From covalent transition states in chemistry to noncovalent in biology: from β- to Φ-value analysis of protein folding

Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.

Predicting and Simulating Mutational Effects on Protein Folding Kinetics

Mutational perturbations of protein structures, i.e., phi-value analysis, are commonly employed to probe the extent of involvement of a particular residue in the rate-determining step(s) of folding. This generally involves the measurement of folding thermodynamic parameters and kinetic rate constants for the wild-type and mutant proteins. While computational approaches have been reasonably successful in understanding and predicting the effect of mutations on folding thermodynamics, it has been challenging to explore the same on kinetics due to confounding structural, energetic, and dynamic factors. Accordingly, the frequent observation of fractional phi-values (mean of ~0.3) has resisted a precise and consistent interpretation. Here, we describe how to construct, parameterize, and employ a simple one-dimensional free energy surface model that is grounded in the basic tenets of the energy landscape theory to predict and simulate the effect of mutations on folding kinetics. As a proof of principle, we simulate one-dimensional free energy profiles of 806 mutations from 24 different proteins employing just the experimental destabilization as input, reproduce the relative unfolding activation free energies with a correlation of 0.91, and show that the mean phi-value of 0.3 essentially corresponds to the extent of stabilization energy gained at the barrier top while folding.

Extracting the Hidden Distributions Underlying the Mean Transition State Structures in Protein Folding

The inherent conflict between noncovalent interactions and the large conformational entropy of the polypeptide chain forces folding reactions and their mechanisms to deviate significantly from chemical reactions. Accordingly, measures of structure in the transition state ensemble (TSE) are strongly influenced by the underlying distributions of microscopic folding pathways that are challenging to discern experimentally. Here, we present a detailed analysis of 150,000 folding transition paths of five proteins at three different thermodynamic conditions from an experimentally consistent statistical mechanical model. We find that the underlying TSE structural distributions are rarely unimodal, and the average experimental measures arise from complex underlying distributions. Unfolding pathways also exhibit subtle differences from folding counterparts due to a combination of Hammond behavior and native-state movements. Local interactions and topological complexity, to a lesser extent, are found to determine pathway heterogeneity, underscoring the importance of the balance between local and nonlocal energetics in protein folding.

Estimating the mean first passage time of protein misfolding

Most theoretical and experimental studies confirm that proteins fold in the time scale of microseconds to milliseconds, but the kinetics of the protein misfolding remains largely unexplored. The kinetics of unfolding-folding-misfolding equilibrium in proteins is formulated in the analytical framework of the Master equation. The folded, unfolded and the misfolded state are characterized in terms of their respective contacts. The Mean First Passage Time (MFPT) to acquire the misfolded conformation from the native or folded state is derived from this equation with different boundary conditions. The MFPT is found to be practically independent of the length of the protein, the number of native contacts and the rate constant for the misfolded to the folded state. The results obtained from the survival probability are directly correlated to the age of onset and appearance of misfolding diseases in humans.

Imprints of function on the folding landscape: functional role for an intermediate in a conserved eukaryotic binding protein

In the computational characterization of single domain protein folding, the effective free energies of numerous microstates are projected onto few collective degrees of freedom that in turn serve as well-defined reaction coordinates. In this regard, one-dimensional (1D) free energy profiles are widely used mainly for their simplicity. Since folding and functional landscapes are interlinked, how well can these reduced representations capture the structural and dynamic features of functional states while being simultaneously consistent with experimental observables? We investigate this issue by characterizing the folding of the four-helix bundle bovine acyl-CoA binding protein (bACBP), which exhibits complex equilibrium and kinetic behaviours, employing an Ising-like statistical mechanical model and molecular simulations. We show that the features of the 1D free energy profile are sufficient to quantitatively reproduce multiple experimental observations including millisecond chevron-like kinetics and temperature dependence, a microsecond fast phase, barrier heights, unfolded state movements, the intermediate structure and average ϕ-values. Importantly, we find that the structural features of the native-like intermediate (partial disorder in helix 1) are intricately linked to a unique interplay between packing and electrostatics in this domain. By comparison with available experimental data, we propose that this intermediate determines the promiscuous functional behaviour of bACBP that exhibits broad substrate specificity. Our results present evidence to the possibility of employing the statistical mechanical model and the resulting 1D free energy profile to not just understand folding mechanisms but to even extract features of functionally relevant states and their energetic origins.

Influences of heterogeneous native contact energy and many-body interactions on the prediction of protein folding mechanisms

Combining heterogenous native contact energies and many-body interactions could improve the prediction of Brønsted plots using a structure-based model.

Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics

Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.

How well does a funneled energy landscape capture the folding mechanism of spectrin domains?

Three structurally similar domains from α-spectrin have been shown to fold very differently. First, there is a contrast in the folding mechanism, as probed by Φ-value analysis, between the R15 domain and the R16 and R17 domains. Second, there are very different contributions from internal friction to folding: the folding rate of the R15 domain was found to be inversely proportional to solvent viscosity, showing no apparent frictional contribution from the protein, but in the other two domains, a large internal friction component was evident. Non-native misdocking of helices has been suggested to be responsible for this phenomenon. Here, I study the folding of these three proteins with minimalist coarse-grained models based on a funneled energy landscape. Remarkably, I find that, despite the absence of non-native interactions, the differences in folding mechanism of the domains are well captured by the model, and the agreement of the Φ-values with experiment is fairly good. On the other hand, within the context of this model, there are no significant differences in diffusion coefficient along the chosen folding coordinate, and the model cannot explain the large differences in folding rates between the proteins found experimentally. These results are nonetheless consistent with the expectations from the energy landscape perspective of protein folding, namely, that the folding mechanism is primarily determined by the native-like interactions present in the Gō-like model, with missing non-native interactions being required to explain the differences in "internal friction" seen in experiment.

Energy landscape and dynamics of proteins: an exact analysis of a simplified lattice model

We present the results of exact numerical studies of the energy landscape and the dynamics of a 12-monomer chain with contact interactions encoding the ground state on a square lattice. In spite of its simplicity, the model is shown to exhibit behavior at odds with the standard picture of proteins.

Single molecule unfolding and stretching of protein domains inside a solid-state nanopore by electric field

Single molecule methods have provided a significantly new look at the behavior of biomolecules in both equilibrium and non-equilibrium conditions. Most notable are the stretching experiments performed by atomic force microscopes and laser tweezers. Here we present an alternative single molecule method that can unfold a protein domain, observed at electric fields greater than 10(6) V/m, and is fully controllable by the application of increasing voltages across the membrane of the pore. Furthermore this unfolding mechanism is characterized by measuring both the residence time of the protein within the nanopore and the current blockade. The unfolding data supports a gradual unfolding mechanism rather than the cooperative transition observed by classical urea denaturation experiments. Lastly it is shown that the voltage-mediated unfolding is a function of the stability of the protein by comparing two mutationally destabilized variants of the protein.

Predictions from an Ising-like Statistical Mechanical Model on the Dynamic and Thermodynamic Effects of Protein Surface Electrostatics

Charged residues on the surface of a protein are known hot-spots for post-translational modification, protein/ligand-binding, and tuning conformational stabilities. Recent experimental evidence points to the fact that surface electrostatics can also modulate thermodynamic barriers and hence folding mechanisms. To probe for this behavior across different proteins, we develop a novel version of the Wako-Saitô-Muñoz-Eaton (WSME) model in which we include an electrostatic potential term in the energy function while simplifying the treatment of solvation free energy. Both of the energy terms are obtained by quantitatively fitting the model to differential scanning calorimetry (DSC) experiments that carry critical information on the protein partition function. We characterize four sets of structural/functional homologues (HEWL/BLA, CspB, engrailed, α-spectrin) either by fitting the experimental data of a single domain in the homologous set and predicting the conformational behavior of the rest with the same set of parameters or by performing semiblind predictions. The model with the added electrostatic term is able to successfully reproduce the order of thermodynamic stabilities and relaxation rates of most of the homologues. In parallel, we predict diverse conformational features including a wide range of thermodynamic barriers (∼9-40 kJ/mol), broad native ensembles in helical proteins, structured unfolded states and intermediates, rugged folding landscapes, and further provide an independent protein-specific estimate of the folding speed limit at 298 K (1/(7-300 μs)). Our results are evidence that protein surface electrostatics can be tailored to not only engineer stabilities but also folding mechanisms and the ruggedness of the underlying landscape.