Cellulose physical properties like crystallinity, porosity, and particle size are known to influence cellulase activity, but knowledge is still insufficient for activity prediction from such measurable substrate characteristics. With the aim of illuminating enzyme-substrate relationships, this work evaluates a purified hyperthermophilic endo-1,4-beta-glucanase (from Pyrococcus furiosus) acting on 13 celluloses characterized for crystallinity and crystal width (by X-ray diffraction), wet porosity (by thermoporometry), and particle size (by light scattering). Activities are analyzed by the Michaelis-Menten kinetic equation, which is justified by low enzyme-substrate affinity. Michaelis-Menten coefficients K(m) and k(cat) are reinterpreted in the context of heterogeneous cellulose hydrolysis. For a set of as-received and milled microcrystalline celluloses, activity is successfully described as a function of accessible substrate concentration, with accessibility proportional to K(m)(-1). Accessibility contribution from external particle areas, pore areas, and crystalline packing are discriminated to have comparable magnitudes, implying that activity prediction demands all these substrate properties to be considered. Results additionally suggest that looser crystalline packing increases the lengths of released cello-oligomers as well as the maximum endoglucanase specific activity (k(cat)).