Food chains present an interconnected set of structural, functional and dynamical properties. Their most conspicuous feature is the static distribution of biomass across trophic levels. But decades of ecological research have affirmed the importance of another, harder to measure, feature: the dynamical propagation of perturbations up and down these chains, creating trophic cascades. These two features are shaped by the same physiological and environmental variables, and seem intuitively related: for instance, more abundant predators should indicate the potential for stronger downward cascades. We interrogate this intuition, combining theory and data from 31 pelagic experiments. We find that basic expectations do not necessarily hold: while for bottom-up perturbations trophic levels respond proportionally to their biomass, for top-down perturbations more top-heavy communities show stronger amplifications. Our framework points at self-regulation (e.g. intra-guild competition) as a major determinant of dynamical-structural relationships. Our approach provides a comprehensive understanding of the link that binds structural and dynamical properties of food chains, and its possible determinants.