Python Programming for Biology: Bioinformatics and Beyond

Protein isoelectric point

The last of the examples in this chapter is an example that involves an optimisation. So far

all  of  the  numerical  values  that  we  have  calculated  have  been  deduced  analytically  by

applying some equation: there is a direct method to get from the data to a precise answer.

---

However, it is commonplace to come across problems where the values we are interested

in are not directly accessible. In reality such problems may range from those for which it

is genuinely difficult to imagine any formulaic method (hard problems: see

Chapter 25

) to

those where a direct formulation is merely inconvenient or slow.

The topic of this example is the estimation of the isoelectric point of a protein, which

we will call the pI. This is a measurable property of a protein: it is the pH

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at which the

protein  carries  no  overall  electric  charge.  This  is  something  that  is  often  used  to

characterise  and  isolate  proteins,  for  example,  by  performing  electrophoresis  (moving

particles through a porous substance with an electric current) in a gel with a pH gradient.

Proteins  have  electric  charges  because  certain  kinds  of  amino  acids,  together  with  the

chain termini (the unlinked ends), are capable of accepting or losing a hydrogen ion (H

+

).

The  groups  that  are  capable  of  gaining  a  hydrogen  ion,  and  thus  a  positive  charge,  are

called  basic:  this  includes  the  residues  arginine,  lysine  and  histidine

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 and  also  the  N-

terminus  of  the  protein,  the  start  of  the  chain  where  there  is  a  free  amine  group.  The

groups which lose a hydrogen ion gain a negative charge; they are neutral before the loss.

These  groups  are  called  acidic  and  include  the  residues  aspartic  acid,  glutamic  acid,

cysteine,  tyrosine  and  the  C-terminus  of  the  protein:  the  end  of  the  protein  chain  where

there is a free carboxylic acid group.

In  any  given  situation  whether  or  not  these  basic  and  acidic  groups  carry  a  charge

depends on the hydrogen ion concentration of the environment: the pH. In a solution with

a low pH the concentration of H

+

is high,

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and so there are lots of free ions to bind to the

basic groups, giving them a positive charge, and also lots of free ions to bind to the acidic

groups, removing the negative charge and making them neutral. Conversely, with a high

pH,  the  concentration  of  H

+

 is  low,  whereupon  the  ions  are  lost  from  the  protein;  basic

groups become neutral and acidic groups are left with a negative charge.

The different basic and acidic groups do not bind to hydrogen ions equally strongly. For

example, aspartic acid very easily loses H

+

; at neutral pH 7.0 they are almost all lost, but

for  tyrosine  at  a  neutral  pH  hardly  any  are  lost.  The  strength  of  any  acid  or  base  can  be

described  by  the  acid  dissociation  constant,  referred  to  as  the  pK

a

.  This  has  a  formal

mathematical  definition  using  the  concentrations  of  hydrogen-bound  and  unbound

components,

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 but  is  most  easily  remembered  as  the  pH  at  which  on  average  half of the

groups will be bound with H

+

. Any one specific group can of course only be bound to a

whole hydrogen ion or no hydrogen ion, so these constants represent the average over time

as H

+

is dynamically lost and gained. The pK

a

value for aspartic acid is 4.4, so at pH 4.4 it

will  have  H

+

 half  of  the  time,  and  thus  its  average  electric  charge  will  be  −0.5:  half

negative  because  the  free  half  is  negative.  For  aspartic  acid,  as  pH  increases  it  will

become  increasingly  negatively  charged  as  it  will  be  bound  to  H

+

 less  of  the  time.

Conversely the pK

a

value for lysine is 10.0, thus at pH 10.0 it will be half bound by H

+

,

but  because  this  residue  is  basic  the  ions  add  a  positive  charge,  rather  than  neutralise  a

negative  one.  So  for  lysine,  as  the  pH  decreases  more  H

+

 binds  and  it  becomes  more

positively charged.

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