Buffers

Proteins have a pH dependent charge and many of the properties of proteins change with pH.  Consequently, in working with proteins,  it is important to  control the pH.  This  is  achieved  by the  use of buffers, and so at the outset it is important to have some insight into buffers, to know which buffer to use for any particular purpose, and how to make up the buffer.

Buffers are solutions of weak acids or bases and their  salt(s),  which resist changes  in pH.  Weak acids  and  bases are  distinguished  from  strong acids and bases by their  incomplete  dissociation.  In the  case of a weak acid the dissociation is:-

and the dissociation constant is:-

For a weak base (e.g.  Tris) the  dissociation is:-

Using similar arguments to those above, it can be shown that in this case,

Equations 1  and 2  are  forms  of the  Henderson-Hasselbalch equation, which can be written in a general form as:-

From which it can be seen that, when [basic species] = [acidic species], then,

A simple monoprotic weak acid, such as acetic acid, yields a titration curve such as that shown schematically in  Fig. 1.  It  will be noticed  that when pH = pKa, the solution resists changes in pH, i.e. it functions best as a buffer in the range pH = pKa ± 0.5.

CH₃COOH is the acidic species in this buffer and CH₃COO- is the  basic species. It may be observed that a solution of acetic acid itself (CH₃COOH) will have a pH less than the pKa of acetic acid.  Conversely, a solution containing only sodium acetate will have a pH greater than  the pKa of acetic acid.  It is important  to understand this point in order to appreciate how to make an acetate buffer using the approach  described in Section 1.1.

Figure 1. Schematic titration curve of a monoprotic acid, such as acetic acid.

A triprotic acid, such as phosphoric acid will yield a titration  curve having three  inflexion points  (Fig.  2), corresponding  to  the  three  pKa values of phosphoric acid.

Figure 2.  Schematic titration curve of phosporic acid.

For most biochemical purposes, pKa₂ is of greatest  interest,  since  it  is Note that:-closest to the  pH of the extracellular fluid of animals.

Put another way, a solution NaH₂PO₄ will have a pH less than pKa₂and a  solution  of  Na₂HPO₄ will have  a  pH greater than  pKa₂.  It  is important to understand this point in order to  appreciate  how to  make  a phosphate buffer using the approach described below.

1.1 Making a buffer

A simple approach to the making  of a buffer is described below.  The advantage of this approach is that only  one solution needs be made up. Several books suggest that buffers should be made up by adding “x” ml of a 1 M solution of “A” to “y” ml of a 1 M solution of “B”. The problem with this  approach  is that  it  involves  extra  work  (making  up  two solutions when one  will do), waste (the  unused volumes of “A”  and  “B” are discarded) and is usually inaccurate  (the  presence  of extra  salts and preservatives, for example, can change the pH due to  common  ion effects).

A simpler method follows the following steps:-

•  Choose the buffer.  A buffer works best at its pK, so the  first  step  is to choose a buffer with a pKa as close as possible to the desired pH.

•  Identify the  buffering  species.  a buffer consists of two components:  a weak acid and its salt  or  a weak base and its salt.  The second step is thus to  identify  the  species which will constitute the buffer.  For example,  in the  case of an  acetate  buffer, the buffering species are  CH₃COOH and CH₃COONa. In a phosphate

buffer at pKa₂, the buffer species are NaH₂PO₄ and Na₂HPO₄.

•  Identify whether the buffer is made from  an  acid or a  base.  The two buffer examples shown above  are  made  from  acids, acetic  acid or phosphoric acid.  In the case  of phosphate  buffer at  pKa2, the  acid is NaH2PO4. An example of a buffer made from a base is Tris/Tris-HCl, which buffers best at pH 8.1, the pKa of Tris.

•  Choose the species that gives no by-products when titrated.  Almost all buffers can be made up by weighing out one component, dissolving in a volume just short of the final volume, titrating to the right pH, and making up to volume.  It  is  not necessary  to make up separate solutions of the two buffer constituents  - the required salt can be generated in situ by titrating the acid with an appropriate base - or vice versa in the case of a buffer made from a base.  [Remember: Titrate an acid “up” (i.e. with a strong base) and titrate a base “down” (i.e. with a strong acid)].

Remember,   acid + base = salt + water

and, a buffer = (acid + its salt )  or  (base + its salt).

The term  “its  salt”  is  important. For example,  if we wanted to  make  an  acetate  buffer,  it  is easy  to identify that this buffer is made from acetic acid and its  salt,  say, sodium acetate.  But,

Q: Could the required mixture of CH₃COOH and CH₃COONa be made

by titrating a solution of CH₃COONa to the correct pH with HCl?

A: No! Because the reaction in this case is:-

and the  resultant  solution  contains  NaCl, which is an unwanted by-product and which is not a salt of acetic acid (i.e. it is not “its  salt”). On the other hand,

Q: Could the required mixture be  made  by  titrating  a  solution  of

A: Yes! The reaction in this case is:-CH₃COOH with NaOH?

which yields only the salt of acetic acid and water, i.e. there are no  by-products. Similarly, in the case of a phosphate buffer, if one chooses Na₂HPO₄, the pH of a solution  of this  salt  will be  higher than  pKa, (see Fig. 2) and this  will require titration  with an acid.  If one chooses  HCl,  the reaction will be:-

which yields NaCl as an  unwanted  by-product. (And if one chooses NaH₂PO₄, this will change the  phosphate  molarity.)  However,  if one starts with NaH₂PO₄, the  pH of a solution  of this  salt  will be  lower than pKa, and this will require titration with a base.  If one  chooses NaOH, the reaction will be:-

volume. For example, the molarity of a phosphate buffer is determined by the  molarity  of the phosphate  moiety,  which does not change when NaH₂PO₄ is titrated to Na₂HPO₄. If a litre of a 0.1 M buffer is required, then 0.1 moles of NaH2PO4 can be weighed out.

•  Add all other components,  titrate  and  make  up  to  volume.  Buffers

often contain ingredients other than the two buffering species.  For ion-exchange elution the buffer might contain extra NaCl, and buffers often contain preservatives such as NaN₃ or chelating agents such as EDTA. Except for NaN3, these  should all be added before the titration. All constituents should be dissolved in the same solution to just less than  the  final volume,  i.e. a volume  must  be  left  for  the titration but the final dilution after titration  should be as small as possible. (The Henderson-Hasselbalch equation predicts  that  the  pH of a  buffer  should  not  change  with  dilution,  but this  is  only  true  over  a small range, due to non-ideal behaviour of ions in  solution.)  Finally the solution is titrated to the desired pH and made up to volume.

NaN₃ should be added after titration  as it  liberates the  toxic  gas, HN₃, when exposed to  acid.  Manganese salts should  also  be  added after adjustment of the pH as these may form irreversibly insoluble salts at pH extremes.

1.2 Buffers of constant ionic strength

Besides pH, which influences the sign and magnitude  of the  charge  on a protein, proteins are also influenced by the specific ions present  in solution and by the solution ionic strength.  In a buffer, the pH and the ionic strength  are related.  The  Henderson-Hasselbalch equation, for a buffer made  from an  acid,  is:-

The ionic strength of the buffer is a function of the [salt].  Therefore, in this case as the  pH rises, the  buffer ionic  strength  also  rises.  Ionic strength is also a function of the molarity of the buffer.  One can picture the relationship between the three  variables, molarity  (M), pH and ionic strength (I) as a lever, for which any one of the  three  could be fixed as a fulcrum and the relative movements of the other two observed (Fig. 3).

Figure 3.  The relationship between molarity, pH and ionic strength for a buffer made from a weak acid.

For a buffer made  from a weak base, the  relevant  form  of the Henderson-Hasselbalch equation is:-

In this case, therefore, the ionic strength increases as the pH decreases and the relationship between “M” (molarity), “I” (ionic strength) and pH can be visualized by reversing the positions of M and I in Fig. 3. The lever model shown in Fig. 5  must not  be taken  to  imply a linear relationship between the  variables.  In fact,  ionic strength  changes sigmoidally with pH as shown in Fig. 4.  The “rate” of change,  i.e. d(ionic strength) ld (pH), is greatest at the pKa, pKa2 in this case.  The  pKa  itself also changes slightly with ionic strength. The data in Fig.4 were calculated according to Ellis and Morrison.

Figure 4.  The relationship between ionic strength and pH for a 0.1 M phosphate buffer.

The relationship between pH, M and I is important  when establishing the pH optimum of an enzyme.  This is commonly done by using a range of buffers of constant  M  and  varying  pH.  However,  if the  enzyme  in question is affected by ionic strength (which is often the  case) it  is better to keep I constant and to  vary M with pH (For an example,  see ref. 4). The  preparation  of buffers  of constant  ionic  strength  is  discussed by  Ellis and Morrison². An in depth discussion of buffers is provided by Perrin and Dempsey⁵.

References

Dennison, C. (2002). A guide to protein isolation . School of Molecular mid Cellular Biosciences, University of Natal . Kluwer Academic Publishers new york, Boston, Dordrecht, London, Moscow .

Ellis, K.  J.  and Morrison J.  F.  (1982) Buffers of constant ionic  strength for  studying pH-dependent processes.  Methods Enzymol.  87, 405-426.

Scopes, R. K. (1994) Protein Purification: Principles and Practice.  3rd Ed, Springer-Verlag, New York,  pp326-330.

Dehrmann, F. M., Coetzer, T. H. T., Pike, R. N. and Dennison, C. (1995) Mature cathepsin L is substantially active in the ionic milieu of the extracellular matrix. Arch. Biochem. Biophys. 324, 93-98.

Perrin, D. D. and Dempsey, B. (1974) Buffers for pH  and  metal  ion  control.  Chapman and Hall, London.