# Are these chemical reactions with amino acids possible, and if so, what are they called?

In high school, I am taught that the synthesis of two amino acids of the form $$\ce{H2NR1COOH}$$ and $$\ce{H2NR2COOH}$$ is a condensation reaction that produces a polypeptide $$\ce{H2NR1COOH}+\ce{H2NR2COOH}\to\ce{H2NR1CONHR2COOH}+\ce{H2O}$$ where $$\ce{R1}$$ and $$\ce{R2}$$ are arbitrary components within each acid. Then I started experimenting with different positions that yield isomers of the polypeptide.

Examples

1. Water is formed though the pairing of the two $$-\ce{OH}$$ groups $$\ce{H2NR1COOH}+\ce{HOOCR2NH2}\to\ce{H2NR1COOCOR2NH2}+\ce{H2O}$$ which forms something that resembles an ester?

2. Water is formed through the pairing of the $$-\ce{OH}$$ and $$\ce{H2N}-$$ groups but the oxygen atom is taken instead from $$\ce{C=O}$$ $$\ce{H2NR1COOH}+\ce{H2NR2COOH}\to\ce{H2NR1C(OH)NR2COOH}+\ce{H2O}$$ where essentially the hydrogen atom from $$-\ce{CONH}$$ has shifted one place.

Are these reactions directly possible? If so, are there special names for

a) the reaction and

b) the type of product formed?

I am at an elementary level in chemistry so more detailed explanations would be appreciated.