De novo polynucleotide synthesis is performed with a substrate-bound polymerase. The polymerase is attached to a solid substrate such as a microelectrode array. The polymerase adds nucleotides to growing polynucleotides strands that are also attached to the solid substrate. Spatial control of polymerase activity is achieved by changing the rate of nucleotide polymerization at selected locations on the surface of the solid substrate. The rate of polymerization is changed by inhibiting or promoting activity of the polymerase. In some implementations, activation of electrodes in the microelectrode array changes the rate of nucleotide polymerization. Nucleotides are added to the growing polynucleotide strands at areas where the polymerase is active. By varying the locations where the substrate-bound polymerase is active and the species of nucleotide added, a population of polynucleotides with different, arbitrary sequences is synthesized on the surface of the solid substrate.