Bleeding air from brakes

I have replaced all four brake wheel cylinders and the master brake cylinder, all four wheels have new pads. I can't seem to get the air out of the brake lines. I have a piece of plastic tubing hooked to the bleed screw and into a plastic bottle partially filled with brake fluid. As I pump the pedal I see the fluid with air bubbles pumping through. I have ran 4 quarts (yes quarts) of brake fluid through the system but cannot get rid of the air. There is not any evidence of brake fluid leaking any where and I have gone over each connection multiple time ensuring all connections are tight. I even adjusted each brake all the way to the point that the wheel is locked down. It appears that I get the most air when bleeding from the driver rear. The master cylinder and wheel cylinders are new not rebuilt. Any suggestions?