Final answer:
The two substances required for the regulation of the myosin cross-bridge cycle in smooth muscle cells are calcium and calmodulin.
Step-by-step explanation:
Different from striated muscle which uses troponin for this process, smooth muscle's regulation is achieved through the interaction of calcium ions that enter through calcium channels in the sarcolemma, or release from the sarcoplasmic reticulum (SR), and bind to the protein calmodulin. This Ca++-calmodulin complex then activates an enzyme known as myosin (light chain) kinase, leading to the phosphorylation of myosin heads and allowing them to attach to actin, initiating muscle contraction.