In this article we present a new kind of computing device that uses biochemical reactions networks as building blocks to implement logic gates. The architecture of a computing machine relies on these generic and composable building blocks, computation units, that can be used in multiple instances to perform complex boolean functions. Standard logical operations are implemented by biochemical networks, encapsulated and insulated within synthetic vesicles called protocells. These protocells are capable of exchanging energy and information with each other through transmembrane electron transfer. In the paradigm of computation we propose, protoputing, a machine can solve only one problem and therefore has to be built specifically. Thus, the programming phase in the standard computing paradigm is represented in our approach by the set of assembly instructions (specific attachments) that directs the wiring of the protocells that constitute the machine itself. To demonstrate the computing power of protocellular machines, we apply it to solve a NP-complete problem, known to be very demanding in computing power, the 3-SAT problem. We show how to program the assembly of a machine that can verify the satisfiability of a given boolean formula. Then we show how to use the massive parallelism of these machines to verify in less than 20 min all the valuations of the input variables and output a fluorescent signal when the formula is satisfiable or no signal at all otherwise.