Coumarin is a plant product which competes with Vitamin K. Since this is a competitive inhibition the degree of anticoagulant effect can be regulated. Conversely, administering Vitamin K will increase the level of plasma clotting proteins somewhat.
Antithrombins are naturally present and remove the small amount of thrombin produced spontaneously. Heparin is also present in small amounts which normally have little effect. But when released from mast cells or basophils heparin significantly increases the effect of the antithrombins, thus inhibiting clotting. This effect is used clinically as a short-term anticoagulant. Giving Ca+2 will neutralize the heparin.