Before revision:  In this paper, we make use of the Koopman observability gramian to develop an algorithm for optimal sensor placement of discrete time autonomous nonlinear dynamical systems . The Koopman operator lifts nonlinear dynamics to a higher dimensional space where the dynamics evolve approximately linearly in time. Data in biology are often sampled sparsely in time , therefore a method is developed to compute a temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator .
After revision:  In this paper, we make use of the Koopman observability gramian to develop an algorithm for optimal sensor placement of discrete time autonomous nonlinear dynamical systems to ease the difficulty of design of the promoter library. This ease is enabled due to the fact that the Koopman operator represents the evolution of a nonlinear system linearly by lifting the states to an infinite-dimensional space of observables. The Koopman framework ideally demands high temporal resolution, but data in biology are often sampled sparsely in time , therefore a method is developed to compute a temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator .