This paper presents a compilation strategy and a toolkit for biochemical reactions that perform sequential arithmetic computation on protein quantities, analogous to registerbased computation in digital systems. From a Verilog-like input specification file, we generate biochemical reactions that produce output quantities as a function of input quantities, performing operations such as addition, subtraction, and multiplication. Sequential operations are implemented by transferring quantities between protein types, based on a clocking mechanism. Synthesis first is performed at a conceptual level, in terms of abstract biochemical reactions - a task analogous to technology-independent logic synthesis in circuit design. Then the results are mapped onto specific biochemical reactions, selected from libraries - a task analogous to technology mapping in circuit design. Our method targets the universal DNA substrate developed by Erik Winfree's group at Caltech as the experimental chassis. We demonstrate the algorithm on the synthesis of a variety of standard sequential functions: signal processing functions (FIR filters and IIR filters), vector multiplication, integration and differentiation. The designs are validated through transient stochastic simulation of the chemical kinetics.