Comment on "Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition"

Abstract

The authors of the commented article claim that the exact time-dependent solutions of the stochastic model for a self-repressing gene previously obtained by us are both "incomplete and incorrect" because their calculations issued complex numbers as decaying rates of the system to steady state. We show that the imaginary decaying rates result from a methodological artifact. We use a linear algebraic approach to show that the decaying rates are those reported in [ Exact time-dependent solutions for a self-regulating gene. Phys. Rev. E 83: 062902 (2011)]. Thus, our solution is both complete and correct. Additionally, the authors claim that they have discovered a new class of operator having complex eigenvalues and non-orthogonal eigenfunctions. We show that the operator can actually be written in the usual self-adjoint form, and, hence, it has real eigenvalues and orthogonal eigenfunctions.