Slow query and use of indexes in MySQL - mysql

Question

I have the following query:
SELECT final_query.chr
, final_query.start
, final_query.end
, co.chr
, co.start
, co.end
, final_query.count
FROM (SELECT ed.chr
, ed.start
, ed.end
, case when e.bin1=ed.bin then e.bin2 else e.bin1 end AS target
, count
FROM (SELECT * FROM coordinates
WHERE chr="chr1" AND (start between 3960000 AND 4000000 OR end between 3960000 AND 4000000)
) ed
JOIN counts e ON (e.bin1 = ed.bin OR e.bin2=ed.bin)
SORT BY count LIMIT 1,20)
AS final_query
JOIN coordinates co ON final_query.target=co.bin;
and the output of EXPLAINED is:
+------+-------------+-------------+--------+---------------+---------+---------+-------+----------+------------------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+------+-------------+-------------+--------+---------------+---------+---------+-------+----------+------------------------------------+
| 1 | SIMPLE | e | ALL | bin1,bin2 | NULL | NULL | NULL | 30763816 | Using filesort |
| 1 | SIMPLE | coordinates | ref | PRIMARY,chr | chr | 22 | const | 4929 | Using index condition; Using where |
| 1 | SIMPLE | co | eq_ref | PRIMARY | PRIMARY | 22 | func | 1 | Using where |
+------+-------------+-------------+--------+---------------+---------+---------+-------+----------+------------------------------------+
What I am doing is to perform the following query of table coordinates, which has field chr indexed. So, in the subquery shown below, I filter those rows that match my conditions.
... (SELECT * FROM coordinates
WHERE chr="chr1" AND (start between 3960000 AND 4000000 OR end between 3960000 AND 4000000)
) ...
This table outputs field bin, also indexed. This field bin links with bin1 and bin2 both from table counts and indexed as well. So, here, what I want is to get all those rows in table counts having coordinates.bin in fields bin1 and bin2. Why in this step no index is used?
Besides of it, I would like to add an ORDER BY in my query, just before the LIMIT statement. But it slows too much my query. I don't know why, because it have to sort a maximum of 4000 rows...
How can I optimize my query?
My tables, from the DESCRIBE statement:
Table counts
+-------+-------------+------+-----+---------+----------------+
| Field | Type | Null | Key | Default | Extra |
+-------+-------------+------+-----+---------+----------------+
| id | int(11) | NO | PRI | NULL | auto_increment |
| bin1 | varchar(20) | NO | MUL | NULL | |
| bin2 | varchar(20) | NO | MUL | NULL | |
| count | float(6,2) | NO | | NULL | |
+-------+-------------+------+-----+---------+----------------+
Table coordinates
+-------+-------------+------+-----+---------+-------+
| Field | Type | Null | Key | Default | Extra |
+-------+-------------+------+-----+---------+-------+
| bin | varchar(20) | NO | PRI | NULL | |
| chr | varchar(20) | NO | MUL | NULL | |
| start | int(11) | NO | | NULL | |
| end | int(11) | NO | | NULL | |
+-------+-------------+------+-----+---------+-------+