To the protein folding question:
Translation (the making of protein from information encoded on mRNA) is poorly understood. As jmullaney’s previous post indicated, we know all of the forces involved in protein folding. These are van der Waals forces (hydrophobic interactions), ionic forces, and hydrogen bonding between the nascent polypeptide strand, the ribosome, the cellular ionic environment, the endoplasmic reticulum (for membranous proteins tranlated on the rough ER), and proteins involved in assisting folding (chaperones and so forth).
We have many problems like this in biology: Enhancer/promoter signals signalling transcription factors to tell when and where genes are turned on (what Spiritus was getting at), epigenetic regulation (methylation, histone acetylation in gene regulation) incredibly complex feedback loops in the most simple developmental processes, ecology/niche interactions and interspecies interactions, etc.
These are all systems with many, many variables and we have no way to reduce the number of variables in order to model them appropriately with current mathematical and computer techniques.
What we are left with is a situation akin to many problems with quantum theory – every particle interaction can be described by an infinite number of Feynmann diagrams, and we have no mathematical way to reduce or model these possible interactions.
All it means is we need better math. What we do in the mean time is we simplify, which sometimes doesn’t work. In biology, we predict protein homolgy by BLAST searching and run computer programs to predict motifs based on primary sequence homology. We have a catalog of motifs, for instance SH2 and peptidase and kinase regions, which give us hints at what proteins do. It takes honest-to-god research into the proteins to actually prove this. There are lots of examples of function predicted by homology being totally uninformative to the real-world job of a gene product, though.
To answer the OP, I agree with jmullaney on a number of points. There are few fundamental things going on that we don’t have a theory for. This is a bit of a skewed question though – the science community is large enough that theories for newly discovered anomalies in measurement are quickly cranked out. New particle seen at CERN? New additions to the Yang-Mills theory. Higher cosmic background? New interpretation of the Big Bang theory. The same happens in chemistry and biology as well. The scientific theories are based on observation, so we can’t say there is anything out there without a theory explaining it. Circular reasoning. It just takes a lot longer to find out which theories have predictive value.
So, to answer the OP:
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We still have no conceptual foundation of how gravity works on a quantum level. We have many theories, but many of them (for instance superstring) may only be corroborated by evidence produced during collisions at Planck energies, which is nowhere close to where we are nowadays.
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Next, the Standard Model of Quantum Mechanics, alluded to above, is a pragmatic interpretation. It is accepted because it works. We are given a set of mathematical formulae that hold up to a high degree of accuracy in every experiment to date. But, the mathematical formulae tell us absolutely nothing about the particles, interactions, forces, or space/time. The equations work because they work. The actual physical properties which underlie the equations are a black box. This feeds into 1.