Mathematical models are widely used to gain insight into biological processes on a variety of different scales, including whole organs on the macroscale and intracellular processes on the microscale. Mechanistic models are particularly useful because they can immediately disclose causal mechanism. One important type of mechanistic models are differential equations. They can be used to describe the temporal evolution of the abundance of biological species in a system. Letting these models explicitly account for the inherently stochastic nature of biological processes can help improve our ability to determine model parameters based on experimental data.
In this talk, I will demonstrate how we applied stochastic differential equations (SDE) to model the translation kinetics after mRNA transfection and how we inferred model parameters from experimental time-lapse fluorescence microscopy data. One focus will be on advantages of SDE in terms of parameter identifiability compared to a deterministic ordinary differential equation (ODE) model.