Trypanosoma brucei causes African trypanosomiasis in humans (HAT or African sleeping sickness) and Nagana in cattle. The disease threatens over 60 million people and uncounted numbers of cattle in 36 countries of sub-Saharan Africa and has a devastating impact on human health and the economy. On the other hand, Trypanosoma cruzi is responsible in South America for Chagas disease, which can cause acute illness and death, especially in young children. In this context, the discovery of novel drug targets in Trypanosome proteome is a major focus for the scientific community. Recently, many researchers have spent important efforts on the study of protein-protein interactions (PPIs) in pathogen Trypanosome species concluding that the low sequence identities between some parasite proteins and their human host render these PPIs as highly promising drug targets. To the best of our knowledge, there are no general models to predict Unique PPIs in Trypanosome (TPPIs). On the other hand, the 3D structure of an increasing number of Trypanosome proteins is reported in databases. In this regard, the introduction of a new model to predict TPPIs from the 3D structure of proteins involved in PPI is very important. For this purpose, we introduced new protein-protein complex invariants based on the Markov average electrostatic potential E_k(Ri) for amino acids located in different regions (Ri) of i-th protein and placed at a distance k one from each other. We calculated more than 30 different types of parameters for 7866 pairs of proteins (1023 TPPIs and 6823 non-TPPIs) from more than 20 organisms, including parasites and human or cattle hosts. We found a very simple linear model that predicts above 90% of TPPIs and non-TPPIs both in training and independent test subsets using only two parameters. The parameters were d_E_k(s) = |E_k(s1) - E_k(s2)|, the absolute difference between the E_k(si) values on the surface of the two proteins of the pairs. We also tested nonlinear ANN models for comparison purposes but the linear model gives the best results. We implemented this predictor in the web server named TrypanoPPI freely available to public at http://miaja.tic.udc.es/Bio-AIMS/TrypanoPPI.php. This is the first model that predicts how unique a protein-protein complex in Trypanosome proteome is with respect to other parasites and hosts, opening new opportunities for antitrypanosome drug target discovery.