From the CAT4201 datasheet:
When the CTRL voltage is less than 0.9 V (typ), the LEDs will shutdown to zero current. When the CTRL voltage is greater than about 2.6 V, full scale brightness is applied to the LED output.
The TLC5940 sinks current (acts like a ground when turned on) so the CTRL voltage will never go positive. You want a schematic closer to Fig. 27 of the datasheet. Instead of the mosfet, however, the connection would be to one of the outputs of the TLC5940. R1 would be 90K (highest recommended value to output minimum current) and Rmax would be 11.25K (90K and 11.25K in parallel = 10K). Fig 27 also shows a transistor Q1 but that is not required -- Just connect directly to CTRL through R2.
- Hopefully someone will check my work or offer a second opinion.