In this paper we show how to model biochemical reactions in Concurrent Constraint Programming (CCP) taking into account space and locality. In fact, in many cases, the distribution of the reactants in the cellular space is critical for the correct dynamics of the reactions. Thus, we propose a modelling framework which allows us to take into account space domains. Resorting on our approach, it is possible to describe accurately biochemical processes without abstracting away from features related to the spatial localisation. In order to describe locality in CCP, we add subexponentials, a concept coming from linear logic, to the constraint system and then, we can model declaratively when a certain reaction occurs within one location of the space domain. Clearly we can also express interactions between agents, taking place either in different spaces or in the same space. Metabolic pathways and, in particular, signalling pathways tend to be arranged in a physical space such that the product of one reaction is in the right place to become the reactant for the subsequent reaction in the pathway. Following this idea, we show through a simple case study how we can model a signalling cascade. Then, we exploit our framework to model a more complex signalling pathway, namely the TWEAK (TNF related Weak inducer of apoptosis), whose misfunctioning has implications in several important diseases.