And depending of the details about what you consider an explanation, we can include gravity https://en.wikipedia.org/wiki/Graviton It probably involves a family of alleged particle that nobody had seen, but with a few approximations you will probably get General Relativity and with more approximations Newtonian Gravity. Anyway, why do gravitons interact with quarks?
I'll try to answer your last question ("why do gravitons interact with quarks") and the implicit one ("why hasn't anyone seen a graviton?") as well.
You yourself are a pile of mostly quarks (and gluons) whose behaviour with respect to the surface of the Earth is extremely well described by General Relativity. There are plenty of large astrophysical objects which are mainly quarks-and-gluons and they follow General Relativity (GR) exactly.
The non-gravitational behaviour of all these objects is (within measurability) exactly described by the Standard Model, and if we divide them up into constituent parts -- right down to subatomic particles -- the description remains accurate. The description of the gravitational behaviour of these objects should also continue as we divide them into ever smaller parts. Quarks feel all four fundamental forces, so they must interact with the respective force carriers.
Gauge bosons are exchanged between elementary particles in a gauge theory (like the Standard Model), and carry the fundamental forces. Gravitons are directly comparable with photons, which mediate the other long range fundamental force; both should be massless because they are long-range. Classical light waves have spin-0 symmetry, and photons are spin-0; classical gravitational gravitational waves have spin-2 symmetry, so a quantization of them must preserve that.
The simplest graviton extension to the Standard Model works very well when gravitational effects are weak, but fails when gravitational effects are strong, largely because gravitons are self-interacting (unlike photons, at least at tree level).
This seen in classical theories: the Maxwell equations are linear; the Einstein Field Equations are not.
Schrödinger's equation is linear; quantum gravitational equations almost certainly will not be.
Weinberg's dimensional power counting of Feynman diagrams works for renormalizing field content described by Schrödinger's equation; that approach doesn't work for the gravitational field content for diagrams with more than one loop of gravitons.
Directly detecting an individual graviton will be difficult; you're interacting with enormous numbers of gravitational waves (even more than the number of light waves you are interacting with), but unlike the photon, the individual effect of each graviton is too weak to detect with anything close to current technology. (see for example http://arxiv.org/abs/gr-qc/0601043 )
Finally, we might arrive at another theory of gravity that doesn't have gravitons, although that would be a surprising result.
