Downhill folding
Encyclopedia
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.
bias, i.e. at low temperatures or in the absence of denaturant
s. This corresponds to the type 0 scenario 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.
structures in two-state folding are not experimentally accessible (by definition they are the least populated along the reaction co-ordinate), but the folding sub-ensembles in downhill folding processes are theoretically distinguishable by spectroscopy
. 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. 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. 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. Nevertheless, in some proteins such as the yeast
phosphoglycerate kinase
and a mutant human ubiquitin
, non-exponential kinetics suggesting downhill folding have been observed.
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.
(Tms) when monitored by different techniques. 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. 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. 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.
. 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. Interestingly, 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. 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. 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.
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. 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 contact
s 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 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. Coarse-grained simulations by Knott and Chan also support the experimental observation of global downhill folding in BBL.
Protein folding
Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure from random coil....
without encountering any significant macroscopic free energy
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...
barrier
Activation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
. It is a key prediction of the folding funnel
Folding funnel
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...
hypothesis of the energy landscape
Energy landscape
In physics, an energy landscape is a mapping of all possible conformations of a molecular entity, or the spatial positions of interacting molecules in a system, and their corresponding energy levels, typically Gibbs free energy, on a two- or three-dimensional Cartesian coordinate system.In...
theory of proteins.
Overview
Downhill folding is predicted to occur under conditions of extreme nativeNative state
In biochemistry, the native state of a protein is its operative or functional form. While all protein molecules begin as simple unbranched chains of amino acids, once completed they assume highly specific three-dimensional shapes; that ultimate shape, known as tertiary structure, is the folded...
bias, i.e. at low temperatures or in the absence of denaturant
Denaturation (biochemistry)
Denaturation is a process in which proteins or nucleic acids lose their tertiary structure and secondary structure by application of some external stress or compound, such as a strong acid or base, a concentrated inorganic salt, an organic solvent , or heat...
s. This corresponds to the type 0 scenario in the energy landscape theory. At temperatures or denaturant concentrations close to their apparent midpoints
Denaturation midpoint
Assuming two-state protein folding, denaturation midpoint is defined as that temperature or denaturant concentration at which both the folded and unfolded states are equally populated at equilibrium....
, 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
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
and entropic
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
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 stateTransition state
The transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules will always...
structures in two-state folding are not experimentally accessible (by definition they are the least populated along the reaction co-ordinate), but the folding sub-ensembles in downhill folding processes are theoretically distinguishable by spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
. 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
Escherichia coli
Escherichia coli is a Gram-negative, rod-shaped bacterium that is commonly found in the lower intestine of warm-blooded organisms . Most E. coli strains are harmless, but some serotypes can cause serious food poisoning in humans, and are occasionally responsible for product recalls...
, has been experimentally shown to fold globally downhill. 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. 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
Sigmoidal
Sigmoidal or sigmoid, literally means S-shaped and can refer to:* Sigmoid function* Sigmoidal artery* Sigmoid colon...
unfolding curve, irrespective of the degree of cooperativity
Cooperativity
Cooperativity is a phenomenon displayed by enzymes or receptors that have multiple binding sites where the affinity of the binding sites for a ligand is increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to a binding site...
, can be fit to a two-state model. Kinetically, the presence of a barrier guarantees a single-exponential, but not vice-versa. Nevertheless, in some proteins such as the yeast
Yeast
Yeasts are eukaryotic micro-organisms classified in the kingdom Fungi, with 1,500 species currently described estimated to be only 1% of all fungal species. Most reproduce asexually by mitosis, and many do so by an asymmetric division process called budding...
phosphoglycerate kinase
Phosphoglycerate kinase
Phosphoglycerate kinase is a transferase enzyme used in the seventh step of glycolysis. It transfers a phosphate group from 1,3-bisphosphoglycerate to ADP, forming ATP and 3-Phosphoglycerate....
and a mutant human ubiquitin
Ubiquitin
Ubiquitin is a small regulatory protein that has been found in almost all tissues of eukaryotic organisms. Among other functions, it directs protein recycling.Ubiquitin can be attached to proteins and label them for destruction...
, non-exponential kinetics suggesting downhill folding have been observed.
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.
Differences in apparent melting temperatures
An analysis based on an extension of Zwanzig's model of protein folding indicates that global downhill folding proteins should reveal different apparent melting temperaturesDenaturation midpoint
Assuming two-state protein folding, denaturation midpoint is defined as that temperature or denaturant concentration at which both the folded and unfolded states are equally populated at equilibrium....
(Tms) when monitored by different techniques. This was experimentally confirmed in the protein BBL mentioned above. The unfolding followed by differential scanning calorimetry
DSC
-in academia:* D.Sc., Doctor of Science* Doctor of Surgical Chiropody, superseded in the 1960s by Doctor of Podiatric Medicine* Dalton State College, Georgia* Daytona State College, Florida* Deep Springs College, California* Dixie State College of Utah...
(DSC), circular dichroism
Circular dichroism
Circular dichroism refers to the differential absorption of left and right circularly polarized light. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. It is exhibited in the absorption bands of optically active chiral...
(CD), fluorescence resonance energy transfer
Fluorescence resonance energy transfer
Förster resonance energy transfer , also known as fluorescence resonance energy transfer, resonance energy transfer or electronic energy transfer , is a mechanism describing energy transfer between two chromophores.A donor chromophore, initially in its electronic excited state, may transfer energy...
(FRET) and fluorescence
Fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation of a different wavelength. It is a form of luminescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation...
all revealed different apparent melting temperatures. A wavelength-dependent melting temperature was also observed in the CD experiments. The data analyzed with a structure-based statistical mechanical
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
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
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
changes (and hence enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...
) 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
Secondary structure
In biochemistry and structural biology, secondary structure is the general three-dimensional form of local segments of biopolymers such as proteins and nucleic acids...
.
A more stringent test would involve following the chemical shifts of each and every atom in the molecule by nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
(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. 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 denaturantDenaturation (biochemistry)
Denaturation is a process in which proteins or nucleic acids lose their tertiary structure and secondary structure by application of some external stress or compound, such as a strong acid or base, a concentrated inorganic salt, an organic solvent , or heat...
. This assumes even more importance in case of DSC experiments as the changes in heat capacity correspond to both fluctuations
Fluctuations
Fluctuations may refer to:* Quantum fluctuations arising from the uncertainty principle* Primordial fluctuations, density variations in the early universe* Statistical fluctuations, very important in statistics, statistical mechanics, and thermodynamics...
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. Interestingly, 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. Instead of attempting a model-free inversion of the DSC profile to extract the underlying probability density function
Probability density function
In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...
, they assumed a specific free energy functional with either one or two minima (similar to the Landau theory
Landau theory
Landau theory in physics was introduced by Lev Landau in an attempt to formulate a general theory of second-order phase transitions. He was motivated to suggest that the free energy of any system should obey two conditions: that the free energy is analytic, and that it obeys the symmetry of the...
of phase transitions) thus enabling the extraction of free energy barrier heights. This model is the first of its kind in physical biochemistry
Biochemistry
Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...
that enables the determination of barrier heights from equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
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
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
of 0.95 was obtained between the rates and barrier heights. 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 dynamicsMolecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
and Monte Carlo
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
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. 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 contact
Native contact
In protein folding, a native contact is a contact between the side chains of two amino acids that are not neighboring in the amino acid sequence but are spatially close in the protein's native state tertiary structure...
s during the folding process; that is, a low contact order
Contact order
The contact order of a protein is a measure of the locality of the inter-amino acid contacts in the protein's native state tertiary structure. It is calculated as the average sequence distance between residues that form native contacts in the folded protein divided by the total length of the protein...
. The link between lack of cooperativity and low contact order was also observed in the context of Monte Carlo
Monte Carlo
Monte Carlo is an administrative area of the Principality of Monaco....
lattice simulations These data suggest that the average number of "nonlocal contacts" per residue
Amino acid
Amino acids are molecules containing an amine group, a carboxylic acid group and a side-chain that varies between different amino acids. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen...
in a protein serves as an indicator of the barrier height, where very low nonlocal contact values imply downhill folding. Coarse-grained simulations by Knott and Chan also support the experimental observation of global downhill folding in BBL.
Further reading
- Bieri O, Kiefhaber T. (2000). Kinetic models in protein folding. In Mechanisms of Protein Folding 2nd ed. Ed. RH Pain. Frontiers in Molecular Biology series. Oxford University Press: Oxford, UK.
- Gruebele M. (2008) Fast protein folding. In Protein Folding, Misfolding and Aggregation Ed. V Muñoz. RSC Biomolecular Sciences series. Royal Society of Chemistry Publishing: Cambridge, UK.