NationMaster - Encyclopedia: Equilibrium unfolding

In biochemistry, equilibrium unfolding is the process of unfolding a protein or RNA molecule by gradually changing its solution conditions, i.e., its environment. Since equilibrium is maintained at all steps, the process is reversible (equilibrium folding). Equilibrium unfolding is used to determine the conformational stability of the molecule. This article or section does not cite its references or sources. ... Protein folding is the process by which a protein structure assumes its functional shape or conformation. ...

Theoretical background

In its simplest form, equilibrium unfolding assumes that the molecule may belong to only two thermodynamic states, the folded state (typically denoted N for "native" state) and the unfolded state (typically denoted U). This "all-or-none" model of protein folding was first proposed by Tim Anson (1945), but is believed to hold only for small, single structural domains of proteins (Jackson, 1998); larger domains and multi-domain proteins often exhibit intermediate states. As usual in statistical mechanics, these states correspond to ensembles of molecular conformations, not just one conformation. Mortimer (Tim) Louis Anson (1901- 16 October 1968) was an early protein scientist. ... Within a protein, a structural domain (domain) is an element of overall structure that is self-stabilizing and often folds independently of the rest of the protein chain. ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... The word ensemble can refer to a musical ensemble a statistical ensemble a quantum ensemble a DAB ensemble a fluid mechanical ensemble This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

The molecule may transition between the native and unfolded states according to a simple kinetic model

with rate constants

k f

and

k u

for the folding () and unfolding () reactions, respectively. The dimensionless equilibrium constant can be used to determine the conformational stability

Δ G

by the equation Image File history File links Gleichgewicht. ... In chemical kinetics a reaction rate constant quantifies the speed of a chemical reaction. ... In chemistry, the equilibrium constant is a quantity characterizing a chemical equilibrium in a chemical reaction which is a useful tool to determine the concentration of various reactants or products in a system where chemical equilibrium occurs. ...

where

R

is the gas constant and

T

is the absolute temperature in Kelvin. Thus,

Δ G

is positive if the unfolded state is less stable (i.e., disfavored) relative to the native state. The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... This article is about the technical details of the thermodynamic concept of temperature. ... The kelvin (symbol: K) is the SI unit of temperature, and is one of the seven SI base units. ...

The most direct way to measure the conformational stability

Δ G

of a molecule with two-state folding is to measure its kinetic rate constants

k f

and

k u

under the solution conditions of interest. However, since protein folding is typically completed in milliseconds, such measurements can be difficult to perform, usually requiring expensive stopped-flow or (more recently) continuous-flow mixers to provoke folding with a high time resolution.

Chemical denaturation

In the less expensive technique of equilibrium unfolding, the fractions of folded and unfolded molecules (denoted as

p N

and

p U

, respectively) are measured as the solution conditions are gradually changed from those favoring the native state to those favoring the unfolded state, e.g., by adding a denaturant such as guanidinium hydrochloride or urea. (In equilibrium folding, the reverse process is carried out.) Given that the fractions must sum to one and their ratio must be given by the Boltzmann factor, we have Irreversible egg protein denaturation and loss of solubility, caused by the high temperature (while cooking it) In biochemistry, denaturation is a structural change in biomolecules such as nucleic acids and proteins, such that they are no longer in their native state, and their shape which allows for optimal activity. ... Guanidine is a crystalline compound of strong alkalinity formed by the oxidation of guanine. ... Urea is an organic compound of carbon, nitrogen, oxygen and hydrogen, with the formula CON2H4 or (NH2)2CO. Urea is also known as carbamide, especially in the recommended International Non-proprietary Names (rINN) in use in Europe. ... In physics, the Boltzmann factor is a weighting factor determining the relative probability of a system in thermodynamic equilibrium at a temperature T being in a state with energy E: (kB is Boltzmanns constant. ...

Protein stabilities are typically found to vary linearly with the denaturant concentration. A number of models have been proposed to explain this observation prominent among them being the denaturant binding model, solvent-exchange model (both by Schellman, JA) and the Linear Energy Model (LEM; Pace, NC). All of the models assume that only two thermodynamic states are populated/de-populated upon denaturation. They could be extended to interpret more complicated reaction schemes.

The denaturant binding model assumes that there are specific but independent sites on the protein molecule (folded or unfolded) to which the denaturant binds with an effective (average) binding constant k. The equilibrium shifts towards the unfolded state at high denaturant concentrations as it has more binding sites for the denaturant relative to the folded state (

Δ n

). In other words, the increased number of potential sites exposed in the unfolded state is seen as the reason for denaturation transitions. An elementary treatment results in the following functional form:

where

Δ G w

is the stability of the protein in water and [D] is the denaturant concentration. Thus the analysis of denaturation data with this model requires 7 parameters:

Δ G w

Δ n

, k, and the slopes and intercepts of the folded and unfolded state baselines.

The solvent exchange model (also called the ‘weak binding model’ or ‘selective solvation’) of Schellman invokes the idea of an equilibrium between the water molecules bound to independent sites on protein and the denaturant molecules in solution. It has the form:

where

K

is the equilibrium constant for the exchange reaction and

X d

is the mole-fraction of the denaturant in solution. This model tries to answer the question of whether the denaturant molecules actually bind to the protein or they seem to be bound just because of the fact that denaturants occupy about 20-30 % of the total solution volume at high concentrations used in experiments, i.e. non-specific effects – and hence the term ‘weak binding’. As in the denaturant-binding model, fitting to this model also requires 7 parameters. One common theme obtained from both these models is that the binding constants (in the molar scale) for urea and guanidinium hydrochloride are small: ~ 0.2

M - 1

for urea and 0.6

M - 1

for GuHCl.

Intuitively, the difference in the number of binding sites between the folded and unfolded states is directly proportional to the differences in the accessible surface area. This forms the basis for the LEM which assumes a simple linear dependence of stability on the denaturant concentration. The resulting slope of the plot of stability versus the denaturant concentration is called the m-value. In pure mathematical terms, m-value is the derivative of the change in stabilization free energy upon the addition of denaturant. However, a strong correlation between the accessible surface area (ASA) exposed upon unfolding, i.e. difference in the ASA between the unfolded and folded state of the studied protein (dASA), and the m-value has been documented by Pace and co-workers. In view of this observation, the m-values are typically interpreted as being proportional to the dASA. There is no physical basis for the LEM and is purely empirical, though it is widely used in interpreting solvent-denaturation data. It has the general form:

where the slope

m

is called the "m-value"(> 0 for the above definition) and (also called C_m) represents the denaturant concentration at which 50% of the molecules are folded (the denaturation midpoint of the transition, where

p N = p U = 1 / 2

In practice, the observed experimental data at different denaturant concentrations are fit to a two-state model with this functional form for

Δ G

, together with linear baselines for the folded and unfolded states. The

m

and are two fitting parameters, along with four others for the linear baselines (slope and intercept for each line); in some cases, the slopes are assumed to be zero, giving four fitting parameters in total. The conformational stability

Δ G

can be calculated for any denaturant concentration (including the stability at zero denaturant) from the fitted parameters

m

and . When combined with kinetic data on folding, the m-value can be used to roughly estimate the amount of buried hydrophobic surface in the folding transition state.

Structural probes

Unfortunately, the probabilities

p N

and

p U

cannot be measured directly. Instead, we assay the relative population of folded molecules using various structural probes, e.g., absorbance at 287 nm (which reports on the solvent exposure of tryptophan and tyrosine), far-ultraviolet circular dichroism (180-250 nm, which reports on the secondary structure of the protein backbone) and near-ultraviolet fluorescence (which reports on changes in the environment of tryptophan and tyrosine). However, nearly any probe of folded structure will work; since the measurement is taken at equilibrium, there is no need for high time resolution. Thus, measurements can be made of NMR chemical shifts, intrinsic viscosity, solvent exposure (chemical reactivity) of side chains such as cysteine, backbone exposure to proteases, and various hydrodynamic measurements. In spectroscopy, the absorbance A is defined as , where I is the intensity of light at a specified wavelength Î» that has passed through a sample (transmitted light intensity) and is the intensity of the light before it enters the sample (or incident light intensity). ... Tryptophan is an amino acid and essential in human nutrition. ... Tyrosine (from the Greek tyros, meaning cheese, as it was first discovered in cheese), 4-hydroxyphenylalanine, or 2-amino-3(4-hydroxyphenyl)-propanoic acid, is one of the 20 amino acids that are used by cells to synthesize proteins. ... Ultraviolet (UV) light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than soft X-rays. ... Ultraviolet (UV) light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than soft X-rays. ... Fluorescence induced by exposure to ultraviolet light in vials containing various sized Cadmium selenide (CdSe) quantum dots. ... Tryptophan is an amino acid and essential in human nutrition. ... Tyrosine (from the Greek tyros, meaning cheese, as it was first discovered in cheese), 4-hydroxyphenylalanine, or 2-amino-3(4-hydroxyphenyl)-propanoic acid, is one of the 20 amino acids that are used by cells to synthesize proteins. ... Pacific Northwest National Laboratorys high magnetic field (800 MHz, 18. ... In nuclear magnetic resonance (NMR), the chemical shift describes the dependence of nuclear magnetic energy levels on the electronic environment in a molecule. ... Intrinsic viscosity is a measure of a solutes contribution to the viscosity of a solution. ...

To convert these observations into the probabilities

p N

and

p U

, one generally assumes that the observable

A

adopts one of two values,

A N

A U

, corresponding to the native or unfolded state, respectively. Hence, the observed value equals the linear sum

By fitting the observations of

A

under various solution conditions to this functional form, one can estimate

A N

and

A U

, as well as the parameters of

Δ G

. The fitting variables

A N

and

A U

are sometimes allowed to vary linearly with the solution conditions, e.g., temperature or denaturant concentration, when the asymptotes of

A

are observed to vary linearly under strongly folding or strongly unfolding conditions. An asymptote is a straight line or curve which a curve approaches as one moves along the curve. ...

Thermal denaturation

A similar formalism may be applied to other types of denaturation by changing the assumed functional form of

Δ G

. For example, in thermal denaturation, the following functional form is often adopted Irreversible egg protein denaturation and loss of solubility, caused by the high temperature (while cooking it) In biochemistry, denaturation is a structural change in biomolecules such as nucleic acids and proteins, such that they are no longer in their native state, and their shape which allows for optimal activity. ...

where

T m i d

is the thermal unfolding midpoint temperature (in Kelvin),

Δ H m i d

is the enthalpy of folding at the midpoint, and

Δ C p

is the difference in specific heats at constant presure between the folded and unfolded states. Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... Protein folding is the process by which a protein structure assumes its functional shape or conformation. ... The specific heat capacity (symbol c or s, also called specific heat) of a substance is defined as heat capacity per unit mass. ...

Other forms of denaturation

Analogous functional forms are posssible for denaturation by pressure, pH, etc. The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... pH is a measure of the acidity of a solution in terms of activity of hydrogen ions (H+). For dilute solutions, however, it is convenient to substitute the activity of the hydrogen ions with the molarity (mol/L) of the hydrogen ions (however, this is not necessarily accurate at higher...

References

Categories: Protein stubs | Protein structure Proteins are amino acid chains, made up from 20 different L-Î±-amino acids, also referred to as residues, that fold into unique three-dimensional protein structures. ... X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of X-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. ... Pacific Northwest National Laboratorys high magnetic field (800 MHz) NMR spectrometer being loaded with a sample. ... Electron crystallography is a method to determine protein structures using electron diffraction. ... Cryo-electron microscopy (sometimes called cryoEM or electron cryomicroscopy) is a form of electron microscopy (EM) where the sample is studied at cryogenic temperatures (generally liquid nitrogen temperatures). ... Basic schematic of a mass spectrometer Mass spectrometry (also know as mass spectroscopy (incorrect)[1] or in common speech mass-spec) is an analytical technique used to measure the mass-to-charge ratio of ions. ... Pacific Northwest National Laboratorys high magnetic field (800 MHz) NMR spectrometer being loaded with a sample. ... Circular dichroism (CD), is the differential absorption of left and right hand circularly polarized light. ... In spectroscopy, the absorbance A is defined as , where I is the intensity of light at a specified wavelength Î» that has passed through a sample (transmitted light intensity) and is the intensity of the light before it enters the sample (or incident light intensity). ... Fluorescence induced by exposure to ultraviolet light in vials containing various sized Cadmium selenide (CdSe) quantum dots. ... The ultracentrifuge is a centrifuge optimized for spinning a rotor at very high speeds, capable of generating acceleration as high as 1,000,000 G (9,800 km/sÂ²) There are two kinds of ultracentrifuges, the preparative and the analytical ultracentrifuge. ... Equipment for running size exclusion chromatography. ... In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. ... Pacific Northwest National Laboratorys high magnetic field (800 MHz) NMR spectrometer being loaded with a sample. ... In biochemistry, flow birefringence is a hydrodynamic technique for measuring the rotational diffusion constants (or, equivalently, the rotational drag coefficients]]. The birefringence of a solution sandwiched between two concentric cylinders is measured as a function of the difference in rotational speed between the iner and outer cylinders. ... In physics, dielectric relaxation refers to the relaxation reponse of a dielectric medium to an external field of microwave frequencies. ... Pacific Northwest National Laboratorys high magnetic field (800 MHz) NMR spectrometer being loaded with a sample. ... Hydrogen-deuterium exchange (also called H-D or H/D exchange) is a chemical reaction in which a covalently bonded hydrogen atom is replaced by a deuterium atom, or vice versa. ... Site-directed mutagenesis is a molecular biology technique in which a mutation is created at a defined site in a DNA molecule, usually a circular molecule known as a plasmid. ... In biochemistry, chemical modification is the technique of chemically reacting a protein or nucleic acid with chemical reagents. ... Protein structure prediction is one of the most significant technologies pursued by computational structural biology and theoretical chemistry. ... Computational molecular docking is a research technique for predicting whether one molecule will bind to another, usually a protein. ...

Contents

Theoretical background GA_googleFillSlot("encyclopedia_square");

Chemical denaturation

Structural probes

Thermal denaturation

Other forms of denaturation

References

Theoretical background