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The Categorical Compositional Distributional (DisCoCat) Model is a powerfulmathematical model for composing the meaning of sentences in natural languages.Since we can think of biological sequences as the "language of life", it isattempting to apply the DisCoCat model on the language of life to see if we canobtain new insights and a better understanding of the latter. In this work, wetook an initial step towards that direction. In particular, we choose to focuson proteins as the linguistic features of protein are the most prominent ascompared with other macromolecules such as DNA or RNA. Concretely, we treateach protein as a sentence and its constituent domains as words. The meaning ofa word or the sentence is just its biological function, and the arrangement ofdomains in a protein corresponds to the syntax. Putting all those into theDisCoCat framework, we can "compute" the function of a protein based on thefunctions of its domains with the grammar rules that combine them together.Since the functions of both the protein and its domains are represented invector spaces, we provide a novel way to formalize the functionalrepresentation of proteins.

A Categorical Compositional Distributional Modelling for the Language of Life