Downhill folding is a process in which a protein
folds without encountering any significant macroscopic
free energy barrier
A barrier or barricade is a physical structure which blocks or impedes something.
Barrier may also refer to:
Places
* Barrier, Kentucky, a community in the United States
* Barrier, Voerendaal, a place in the municipality of Voerendaal, Netherl ...
. It is a key prediction of the
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. A ...
hypothesis of the
energy landscape
An energy landscape is a mapping of possible states of a system. The concept is frequently used in physics, chemistry, and biochemistry, e.g. to describe all possible conformations of a molecular entity, or the spatial positions of interacting m ...
theory of proteins.
Overview
Downhill folding is predicted to occur under conditions of extreme
native
Native may refer to:
People
* Jus soli, citizenship by right of birth
* Indigenous peoples, peoples with a set of specific rights based on their historical ties to a particular territory
** Native Americans (disambiguation)
In arts and entert ...
bias, i.e. at low temperatures or in the absence of
denaturants. 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
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object.
Unimodal probability distribution
In statistics, a unimodal p ...
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
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
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
In chemistry, 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 potential energy along this reaction coordinate. It is often marked ...
structures in
two-state folding are not experimentally accessible (by definition they are the least populated along the
reaction coordinate
In chemistry, a reaction coordinate is an abstract one-dimensional coordinate which represents progress along a reaction pathway. It is usually a geometric parameter that changes during the conversion of one or more molecular entities. In molecu ...
), 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
Yeasts are eukaryotic, single-celled microorganisms classified as members of the fungus kingdom. The first yeast originated hundreds of millions of years ago, and at least 1,500 species are currently recognized. They are estimated to constit ...
phosphoglycerate kinase
Phosphoglycerate kinase () (PGK 1) is an enzyme that catalyzes the reversible transfer of a phosphate group from 1,3-bisphosphoglycerate (1,3-BPG) to ADP producing 3-phosphoglycerate (3-PG) and ATP :
:1,3-bisphosphoglycerate + ADP glycerat ...
and a mutant human
ubiquitin
Ubiquitin is a small (8.6 kDa) regulatory protein found in most tissues of eukaryotic organisms, i.e., it is found ''ubiquitously''. It was discovered in 1975 by Gideon Goldstein and further characterized throughout the late 1970s and 1980s. Fo ...
, 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.
Equilibrium criteria
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 temperatures (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
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
(FRET) and
fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
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
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object.
Unimodal probability distribution
In statistics, a unimodal p ...
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 or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity ...
changes (and hence
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
) 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
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
(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
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
In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water (known as a hydrophobe). In contrast, hydrophiles are attracted to water.
Hydrophobic molecules tend to be nonpolar and, t ...
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.
Instead of attempting a model-free inversion of the DSC profile to extract the underlying
probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) ca ...
, they assumed a specific free energy functional with either one or two minima (similar to the
Landau theory
Landau theory in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. It can also be adapted to systems under externally-applied fields, and used as a qu ...
of
phase transitions
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
) thus enabling the extraction of free energy barrier heights. This model is the first of its kind in physical
biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
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.
Simulations
Because downhill folding is difficult to measure experimentally,
molecular dynamics
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 t ...
and
Monte Carlo
Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...
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
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 (i.e., they are more than four residues apart in the primary sequence in order to remove trivial i to ...
s during the folding process; that is, a low
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 folde ...
. The link between lack of cooperativity and low contact order was also observed in the context of
Monte Carlo
Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...
lattice simulations
These data suggest that the average number of "nonlocal contacts" per
residue
Residue may refer to:
Chemistry and biology
* An amino acid, within a peptide chain
* Crop residue, materials left after agricultural processes
* Pesticide residue, refers to the pesticides that may remain on or in food after they are applied ...
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.
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.
[{{cite journal , last1=Yue , first1=Zhi , last2=Shen , first2=Jana , title=pH-Dependent cooperatively and existence of a dry molten globule in the folding of a mini protein BBL , journal=Physical Chemistry Chemical Physics , publisher=Royal Society of Chemistry , volume=20 , issue=5 , date=2018 , issn=1463-9084 , doi=10.1039/c7cp08296g , pages=3523–3530, pmid=29336449 , pmc=5794518 , bibcode=2018PCCP...20.3523Y , s2cid=3594552 ]
See also
*
Dr. Victor Muñoz
References
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.
Protein structure
Statistical mechanics