  Long-term behaviors of biochemical systems are described by steady states in
deterministic models and stationary distributions in stochastic models.
Obtaining their analytic solutions can be done for limited cases, such as
linear or finite-state systems, as it generally requires solving many coupled
equations. Interestingly, analytic solutions can be easily obtained when
underlying networks have special topologies, called weak reversibility (WR) and
zero deficiency (ZD), and the kinetic law follows a generalized form of
mass-action kinetics. However, such desired topological conditions do not hold
for the majority of cases. Thus, translating networks to have WR and ZD while
preserving the original dynamics was proposed. Yet, this approach is limited
because manually obtaining the desired network translation among the large
number of candidates is challenging. Here, we prove necessary conditions for
having WR and ZD after translation, and based on these conditions, we develop a
user-friendly computational package, TOWARDZ, that automatically and
efficiently identifies translated networks with WR and ZD. This allows us to
quantitatively examine how likely it is to obtain WR and ZD after translation
depending on the number of species and reactions. Importantly, we also describe
how our package can be used to analytically derive steady states of
deterministic models and stationary distributions of stochastic models. TOWARDZ
provides an effective tool to analyze biochemical systems.
