Shrinking Too SmallNoise in Biochemical Systems

We discuss the astronomical scale of the molecular constituents of macroscopic systems. We find that even very small cells have an enormous number of molecules in them. Noting that our models so far have considered biochemical species as continuous concentrations, we ask whether models that treat individual molecules as discrete entities provide improved accuracy. We find that even in bacterial cells, the continuous approximation is likely valid. However, we then recognize that the DNA molecule is only present in one or two copies per cell, making the continuous approximation invalid for considering the central dogma of molecular biology. We create a stochastic model of the central dogma, finding that both the mRNA molecules and the protein molecules in the cell experience random fluctuations due to the small numbers of molecules involved. However, we see that the fluctuations are larger for the mRNA molecules, as would be expected if natural selection had acted to reduce noise in protein levels inside the cell.