Phi value analysis,
analysis, or
-value analysis is an experimental
protein engineering
Protein engineering is the process of developing useful or valuable proteins. It is a young discipline, with much research taking place into the understanding of protein folding and recognition for protein design principles. It has been used to imp ...
technique for studying the structure of the folding
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 wi ...
of small
protein domain
In molecular biology, a protein domain is a region of a protein's polypeptide chain that is self-stabilizing and that folds independently from the rest. Each domain forms a compact folded three-dimensional structure. Many proteins consist of s ...
s that
fold in a two-state manner. The structure of the folding transition state is hard to find using methods such as
protein NMR Nuclear magnetic resonance spectroscopy of proteins (usually abbreviated protein NMR) is a field of structural biology in which NMR spectroscopy is used to obtain information about the structure and dynamics of proteins, and also nucleic acids, and ...
or
X-ray crystallography
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
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
The wild type (WT) is the phenotype of the typical form of a species as it occurs in nature. Originally, the wild type was conceptualized as a product of the standard "normal" allele at a locus, in contrast to that produced by a non-standard, "m ...
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.
The protein's residues are mutated one by one to identify residue clusters that are well-ordered in the folded transition state. These residues' interactions can be checked by ''double-mutant-cycle
'' ''analysis'', in which the single-site mutants' effects are compared to the double mutants'. Most mutations are conservative and replace the original residue with a smaller one (''cavity-creating mutations'') like
alanine
Alanine (symbol Ala or A), or α-alanine, is an α-amino acid that is used in the biosynthesis of proteins. It contains an amine group and a carboxylic acid group, both attached to the central carbon atom which also carries a methyl group side c ...
, though
tyrosine
-Tyrosine or tyrosine (symbol Tyr or Y) or 4-hydroxyphenylalanine is one of the 20 standard amino acids that are used by cells to synthesize proteins. It is a non-essential amino acid with a polar side group. The word "tyrosine" is from the Gr ...
-to-
phenylalanine
Phenylalanine (symbol Phe or F) is an essential α-amino acid with the formula . It can be viewed as a benzyl group substituted for the methyl group of alanine, or a phenyl group in place of a terminal hydrogen of alanine. This essential amino a ...
,
isoleucine
Isoleucine (symbol Ile or I) is an α-amino acid that is used in the biosynthesis of proteins. It contains an α-amino group (which is in the protonated −NH form under biological conditions), an α-carboxylic acid group (which is in the deprot ...
-to-
valine
Valine (symbol Val or V) is an α-amino acid that is used in the biosynthesis of proteins. It contains an α-amino group (which is in the protonated −NH3+ form under biological conditions), an α- carboxylic acid group (which is in the deprotonat ...
and
threonine
Threonine (symbol Thr or T) is an amino acid that is used in the biosynthesis of proteins. It contains an α-amino group (which is in the protonated −NH form under biological conditions), a carboxyl group (which is in the deprotonated −COOâ ...
-to-
serine
Serine (symbol Ser or S) is an α-amino acid that is used in the biosynthesis of proteins. It contains an α-amino group (which is in the protonated − form under biological conditions), a carboxyl group (which is in the deprotonated − form un ...
mutants can be used too.
Chymotrypsin inhibitor,
SH3 domain
The SRC Homology 3 Domain (or SH3 domain) is a small protein domain of about 60 amino acid residues. Initially, SH3 was described as a conserved sequence in the viral adaptor protein v-Crk. This domain is also present in the molecules of phos ...
s,
WW domain
The WW domain, (also known as the rsp5-domain or WWP repeating motif) is a modular protein domain that mediates specific interactions with protein ligands. This domain is found in a number of unrelated signaling and structural proteins and may be ...
, individual domains of proteins L and G,
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 ...
, and
barnase
Barnase (a portmanteau of "BActerial" "RiboNucleASE") is a bacterial protein that consists of 110 amino acids and has ribonuclease activity. It is synthesized and secreted by the bacterium '' Bacillus amyloliquefaciens'', but is lethal to the cel ...
have all been studied by
analysis.
Mathematical approach
Phi is defined thus:
[ Daggett V, Fersht AR. (2000). Transition states in protein folding. In ''Mechanisms of Protein Folding'' 2nd ed, editor RH Pain. Oxford University Press.]
is the difference in energy between the wild-type protein's
transition and denatured state,
is the same energy difference but for the mutant protein, and the
bits are the differences in energy between the native and denatured state. The phi value is interpreted as how much the mutation destabilizes the transition state versus the folded state.
Though
may have been meant to range from zero to one, negative values can appear. A value of zero suggests the ''mutation'' doesn't affect the structure of the folding pathway's rate-limiting transition state, and a value of one suggests the mutation destabilizes the transition state as much as the folded state; values near zero suggest the ''area around the mutation'' is relatively unfolded or unstructured in the transition state, and values near one suggest the transition state's local structure near the mutation site is similar to the native state's. Conservative substitutions on the protein's surface often give phi values near one. When
is well between zero and one, it is less informative as it doesn't tell us which is the case:
# The transition state itself is partly structured; or
# There are two
protein populations of near-equal numbers, one kind which is mostly-unfolded and the other which is mostly-folded.
Key assumptions
# Phi value analysis assumes
Hammond's postulate
Hammond's postulate (or alternatively the Hammond–Leffler postulate), is a hypothesis in physical organic chemistry which describes the geometric structure of the transition state in an organic chemical reaction
A chemical reaction is a pro ...
, which states that energy and chemical structure are correlated. Though the relationship between the folding intermediate and native state's structures may correlate that between their energies when 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 ...
has a well-defined, deep global minimum, free energy destabilizations may not give useful structural information when the energy landscape is flatter or has many local minima.
# Phi value analysis assumes the folding ''pathway'' isn't significantly altered, though the folding ''energies'' may be. As nonconservative mutations may not bear this out, conservative substitutions, though they may give smaller energetic destabilizations which are harder to detect, are preferred.
# Restricting
to numbers greater than zero is the same as assuming the mutation increases the stability and lowers the energy of neither the native nor the transition state. It is in the same line assumed that interactions that stabilize a folding transition state are like those of the native structure, though some protein folding studies found that stabilizing non-native interactions in a transition state facilitates folding.
Example: barnase
Alan Fersht
Sir Alan Roy Fersht (born 21 April 1943) is a British chemist at the MRC Laboratory of Molecular Biology, Cambridge, and an Emeritus Professor in the Department of Chemistry at the University of Cambridge. He was Master of Gonville and Caius C ...
pioneered phi value analysis in his study of the small
bacteria
Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among ...
l protein
barnase
Barnase (a portmanteau of "BActerial" "RiboNucleASE") is a bacterial protein that consists of 110 amino acids and has ribonuclease activity. It is synthesized and secreted by the bacterium '' Bacillus amyloliquefaciens'', but is lethal to the cel ...
. Using
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 the ...
simulations, he found that the transition state between folding and unfolding looks like the native state and is the same no matter the reaction direction. Phi varied with the mutation location as some regions gave values near zero and others near one. The distribution of
values throughout the protein's sequence agreed with all of the simulated transition state but one helix which folded semi-independently and made native-like contacts with the rest of the protein only once the transition state had formed fully. Such variation in the folding rate in one protein makes it hard to interpret
values as the transition state structure must otherwise be compared to folding-unfolding simulations which are computationally expensive.
Variants
Other 'kinetic perturbation' techniques for studying the folding transition state have appeared recently. Best known is the psi (
) value which is found by engineering two metal-binding amino acid residues like
histidine
Histidine (symbol His or H) is an essential amino acid that is used in the biosynthesis of proteins. It contains an α-amino group (which is in the protonated –NH3+ form under biological conditions), a carboxylic acid group (which is in the de ...
into a protein and then recording the
folding kinetics as a function of metal ion concentration, though Fersht thought this approach difficult. A '
cross-link
In chemistry and biology a cross-link is a bond or a short sequence of bonds that links one polymer chain to another. These links may take the form of covalent bonds or ionic bonds and the polymers can be either synthetic polymers or natural ...
ing' variant of the
-value was used to study segment association in a folding transition state as covalent crosslinks like
disulfide bond
In biochemistry, a disulfide (or disulphide in British English) refers to a functional group with the structure . The linkage is also called an SS-bond or sometimes a disulfide bridge and is usually derived by the coupling of two thiol groups. In ...
s were introduced.
-T value analysis has been used as an extension of
-value analysis to measure the response of mutants as a function of temperature to separate enthalpic and entropic contributions to the transition state free energy.
Limitations
The error in equilibrium stability and aqueous (un)folding rate measurements may be large when values of
for solutions with
denaturants must be extrapolated to
aqueous solution
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be re ...
s that are nearly pure or the stability difference between the native and mutant protein is 'low', or less than 7 kJ/mol. This may cause
to fall beyond the zero-one range. Calculated values
depend strongly on how many data point are available. A study of 78 mutants of WW domain with up to four mutations per residue has quantified what types of mutations avoid interference from native state flexibility, solvation, and other effects, and statistical analysis shows that reliable information about transition state perturbation can be obtained from large mutant screens.
See also
*
Chevron plot
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' ...
*
Denaturation midpoint
*
Equilibrium unfolding
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 ...
References
{{Reflist, 2
Protein structure
Protein folding
Protein engineering
Protein methods