Sequestration and delays enable the synthesis of a molecular derivative operator

Abstract

Many biological systems need to sense and respond to chemical gradients in order to find nutrients and adapt to their environment. In nature, molecular networks able to compute molecular gradients are complex, making it challenging to build minimal components for use in synthetic biology. In this work, we propose a motif that relies on molecular sequestration and delays to perform an approximate derivative operation. We analyze and discuss the properties and physical limitations of this network. We outline potential biological implementations of the motif, and we show its capacity for gradient computation with simulations. Other molecular architectures with the topology of an incoherent feed forward loop could be used for derivative computation, but they present nonlinear behavior that is avoided in our motif.