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# Isoelectric Point Formula, Calculation, & Examples

Lakshmi Vasudevan, Sarah Erhart
• Author
Lakshmi Vasudevan

Lakshmi Vasudevan is a scientific professional with more 7 years of experience in Cell biology, Pharmacology, Molecular Biology, and Biochemistry. She is a doctorate from Ghent University, Belgium with 10 publications in several, good-ranking journals. She did her Bachelors and Masters in Biochemistry from University of Mumbai, India. She has taught Biochemistry at both graduate and postgraduate level , and biology at high school level.

• Instructor
Sarah Erhart

Sarah has taught college physical, organic, and general chemistry and high school biology. She has a master's degree in chemistry.

Discover what the isoelectric formula in chemistry is, its role, functions, and importance. Know its formula and learn how to compute it through given examples. Updated: 03/23/2022

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The pH at which the net charge on the molecule is zero is defined as the isoelectric point (pI) of that molecule. Note that the molecule at its pI exists as a zwitterion with an equal number of positive and negative charges. In order to understand more about the pI of a molecule and the related concepts better, read further.

## What are pH and pKa?

A pH meter is very common in chemistry labs. This instrument simply measures the hydrogen ion concentration (or proton concentration) of a solution in a range from 0 to 14. Acids that are proton donors have a pH value anywhere between 0 to 7, while bases that accept protons have a pH value from 7 to 14 depending on their strength. In simple words, the stronger the acid, the greater the tendency to lose a proton, the lower the pH. Similarly, the stronger the base, the greater the tendency to accept a proton, the higher the pH. Pure water has a neutral pH of 7.0 at 25o C.

On the other hand, weak acids (or weak bases) dissociate only partially in solution. For a given weak acid (HA), its dissociation reaction could be written as follows:

The acid dissociation constant (Ka) for this reaction is:

where [HA], [ A- ] and [ H+ ] are the molar concentrations of the undissociated weak acid, its conjugate base, and hydrogen ion respectively.

Now, draw comparisons between pH and pKa:

• pH is the negative logarithm of hydrogen ion concentration, thus dependent only on hydrogen concentration. pKa is the negative logarithm of Ka, thus dependent on the concentration of undissociated acid, its conjugate base, and hydrogen ion.
• pH determines the acidity or alkalinity of the solution. pKa determines the strength of an acid (or base) in the solution.
• The stronger the acid, the lower the pH. The stronger the acid, the higher the Ka (because it dissociates completely), and the lower the pKa.

The pKa of a weak acid can be determined experimentally by titrating with a known concentration of a strong base like NaOH. With the slow increments in the addition of the base (NaOH), the OH- ion from NaOH combines with H+ ion from the acid to produce water, which further promotes the forward reaction in the acid dissociation reaction (Figure 1). Eventually, at the midpoint of the titration, there is an equimolar concentration of undissociated acid (proton donor) and its conjugate base (proton acceptor). The pH at this midpoint is called the pKa of the weak acid. Finally, at the end of the titration, all the acid molecules are deprotonated.

Keeping these concepts in mind, dive further to understand the isoelectric point.

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## What is Isoelectric Point?

Different functional groups on a molecule can donate or accept protons depending on their pKa values. One of the best-understood examples is amino acids. In amino acids, the amino group acts as a proton acceptor and the acid group as a proton donor.

One can understand how the pKa of different groups comes into play upon titration of a simple amino acid (here, glycine as an example) with alkali, as explained earlier.

At the start of the titration at a very low pH, the predominant species present is H3 N+ -CH2 -COOH with both the amino (NH3+ ) group and carboxylic acid (COOH) group protonated. As the titration proceeds, the carboxylic acid starts losing its proton. At the pKa of the carboxylic acid group, which is 2.34 in the case of glycine, an equimolar concentration of the protonated species ( H3 N+ -CH2 -COOH ) and the deprotonated species ( H3 N+ -CH2 -COO- ) are present.

Further, upon titration, the deprotonation from the carboxylic acid group is complete such that the predominant species at this point is H3 N+ -CH2 -COO-. This species which has an equal number of positive and negative charges is known as zwitterion and the pH at which the net electric charge on a molecule is zero is known as the isoelectric point (pI) of the molecule. The isoelectric point of glycine is 5.94. Next, upon further titration, the amino group starts losing its proton, and at the pKa of the amino group (9.60 in the case of glycine), an equimolar concentration of the protonated species ( H3 N+ -CH2 -COO- ) and the deprotonated species ( H2 N-CH2 -COO- ) are present. At the end of the titration, the deprotonation from the amino group is complete with the predominant species being H2 N-CH2 -COO- at this point.

Essentially:

At pH < pI, the amino acid is protonated, hence, positively charged.

At pH > pI, the amino acid is deprotonated, hence, negatively charged.

## Isoelectric Point Examples

The isoelectric point can be calculated for a compound that has two or more pKa values. The amino acids that have a single amino and acid group with no ionizable functional R groups, the titration pattern resembles that of glycine with similar pKa values for each group. However, for amino acids with ionizable functional R groups, the titration curve is more complicated to accommodate the pKa of the R group. Take arginine as an example here.

Arginine has a positively charged R group, therefore in titration, there are three ionizable steps with three pKa values corresponding to the carboxylic acid group, the alpha-amino group, and the guanidium R group. The pI value depends on the nature of the ionizable groups. Note that the pI of arginine (10.76) is higher than that of glycine due to the presence of two amino groups (the alpha-amino group, and the guanidium R group) with pKa values of 9.04 and 12.48, which brings the average to 10.76 because the zwitterionic species exists in the middle of these two pKa values. Therefore, in amino acids (or compounds) with more than two ionizable groups, the pI is the average of the pKa values of two similar ionizable groups. Neutral amino acids have a pI value like that of glycine, while basic amino acids (histidine, lysine, arginine) have a pI value greater than that of glycine, and acidic amino acids (aspartic acid, glutamic acid) have a pI value lesser than that of glycine.

After understanding the concepts with single amino acids, now take the next step in understanding the pI of a protein. Amino acids are the building blocks of a protein. The type of amino acids that make up a protein determines the pI of the protein. The isoelectric point of protein is the pH at which the net electrical charge of the protein is zero because the total number of positive charges equals the total number of negative charges on the protein. When the pH is greater than the pI of the protein, the protein is negatively charged and vice versa. Thus, the pI of a protein gives us valuable information about the charge on the protein under physiological conditions.

## Isoelectric Point Formula

For amino acids with two ionizable groups, the isoelectric point equation is:

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#### How does one find an isoelectric point?

Isoelectric point (pI) can be calculated using the formula, pI = pKa1 + pKa2/ 2 for molecules with two ionizable groups (e.g. amino acids like glycine). The pKa1 of the carboxylic acid group of glycine is 2.34 and pKa2 of the amino group is 9.60, therefore, pI (glycine) = (2.34+9.60)/2 = 5.94.

However, for molecules with more than two ionizable groups (e.g. arginine), pI is the average of two pKa values that are close to each other.

Arginine has 3 pKa values: pKa1 (carboxylic acid group) = 2.17, pKa2 (alpha-ammonium group), = 9.04, pKa3 (guanidium R group) = 12.48. Therefore, pI (arginine) = (9.04 + 12.48)/2 = 10.76.

#### What is an isoelectric point and how it is calculated?

Isoelectric point (pI) is the pH at which the net electric charge on a molecule/protein is zero. At its pI, the molecule/protein is electrically neutral. pI can be easily calculated using the formula, pI = pKa1 + pKa2/ 2 for molecules with two ionizable groups, while for molecules with more than two ionizable groups, pI is the average of two pKa values that are close to each other.

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