The concept of PZC should not be used for proteins due to their zwitterionic nature. It is appropriate to use IEP (obtained via electrophoresis and includes all charged speacies), and IIP (obtained by potentiometric titration) which only includes protonic charge.

In general, none of the methods can provide information about the location of the charge. If you measure mobility at across a wide range of pH and ionic strength, it is possible to obtain some information about the location of charge.

Here's some text from a manuscript I am preparing:

"At a particular pH, the number of ionized carboxylate groups will exactly equal the number of ionized amino groups. This pH is the isoionic point (iip) and can be determined by the intersection of multiple acid titration curves over a range of ionic strengths.37,38 The isoelectric point, iep, is defined as the pH at which the velocity of protein molecules in response to an applied electric field is zero. iep is an electrokinetic property and indicates the pH at which the net charge of the protein is zero. Thus, if the protein binds with other ions, such as chloride counterions, the contribution to the zero net charge by the zwitterion protonation will be non-zero. As a result, iip and iep will not be the same, and their difference will increase with an increasing amount of bound non-protonic ions, such as counterions adsorbed from the dispersion medium. iep may be measured by electrophoresis. The corresponding electrophoretic mobility can be expressed as the sum of a contribution due to protonic charge and a contribution due to counterion charge."

" The Henry equation assumes non-conducting spherical particles with smooth, impenetrable ("hard") surfaces, and does not account for the finite size and hydration of ions at or near the particle surface. Thus, although it may be reasonably valid for lyophobic inorganic oxides, it is not appropriate for protein molecules in free solution or adsorbed onto carrier particles.

The conformation of globular proteins in aqueous solution resembles a core of densely-packed hydrophobic amino acid side chains surrounded by a less densely-packed shell of hydrophilic amino acid side chains. The core is likely to carry little electrical charge, whereas the shell will possess charge according to the zwitterionic equilibria and any bound non-protonic ions. These charges are spatially fixed and nominally evenly distributed. Unlike the hydrophobic core, the hydrophilic shell is permeable to the surrounding liquid. Bound ions such as chloride are likely to be located within the protein structure as a result of co-ordination between the ions and multiple amino acid residues. Therefore, the overall structure of a globular protein in aqueous solution resembles a "soft" particle with protonic charges at the exterior surface and nonprotonic charges within the interior of the molecule. There are two limiting cases of a soft sphere. In the case of a shell of zero thickness, the particle is the same as a rigid, hard sphere. A particle with a core diameter of zero behaves as a solvated polymer molecule and, more specifically, a polyelectrolyte in the instance of a charged particle. Several theoretical treatments of the electrophoretic behavior of polyelectrolytes (including proteins) have been reported. Most of these require numerical analysis or semi-analytical computation and, therefore, are of limited practical application. The theories of the electrophoresis of rigid spheres and, separately, spherical polyelectrolytes often are considered mutually inconsistent. Ohshima has developed an analytical electrokinetic model for the electrophoretic mobility of soft particles that is consistent with both theoretical frameworks. He uses the Smoluchowski and related models for the limiting case of spherical hard particles. The other limiting case, namely for porous spherical polyelectrolytes, follows the models described Hermans that consider the flow of liquid through a porous sphere. In the case of a polymer molecule, the liquid flow is determined by the forces arising from the interaction between the liquid and the polymer chain segments when the polymer molecule is moving in response to an external field. In the case of a gravitational field, the polymer motion is sedimentation. The electrophoretic mobility for a non-free draining porous particle containing spatially fixed charges limits to a constant value with increasing electrolyte concentration. This is unlike the case for a rigid impermeable spherical particle for which the electrophoretic mobility is predicted to limit to zero with increasing electrolyte concentration."

The definitions of these terms have no relationship to the location of the charge.

*By definition* the isoelectric point (IEP) is the pH at which there is zero velocity for particles subjected to an external electric field. It is strictly determined by electrokinetics (e.g., electrophoresis). This doesn't mean there is zero charge. Consider proteins - at the isoelectric point, there will be positive and negative charges present at the same (iso) extent. For simpler materials, notably inorganic oxides, zero velocity usually means zero absolute charge (rather than zero net charge). There's only one charged species so it cannot be "iso" with anything else - hence "IEP" doesn't apply but PZC does. PZC can be determined using potentiometric titration.

Remember that the electrophoretic mobility says nothing about double layers, planes of shear etc. These are encompassed in the electrokinetic models relating mobility to zeta potential etc. No matter what the model, zero is zero. You don't even need to quantify the velocity to get the IEP.

Another related - and often confused - property is the isoionic point (IIP). This is has a rather complex formal definition but, in practical terms, is the pH at which the net protonic charge of a protein is zero. It only relates to protons. IEP on the other hand, relates to all types of charges such as bound counterions (e.g., chloride). Unless all the charge is protonic, IEP and IIP are not the same.

Thus, none of these three terms should be used interchangeably.

Most of these definitions were established in the first half of the 20th century but, as seems to be all too common, misunderstood/redefined/ignored in the last two or three decades.

Thank you, Dr. John Francis Miller .

A few follow-up question, if I may:

1) So for the case of proteins that you mentioned, would it be accurate to say that the mean surface charge density will be zero at the PZC (i.e., as many positive charges as negative charges)?

2) Also, would it be accurate to say that when H+/OH- are the only potential-determining ions, then the IEP and PZC will be equal?

3) Finally, does the IEP tell us anything about the "net charge" at the surface of shear?

The concept of PZC should not be used for proteins due to their zwitterionic nature. It is appropriate to use IEP (obtained via electrophoresis and includes all charged speacies), and IIP (obtained by potentiometric titration) which only includes protonic charge.

In general, none of the methods can provide information about the location of the charge. If you measure mobility at across a wide range of pH and ionic strength, it is possible to obtain some information about the location of charge.

Here's some text from a manuscript I am preparing:

"At a particular pH, the number of ionized carboxylate groups will exactly equal the number of ionized amino groups. This pH is the isoionic point (iip) and can be determined by the intersection of multiple acid titration curves over a range of ionic strengths.37,38 The isoelectric point, iep, is defined as the pH at which the velocity of protein molecules in response to an applied electric field is zero. iep is an electrokinetic property and indicates the pH at which the net charge of the protein is zero. Thus, if the protein binds with other ions, such as chloride counterions, the contribution to the zero net charge by the zwitterion protonation will be non-zero. As a result, iip and iep will not be the same, and their difference will increase with an increasing amount of bound non-protonic ions, such as counterions adsorbed from the dispersion medium. iep may be measured by electrophoresis. The corresponding electrophoretic mobility can be expressed as the sum of a contribution due to protonic charge and a contribution due to counterion charge."

" The Henry equation assumes non-conducting spherical particles with smooth, impenetrable ("hard") surfaces, and does not account for the finite size and hydration of ions at or near the particle surface. Thus, although it may be reasonably valid for lyophobic inorganic oxides, it is not appropriate for protein molecules in free solution or adsorbed onto carrier particles.

The conformation of globular proteins in aqueous solution resembles a core of densely-packed hydrophobic amino acid side chains surrounded by a less densely-packed shell of hydrophilic amino acid side chains. The core is likely to carry little electrical charge, whereas the shell will possess charge according to the zwitterionic equilibria and any bound non-protonic ions. These charges are spatially fixed and nominally evenly distributed. Unlike the hydrophobic core, the hydrophilic shell is permeable to the surrounding liquid. Bound ions such as chloride are likely to be located within the protein structure as a result of co-ordination between the ions and multiple amino acid residues. Therefore, the overall structure of a globular protein in aqueous solution resembles a "soft" particle with protonic charges at the exterior surface and nonprotonic charges within the interior of the molecule. There are two limiting cases of a soft sphere. In the case of a shell of zero thickness, the particle is the same as a rigid, hard sphere. A particle with a core diameter of zero behaves as a solvated polymer molecule and, more specifically, a polyelectrolyte in the instance of a charged particle. Several theoretical treatments of the electrophoretic behavior of polyelectrolytes (including proteins) have been reported. Most of these require numerical analysis or semi-analytical computation and, therefore, are of limited practical application. The theories of the electrophoresis of rigid spheres and, separately, spherical polyelectrolytes often are considered mutually inconsistent. Ohshima has developed an analytical electrokinetic model for the electrophoretic mobility of soft particles that is consistent with both theoretical frameworks. He uses the Smoluchowski and related models for the limiting case of spherical hard particles. The other limiting case, namely for porous spherical polyelectrolytes, follows the models described Hermans that consider the flow of liquid through a porous sphere. In the case of a polymer molecule, the liquid flow is determined by the forces arising from the interaction between the liquid and the polymer chain segments when the polymer molecule is moving in response to an external field. In the case of a gravitational field, the polymer motion is sedimentation. The electrophoretic mobility for a non-free draining porous particle containing spatially fixed charges limits to a constant value with increasing electrolyte concentration. This is unlike the case for a rigid impermeable spherical particle for which the electrophoretic mobility is predicted to limit to zero with increasing electrolyte concentration."

Dear all, thanks for detailled explation Dr. John Francis Miller, I would like to know your opinion about the usefullness of ellipsometry with respect to the techniques you already explained. My Regards

Hi;

The isoelectric point (IEP) is only representative of the external surface charges of particles in solution, whereas the point of zero charge (PZC) varies in response to the net total (external and internal) surface charge of the particles.

With my best regards

Doufnoune RACHIDA Rachida That isn't true. As I stated, the definition of IEP is the pH at which the velocity of particles in an electric field is zero. It doesn't matter how the charges are distributed.

e.g.,

Abramson, H. A. ELECTROKINETIC PHENOMENA: XIII. A COMPARISON OF THE ISOELECTRIC POINTS OF DISSOLVED AND CRYSTALLINE AMINO ACIDS. The Journal of General Physiology 1938, 21 (6), 729–744. https://doi.org/10.1085/jgp.21.6.729.

To follow up, I have just had a paper published that clearly illustrates the difference between IEP and IIP:

Article Determination of Protein Charge in Aqueous Solution Using El...

Video link for determination of Point of zero charge (PZC)

https://youtu.be/vCJE7kDDYRU