Give the amino acid sequence of the following polypeptides using the data given by partial hydrolysis.
(a) `(Ser,Hyp,Pro,Thr) overset(H_(3)O+) rarr Ser, Thr +Thr,Hyp +Pro,Ser`
`(Ala,Arg,Cys,Val,Leu) overset(H_(3)O+) rarr Ala,Cys+Cys,Arg+Arg,Val+Leu,Ala`.

Explanation

To determine the amino acid sequence of the given polypeptides based on the provided data from partial hydrolysis, we will analyze the information step by step.

### Solution:

**(a)** For the first polypeptide: `(Ser, Hyp, Pro, Thr) overset(H_(3)O+) rarr Ser, Thr + Thr, Hyp + Pro, Ser`

1. **Identify the amino acids involved**: The polypeptide consists of Serine (Ser), Hydroxyproline (Hyp), Proline (Pro), and Threonine (Thr).

2. **Analyze the products of hydrolysis**:
- The first product is Ser, Thr, indicating that Serine and Threonine are linked.
- The second product is Thr, Hyp, indicating that Threonine and Hydroxyproline are linked.
- The third product is Pro, Ser, indicating that Proline and Serine are linked.

3. **Determine the sequence**:
- From Ser, Thr, we can denote that Serine is at the N-terminal and Threonine at the C-terminal.
- From Thr, Hyp, we can denote that Threonine is at the N-terminal and Hydroxyproline at the C-terminal.
- From Pro, Ser, we can denote that Proline is at the N-terminal and Serine at the C-terminal.

4. **Construct the sequence**:
- Start with Pro (N-terminal) → Ser (C-terminal from Pro, Ser) → Thr (N-terminal from Thr, Hyp) → Hyp (C-terminal from Thr, Hyp).
- The sequence is: **Pro - Ser - Thr - Hyp**.

**(b)** For the second polypeptide: `(Ala, Arg, Cys, Val, Leu) overset(H_(3)O+) rarr Ala, Cys + Cys, Arg + Arg, Val + Leu, Ala`

1. **Identify the amino acids involved**: The polypeptide consists of Alanine (Ala), Arginine (Arg), Cysteine (Cys), Valine (Val), and Leucine (Leu).

2. **Analyze the products of hydrolysis**:
- The first product is Ala, Cys, indicating that Alanine and Cysteine are linked.
- The second product is Cys, Arg, indicating that Cysteine and Arginine are linked.
- The third product is Arg, Val, indicating that Arginine and Valine are linked.
- The fourth product is Leu, Ala, indicating that Leucine and Alanine are linked.

3. **Determine the sequence**:
- From Ala, Cys, we can denote that Alanine is at the N-terminal and Cysteine at the C-terminal.
- From Cys, Arg, we can denote that Cysteine is at the N-terminal and Arginine at the C-terminal.
- From Arg, Val, we can denote that Arginine is at the N-terminal and Valine at the C-terminal.
- From Leu, Ala, we can denote that Leucine is at the N-terminal and Alanine at the C-terminal.

4. **Construct the sequence**:
- Start with Leu (N-terminal) → Ala (C-terminal from Leu, Ala) → Cys (N-terminal from Cys, Arg) → Arg (C-terminal from Cys, Arg) → Val (C-terminal from Arg, Val).
- The sequence is: **Leu - Ala - Cys - Arg - Val**.

### Final Amino Acid Sequences:
- **(a)** Pro - Ser - Thr - Hyp
- **(b)** Leu - Ala - Cys - Arg - Val