  Biochemists know that the law of mass action is not exact and not very useful
because we cannot transfer it (with unchanged parameters) from one condition to
another. I argue that exact equations require calibrated multiscale analysis to
deal with ions. Exact theories in biochemistry must use mathematics of
interactions because biological ionic solutions, derived from seawater, are
complex (not simple) fluids. The activity of one ion depends on every other
ion. Mathematics of conservative interactions is well understood but friction
is another matter. Mathematicians now have now an energetic variational
calculus dealing with friction. Complex fluids need variational methods because
everything interacts with everything else. Mathematics designed to handle
interactions is needed to produce exact equations. If interactions are not
addressed with variational mathematics, they are bewildering. The mathematics
must include the global properties of the electric field. Flow of charge in one
place changes the flow everywhere by Kirchoff and Maxwell laws. Charge changes
physical nature as it flows through a circuit. It is ions in salt water; it is
electrons in a vacuum tube; it is quasi-particles in a semiconductor; and it is
nothing much in a vacuum capacitor (i.e., displacement current). Charge is
abstract. The physical nature of charge and current is strikingly diverse; yet,
the flow of current is exactly the same in every element in a series circuit.
The global nature of electric flow prevents the law of mass action from being
exact. The law of mass action (with rate constants that are constant) does not
know about charge. The law of mass action is about mass conservation. I believe
the law of mass action must be modified to be consistent with the Kirchoff
current law if biochemistry is to be an exact science.
