We present an $\textit{ab initio}$ calculation of the individual up, down, and strange quark unpolarized, helicity, and transversity parton distribution functions for the proton. The calculation is performed within the Wilson twisted mass clover-improved fermion formulation in lattice QCD. We use a $N_f=2+1+1$ gauge ensemble simulated with pion mass $m_\pi\approx 260$~MeV, $m_\pi L\approx 3.8$ and lattice spacing $a \approx 0.0938$~fm. Momentum smearing is employed in order to improve the signal-to-noise ratio, allowing for the computation of the matrix elements up to nucleon boost momentum of $P_3=1.24$~GeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $\overline{MS}$ scheme at a scale of $2$~GeV (unpolarized and helicity) and $\sqrt{2}$~GeV (transversity).