Interval running benefits your muscle cells, but what else happens at the cellular level.

As stated in week three, your weekly long run increases aerobic
base or stamina. Long runs improve your:
aerobic pathways at the cellular level, 
stimulate more and larger mitochondria, 
more red blood cells, 
increase your blood volume and 
Builds bigger heart, breathing and running muscle cells
increases the quantity of blood pumped out with each heart
The net result is an enhanced capacity to take in and distribute
This increased aerobic ability is technically called an increased
maximum oxygen uptake capacity--VO2 max.

Interval running makes additional increases to the above and stimulates better or faster enzyme action at the cellular level.

VO2 max, or Maximum Oxygen Uptake Capacity, to use its
formal name, is the amount of oxygen we can absorb into our cells
in one minute while working at full capacity. 
British coach, Frank Horwill, says that:
“The best way to improve VO2 max is to run between 80 and 100
percent of VO2 max. One hundred percent equals the runner’s 3K
or two mile race pace; 95 % equals 5K speed; 90 % is 10K
running speed.
“Work physiologists believe training at 95 % VO2 max brings the
best results--though one Russian physiologist of note--Karibosk,
thinks 100 % (3K or two mile pace) is better because it tunes up
the anaerobic pathway.” 

Logic agrees with scientists

Once in a blue moon, so twice in 1999, logic meets science.
Running a bit faster than 10K pace is obviously a good training
idea because it prepares you for race pace.
Running a bit slower than 2 mile pace intensity is easier on your
body, which decreases injury and burnout risk (the full results of
interval running take 12 or more weeks).
Running at 5K pace, at 95 percent of VO2 max is recommended
by most exercise physiologists, and it makes the most
phase 4 of 10K running.

Interval running should be progressive

Interval running is simple but progressive: You run moderately
fast for a tolerable duration: then you take a rest. You vary your
rest period and hence you vary the stimulation to your body. Over
the course of many running sessions you improve your VO2 max
and you running economy.
It is this modest stimulation to your body from running 1 to 2
minutes at 5K pace which stimulates additional improvements in
your VO2 max and your running efficiency.
Blasting a few reps faster than 2 mile pace will not help your VO2
max. Experienced runners: restrain yourself to 2 mile race pace if
you’ve done lots of races recently. Running at 5K pace is better for
most runners. Don’t let exuberance and training partners make you
run faster than is good for you.

This web page is based on running 30 miles per week? Go here if you're running 40-60 miles per week
Practice good running form, and the clever use of interval training at 5K pace will:
Week 11 of 20 for 30 miles per week 10K racers...nutrition
10K running week 13 of 20...long intervals for experienced runners
Summary of 20 week 10K training schedule for 30 mile per week runners with connections to all 20 weeks

10K Running, Training & Racing: The Running Pyramid book summary.
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This page is 10K running week 12 of 20: Interval running benefits in the muscle cell or at the cellular level