native sql to Doctrine_RawSql

Question

I have this SQL Query.

SELECT
    c.id, 
    c.name,
    c.slug,
    sc.id,
    sc.name,
    sc.slug,
    COUNT(bsc.id) AS business_count
FROM
    fi_category c
LEFT JOIN
    fi_subcategory sc ON c.id = sc.category_id AND (sc.deleted_at IS NULL)
LEFT JOIN (
        fi_business b
    INNER JOIN
        fi_business_subcategory bsc ON b.id = bsc.business_id AND (bsc.deleted_at IS NULL)
    INNER JOIN
        fi_suburb su ON su.id = b.suburb_id AND su.city_id = 1
    ) ON sc.id = bsc.subcategory_id
WHERE 
    (c.deleted_at IS NULL) 
GROUP BY 
    c.id, sc.id

as this type of query is not supported by DQL. i want to use it with Doctrine_RawSql

i tried using it this way.

$q = new Doctrine_RawSql();
$q->select('{c.name}, {c.slug}, {sc.name}, {sc.slug}, {COUNT(bsc.id) AS business_count}');
$q->from('fi_category c LEFT JOIN fi_subcategory sc ON c.id = sc.category_id AND (sc.deleted_at IS NULL) LEFT JOIN (fi_business b INNER JOIN fi_business_subcategory bsc ON b.id = bsc.business_id AND (bsc.deleted_at IS NULL) INNER JOIN fi_suburb su ON su.id = b.suburb_id AND su.city_id = 1) ON sc.id = bsc.subcategory_id');
$q->groupBy('GROUP BY c.id, sc.id');
$q->addComponent('c', 'Model_Category c');
$q->addComponent('sc', 'c.Subcategory sc');
$q->addComponent('bsc', 'sc.BusinessSubcategory bsc');
$q->addComponent('b', 'bsc.Business b');
$q->addComponent('su', 'b.Suburb su');
$q->execute();

this query is not working, which is the correct way of building Doctrine_Rawsql for the above SQL query?

if incase if someone wants to check the tables here is the link to fiddle http://sqlfiddle.com/#!2/5adaa

UPDATE: this is continuation of this question, select query and count based on condition if someone could help me build Doctrine_Rawsql by using any of the query from the solution provided by @MvG