  Given an $\infty$-bicategory $\mathbb{D}$ with underlying $\infty$-category
$\mathcal{D}$, we construct a Cartesian fibration
$\operatorname{Tw}(\mathbb{D})\to \mathcal{D} \times
\mathcal{D}^{\operatorname{op}}$, which we call the enhanced twisted arrow
$\infty$-category, classifying the restricted mapping category functor
$\operatorname{Map}_{\mathbb{D}}:\mathcal{D}^{\operatorname{op}}\times
\mathcal{D} \to \mathbb{D}^{\operatorname{op}} \times \mathbb{D} \to
\operatorname{Cat}_{\infty}$. With the aid of this new construction, we provide
a description of the $\infty$-category of natural transformations
$\operatorname{Nat}(F,G)$ as an end for any functors $F$ and $G$ from an
$\infty$-category to an $\infty$-bicategory. As an application of our results,
we demonstrate that the definition of weighted colimits presented in
arXiv:1501.02161 satisfies the expected 2-dimensional universal property.
