Despite progress in the understanding of how nanostructuring affects activity of heterogeneous catalysts, there are still fundamental questions to be answered. Do nanoparticle edges have the same catalytic properties as steps on single-crystal surfaces? How much does the increased structural flexibility of nanoparticles contribute to their activity? How do reaction barriers depend on the nanoparticle size? Herein we address these questions regarding an exemplary reaction sequence of complete methane dehydrogenation. Using density functional theory methods we calculate energy profiles of this reaction on edges of 1.2 nm large Pd-79 and 1.6 nm large Pd-140 particles as well as on Pd(1 1 1) and steps on Pd (21 1) single-crystal surfaces. The barriers of the two slowest reaction steps, CH4 - CH3 + H and CH C + H, notably decrease in the following series of substrates: Pd(1 1 1) greater than or similar to Pd(2 1 1) > Pd-140 > Pd-79. Importantly, these barriers differ by >= 20 kJ/mol on Pd-140 and Pd(2 1 1), whereas the differences between the barriers on Pd(1 1 1) and Pd(2 1 1) are only <= 11 kJ/mol. Also, the structural flexibility contributes to higher reactivity several times stronger for Pd-79 than for Pd(1 1 1). All calculated elementary steps follow Bronsted-Evans-Polanyi relationships. This study advances the understanding of heterogeneous catalysis by shedding light on several fundamental questions concerning structure-property relationships in nanostructured catalysts. (C) 2016 Elsevier Inc. All rights reserved.