  We have a general knowledge of the principles by which catalysts accelerate
the rate of chemical reactions but no precise understanding of the geometrical
and physical constraints to which their design is subject. To analyze these
constraints, we introduce a minimal model of catalysis based on elastic
networks where the implications of the geometry and flexibility of a catalyst
can be studied systematically. The model demonstrates the relevance and
limitations of the principle of transition-state stabilization: optimal
catalysts are found to have a geometry complementary to the transition state
but a degree of flexibility that non-trivially depends on the parameters of the
reaction as well as on external parameters such as the concentrations of
reactants and products. The results illustrate how simple physical models can
provide valuable insights on the design of catalysts.
