We study brane-world models and demonstrate that such models do not admit self-similar solutions through the matter collineation approach. By introducing the hypothesis of variable brane tension, λ, we outline the new effective field equation (EFE) in the most simple case (symmetric embedding) under the assumption that the fundamental constants in five dimensions (5D) are constants. In this case, we find the exact form that each physical quantity may take in order that the EFE become invariant under scale transformations. By taking into account such assumptions, we find that in four dimensions the gravitational constant κ2 ~ λ, while the cosmological constant ʌ ~ λ2 is always decreasing. These results are quite general and valid for any homogeneous self-similar metric. Nevetheless, the study of the EFE under scale symmetries suggests that ρ ~ λ (as a functional relationship). This allows us to get a growing κ2 but, in this case, the fundamental constants in 5D must vary as well. We outline a toy model allowing such a possibility. © 2022 The Author(s).