Allosteric control model of bone remodelling containing periodical modes

Area of Science:

• Biomedical Engineering
• Mathematical Biology
• Skeletal Biology

Background:

• Bone remodeling is a complex process crucial for skeletal health and scaffold integration.
• Understanding native bone remodeling is vital for developing effective bone scaffolds.
• Existing models may not fully capture the dynamic regulatory mechanisms involved.

Purpose of the Study:

• To formulate a mathematical model predicting osteoactivity in bone and scaffolds.
• To extend the model using a bio-cybernetic approach incorporating allosteric regulation.
• To investigate the cyclic behavior and potential conservative values in bone remodeling.

Main Methods:

• Developed a mathematical model for osteoactivity prediction.
• Integrated bio-cybernetic principles and allosteric control mechanisms (e.g., Hill, Monod-Wyman-Changeux).
• Analyzed a four-dimensional system exhibiting cyclic behavior and performed linear stability analysis.

Main Results:

• The model demonstrates steady cyclic behavior across a range of biological constants.
• A limiting cycle in multi-dimensional phase space represents a local steady state.
• Identified a conservative value analogous to energy, representing the bone remodeling system's regenerative potential.

Conclusions:

• The proposed model accurately reflects normal bone remodeling processes.
• The existence of a conservative value, akin to energy, characterizes bone recovery potential.
• The cyclic attractor is robust under various feedback controls, supporting the model's viability.