Dissociation constants of leucine

Leucine is a type of amino acid. Let me write its chemical formula as $\ce{NH2-C5H10-COOH}$. On the wikipedia page, <https://en.wikipedia.org/wiki/Leucine>, there are two dissociation constants, one for $\ce{-COOH}\,$ given by $\mathrm{pK}\_{a1}=2.36$, and one for $\ce{-NH3+}$ given by $\mathrm{pK}\_{a2}=9.60$. But I also know that once $\ce{-COOH}\,$ loses its proton $\ce{H+}$ into the solution, the proton may combine with the $\ce{-NH2}\,$ group of the same molecule to form the zwitterion $\ce{NH3+-C5H10-COO-}$ so that the solution now has $4$ species with $4$ dissociation equilibria


$$\begin{array}{rclll}
\ce{NH3+-C5H10-COOH}\!\!&\!\!\ce{<=>}\!\!&\!\!\ce{NH2-C5H10-COOH +H+},& \ &(1)\\
\ce{NH3+-C5H10-COOH}\!\!&\!\!\ce{<=>}\!\!&\!\!\ce{NH3+-C5H10-COO- +H+},& \ &(2)\\
\ce{NH2-C5H10-COOH}\!\!&\!\!\ce{<=>}\!\!&\!\!\ce{NH2-C5H10-COO- +H+},& \ &(3)\\
\ce{NH3+-C5H10-COO-}\!\!&\!\!\ce{<=>}\!\!&\!\!\ce{NH2-C5H10-COO- +H+}.& \ &(4)
\end{array}$$


So there should be $4$ equilibrium constants. Which two do $K\_{a1}$ and $K\_{a2}$ refer to and how do I know the other two? Or is it that we can assume that $\ce{-COOH}\,$ and $\ce{-NH3+}$ dissociate independently so that the equilibrium constants of the $4$ equations are $K\_{a2},K\_{a1},K\_{a1},K\_{a2}$ respectively? I've also seen in some calculation that the zwitterion $\ce{NH3+-C5H10-COO-}$ and the original molecule $\ce{NH2-C5H10-COOH}$ are treated as the same species. But I don't quite understand why this is allowed. They clearly have different charge distributions and should be treated as distinguishable particles in entropy (or Gibbs free energy) calculations.




Among the $4$ equilibria, only $3$ are linearly independent, because we have $(1)+(3)=(2)+(4)$. Let's then choose only three independent reactions


\begin{align}
\ce{NH3+-C5H10-COOH}&\ce{<=> NH3+-C5H10-COO- + H+},\\
\ce{NH3+-C5H10-COO-}&\ce{<=> NH2-C5H10-COO- + H+},\\
\ce{NH3+-C5H10-COO-}&\ce{<=> NH2-C5H10-COOH},
\end{align}


as the basis equations, which are obtained from $(2)$, $(4)$, and $(1)-(2)$. The equilibrium constants of these equations are $K\_{a1}$, $K\_{a2}$, and $K\_{a2}/K\_{a1}=10^{-7.24}\ll 1$. Therefore most of the neutral amino acid molecules would exist in the zwitterionic form $\,\ce{NH3+-C5H10-COO-}$. Neglecting the last equilibrium, the equilibrium constants $K\_{a1}$ and $K\_{a2}$ are those of the $\ce{-COOH}\,$ and $\ce{-NH3+}$ groups in the zwitterions $\,\ce{NH3+-C5H10-COO-}$, which is much more abundant than the original molecules $\,\ce{NH2-C5H10-COOH}\,$ making the latter negligible.


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