  In the note we study the multipoint Seshadri constants of
$\mathcal{O}_{\mathbb{P}^{2}_{\mathbb{C}}}(1)$ centered at singular loci of
certain curve arrangements in the complex projective plane. Our first aim is to
show that the values of Seshadri constants can be approximated with use of a
combinatorial invariant which we call the configurational Seshadri constant. We
study specific examples of point-curve configurations for which we provide
actual values of the associated Seshadri constants. In particular, we provide
an example based on Hesse point-conic configuration for which the associated
Seshadri constant is computed by a line. This shows that multipoint Seshadri
constants are not purely combinatorial.
