# Structural Biochemistry/Buffer
## General Information of Buffers

A significant change in pH can lead to harmful reaction to molecular structure, biological activity and function. Protein structure can be disrupted and enzymes denatured due to the effects of pH on cellular structure. Fortunately, nature has evolved a solution to this problem; solutions that resist changes in pH are called buffers. If an acid is added to an unbuffered solution, the pH will change suddenly and proportional to the amount of acid added. However, the pH will drop gradually in buffer solution when acid is added. Buffers also mitigate the pH increase caused by adding base.
Buffers are aqueous systems that resist changes in pH as acid or base is added. They are usually composed of a weak acid and its conjugate base. Biological buffers, mixture of weak acids (the proton donors) and their conjugate bases (the proton acceptors), help maintain biomolecules in optimal ionic state of pH 7. Buffering is a result of two reversible reaction equilibrium occurring in a solution of about equal concentration of proton donor and its conjugate proton acceptor; when acid or base is added to a buffer, it results in a change in the ratio of the relative concentrations of the weak acid and its anion, or the pH. However, this change in pH is significantly greater than it would be without a buffering solution to accommodate excess hydronium or hydroxide ions.

## Properties

A buffer solution usually contains a weak acid and its conjugate base, but it can also contain a weak base and its conjugate acid. When H$^+$ are added to a buffer, the weak acid's conjugate base will become protonated, thereby "absorbing" the H$^+$ before the pH of the solution lowers significantly. Similarly, when OH$^-$ is added, the weak acid will become deprotonated to its conjugate base, thereby resisting any increase in pH before shifting to a new equilibrium point. In biological systems, buffers prevent the fluctuation of pH by processes that produce acid or base by-products to maintain an optimal pH.
Each conjugate acid-base pair has a characteristic pH range as an effective buffer. The buffering region is about 1 pH unit on either side of the pKa of the conjugate acid, where it has the most effectiveness for resisting large changes in pH when either acid or base is added.

## Henderson-Hasselbalch Equation

The equilibrium constant for the deprotonation of an acid is written as:
$\mathrm {K_{a}={\frac {[H^{+}][A^{-}]}{[HA]}}}$ (1)
Where $[A^{-}]$ is the concentration of a conjugate base and [HA] is the concentration of an acid
Taking logarithms of both sides, we get
$\mathrm {\log K_{a}=\log H^{+}-\log {\frac {[A^{-}]}{[HA]}}}$ (2)
subtract both sides by $log([A^{-}]/[HA])$, we get
$\mathrm {pH=pK_{a}+\log {\frac {[A^{-}]}{[HA]}}}$ (3)
This is the Henderson-Hasselbalch Equation. It describes the dissociation of a weak acid (HA) in the presence of its conjugate base (A$^-$).
The midpoint of the buffering region is when one half of the acid reacts to dissociation and where the concentration of the proton donor (acid) equals that of the proton acceptor (base); the pH of the equimolar solution of acid is equal to the pKa. (When the concentration ratio for conjugated base and weak acid, [A$^-$]/[HA], is 1:1)

## Limitations

Buffers usually work well at a pH close to the pKa value of the acidic component. If too much acid is added to the buffer, or if the concentration is too strong, extra protons remain free and the pH will fall sharply. This is reflected in the titration curve and is known as the buffer capacity.

## Titration curve

This curve demonstrated the capacity of a buffer. In the middle part of the curve, it is flat because the addition of base or acid does not affect the pH of the solution drastically - this is the buffer zone. However, once the curve extends out of the buffer region, it will increase tremendously when a small amount of acid or base added to the buffer system. This effect demonstrated the buffer capacity of the solution.
H$_3$PO$_4$ titration curve
HCl titration curve

## Physiological Buffers

Phosphoric acid system (pK$_a$ = 7.4) and carbonic acid system (pK$_a$ = 3.6) are two important buffer systems in human body. The phosphate buffer system is an effective buffer in the cytoplasm of all cells. H$_2$PO$_4$$^–$ acts as the proton donor and HPO$_4$$^{2–}$- acts as the proton acceptor.
H$_2$PO$_4$$^–$ ⇋ H$^+$ + HPO$_4$$^{2–}$
The bicarbonate buffer system is used to buffer blood plasma where the carbonic acid (H$_2$CO$_3$) acts as a proton donor and bicarbonate (HCO$_3$$^−$ acts as a proton acceptor.
H$_2$CO$_3$ ⇋ HCO$_3$$^−$ + H$^+$
In this buffer system, when the pH of the blood plasma is too high, the H$^+$ of blood plasma is lowered. The H$_2$CO$_3$ is dissociated to H$^+$ and HCO$_3$$^−$. The CO$_2$ from the lungs is dissolved in the blood plasma resulting in a lower pH. On the other hand if the pH of the blood plasma is too low, H$^+$ is added to the blood increasing the concentration of H$_2$CO$_3$. This results in an increase of CO$_2$ in the blood plasma. The increase in the partial pressure of CO$_2$ in the air space of the lungs causes extra CO$_2$ to be exhaled ultimately resulting in a raise in pH. Since the concentration of CO$_2$ can be adjusted rapidly through changes in the rate of respiration, a large reservoir of CO$_2$ can quickly adjust this equilibria to keep blood pH at a nearly constant rate.
Buffers are also important for enzyme activities. There is an optimal pH for each enzyme. For example protein cleavage enzyme pepsin works at pH 1-6 (pH=2 max), trypsin at pH 2-9 (ph=6 max) and alkaline phospatase at pH 4-10(pH=8 max).
In addition to this, some reactions should be carried out at constant pH which is provided by buffer systems.