This invention provides a method for treating a subject having a tumor and a method for inhibiting angiogenesis in a subject, both comprising administering to the subject an effective amount of a composition of matter comprising the extracellular domain of a Notch receptor protein operably affixed to a half-life-increasing moiety. This invention also provides a composition of matter comprising the extracellular domain of Notch4 receptor protein operably affixed to a half-life-increasing moiety. This invention further provides an article of manufacture. Finally, this invention provides a replicable vector which encodes a polypeptide comprising the extracellular domain of a Notch receptor protein operably affixed to a half-life-increasing moiety, a host vector system which comprises such replicable vector and a method of producing such polypeptide.