Using your favorite text editor, as root, open up the /etc/my.cnf file (the location of the file may vary according to your distribution). You should see something like this:
# vi /etc/my.cnf

Your MySQL settings should be adjusted for the heavier load.

Default Setting:
max_connections = 60
max_user_connections = 60

Should increase to:
max_connections = 1200
max_user_connections = 1200

You should allow consider the following changes:
max_allowed_packet=1M (sanity check to stop runaway queries)
max_connect_errors=999999
table_cache=1200

These changes are made in your /etc/my.cnf file.  You must restart mysqld after making any changes.

#/etc/init.d/mysqld restart

NOTE:  These are performance tuning best practice recommendations only.  Before making these changes you should consider the servers available resources.