Systems and methods for executing trades on an interconnected computer network, such as the Internet, using a catalog of protocol-independent fundamental asset trading messages, called “gestures,” that support multiple higher-level trading protocols which characterize most asset trading transactions. Trading transactions requiring protocol-dependent workflows are composed from protocol-independent gestures selected from the catalogue of gestures and then passed one at a time to an online asset trading server. The online asset trading server transitions pending quotes and trades through a series of distinct states, based on the current state, the selected protocol-independent gestures it receives and a set of state transition rules, thereby implementing the higher-level protocol-dependent workflows.