  A multi-phase transport (AMPT) model has been successful in explaining a wide
range of observables in relativistic heavy ion collisions. In this work, we
implement a modern set of free proton parton distribution functions and an
impact parameter-dependent nuclear shadowing in the AMPT model. After refitting
the parameters of the two-component initial condition model to the experimental
data on $pp$ and $p \bar p$ total and inelastic cross sections from $\sqrt s
\sim $ 4 GeV to 13 TeV, we study particle productions in $pp$ and $AA$
collisions. We show that the updated AMPT model with string melting can
reasonably describe the overall particle yields and transverse momentum spectra
for both $pp$ and $AA$ collisions at RHIC and LHC energies after we introduce a
nuclear scaling of the minijet transverse momentum cutoff for $AA$ collisions
at LHC energies that is motivated by the color glass condensate. Since heavy
flavor and high-$p_{\rm T}$ particles are produced by perturbative-QCD
processes and thus directly depend on parton distribution functions of nuclei,
the updated AMPT model is expected to provide a more reliable description of
these observables.
