Properly representing the principle physical interactions of complex biological systems is paramount for building powerful, yet simple models. As an in depth look into different biological systems at different scales, multiple models are presented. At the molecular scale, an analytical solution to the (linearized) Poisson-Boltzmann equation for the electrostatic potential of any size biomolecule is derived using spherical geometry. The solution is tested both on an ideal sphere relative to an exact solution and on a multitude of biomolecules relative to a numerical solution. In all cases, the bulk of the error is within thermal noise. The computational power of the solution is demonstrated by finding the electrostatic potential at the surface of a viral capsid that is nearly half a million atoms in size.

Next, a model of the nucleosome using simplified geometry is presented. This system is a complex of protein and DNA and acts as the first level of DNA compaction inside the nucleus of eukaryotes. The analytical model reveals a mechanism for controlling the stability of the nucleosome via changes to the total charge of the protein globular core. The analytical model is verified by a computational study on the stability change when the charge of individual residues is altered.

Finally, a multiple model approach is taken to study bacteria that are capable of different responses depending on the size of their surrounding colony. The first model is capable of determining how the system propagates the information about the colony size to those specific genes that control the concentration of a master regulatory protein. A second model is used to analyze the direct RNA interference mechanism the cell employs to tune the available gene transcripts of the master regulatory protein, i.e. small RNA - messenger RNA regulation. This model provides a possible explanation for puzzling experimentally measured phenotypic responses.