Nonchaoticity of Ordinary Differential Equations Describing Autonomous Transcriptional Regulatory Circuits

Gene transcriptional regulation （TR） processes are often described by coupled nonlinear ordinary differential equations （ODEs）. When the dimension of TR circuits is high （e.g. n≥3） the motions of the corresponding ODEs may, very probably, show self-sustained oscillations and chaos. On the other hand, chaoticity may be harmful for the normal biological functions of TR processes. In this letter we numerically study the dynamics of 3-gene TR ODEs in great detail, and investigate many 4-, 5-, and lO-gene TR systems by randomly choosing figures and parameters in the conventionally accepted ranges. And we find that oscillations are very seldom and no chaotic motion is observed, even if the dimension of systems is sufficiently high （n≥3）. It is argued that the observation of nonchaoticity of these ODEs agrees with normal functions of actual TR processes.