Optimize my.cnf settings on linux sever

I run a website for my customers where it gets extremely busy during peak hours. top command shows mysql at 300%. This is because we have a lot of simultaneous entries being made on the database - approx 1000 entries per min during peak hours. At this point server goes down and my customers start facing problems and inconvenience. I need someone to look at the below config and advice what needs changing. Server Info CPU GenuineIntel, Intel(R) Xeon(R)CPU E3-1270 v3 @ 3.50GHz Version Plesk v12.0.18_build1200140606.15 os_CentOS 6 16GB RAM This is my current configuration [mysqld] bind-address=[login to view URL] datadir=/var/lib/mysql socket=/var/lib/mysql/[login to view URL] user=mysql symbolic-links=0 local-infile=0 max_connections = 600 max_user_connections=1000 key_buffer_size = 512M myisam_sort_buffer_size = 512M read_buffer_size = 1M table_open_cache = 5000 thread_cache_size = 384 wait_timeout = 300 connect_timeout = 300 tmp_table_size = 768M max_heap_table_size = 256M max_allowed_packet = 64M net_buffer_length = 16384 max_connect_errors = 150 concurrent_insert = 2 read_rnd_buffer_size = 786432 bulk_insert_buffer_size = 8M query_cache_limit = 4M query_cache_size = 256M query_cache_type = 1 query_prealloc_size = 262144 query_alloc_block_size = 65535 transaction_alloc_block_size = 8192 transaction_prealloc_size = 4096 max_write_lock_count = 8 slow_query_log log-error external-locking=FALSE open_files_limit=50000 innodb_buffer_pool_size=8G [mysqld_safe] log-error=/var/log/[login to view URL] pid-file=/var/run/mysqld/[login to view URL] [mysqldump] quick max_allowed_packet = 64M [isamchk] key_buffer = 384M sort_buffer = 384M read_buffer = 256M write_buffer = 256M [myisamchk] key_buffer = 384M sort_buffer = 384M read_buffer = 256M