cc power supply
In the Constant-Current mode the output of the opamp takes control over the ADJ pin of the LM317 voltage regulator by pulling the voltage down through the LED diode and D1 ..
In the voltage control mode the volatage at the ADJ pin is around 1.25V (Vref) .. So if you take into account that the voltage drop across LED ≈2V and across D1 ≈0.75V the output of the opamp has to go below -1.5V, and that is the reason the designer used that -6V negative voltage ..
You can easily replace 301 opamp with any other opamp including the TL081 (C4 and D2 are for frequency compensation and will not be required with other opamps) ..
Just connect -Vcc to -6 and and +Vcc to max 30Vdc (TL081 is rated for +/-18V =36V) ..
If you replace D1 with a Schottky diode (Vf≈0.3V) and connect it directly to the opamp's output, increase the value of R4 to >3kΩ and insted of connecting it to the LM317 output wire it directly to your +Vcc supply, you will be able to supply the whole circuit without any need for negative (in this case -6V) voltages, so keep this option in mind ..
Regards,
IanP