  Analysis of the band structure of TiS$_3$ single-layers suggests the
possibility of changing their physical behaviour by injecting electron
carriers. The anisotropy of the valence and conduction bands is explained in
terms of their complex orbital composition. The nature of the Fermi surface and
Lindhard response function for different doping concentrations is studied by
means of first-principles DFT calculations. It is suggested that for electron
doping levels $x$ (number of electrons per unit cell) $\sim$ 0.18-0.30$e^-$ the
system could exhibit incommensurate charge or spin modulations which, however,
would keep the metallic state whereas systems doped with smaller $x$ would be
2D metals without any electronic instability. The effect of spin-orbit coupling
in the band dispersion is analysed. The DFT effective masses are used to study
the plasmon spectrum from an effective low energy model. We find that this
material supports highly anisotropic plasmons, with opposite anisotropy for the
electron and hole bands.
