How to tie the last note of one variable to the first note of another variable?

[Disc Magnet]

partOne = \relative c' {
    c4 e g e~
}

partTwo = \relative c' {
    e1
    c4 e g e~
    e1
}

\score {
    \new PianoStaff <<
        \set PianoStaff.midiInstrument = "acoustic grand"

        \new Staff {
            \tempo 4 = 120
            \partOne
            \partTwo
        }
    >>
    \midi { }
    \layout {}
}

I expect the last e of partOne and first e of partTwo to be tied
together. However, it doesn't happen so. What is the right way to do
this?