There have been a number of studies made over the years on the biarticular muscles in jumping (see links below). These studies indicate that a standing vertical jump may be accomplished without change in the lengths of the several bi-articular muscles of the legs – that, in jumping, the biarticular muscles work almost like tendons, maintaining tone without shortening or lengthening to deliver the work of powerful uniarticular muscles (gluteus) to the toes. Unless jumping conferred an advantage at some distant period in man’s evolution (getting that low-hanging fruit first), then one can assume that these muscles have evolved with running, and can function similarly in running. I believe that most young children (pre-schoolers, at least) naturally run in a manner that uses the biarticular muscles as they can be used in jumping, and I believe that training with this use of the biarticular musculature in mind can lead to improvements in adults who have lost this natural way of running.
Most of the major muscles involved in running do not do the work required to advance the body for running. That is, they not need to change length in the extension phase of running. These muscles are the bi-articular muscles.
A bi-articular muscle is one that crosses two joints. There are, in the legs, three primary muscles that fit the definition bi-articular. They are the rectus femoris at the front of the thighs, the biceps femoris or hamstrings at the back of the thighs, and the gastrocnemius, or calf muscles. (There are four others, partners to those in the upper leg, but it will suffice to work with these three to describe general principles of running mechanics.) Bi-articular muscles function to link the action of muscles along a limb so that the work of powerful mono-articular muscles is transmitted to an extremity. In the case of a leg, this means that it is possible to deliver the power of the gluteus muscles to the feet without changing the lengths of the major leg muscles. For example, in a pure vertical jump, the length of the bi-articular muscles will/can remain constant throughout all phases of the movement, allowing mono-articular muscles, particularly the gluteus maximus (butt) muscles, to extend the entire leg. Stated otherwise, the gluteus maximus muscles, the largest and strongest muscles in the body, when contracted, extend the whole leg through the linking action of the bi-articular muscles. (I am over-simplifying things a bit, as there are other mono-articular muscles that are important in running, such as the vastus lateralis,intermedius and medialis, which are increasingly active in sprinting.)
If we do a kind of slow-motion jump, beginning with the hips, knees and ankles folded to equivalent degrees, then simultaneously extending the three joints together, so that we end up on the toes with all joints fully extended, we can see how the bi-articular muscles might work in running.
In the movement from flexed to extended, the rectus femoris (thigh) muscles will shorten at the knee, and will lengthen an equivalent degree at the hip, thus retaining constant length throughout the movement. The hamstrings will shorten at the knee and lengthen at the hip, and the gastrocnemius muscles will shorten at the ankle, and lengthen at the knee. This assures that adjoining joints are flexed or extended to exactly corresponding degrees, assuring even distribution of effort in extension of the limb. Again, the bi-articular muscles function in pure extension to link the action of mono-articular muscles. In pure extension, these muscles could be replaced by tendons, without loss of function or power. These bi-articular systems have evolved to allow efficient locomotion (they exist in the arms, as well). [See: Effects of the lower leg biarticular muscles in jumping]
However, as soon as any particular joint in the leg is stabilized or fixed, the bi-articular muscles will shorten or lengthen to create movement in the adjoining joint. If you keep the upper leg in a position relation to the pelvis, contracting the rectus femoris will extend the knee (in this case, the opposing muscle, the biceps femoris, is inhibited, or allowed to lengthen).
In natural running, at least in steady, level conditions, the biarticular leg muscles do nothing to generate movement. They need to be strong, but they acquire the strength they need by resisting the forces applied to them in running. Working in an isolated manner to strengthen individual leg muscles does little or nothing to improve running. Leg curls or extensions or toe lifts, or any exercise that works on shortening a leg muscle, are pretty useless for runners. See Running is jumping for a more thorough explanation of the bi-articular muscles in running.
Here are a couple of studies: