A lot of new applications of main disciplines such as physics, mathematics, and engineering to the study of biological systems arise at an impressive rate. The mathematically-oriented research of biosystems can lead to useful ways of understanding and transforming many naturally-ocurring mechanisms in such systems. This book provides two different mathematical approaches for studying some processes at the intracellular and cell membrane level, as well as their application to other interesting problems in physics. The first part deals with factorization and supersymmetric methods, developed in the context of mathematical-physics, as applied to the polymerization of tubulin dimers and the motion of domain walls in microtubules, which are one of the basic components of cell skeleton. The second part deals with the control of neuronal dynamics through synchronization in a minimal ensemble of two Hodgkin-Huxley neurons by using the nonlinear control theory. These methods may be especially useful to proffesionals in the fields of physics, mathematics, control theory, biology, and to anyone else who may be interested in interdisciplinary scientific investigations.