Living organisms need to obtain and process information crucial for their survival. Information processing in living systems, ranging from signal transduction in a single cell to image processing in the human brain, are performed by biological circuits (networks), which are driven out of equilibrium. These biochemical and neural circuits are inherently noisy. However, certain accuracy is required to carry out proper biological functions. How do biological networks process information with noisy components? What is the free energy cost of accurate biological computing? Is there a fundamental limit for its performance of the biological functions? In this talk, we will describe our recent work in trying to address these general questions in the context of two basic cellular computing tasks: sensory adaptation for memory encoding [1,2]; biochemical oscillation for accurate timekeeping .
 The energy-speed-accuracy trade-off in sensory adaptation, G. Lan, P.
Sartori, S. Neumann, V. Sourjik, and Yuhai Tu, Nature Physics 8, 422-428,
 Free energy cost of reducing noise while maintaining a high sensitivity, Pablo Sartori and Yuhai Tu, Phys. Rev. Lett. 2015. 115: 118102.
 The free-energy cost of accurate biochemical oscillations, Y. Cao, H. Wang, Q. Ouyang, and Yuhai Tu, Nature Physics 11, 772, 2015.