Downhill folding

Last updated February 22, 2022

Downhill folding is a process in which a protein folds without encountering any significant macroscopic free energy barrier. It is a key prediction of the folding funnel hypothesis of the energy landscape theory of proteins.

Overview

Downhill folding is predicted to occur under conditions of extreme native bias, i.e. at low temperatures or in the absence of denaturants. This corresponds to the type 0 scenario^{[ clarification needed ]} in the energy landscape theory. At temperatures or denaturant concentrations close to their apparent midpoints, proteins may switch from downhill to two-state folding, the type 0 to type 1 transition.

Global downhill folding (or one-state folding) is another scenario in which the protein folds in the absence of a free energy barrier under all conditions. In other words, there is a unimodal population distribution at all temperatures and denaturant concentrations, suggesting a continuous unfolding transition in which different ensembles of structures populate at different conditions. This is in contrast to two-state folding, which assumes only two ensembles (folded and unfolded) and a sharp unfolding transition.

Free energy barriers in protein folding are predicted to be small because they arise as a result of compensation between large energetic and entropic terms. Non-synchronization between gain in stabilizing energy and loss in conformational entropy results in two-state folding, while a synchronization between these two terms as the folding proceeds results in downhill folding.

Experimental studies

Transition state structures in two-state folding are not experimentally accessible (by definition they are the least populated along the reaction coordinate), but the folding sub-ensembles in downhill folding processes are theoretically distinguishable by spectroscopy.^[1]^[2] The 40-residue protein BBL, which is an independently folding domain from the E2 subunit of the 2-oxoglutarate dehydrogenase multi-enzyme complex of E. coli, has been experimentally shown to fold globally downhill.^[3]^[4] Also, a mutant of lambda repressor protein has been shown to shift from downhill to two-state upon changing the temperature/solvent conditions. However, the status of BBL as a downhill-folding protein, and by extension the existence of naturally occurring downhill folders, has been controversial.^[5]^[6]^[7] The current controversy arises from the fact that the only way a protein can be labeled as two-state or downhill is by analyzing the experimental data with models that explicitly deal with these two situations, i.e. by allowing the barrier heights to vary. Unfortunately, most of the experimental data so far have been analyzed with a simple chemical two-state model. In other words, the presence of a rather large free energy barrier has been pre-assumed, ruling out the possibility of identifying downhill or globally downhill protein folding. This is critical because any sigmoidal unfolding curve, irrespective of the degree of cooperativity, can be fit to a two-state model. Kinetically, the presence of a barrier guarantees a single-exponential, but not vice versa.^[8] Nevertheless, in some proteins such as the yeast phosphoglycerate kinase and a mutant human ubiquitin, non-exponential kinetics suggesting downhill folding have been observed.^[9]

A proposed solution to these problems is to develop models that can differentiate between the different situations, and identify simple but robust experimental criteria for identifying downhill folding proteins. These are outlined below.

Equilibrium criteria

Differences in apparent melting temperatures

An analysis based on an extension of Zwanzig's model of protein folding^[10] indicates that global downhill folding proteins should reveal different apparent melting temperatures (Tms) when monitored by different techniques.^[2] This was experimentally confirmed in the protein BBL mentioned above. The unfolding followed by differential scanning calorimetry (DSC), circular dichroism (CD), fluorescence resonance energy transfer (FRET) and fluorescence all revealed different apparent melting temperatures.^[3] A wavelength-dependent melting temperature was also observed in the CD experiments. The data analyzed with a structure-based statistical mechanical model resulted in a unimodal population distribution at all temperatures, indicating a structurally uncoupled continuous unfolding process. The crucial issue in such experiments is to use probes that monitor different aspects of the structure. For example, DSC gives information on the heat capacity changes (and hence enthalpy) associated with unfolding, fluorescence on the immediate environment of the fluorophore, FRET on the average dimensions of the molecule and CD on the secondary structure.

A more stringent test would involve following the chemical shifts of each and every atom in the molecule by nuclear magnetic resonance (NMR) as a function of temperature/denaturant. Though time-consuming, this method does not require any specific model for the interpretation of data. The Tms for all the atoms should be identical within experimental error if the protein folds in a two-state manner. But for a protein that folds globally downhill the unfolding curves should have widely different Tms. The atomic unfolding behavior of BBL was found to follow the latter, showing a large spread in the Tms consistent with global downhill behavior.^[4] The Tms of some atoms were found to be similar to that of the global Tm (obtained from a low-resolution technique like CD or fluorescence), indicating that the unfolding of multiple atoms has to be followed, instead of a few as is frequently done in such experiments. The average atomic unfolding behavior was strikingly similar to that of CD, underlining the fact that unfolding curves of low resolution experiments are highly simplified representations of a more complex behavior.

Calorimetry and crossing baselines

Baselines frequently used in two-state fits correspond to the fluctuations in the folded or unfolded well. They are purely empirical as there is little or no information on how the folded or unfolded states' property changes with temperature/chemical denaturant. This assumes even more importance in case of DSC experiments as the changes in heat capacity correspond to both fluctuations in the protein ensemble and exposure of hydrophobic residues upon unfolding. The DSC profiles of many small fast-folding proteins are broad, with steep pre-transition slopes. Two-state fits to these profiles result in crossing of baselines indicating that the two-state assumption is no longer valid. This was recognized by Munoz and Sanchez-Ruiz, resulting in the development of the variable-barrier model.^[11] Instead of attempting a model-free inversion of the DSC profile to extract the underlying probability density function, they assumed a specific free energy functional with either one or two minima (similar to the Landau theory of phase transitions) thus enabling the extraction of free energy barrier heights. This model is the first of its kind in physical biochemistry that enables the determination of barrier heights from equilibrium experiments. Analysis of the DSC profile of BBL with this model resulted in zero barrier height, i.e. downhill folding, confirming the earlier result from the statistical mechanical model. When the variable-barrier model was applied to a set of proteins for which both the rate and DSC data are available, a very high correlation of 0.95 was obtained between the rates and barrier heights.^[12] Many of the proteins examined had small barriers (<20 kJ/mol) with baseline crossing evident for proteins that fold faster than 1 ms. This is in contrast to the traditional assumption that the free energy barrier between the folded and unfolded states are large.

Simulations

Because downhill folding is difficult to measure experimentally, molecular dynamics and Monte Carlo simulations have been performed on fast-folding proteins to explore their folding kinetics. Proteins whose folding rate is at or near the folding "speed limit", whose timescales make their folding more accessible to simulation methods, may more commonly fold downhill.^[13] Simulation studies of the BBL protein imply that its rapid folding rate and very low energy barrier arise from a lack of cooperativity in the formation of native contacts during the folding process; that is, a low contact order. The link between lack of cooperativity and low contact order was also observed in the context of Monte Carlo lattice simulations ^[14] These data suggest that the average number of "nonlocal contacts" per residue in a protein serves as an indicator of the barrier height, where very low nonlocal contact values imply downhill folding.^[15] Coarse-grained simulations by Knott and Chan also support the experimental observation of global downhill folding in BBL.^[16] A more recent study using constant-pH molecular dynamics (CpHMD) simulation has reconciled the opposing downhill and two-state folding mechanisms and found that the folding barrier vanishes at acidic pH conditions, leading to downhill folding.^[17]

Related Research Articles

Denaturation is a process in which proteins or nucleic acids lose the quaternary structure, tertiary structure, and secondary structure which is present in their native state, by application of some external stress or compound such as a strong acid or base, a concentrated inorganic salt, an organic solvent, agitation and radiation or heat. If proteins in a living cell are denatured, this results in disruption of cell activity and possibly cell death. Protein denaturation is also a consequence of cell death. Denatured proteins can exhibit a wide range of characteristics, from conformational change and loss of solubility to aggregation due to the exposure of hydrophobic groups. Denatured proteins lose their 3D structure and therefore cannot function.

Protein folding is the physical process by which a protein chain is translated to its native three-dimensional structure, typically a "folded" conformation by which the protein becomes biologically functional. Via an expeditious and reproducible process, a polypeptide folds into its characteristic three-dimensional structure from a random coil. Each protein exists first as an unfolded polypeptide or random coil after being translated from a sequence of mRNA to a linear chain of amino acids. At this stage the polypeptide lacks any stable (long-lasting) three-dimensional structure. As the polypeptide chain is being synthesized by a ribosome, the linear chain begins to fold into its three-dimensional structure.

The term molten globule (MG) refers to protein states that are more or less compact, but are lacking the specific tight packing of amino acid residues which creates the solid state-like tertiary structure of completely folded proteins. It was found, for example, in cytochrome c, which conserves a native-like secondary structure content but without the tightly packed protein interior, under low pH and high salt concentration. For cytochrome c and some other proteins, it has been shown that the molten globule state is a "thermodynamic state" clearly different both from the native and the denatured state, demonstrating for the first time the existence of a third equilibirum state.

Force spectroscopy is a set of techniques for the study of the interactions and the binding forces between individual molecules. These methods can be used to measure the mechanical properties of single polymer molecules or proteins, or individual chemical bonds. The name "force spectroscopy", although widely used in the scientific community, is somewhat misleading, because there is no true matter-radiation interaction.

Molecular dynamics Computer simulations to discover and understand chemical properties

Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanics force fields. The method is applied mostly in chemical physics, materials science, and biophysics.

Folding@home is a distributed computing project aimed to help scientists develop new therapeutics for a variety of diseases by the means of simulating protein dynamics. This includes the process of protein folding and the movements of proteins, and is reliant on simulations run on volunteers' personal computers. Folding@home is currently based at Washington University in St. Louis and led by Greg Bowman, a former student of Vijay Pande.

Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms.

Protein structure is the three-dimensional arrangement of atoms in an amino acid-chain molecule. Proteins are polymers – specifically polypeptides – formed from sequences of amino acids, the monomers of the polymer. A single amino acid monomer may also be called a residue indicating a repeating unit of a polymer. Proteins form by amino acids undergoing condensation reactions, in which the amino acids lose one water molecule per reaction in order to attach to one another with a peptide bond. By convention, a chain under 30 amino acids is often identified as a peptide, rather than a protein. To be able to perform their biological function, proteins fold into one or more specific spatial conformations driven by a number of non-covalent interactions such as hydrogen bonding, ionic interactions, Van der Waals forces, and hydrophobic packing. To understand the functions of proteins at a molecular level, it is often necessary to determine their three-dimensional structure. This is the topic of the scientific field of structural biology, which employs techniques such as X-ray crystallography, NMR spectroscopy, cryo electron microscopy (cryo-EM) and dual polarisation interferometry to determine the structure of proteins.

Lattice proteins are highly simplified models of protein-like heteropolymer chains on lattice conformational space which are used to investigate protein folding. Simplification in lattice proteins is twofold: each whole residue is modeled as a single "bead" or "point" of a finite set of types, and each residue is restricted to be placed on vertices of a lattice. To guarantee the connectivity of the protein chain, adjacent residues on the backbone must be placed on adjacent vertices of the lattice. Steric constraints are expressed by imposing that no more than one residue can be placed on the same lattice vertex.

In the context of chemistry and molecular modelling, a force field is a computational method that is used to estimate the forces between atoms within molecules and also between molecules. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles in molecular mechanics, molecular dynamics, or Monte Carlo simulations. The parameters for a chosen energy function may be derived from experiments in physics and chemistry, calculations in quantum mechanics, or both. Force fields are interatomic potentials and utilize the same concept as force fields in classical physics, with the difference that the force field parameters in chemistry describe the energy landscape, from which the acting forces on every particle are derived as a gradient of the potential energy with respect to the particle coordinates.

Phi value analysis, $analysis, or -value analysis is an experimental protein engineering technique for studying the structure of the folding transition state of small protein domains that fold in a two-state manner. The structure of the folding transition state is hard to find using methods such as protein NMR or X-ray crystallography because folding transitions states are mobile and partly unstructured by definition. In -value analysis, the folding kinetics and conformational folding stability of the wild-type protein are compared with those of point mutants to find phi values . These measure the mutant residue's energetic contribution to the folding transition state, which reveals the degree of native structure around the mutated residue in the transition state, by accounting for the relative free energies of the unfolded state, the folded state, and the transition state for the wild-type and mutant proteins.$

In biochemistry, equilibrium unfolding is the process of unfolding a protein or RNA molecule by gradually changing its environment, such as by changing the temperature or pressure, pH, adding chemical denaturants, or applying force as with an atomic force microscope tip. If the equilibrium was maintained at all steps, the process theoretically should be reversible during equilibrium folding. Equilibrium unfolding can be used to determine the thermodynamic stability of the protein or RNA structure, i.e. free energy difference between the folded and unfolded states.

A chevron plot is a way of representing protein folding kinetic data in the presence of varying concentrations of denaturant that disrupts the protein's native tertiary structure. The plot is known as "chevron" plot because of the canonical v, or chevron shape observed when the logarithm of the observed relaxation rate is plotted as a function of the denaturant concentration.

Denaturation midpoint of a protein is defined as the temperature (T_m) or concentration of denaturant (C_m) at which both the folded and unfolded states are equally populated at equilibrium. T_m is often determined using a thermal shift assay.

The folding funnel hypothesis is a specific version of the energy landscape theory of protein folding, which assumes that a protein's native state corresponds to its free energy minimum under the solution conditions usually encountered in cells. Although energy landscapes may be "rough", with many non-native local minima in which partially folded proteins can become trapped, the folding funnel hypothesis assumes that the native state is a deep free energy minimum with steep walls, corresponding to a single well-defined tertiary structure. The term was introduced by Ken A. Dill in a 1987 article discussing the stabilities of globular proteins.

Hydrophobic collapse is a proposed process for the production of the 3-D conformation adopted by polypeptides and other molecules in polar solvents. The theory states that the nascent polypeptide forms initial secondary structure creating localized regions of predominantly hydrophobic residues. The polypeptide interacts with water, thus placing thermodynamic pressures on these regions which then aggregate or "collapse" into a tertiary conformation with a hydrophobic core. Incidentally, polar residues interact favourably with water, thus the solvent-facing surface of the peptide is usually composed of predominantly hydrophilic regions.

Homology modeling, also known as comparative modeling of protein, refers to constructing an atomic-resolution model of the "target" protein from its amino acid sequence and an experimental three-dimensional structure of a related homologous protein. Homology modeling relies on the identification of one or more known protein structures likely to resemble the structure of the query sequence, and on the production of an alignment that maps residues in the query sequence to residues in the template sequence. It has been seen that protein structures are more conserved than protein sequences amongst homologues, but sequences falling below a 20% sequence identity can have very different structure.

Implicit solvation is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of molecular mechanics. The method is often applied to estimate free energy of solute-solvent interactions in structural and chemical processes, such as folding or conformational transitions of proteins, DNA, RNA, and polysaccharides, association of biological macromolecules with ligands, or transport of drugs across biological membranes.

FoldX is a protein design algorithm that uses an empirical force field. It can determine the energetic effect of point mutations as well as the interaction energy of protein complexes. FoldX can mutate protein and DNA side chains using a probability-based rotamer library, while exploring alternative conformations of the surrounding side chains.

Victor Muñoz is a biochemist whose focus has been on protein folding and design. He provided experimental evidence for a mechanism of protein folding called as "downhill folding". He has pioneered various computational and experimental techniques to study this mechanism as well as to gain insights into the general process of protein folding.

References

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