For the demonstrations, I'll be using a Fractal Audio Systems "Axe-Fx Ultra". The Axe-Fx is one of the most common units in modern metal, not only for effects, but for literally building an entire guitar sound from scratch. Line 6 products come very close, however with the right EQing, amp settings and personal touch, you'll be "djenting" just fine in no time, regardless of equipment.
The input chain in for the guitar sound I'll be using is as follows: Compressor - Gate - Drive - Amp - EQ - Cab -EQ
Compressor - A very important piece of the puzzle - this will give your sound the attack and defnition required in achieving the tightest tone possible. Use low sustain, high attack, release around 10 o'clock and adjust the level accordingly.
Gate - Silence is another fundamental part of achieving a sound like this. It's what will offer the distinction between played notes and dead space. I usually keep the threshold relatively moderate (around 12 o'clock) with a low attack, and a moderate ratio (again, around 12 o'clock).
Amp/Cab - Choose an amp/cab simulation (or real thing, of course) that sounds clean even when heavily distorted. Remember, tight mid-range is all important. I use a Mesa Boogie Dual Rectifier in live situations, and use the Recto amp model on the Axe Fx, it tends to have all the most beneficial properties.
EQ - Use a low and high-pass filter (roll off extreme highs as well as lows) and boost the low as well as high mid-range. This is subjective, however, as all modelers, amps, guitars and pedals do different things. Adjust accordingly.