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This paper studies the molecular communication system where the transmitter has limited productivity and the receiver employs ligand-binding receptors. By simplifying the release and propagation process of the information particles, the ligand-binding process is regarded as a binding channel with peak and average constraints and modeled by a finite-state Markov chain. It is proved that the capacity of the constrained independent and identically distributed (IID) binding channel, defined as the IID capacity, is achieved by a discrete input distribution. The sufficient and necessary conditions of an IID input distribution being capacity-achieving is presented. Moreover, an algorithm called modified steepest ascent cutting-plane algorithm is proposed to efficiently compute the IID capacity-achieving distributions. The numerical results show that the IID capacity is a tight lower bound of the capacity for the binding channel.