![11. The relationship between log10(MW) [where MW — molecular weight in kDa] of a mixture of protein standards and their retention factors (Rf) obtained from native-PAGE is log10(MW) = -2Rf + 3. lf the measured retention factor for a protein with 180 amino acids is 0.5, then the number of identical monomers in the protein is .](https://www.letstalkacademy.com/wp-content/uploads/2026/07/01-11.jpg)
11. The relationship between log10(MW) [where MW — molecular weight in kDa] of a mixture of protein standards and their retention factors (Rf) obtained from native-PAGE is log10(MW) = -2Rf + 3. lf the measured retention factor for a protein with 180 amino acids is 0.5, then the number of identical monomers in the protein is .
How to Calculate the Number of Identical Monomers in a Protein Using Native-PAGE?
Correct Answer: 5 Identical Monomers
The correct answer is 5 identical monomers. The problem can be solved in two major stages. First, the molecular weight of the complete native protein must be calculated from its retention factor using the given native-PAGE equation. Second, the approximate molecular weight of one monomer must be calculated from the number of amino acids. Dividing the molecular weight of the complete native protein by the molecular weight of one monomer gives the number of identical subunits.
The measured retention factor of the protein is Rf = 0.5. Substituting this value into the equation gives a native molecular weight of 100 kDa. A monomer containing 180 amino acids has an approximate molecular weight of 19.8 kDa, using the average molecular mass of an amino acid residue as approximately 110 Da.
Therefore:
Number of monomers = 100 kDa ÷ 19.8 kDa ≈ 5
Thus, the native protein consists of 5 identical monomers and can be described as a homopentamer.
Understanding the Information Given in the Question
This question combines three important concepts in protein biochemistry: native polyacrylamide gel electrophoresis, estimation of molecular weight from electrophoretic mobility, and determination of protein quaternary structure.
The first piece of information is the mathematical relationship between the logarithm of the molecular weight and the retention factor:
log10(MW) = −2Rf + 3
The second piece of information is the experimentally measured retention factor:
Rf = 0.5
The third piece of information is the length of one polypeptide monomer:
Number of amino acids in one monomer = 180
The equation provides the molecular weight of the complete protein under native conditions, whereas the amino acid number allows the approximate molecular weight of one polypeptide chain to be estimated. Comparing these two values reveals how many identical monomers are present in the native protein.
Step 1: Write the Given Native-PAGE Equation
The relationship provided in the question is:
log10(MW) = −2Rf + 3
Here, MW represents the molecular weight of the protein in kilodaltons (kDa), and Rf represents the retention factor or relative migration value obtained from native-PAGE.
The measured value for the unknown protein is:
Rf = 0.5
This value must be substituted into the equation to determine the molecular weight of the complete native protein.
Step 2: Substitute the Retention Factor into the Equation
Starting with:
log10(MW) = −2Rf + 3
Substitute:
Rf = 0.5
Therefore:
log10(MW) = −2(0.5) + 3
Multiplying −2 by 0.5 gives:
log10(MW) = −1 + 3
Therefore:
log10(MW) = 2
This value represents the base-10 logarithm of the molecular weight. The next step is to remove the logarithm and calculate the actual molecular weight.
Step 3: Calculate the Molecular Weight of the Native Protein
From the previous calculation:
log10(MW) = 2
Taking the antilogarithm:
MW = 102 kDa
Therefore:
MW = 100 kDa
The molecular weight of the complete protein under native conditions is therefore approximately 100 kDa.
This value represents the molecular weight of the complete functional protein complex rather than the molecular weight of an individual polypeptide monomer. The question asks for the number of identical monomers, so the molecular weight of one monomer must now be calculated.
Step 4: Calculate the Molecular Weight of One Monomer
The question states that the protein monomer contains 180 amino acids. To estimate the molecular weight of a polypeptide from its amino acid length, the average molecular mass of one amino acid residue is taken as approximately 110 Da.
Therefore:
Molecular weight of one monomer = Number of amino acids × Average molecular weight of one amino acid residue
Substituting the given values:
Molecular weight of one monomer = 180 × 110 Da
Therefore:
Molecular weight of one monomer = 19,800 Da
Since:
1 kDa = 1000 Da
Therefore:
Molecular weight of one monomer = 19.8 kDa
The approximate molecular weight of each identical polypeptide monomer is therefore 19.8 kDa, which is approximately 20 kDa.
Step 5: Calculate the Number of Identical Monomers
The number of identical monomers is determined by dividing the molecular weight of the complete native protein by the molecular weight of one monomer.
Number of monomers = Molecular weight of native protein ÷ Molecular weight of one monomer
Substituting the calculated values:
Number of monomers = 100 kDa ÷ 19.8 kDa
Therefore:
Number of monomers ≈ 5.05
A protein cannot contain 5.05 identical polypeptide subunits. The small difference from the whole number arises because the molecular mass of 110 Da per amino acid residue is an approximate average value.
Therefore:
Number of identical monomers = 5
The protein is consequently composed of five identical polypeptide subunits.
Complete Calculation at a Glance
The complete solution can be expressed as follows:
Given:
log10(MW) = −2Rf + 3
Rf = 0.5
Therefore:
log10(MW) = −2(0.5) + 3
log10(MW) = 2
MW = 102 = 100 kDa
For one monomer:
Molecular weight = 180 × 110 Da
Molecular weight = 19,800 Da = 19.8 kDa
Therefore:
Number of identical monomers = 100 ÷ 19.8
Number of identical monomers ≈ 5
Final Answer = 5 identical monomers
Why Is the Average Molecular Weight of an Amino Acid Taken as 110 Da?
Proteins are composed of amino acid residues linked together by peptide bonds. The 20 common amino acids do not all have the same molecular mass. Some amino acids have relatively small side chains, whereas others have much larger side chains.
For approximate protein molecular weight calculations, the average mass of one amino acid residue in a polypeptide is commonly taken as approximately 110 daltons.
This value is an average rather than an exact molecular mass. The precise molecular weight of a protein depends on its exact amino acid sequence and any post-translational modifications that may be present.
However, when only the number of amino acids is provided in a numerical problem, the standard approximation is:
Average molecular weight of one amino acid residue ≈ 110 Da
This approximation allows the molecular weight of a protein to be estimated quickly from its amino acid length.
Estimating Protein Molecular Weight from Amino Acid Number
The approximate molecular weight of a protein can be calculated using the following relationship:
Protein molecular weight in Da ≈ Number of amino acids × 110
For a protein containing 180 amino acids:
180 × 110 = 19,800 Da
Converting daltons into kilodaltons:
19,800 Da ÷ 1000 = 19.8 kDa
Therefore, a 180-amino-acid polypeptide has an approximate molecular weight of 19.8 kDa.
What Is Native-PAGE?
Native polyacrylamide gel electrophoresis, or native-PAGE, is a technique used to separate proteins while preserving much of their native structure and subunit association.
Unlike denaturing electrophoresis, native-PAGE does not normally use strongly denaturing conditions to unfold proteins and dissociate their subunits. Therefore, a multisubunit protein can remain assembled during electrophoresis.
This property is essential for the present question. The measured molecular weight of 100 kDa corresponds to the complete native protein complex. The individual polypeptide monomer, however, has an estimated molecular weight of only 19.8 kDa.
The difference between these two molecular weights indicates that the native protein contains multiple copies of the same polypeptide chain.
Why Is Native-PAGE Important for Determining Protein Oligomerization?
A protein may function as a single polypeptide chain or as a complex containing multiple subunits. When subunits remain associated under native conditions, the complete complex behaves as a larger molecular entity.
For example, a monomeric protein contains one subunit, a dimer contains two subunits, a trimer contains three, a tetramer contains four, and a pentamer contains five.
In this problem, the native molecular weight is approximately five times the molecular weight of an individual monomer:
100 kDa ÷ 19.8 kDa ≈ 5
Therefore, the native protein is composed of five identical subunits.
What Is the Quaternary Structure of the Protein?
The association of multiple polypeptide chains into a functional protein complex is known as quaternary structure.
The protein described in this question contains five identical monomers. A complex containing five subunits is called a pentamer. Because all five subunits are identical, the protein can more specifically be described as a homopentamer.
The terms can be understood as follows:
Mono = One subunit
Di = Two subunits
Tri = Three subunits
Tetra = Four subunits
Penta = Five subunits
Therefore, the protein in this question is a homopentameric protein.
Why Is the Native Molecular Weight 100 kDa?
The molecular weight is obtained directly from the relationship between log10(MW) and the retention factor. The measured retention factor is 0.5, so:
log10(MW) = −2(0.5) + 3
log10(MW) = 2
The expression log10(MW) = 2 means that the molecular weight is the number whose base-10 logarithm equals 2.
Therefore:
MW = 102 = 100 kDa
The logarithmic step is important because the value 2 is not itself the molecular weight. The antilogarithm must be calculated to obtain the actual molecular weight.
Understanding Logarithm and Antilogarithm in the Calculation
The equation gives log10(MW) rather than MW directly. Therefore, after obtaining the logarithmic value, an antilogarithm calculation is required.
If:
log10(MW) = 2
Then:
MW = 102
Therefore:
MW = 100
Since the question specifies that molecular weight is expressed in kilodaltons, the final native molecular weight is 100 kDa.
What Is the Retention Factor in PAGE?
The retention factor or relative migration value, represented as Rf, describes the relative distance migrated by a molecule during electrophoresis.
It is commonly expressed as a ratio comparing the distance traveled by the protein with a reference migration distance, such as the migration of the tracking dye front.
A general representation is:
Rf = Distance migrated by protein ÷ Distance migrated by reference front
Because both values are measured in the same units, Rf is dimensionless.
In this question, the measured value is:
Rf = 0.5
This experimental value is inserted into the calibration equation generated using protein standards of known molecular weight.
How Are Protein Standards Used to Estimate Molecular Weight?
Proteins of known molecular weight can be separated under defined electrophoretic conditions. Their migration values are measured, and a relationship between molecular weight and electrophoretic mobility is established.
In the present question, the calibration relationship is already provided:
log10(MW) = −2Rf + 3
The unknown protein is run under the same experimental conditions, and its Rf value is measured. The measured value is then substituted into the calibration equation to estimate the molecular weight of the unknown protein.
This approach is useful because it allows the electrophoretic behavior of an unknown protein to be compared with that of standards whose molecular weights are already known.
Why Is the Number of Monomers Calculated by Division?
If a protein consists of identical monomers, the molecular weight of the complete protein is approximately equal to the molecular weight of one monomer multiplied by the number of monomers.
The relationship is:
Molecular weight of native protein = Molecular weight of one monomer × Number of monomers
Rearranging the equation:
Number of monomers = Molecular weight of native protein ÷ Molecular weight of one monomer
For the present problem:
Number of monomers = 100 kDa ÷ 19.8 kDa
Number of monomers ≈ 5
Therefore, the native protein contains five identical monomers.
Why Is the Calculated Value Rounded from 5.05 to 5?
The numerical calculation gives:
100 ÷ 19.8 ≈ 5.05
However, the number of monomers in a discrete protein complex must be a whole number. A protein cannot contain 5.05 identical polypeptide subunits.
The slight deviation from exactly 5 occurs because the value of 110 Da per amino acid residue is an approximation. The exact molecular weight of a polypeptide depends on its specific amino acid sequence.
Therefore, the value 5.05 is interpreted as approximately 5 monomers.
Native-PAGE Versus SDS-PAGE in This Problem
The distinction between native-PAGE and SDS-PAGE is essential for understanding the calculation. Native-PAGE is designed to preserve much of the native protein structure and can allow multisubunit complexes to remain associated.
Therefore, the molecular weight estimated from the native-PAGE relationship corresponds to the complete protein complex, which is approximately 100 kDa.
Under denaturing SDS-PAGE conditions, the interactions maintaining the quaternary structure would generally be disrupted, and the five identical subunits would separate from one another. Since all five monomers are identical and each has a molecular weight of approximately 19.8 kDa, they would migrate together at the same position.
Thus, the native protein behaves as an approximately 100 kDa complex, whereas the individual polypeptide chain has an approximate molecular weight of 19.8 kDa.
How Native and Monomer Molecular Weights Reveal Protein Structure
Comparing the molecular weight of a protein under native conditions with the molecular weight of its individual polypeptide chain is a useful way to infer subunit organization.
If the native and monomer molecular weights are approximately equal, the protein is likely monomeric. If the native molecular weight is approximately twice the monomer molecular weight, the protein may be a dimer. A ratio of three suggests a trimer, a ratio of four suggests a tetramer, and a ratio of five suggests a pentamer.
In this question:
Native molecular weight ≈ 100 kDa
Monomer molecular weight ≈ 19.8 kDa
Therefore:
100 ÷ 19.8 ≈ 5
This ratio demonstrates that the protein contains five identical monomers.
Final Answer
Correct Answer: 5 Identical Monomers
The molecular weight of the complete native protein is first calculated using the given relationship:
log10(MW) = −2Rf + 3
For Rf = 0.5:
log10(MW) = −2(0.5) + 3 = 2
Therefore:
MW = 102 = 100 kDa
The molecular weight of one monomer containing 180 amino acids is:
180 × 110 Da = 19,800 Da = 19.8 kDa
Therefore:
Number of identical monomers = 100 kDa ÷ 19.8 kDa ≈ 5
Thus, the protein contains 5 identical monomers and is a homopentamer.
