For a good introduction to storing trees in mptt form, read this: http://www.sitepoint.com/article/hierarchical-data-database
Here is the code of my component:

Component Class:

<?php 
class MpttComponent extends Object
{

    var $model_name;
    var $rgt_col;
    var $lft_col;

    function getTree(&$model, $root_node_id, $lft_col = 'lft', $rgt_col = 'rgt')
    {
        $this->model_name = $model->name;
        $this->rgt_col = $rgt_col;
        $this->lft_col = $lft_col;
    
        $root = new Object();
        $root->data = $model->read(null, $root_node_id);
        $root->parent = null;
        $lft = $root->data[$model->name][$lft_col];
        $rgt = $root->data[$model->name][$rgt_col];
        $children = $model->findAll($lft_col.'>'.$lft.' AND '.$rgt_col.'<'.$rgt, null, $lft_col.' ASC');

        if (!empty($children)) {

            $current_parent = $root;
            $current_parent->children = array();

            foreach ($children as $current_child_data) {
                $current_child = new Object();
                $current_child->data = $current_child_data;
                $current_child->children = array();
                while(!$this->_isChildOf($current_child, $current_parent)) {
                    $current_parent = $current_parent->parent;
                }
                $current_child->parent = $current_parent;
                $current_parent->children []= $current_child;
                $current_parent = $current_child;
            }

        }
        return $root;
    }

    function _isChildOf($child, $parent)
    {
        $child_lft = $child->data[$this->model_name][$this->lft_col];
        $child_rgt = $child->data[$this->model_name][$this->rgt_col];
        $parent_lft = $parent->data[$this->model_name][$this->lft_col];
        $parent_rgt = $parent->data[$this->model_name][$this->rgt_col];
        return ($child_lft > $parent_lft && $child_rgt < $parent_rgt);
    }

    function printTree(&$tree, $model_name, $disp_col, $ind = '')
    {
        print($ind.$tree->data[$model_name][$disp_col].'<br/>');
        foreach ($tree->children as $child) {
            $this->printTree($child, $model_name, $disp_col, '....'.$ind);
        }
    }

    function insertNode($lft, &$model, &$data, $lft_col= 'lft', $rgt_col = 'rgt')
    {
        $sql_update_rgt = 'UPDATE '.$model->useTable." SET $rgt_col=$rgt_col+2 WHERE $rgt_col>=$lft";
        $model->query($sql_update_rgt);
        $sql_update_lft = 'UPDATE '.$model->useTable." SET $lft_col=$lft_col+2 WHERE $lft_col>=$lft";
        $model->query($sql_update_lft);
        // Insert data.
        $data[$model->name][$lft_col] = $lft;
        $data[$model->name][$rgt_col] = $lft+1;
        $model->id = null;
        if ($model->save($data)) {
            // Return true on success
            return TRUE;
        }
        // Return false on failure
        return FALSE;
    }

    function insertNodeUnder($parent_node_id, &$model, &$data, $lft_col = 'lft', $rgt_col = 'rgt')
    {
        $parent = $model->read(null, $parent_node_id);
        if (!empty($parent)) {
            $parent_rgt = $parent[$model->name][$rgt_col];
            return $this->insertNode($parent_rgt, $model, $data, $lft_col, $rgt_col);
        }
        return FALSE;
    }

    function insertNodeLeftOf($sibling_id, &$model, &$data, $lft_col = 'lft', $rgt_col = 'rgt')
    {
        $sib = $model->read(null, $sibling_id);
        if (!empty($sib)) {
            $sib_lft = $sib[$model->name][$lft_col];
            return $this->insertNode($sib_lft, $model, $data, $lft_col, $rgt_col);
        }
        return FALSE;
    }

    function insertNodeRightOf($sibling_id, &$model, &$data, $lft_col = 'lft', $rgt_col = 'rgt')
    {
        $sib = $model->read(null, $sibling_id);
        if (!empty($sib)) {
            $sib_rgt = $sib[$model->name][$rgt_col];
            return $this->insertNode($sib_rgt+1, $model, $data, $lft_col, $rgt_col);
        }
        return FALSE;
    }

    function deleteNode($node_id, &$model, $lft_col = 'lft', $rgt_col = 'rgt')
    {
        // Retrieve node data.
        $node = $model->read(null, $node_id);
        if (!empty($node)) {
            $lft = $node[$model->name][$lft_col];
            $rgt = $node[$model->name][$rgt_col];
            // Delete node and all children.    
            $del_sql = 'DELETE FROM '.$model->useTable." WHERE $lft_col >= $lft AND $rgt_col <= $rgt";
            $model->query($del_sql);
            // Update table.
            $diff = $rgt-$lft+1;
            $update_lft_sql = 'UPDATE '.$model->useTable." SET $lft_col = $lft_col-$diff WHERE $lft_col > $rgt";
            $model->query($update_lft_sql);
            $update_rgt_sql = 'UPDATE '.$model->useTable." SET $rgt_col = $rgt_col-$diff WHERE $rgt_col > $rgt";
            $model->query($update_rgt_sql);
            return TRUE;
        }
        return FALSE;
    }
}
?>
The code should be fairly straightforward. The getTree function returns an object. The returned object represents a tree node, and has two member variables: data, and children. The data member variable holds the information for the given node from the database. The children member variable is an array of node objects that are children of the current node.