Important subjects for biological systems modelling which subjects and tools are important for a person who wants to start modelling biological systems? For example, everyone knows that calculus is really important to step in any mathematical description about anything but which other topics one needs to cover in order to model biological systems, and why? Are there any essential math tools/topics one needs to know in order to proceed in this area? 
 A: From my experience, the most important topic are


*

*ordinary and partial differential equations and 

*nonlinear dynamical systems. 


To get things started you may refer to Boyd's OR Zill's text on ordinary differential equations, Haberman's partial differential equation, and Strogatz's text on nonlinear physics. 
For example, browse through the modeling of action potential across a neuron http://wwwold.fi.isc.cnr.it/users/alessandro.torcini/ARTICOLI/lezione4-zillmer.pdf
You immediately find application of differential equations, phase portraits, bifurcation, chaos, etc. etc. Many things associated with neurons are modelled by partial differential equations and now increasingly tools from stochastic systems.
In my opinion this is the these are the most important things to know for modeling biological systems. And not simply neurons and biochemical reacions, but also understanding things such muscular contraction (basically a nonlinear mass spring damper system), heart beats (dynamical system on a circle), gait (limit cycle)...
