Rosen's (M,R) system as an X-machine.

Area of Science:

• Systems Biology
• Theoretical Biology
• Computational Biology

Background:

• Robert Rosen's (M,R) system is an abstract biological network model.
• Its self-referential structure poses challenges for reductionist and mechanistic approaches in systems biology.
• The non-computability of the (M,R) system on a Turing machine questions the feasibility of accurate computational modeling.

Purpose of the Study:

• To investigate the limitations of existing formal architectures in modeling the (M,R) system.
• To propose a novel computational framework capable of representing the self-referential properties of the (M,R) system.
• To lay the groundwork for future software instantiations of (M,R) systems.

Main Methods:

• Analysis of finite state machine and stream X-machine formalisms for (M,R) system representation.
• Demonstration of the failure of these architectures to capture self-referential requirements.
• Development of a solution using communicating X-machines and object-orientation.

Main Results:

• Finite state machine and stream X-machine architectures are insufficient for modeling the self-referential (M,R) system.
• Communicating X-machines, through parallel computation, can effectively remove self-reference.
• A synthesis of communicating X-machines with object-orientation provides a formal basis for (M,R) system software.

Conclusions:

• The (M,R) system's complexity necessitates advanced computational approaches beyond traditional models.
• Communicating X-machines offer a viable method for handling the self-referential aspects of biological networks.
• Object-oriented communicating X-machines provide a robust formal foundation for computational systems biology research.