Thermodynamic uncertainty relation constraints information transmission through cell signaling systems

Cell signaling systems are involved in sensing changes in the environment by activating a set of transcription factors (TF) that typically diffuse within the nucleus to trigger transcription of the required genes. The TFs can diffuse randomly in and out of the nucleus leading to fluctuations in different components which severely limits the accuracy of estimating environmental input. The diffusion usually happens through the nuclear pore complexes which enables the tf protein to enter the nucleus either passively or actively depending on its size. In this study, we explored the role of diffusion on the information transmission capacity of a set of tfs using a coupled mathematical and machine learning approaches to experimental data in yeast under several stress conditions. We found that the the activation followed by biased diffusion of transcription factors (TF) towards the nucleus triggers amplifying magnitude of the overall TF currents towards the nucleus as well as reduces the fluctuations. In fact, to our surprise the diffusion rate estimated from the data is found to be positively correlated with the protein mass, indicating the possibility of active diffusion since a negative correlation is expected in case of passive diffusion. The active diffusion in fact facilitates faster entry to the nucleus enabling faster information transmission with nuclear protein concentration as output. Additionally, higher copy number of the TF also improves information transmission by reducing overall noise in the output. However, improved information owing to faster active diffusion and higher copy number comes at an extra cost of increased entropy production due to the inherent thermodynamic uncertainty relation (TUR)for non-equilibrium systems. A linear optimization analysis demonstrates a corelation between the protein size and the optimized protein number which corroborates the actual observation. Thus, experimental measurements coupled with diffusion based theoretical models demonstrate the role of diffusion on optimizing cellular information processing.