Protocols

Experiments to determine the presence of protein subunits and their size and molecular mass

Summary

The size or apparent atomic mass of proteins is perhaps the most common way of distinguishing the nature of a molecule. As a basis for many separation methods, the molecular mass or just the size of the molecule provides direct information on the degree of molecular complexity, such as whether the molecule can be easily produced in large quantities, or whether a particular analytical method is likely to be effective. Understanding whether the target peptide is capable of binding itself or forming a heterogeneous complex with other peptides will be useful for biosynthetic or mechanistic studies. This chapter briefly introduces some key methods to determine the size and mass of a molecule and the presence or absence of a subunit, emphasizing the basic capabilities and limitations of the methods.

Authors: Burgess et al, Translator: Chen Wei, This experiment is from the "Guide to Protein Purification".

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Experiments to determine the presence of protein subunits and their size and molecular mass

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I. Introduction

Protein molecular size is the basis of many separation methods and is a simple and convenient descriptor of a known molecule or an unknown impurity such as a 20 kDa product. However, despite significant improvements in methodology and data handling, caution is still required if molecular size is to be estimated accurately. In this chapter, 'size' refers to the physical dimension of the protein, and molecular mass to the amount of protein. The asymmetry [or axial ratio] of proteins will also be considered in this chapter, as the molecular mass of a molecule is not the same as that of a protein.
This property of molecular mass often affects the determination of the apparent size of a molecule.

Many proteins assemble into large polymers, and each constituent chain is called a subunit (subunit; T i masheff andF a s m a n , 1971). However, the definition of the subunit concept varies from researcher to researcher depending on the context of the study, and needs to take into account the system being studied, as well as the goals for which the system is working. For the purposes of the discussion in this chapter, an independent protein subunit is defined as a protein component that does not contain a continuous polypeptide backbone. Thus, peptides linked by disulfide bonds or noncovalent interactions are identified as subunits, although these subunits may all be hydrolysis products of the same polypeptide chain.

Methods for determining the size and mass of proteins can be divided into three broad categories: chemicalanalysis, such as compositional analysis or analysis of molecular interactions affecting solvent properties (e.g., vapor pressure, freezing point, and boiling point); transport m e t h o d , based on the movement of molecules in response to external forces (e.g., electric field, centrifugal, mechanical, etc.). transport m e t h o d , based on the movement of molecules in response to external forces (e.g., electric field forces, centrifugal forces, mechanical forces); scattering m e t h o d , based on the interaction of emitted radiation (e.g., light, X-rays, neutrons) with molecules. Because these methods target different properties of the molecule, the choice of method depends on what aspect of the system the researcher needs to understand and the degree of accuracy required. Table 39.1 summarizes the capabilities, strengths, and limitations of many methods. In addition to these criteria, proteins and methods need to be compatible with each other, taking into account the amount of protein sample available, the level of purity that can be achieved (Rhodes and L a u e , 2009), solvent requirements, and any other protein properties that may interfere with the specific method. These methods are also effective for the detection of other molecular properties, which will be covered in the discussion of individual techniques below. Many of the techniques can be coupled with each other (e.g., viscosity and sedimentation coefficient methods, composition and S D S gel electrophoresis, high-performance liquid chromatography, and mass spectrometry). Not all methods are listed here, and some (e.g., radiation deactivation and cDNA analysis) may be applicable only in special cases.

ii. chemical methods

2.1 Composition

2.1.1 General

Although compositional assays are currently only used in special cases, these methods can provide quantities of amino acids or specific cofactor substances, and therefore the minimum molecular mass of some proteins can be estimated using the formula Mmin= m/n, where Mmin is the estimated molecular mass of the protein (g/mol, m is the amount of protein used in the analysis, and n is the number of moles of the relevant component of the protein measured in the analysis. m is the amount of protein used in the analysis, and n is the number of moles of protein-related components measured in the analysis. Amino acid analysis, terminal analysis, and quantitative analysis of specific cofactors (NobleandBailey, 2009) can yield very good quantitative values. The amount of material required for such component-based molecular mass analysis depends on the sensitivity of the method used. Since many of the newer analytical techniques are available at the nmol to Pmol level, the amount of material required is dependent on the sensitivity of the method used.
Since many newer analytical techniques are very sensitive at the nmol to Pmol level, micrograms or even less of sample may be required to satisfy the analytical requirements.

Both the mass estimation error and the component-specific analytical error determine the error in the minimum molecular mass estimate. Therefore, the error in the estimation of the minimum molecular mass will be determined by the method of measurement of these two parameters. Combining the analytical data of different components can improve the accuracy. Therefore, independent estimation methods based on amino acid analysis, quantitative analysis of terminal groups, or quantification of nonprotein factors are recommended.

Since the component analysis method can only provide a minimum molecular mass, the mass of the protein can be obtained by combining these data with results obtained by other methods. # An accurate fractional analysis can be used in conjunction with other low-accuracy whole-molecule mass assays to produce high-accuracy results. Perhaps the most common example of this approach is the combination of amino acid analysis [the more commonly used sequence-based methods are described in BUrgeSs (2009), see also Bartolom eo and Maisano (2006)] and SDS gel electrophoresis. Theoretically, the M-value should be estimated by determining the smallest whole that is representative of the entire amino acid composition. In practice, the uncertainty of the concentration of all 20 different amino acids makes this method inherently unreliable. However, the approximate molecular mass obtained by SDS gel electrophoresis can help guide the estimation of M values from
However, the approximate molecular mass obtained by SDS gel electrophoresis can help guide the selection of the approximate absolute concentration from the relative concentrations by indicating to the researcher whether to round up or round down a value.

2.1.2 Methods
The most accurate measurement of protein mass should be the dry weight of the protein in a volatile buffer (e.g. ammonium bicarbonate). Protein mass can be calculated in non-volatile buffers based on the mass difference between the dry weight of the sample containing the protein solution and the buffer-only sample, but this is less accurate and is not suitable for some volatile buffers. Protein concentration tests are often used in place of dry weight measurements (the value of mass is the product of mass concentration and volume). Concentration tests can be measured by refractometry, spectrophotometry or chemical methods. The precision of these methods is acceptable, but accuracy is often limited and the main problem is the difficulty of standardization (Nozaki, 1986). Especially for glycoproteins, lipoproteins, or other proteins of more specific composition, analytical methods may be sensitive only to some protein-specific components (e.g., peptide bonds). Of these listed assays, refractometry [or differential refractometry] is the most accurate for concentration measurements, and amino acid analysis is also a suitable quantitative method.

2.1.3 Problems and limitations

Composition-based minimum molecular mass analysis is more sensitive to sample purity. Any impurities that affect the mass estimation or quantitative analysis will affect the accuracy of the measurement. Since none of these analyses can separate the initial material, impurities or heterogeneous components will affect the final result. Therefore, the sample must be purified prior to analysis. Sample purity requirements depend on the nature of the impurity, the mass estimate, or the sensitivity of the analytical method to the impurity. For all of these methods, it must be assumed that there is only one mole or ^ integer molar value of analyte component per mole of protein. In the absence of available information on the four-level structure, only a minimum molecular mass can be obtained. For example, quantitative analysis of heme iron in hemoglobin or myoglobin will yield nearly identical apparent molecular masses, despite the fact that intact hemoglobin has four times the molecular mass of myoglobin.

2.2 Dependence

2.2.1 General

Dissolution of solutes into solution reduces the chemical potential of the solvent and leads to some visible phenomenon, this common phenomenon is called colligative property (Tinoco et al., 2002). Based on this phenomenon they are related as 象称为依数性(colligative property)(Tinoco et al.,2002)。基于这个现象它们的关系为 - ^ 0a= RTln(XaXa) (39.1) 式 中 ,柃为一个溶质“a”(c a P /mol)的化学势;;4°为柃的标准状态;i? 为气体常数[8. 3144X 107cal/(m〇 l,°K)];: T 为温度(K );y 为溶质V ’ 的活性系数;X a 为 7 ’ 的摩尔成分。当 Xa 小 于 1 时 ,^ 小 于 & ° 。理论上,通过已知量的溶质对溶液活性的改变程度可以确定任何

The molecular mass of a solute. The molecular mass of any such solute, including proteins, can be determined by measuring the decrease in freezing point, the increase in boiling point, the osmotic pressure, or the vapor pressure. Since the change in freezing or boiling point caused by a molecule the size of a protein is usually small, and since protein molecules are generally unstable at these extreme temperatures, they are not applicable to the study of protein solutions. Alternatively, vapor pressure and osmotic pressure can be used to measure protein molecular mass, but are not discussed in detail here. Vapor pressure, freezing point, and membrane osmometers are all commercially available, with vapor pressure and membrane osmometers being the most commonly used in the clinical and pharmaceutical industries. Vapor pressure and freezing point osmometers can reliably measure molecular masses around 25,000 in water, while membrane osmometers can be used to measure proteins with molecular masses greater than 20 0 0 0 . Typically, a protein solution concentration of 0.1 to 1 mg/m L and a sample volume of 10 to 200 uL are required. As with methods for measuring composition, these methods require a high degree of accuracy in terms of sample mass. It should be noted that the molecular mass obtained from any dependent measurement is an average value and is susceptible to the influence of low molecular mass impurities. Additional information can be found in T in o c o et al. (2002) and in the product literature.

Transmission Methods

3.1 Sedimentation equilibrium method

3.1.1 General

The deposition equilibrium method is an accurate and effective method for measuring the mass of natural molecules of protein (Cole et al., 2008). The method is simple, non-destructive and relatively fast. All parameters describing the sedimentation equilibrium are easy to measure or estimate. The method has several unique capabilities to quantify molecular mass, stoichiometry, and binding for a wide range of chemical systems.
constants for a wide range of chemical systems. For example, by settling in a neutral buoyant (non-sedimenting) detergent, it is possible to measure the molecular mass of proteins that are able to dissolve in that detergent (F ish, 1978). There are many other systems that cannot be analyzed by other methods that can be successfully evaluated by the sedimentation equilibrium method. However, because equilibrium methods often require sophisticated and expensive instrumentation, and because other methods have been able to accomplish many of the objectives and obtain sufficient data, the use of equilibrium methods has declined considerably with the maturation of powerful sedimentation rate analysis methods. Nevertheless, equilibrium methods remain one of the most effective assays for the quantitative study of protein-protein binding and play an irreplaceable role in the study of protein systems with weak or moderate binding constants.

3.1.2 Methods

The purpose of the sedimentation equilibrium experiment is to produce a measurable protein concentration gradient along the radial axis of the centrifuge cell. The time to equilibrium depends on the length of the solution column, the reduced molecular weight value (ex), and the diffusion constant. Since the time to equilibrium depends on the square of the column length, many centrifugation cells and techniques utilize short columns (0.75 m m or 3 m m long) (Ralston, 1993). With these centrifugation cells, different proteins can be equilibrated in minutes to hours. The concentration distribution is measured at 30-60 m in intervals at a given rotational speed, and if the concentration distribution does not change over time, equilibrium has been reached. Some software (e.g., HeteroAnalysis) can help automate this process (Cole et al., 2008).

A typical sedimentation equilibrium centrifugation experiment requires 3 to 4 concentrations of 100 to 200 ul of solution each, typically ranging from 0.1 mg/m L to about 3 mg/m L. These solutions need to be prepared with a suitable buffer containing the same components. Sedimentation equilibrium centrifugation experiments are usually carried out at different speeds, with a concentration ratio of 3 to 5 at the top and bottom of the centrifugation tank at low speeds, and a complete absence of solutes in the crescent surface of the centrifuge at high speeds.

Even without an analytical centrifuge, the concentration distribution at equilibrium can be measured by a variety of methods. If a preparative centrifuge (Attri and Minoton, 1986) or an "airfuge" (Bock and Halvorson, 1E 583) is used in the measurement, the centrifuged material can be separated and then subjected to any test method appropriate to the protein concentration. Since any concentration measure can be used (e.g., enzyme activity), analysis of sedimentation equilibrium using a preparative centrifuge can be used to examine the molecular mass of complex mixtures and highly concentrated solutions (Howlett etal., 2006). However, centrifugation experiments of varying lengths of time are required to ensure that the mixture system
equilibrium is achieved. Moreover, the accuracy of these centrifugation methods is lost when the rotor is decelerated or when the centrifugal fraction is separated due to the destruction of the concentration gradient. However, some experimentation is necessary at various points in time to ensure that the mixture system is in equilibrium, but the accuracy of these centrifugation methods is lost when the rotor is decelerated or the centrifugal group is separated due to the destruction of the concentration gradient. Analytical supercentrifuges can alleviate this problem by allowing optical examination of the solvent components while the centrifugal components remain in equilibrium during centrifugation.

Three optical systems are currently available for use in standard analytical centrifuges: ultraviolet or visible light absorption scanners, rayleigh interferometers, and sudden light detectors. These three systems provide complementary information in situations where the selectivity and sensitivity of fluorescence and absorption optics are required, while at other times the precision and accuracy of a rayleigh interferometer system is needed. Fluorescence systems have excellent sensitivity (down to 100 pmol/L fluorescein) but require fluorescent molecules or fluorescent labeling molecules (Kroe and Laue, 2009). Fluorescence optical systems have similar precision to absorption optical systems, but accuracy is limited because the quantum yield of the fluorescent moiety is very sensitive to the environment in which the molecule resides.

The radius of the centrifuge must be calculated accurately, and analyzing the optical system of an ultracentrifuge can provide this information (Ralston, 1993). When using preparative centrifuges, the radius is calculated from geometry. The original article describes how to calculate radii for different rotors and centrifugal coffins (Attri and M nton, 1986; Bock and Halvorson, 1983).

3.1.3 Problems and limitations

The central problem with sedimentation equilibrium analysis is obtaining sufficient quantities of high-purity proteins for analysis. Even for high-purity proteins, it is beneficial to perform a sedimentation rate analysis prior to equilibrium analysis (C o le e t al., 2008). The Rayleigh interferometer optical system requires only 20 uL of solution at a concentration of I mg/m L to measure molecular mass, and the concentration of some fluorescent solutes can be even lower. Although this method uses less material than usual gel electrophoresis, the presence of small amounts of impurities may make interpretation of the data more difficult, especially if the impurities are unknown or unanticipated. If a preparative centrifuge is used and the measurement method is sensitive, less material may be required, but with less accuracy. It is also important to note that sedimentation equilibrium methods do not separate to the same extent as sedimentation rates, gel filtration and gel electrophoresis. Nevertheless, centrifugal force separates the solution to some extent, removing some large particles (e.g., dust, flocs, polymers). This means that although analytical centrifugation requires some suitable techniques, it is not necessary to purify the sample as carefully as scattering methods. It should be noted that buffer components are also separated in the centrifugal force field, so it is best to choose a buffer that is5 close to the solvent (1 ) . Buffers such as Tr is are suitable for sedimentation experiments, whereas phosphate buffers may cause problems in some cases.
(Yphantis, 1964). Adequate dialysis and careful filling of the centrifuge chamber can minimize problems with buffer settling.

There are methods for detecting impurities in samples analyzed by sedimentation equilibrium methods. One such method is to map the apparent molecular mass
(which can be obtained from the local slope of the plot of Inc as a function of r2/ 2) as a function of concentration [M (c)]. If the M (c) plot is independent of the rotor rate, then it is quite certain that the sample is pure. More highly sensitive methods for measuring heterogeneity are outlined in the literature by R hodes and Laue (2009).

3.2 Sedimentation rate methods

3.2.1 General

The sedimentation rate method is a simple, non-destructive method for determining the hydrodynamic properties of proteins. Its advantage over gel chromatography is that it can be used as a basic method (without standards) to determine hydrodynamic parameters. Since sedimentation analysis is based on the first law, it can be applied to systems that cannot be analyzed by any other method. The main result obtained by sedimentation rate experiments is the sedimentation coefficient G ), which is obtained by measuring the ratio of the buoyant mass of the protein to its frictional coefficient:

3.2.2 Methods

Although methods have been developed to improve the accuracy of preparative centrifugation where appropriate, the sedimentation rate method is best performed with an analytical ultracentrifuge. The advantage of analytical equipment is that its accuracy (± 1 % to 3 %) is almost an order of magnitude higher than that of preparative equipment. Also, data is available in real time throughout the experiment, so that any abnormal behavior can be observed and better understood. The benefit of a preparative centrifuge is that it allows the use of sensitive or specific measurement methods, such as ELISA, and can therefore be used in situations where the purity of the sample is unknown. Specific methods can be found in the use of analytical ultracentrifuges (R aIs t o n , , ).
1993) and the use of preparative centrifuges (Freifelder, 1973; M artin an d Am es, 1961).

As mentioned earlier, the primary measurements of any sedimentation experiment are obtained as a function of concentration with respect to radial position. The sedimentation coefficient can be determined from the slope of a plot of the natural logarithm of the molecular sedimentation distance as a function of time (dlnr/ by)

3.2.3 Problems and limitations

Sedimentation rate methods provide molecular biologists with the best and only basic method for measuring hydrodynamic data . Both electrophoresis and gel filtration methods require molecular mass standards, which limits data interpretation. Of all the methods presented in this chapter, the problems and limitations of the sedimentation analysis method are the best documented and the easiest to overcome.

The most demanding aspect of sedimentation is the need for adequate material for analysis. If the standard optical system of the popular Beckman XL-A analytical ultracentrifuge is used, 0.5 m L of protein concentration in the range of 0.1 to 1 mg/m L is required to obtain good data.

For proteins with significant binding to buffer components (e.g., detergent-solubilized proteins), interpretation of the sedimentation coefficients becomes difficult because the binding component will affect the measurement of s by four parameters: M, v, p, and f. Of these four parameters, M, v, p, and f, the sedimentation coefficient is the same as that of the buffer component. Of these four parameters, M, v, and f are usually the most susceptible to the influence of the binding components and, unlike the equilibrium method, the sedimentation rate method cannot "cancel out" the influence of these components. Therefore, the measured sedimentation coefficients are such that protein complexes with bound components are difficult to extract information about the protein itself from.

3.2.4 Derivative methods

The effect of protein concentration on S can be evaluated by measuring s values for different protein concentrations. In general, an approximate linear decrease is observed with increasing protein concentration.

Another widely used method for estimating the molecular mass of proteins is the sucrose concentration gradient sedimentation method introduced by M a rtin and Ames (1961). With this method, a linear gradient of sucrose is obtained in solution using a suspended hanging centrifuge bucket. The sucrose concentration is usually about 5 % at the top of the centrifuge tube and 20 % at the bottom of the centrifuge tube. The actual concentration range is not as important as the linearity and reproducibility of the gradient. The unknown sample is spread over one gradient, and then a series of standard proteins of known molecular mass are spread over another gradient that is balanced against it. The centrifugation process takes a certain amount of time (typically 12-24 h), and then the material on the different gradients is collected in separate fractions. The concentration of proteins in these separated fractions can be determined by spectrophotometric, enzymatic or other assays.

The present method is based on the fact that in a linear sucrose gradient, the distance traveled by the molecules is a linear function of the centrifugation time at a given rate. In addition, this distance is linearly related to s. The ratio of the distance traveled by the unknown protein to the distance traveled by the standard protein is equal to the ratio of their sedimentation coefficients. The sedimentation coefficient is approximately equal to the 2/3 power of the molecular mass ratio. This method gives only approximate values for s and M, but it is simple, requires no special equipment, and with the right method can estimate s and M for very small amounts of material.

3.3 Gel filtration (molecular exclusion) chromatography

3.3.1 General

Gel filtration chromatography is one of the most efficient and simple methods used to estimate the molecular mass of proteins. Sample purity does not need to be high since this method enables the separation of the sample and the application of methods for the specific determination of the target protein (e.g. enzymatic and immunological methods). The method is non-destructive, can be completed in a fairly short time, and is moderately accurate, as long as the shape of the target protein roughly corresponds to the protein standard used to calibrate the analytical column (Ackers, 1970)

Determination of the molecular weight of protein by gel chromatography relies on the comparison of the elution volume of an unknown protein with that of some protein standards of known molecular weight. The molecular mass of unknown proteins is estimated by means of a function plot of the logarithmic value of the molecular mass of the protein standard and the elution volume (or K av, see below). (It is important to note that the actual dependence is on the logarithmic value of the effective hydration radius, or the "Stokes radius" of the protein, if the protein standard can be fitted to this variable). The elution volume (V e) of the protein standard should cover the volume from the void volume (V .); the volume outside of the solid phase should cover the volume from the solid phase (V .); and the volume from the solid phase should cover the volume from the void volume (V .). The elution volume (Ve) should cover the range from void volume (V; volume outside the stationary phase) to internal volume (included volume, %; volume accessible in the stationary phase solenoid). Although this part of the discussion concerns elution volume, most SEC data reports use elution time. For a given flow rate, the elution time is proportional to the elution volume. The column non-dependent measure of protein behavior, K av, is a more favorable comparison of results than a simple elution volume.

3.3.2 Methods

The principles of operation and the choice of gel medium and gel porosity have been described in detail (Stellwagen, 2009). It is now possible to separate SEC solid phase media over a very wide range of molecular sizes, but the resolution may not be sufficient to meet specific needs. In some cases, solid phases with a small measuring range can provide very high resolution, but the size of the target protein needs to be taken into account when choosing one that is within the separation range of the gel. In general, as long as the protein cannot be bound to the matrix, the choice of the solid phase is relatively arbitrary. If more than one type of gel particle is available for a given porosity requirement, the smallest particle should be used, as this will increase the resolution of the column. It is important to check the manufacturer's manual for any solvent limitations, but in general, almost any free-flowing aqueous buffer system can be used. The use of medium ionic strength buffers is recommended to minimize the electrostatic interactions between protein and substrate. For best results and highest resolution, long, thin columns should be used. Column preparation, column buffer equilibrium, and flow rate should be chosen according to the manufacturer's instructions. In general, the lower the flow rate, the better the resolution, since the solutes can equilibrate with the gel matrix at any time, but if the flow rate is too slow it will cause excessive diffusion and affect the resolution. All samples should be in the same buffer used to equilibrate the column. The sample volume should be less than 2% of the bed volume. In addition, the flow rate of the column should be constant throughout the analysis so that the elution volume can be predicted from the flow rate (Ackers, 1970).
The eluted volume (V6) is the volume removed from the column, calculated from the top of the gell bed where half of the sample flows until the maximum value of the target protein (peak) is removed. Column Volume Free (V.) can be measured using commercial glucose blue (M == 2,000,000) in various sizes and monitoring the flow-through fluid at 540 nm or 280 nm. The internal volume ( Vi ) can be measured using buffers at different pH or conductivities (extreme conditions affecting the column should be avoided) as samples, or containing a small amount of dye (e.g., bromophenol blue). The internal volume is the difference between the eluted volume of the small molecules and the void volume ( V0 ) measured using the large molecules that cannot be introduced into the gel. Great care should be taken in the selection of dyes, as many aromatic compounds have an affinity for the solid phase, which will result in unusually high K av values and V i values.

The molecular mass of the protein standard should cover the separable range of the selected stationary phase to ensure that the molecular mass of the protein being analyzed is within the standard. For best results, at least four different standards should be used. Kits containing pre-stained proteins are commercially available. Any analytical method that allows simple detection of the target protein can be used. Columns need to be recalibrated whenever they need to be reloaded for any reason.

There are some special problems associated with using column chromatography to measure the molecular mass of altered proteins (Fish, 1978). This method assumes that the shape of the unknown protein is the same as that of the standard protein, which means that the egg is not the same as the standard protein.
This means that the protein needs to be completely denatured, including reduction of the disulfide bonds. Therefore the buffer should be an alkylate containing a reducing agent or sulfhydryl group, thus preventing the disulfide bond from forming again. Both standards and unknown samples should b


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Da — when not otherwise indicated, molecular weight units are daltons.   Mw — weight-average molecular weight.   Mn — number-average molecular weight.

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