Mathematical Methods in Biophysics

Quantitative relationships between different variables are represented as mathematical functions. For example, the number of proteins of a certain type in a cell can vary with time. We can denote it by the function, N(t). If N is large, one can ignore the discreteness in N and regard it as a smooth differentiable variable. Its time derivative dN/dt(t), the instantaneous rate of change of this number, will be another function of time. Consider a protein that is being created in the cell at a steady rate k1. Furthermore, let there be a mechanism for clearing or removing the protein from the cell. The latter rate must be proportional to the number of proteins. If its rate constant is k2, the rate of change of protein number in the cell is given by the equation.