Gate voltage range - Biasing circuit
When Q2 is on, the output is always −4 V. When Q2 is off, the output is determined by the R13/R5/R14 voltage divider. With the values shown, the voltage can be adjusted between about −1.6 V and −2.4 V.

To allow voltages down to −4 V, drop R13. To allow voltages up to −0.5 V, make R14 one seventh of R5. The wiper of the potentiometer is unlikely to go all the way to the ends, so you will probably not reach these limits.