  We study the application of the novel tensor formats (TT, QTT, QTT-Tucker) to
the solution of $d$-dimensional chemical master equations, applied mostly to
gene regulating networks (signaling cascades, toggle switches,
phage-$\lambda$). For some important cases, e.g. signaling cascade models, we
prove good separability properties of the system operator. The Quantized tensor
representations (QTT, QTT-Tucker) are employed in both state space and time,
and the global state-time $(d+1)$-dimensional system is solved in the
structured form by using the ALS-type iteration. This approach leads to the
logarithmic dependence of the computational complexity on the system size. When
possible, we compare our approach with the direct CME solution and some
previously known approximate schemes, and observe a good potential of the newer
tensor methods in simulation of relevant biological systems.

Numerical Analysis