Prions

Not all infectious diseases are transmitted by bacteria or viruses. Some neurological diseases, such as Creutzfeldt-Jaakob disease (CJD) or mad cow disease are in fact caused by agents called Prions, which are of similar size to viruses but are made up of only protein  

Prions have these characteristics:

1.) "The transmissible agent consists of aggregated forms of a specific protein"

2.) These protein aggregates cannot be degraded by the agents that degrade most other proteins

3.) "The protein is largely or completely derived from a cellular protein called PrP, that is normally present in the brain"

So an aggregated form of a protein (that is already present in the brain) is the infectious agent in prion diseases