabilize proteins, rather than from the super Arrhenius temperature dependence predicted for the configurational diffusion constant on a rough energy landscape. However, because of the limited temperature range accessible to experiment, the results do not rule out models with higher order temperature dependences. The significance of the slope of the stability-corrected Arrhenius plots is discussed.

Characteristic temperatures of folding of a small peptide

We perform a generalized-ensemble simulation of a small peptide taking the interactions among all atoms into account. From this simulation we obtain thermodynamic quantities over a wide range of temperatures. In particular, we show that the folding of a small peptide is a multistage process associated with two characteristic temperatures, the collapse temperature Tθ and the folding temperature Tƒ. Our results give supporting evidence for the energy landscape picture and funnel concept. These ideas were previously developed in the context of studies of simplified protein models, and here are checked in an all-atom Monte Carlo simulation.

Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

Protein fluctuations are sensed by stimulated infrared echoes of the vibrations of carbon monoxide and azide probes

The correlation functions of the fluctuations of vibrational frequencies of azide ions and carbon monoxide in proteins are determined directly from stimulated photon echoes generated with femtosecond infrared pulses. The asymmetric stretching vibration of azide bound to carbonic anhydrase II exhibits a pronounced evolution of its vibrational frequency distribution on the time scale of a few picoseconds, which is attributed to modifications of the ligand structure through interactions with the nearby Thr-199. When azide is bound in hemoglobin, a more complex evolution of the protein structure is required to interchange the different ligand configurations, as evidenced by the much slower relaxation of the frequency distribution in this case. The time evolution of the distribution of frequencies of carbon monoxide bound in hemoglobin occurs on the ≈10-ps time scale and is very nonexponential. The correlation functions of the frequency fluctuations determine the evolution of the protein structure local to the probe and the extent to which the probe can navigate those parts of the energy landscape where the structural configurations are able to modify the local potential energy function of the probe.

Lifetimes of intermediates in the β-sheet to α-helix transition of β-lactoglobulin by using a diffusional IR mixer

The extremely slow α-helix/β-sheet transition of proteins is a crucial step in amylogenic diseases and represents an internal rearrangement of local contacts in an already folded protein. These internal structural rearrangements within an already folded protein are a critical aspect of biological action and are a product of conformational flow along unknown metastable local minima of the energy landscape of the compact protein. We use a diffusional IR mixer with time-resolved Fourier transform IR spectroscopy capable of 400-μs time resolution to show that the trifluoroethanol driven β-sheet to α-helix transition of β-lactoglobulin proceeds via a compact β-sheet intermediate with a lifetime of 7 ms, small compared with the overall folding time of β-lactoglobulin.

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.

Barriers to protein folding: formation of buried polar interactions is a slow step in acquisition of structure.

In the MYL mutant of the Arc repressor dimer, sets of partially buried salt-bridge and hydrogen-bond interactions mediated by Arg-31, Glu-36, and Arg-40 in each subunit are replaced by hydrophobic interactions between Met-31, Tyr-36, and Leu-40. The MYL refolding/dimerization reaction differs from that of wild type in being 10- to 1250-fold faster, having an earlier transition state, and depending upon viscosity but not ionic strength. Formation of the wild-type salt bridges in a hydrophobic environment clearly imposes a kinetic barrier to folding, which can be lowered by high salt concentrations. The changes in the position of the transition state and viscosity dependence can be explained if denatured monomers interact to form a partially folded dimeric intermediate, which then continues folding to form the native dimer. The second step is postulated to be rate limiting for wild type. Replacing the salt bridge with hydrophobic interactions lowers this barrier for MYL. This makes the first kinetic barrier rate limiting for MYL refolding and creates a downhill free-energy landscape in which most molecules which reach the intermediate state continue to form native dimers.

Least activation path for protein folding: investigation of staphylococcal nuclease folding by stopped-flow circular dichroism.

Is the pathway of protein folding determined by the relative stability of folding intermediates, or by the relative height of the activation barriers leading to these intermediates? This is a fundamental question for resolving the Levinthal paradox, which stated that protein folding by a random search mechanism would require a time too long to be plausible. To answer this question, we have studied the guanidinium chloride (GdmCl)-induced folding/unfolding of staphylococcal nuclease [(SNase, formerly EC 3.1.4.7; now called microbial nuclease or endonuclease, EC 3.1.31.1] by stopped-flow circular dichroism (CD) and differential scanning microcalorimetry (DSC). The data show that while the equilibrium transition is a quasi-two-state process, kinetics in the 2-ms to 500-s time range are triphasic. Data support the sequential mechanism for SNase folding: U3 <--> U2 <--> U1 <--> N0, where U1, U2, and U3 are substates of the unfolded protein and N0 is the native state. Analysis of the relative population of the U1, U2, and U3 species in 2.0 M GdmCl gives delta-G values for the U3 --> U2 reaction of +0.1 kcal/mol and for the U2 --> U1 reaction of -0.49 kcal/mol. The delta-G value for the U1 --> N0 reaction is calculated to be -4.5 kcal/mol from DSC data. The activation energy, enthalpy, and entropy for each kinetic step are also determined. These results allow us to make the following four conclusions. (i) Although the U1, U2, and U3 states are nearly isoenergetic, no random walk occurs among them during the folding. The pathway of folding is unique and sequential. In other words, the relative stability of the folding intermediates does not dictate the folding pathway. Instead, the folding is a descent toward the global free-energy minimum of the native state via the least activation path in the vast energy landscape. Barrier avoidance leads the way, and barrier height limits the rate. Thus, the Levinthal paradox is not applicable to the protein-folding problem. (ii) The main folding reaction (U1 --> N0), in which the peptide chain acquires most of its free energy (via van der Waals' contacts, hydrogen bonding, and electrostatic interactions), is a highly concerted process. These energy-acquiring events take place in a single kinetic phase. (iii) U1 appears to be a compact unfolded species; the rate of conversion of U2 to U1 depends on the viscosity of solution. (iv) All four relaxation times reported here depend on GdmCl concentrations: it is likely that none involve the cis/trans isomerization of prolines. Finally, a mechanism is presented in which formation of sheet-like chain conformations and a hydrophobic condensation event precede the main-chain folding reaction.

Foldons, protein structural modules, and exons.

Foldons, which are kinetically competent, quasi-independently folding units of a protein, may be defined using energy landscape analysis. Foldons can be identified by maxima in a scan of the ratio of a contiguous segment's energetic stability gap to the energy variance of that segment's molten globule states, reflecting the requirement of minimal frustration. The predicted foldons are compared with the exons and structural modules for 16 of the 30 proteins studied. Statistical analysis indicates a strong correlation between the energetically determined foldons and Go's geometrically defined structural modules, but there are marked sequence-dependent effects. There is only a weak correlation of foldons to exons. For gammaII-crystallin, myoglobin, barnase, alpha-lactalbumin, and cytochrome c the foldons and some noncontiguous clusters of foldons compare well with intermediates observed in experiment.

A mean field model of ligand-protein interactions: implications for the structural assessment of human immunodeficiency virus type 1 protease complexes and receptor-specific binding.

We propose a general mean field model of ligand-protein interactions to determine the thermodynamic equilibrium of a system at finite temperature. The method is employed in structural assessments of two human immuno-deficiency virus type 1 protease complexes where the gross effects of protein flexibility are incorporated by utilizing a data base of crystal structures. Analysis of the energy spectra for these complexes has revealed that structural and thermo-dynamic aspects of molecular recognition can be rationalized on the basis of the extent of frustration in the binding energy landscape. In particular, the relationship between receptor-specific binding of these ligands to human immunodeficiency virus type 1 protease and a minimal frustration principle is analyzed.