Quantum Graph-Based Differential Models For Dynamic Analysis Of Protein-Protein Interaction Networks
Keywords:
Quantum Graph Theory, Protein-Protein Interaction Networks, Differential Equations, Dynamic Network Analysis, Quantum State Transitions, Biological Network Modeling, Molecular Pathways, System Dynamics,, Biomarker Discovery, Drug Target IdentificationAbstract
Understanding Protein-Protein Interaction (PPI) networks is essential for comprehending intricate biological processes, such as disease development and cellular functions. Due to the dynamic and non-linear nature of these connections, modelling and analysing such complex networks is extremely challenging. Existing graph-based frameworks often fail to capture the stochastic behaviour and quantum-level uncertainty inherent in biological structures. This study enhances the dynamic assessment of PPI systems by introducing Quantum Graph-Based Differential Models (QGDM) to overcome these limitations. The proposed method incorporates quantitative transitions between states and probabilistic behaviour in biological systems while modelling time-evolving interactions using inequality equations and classical graph theory concepts. The process involves constructing quantum graphs to represent PPI systems and applying quantum linear equations to describe the structure of interactions. By integrating quantum effects, the model improves predictions of system shifts, leading to a better understanding of biological pathways and system responses. The goal is to provide a more accurate framework for identifying key proteins and predicting the impact of network modifications on functionality. The effectiveness of the proposed model is validated through experimental simulations using real PPI datasets demonstrating enhanced prediction accuracy and resilience compared to traditional methods. The findings indicate a significant improvement in identifying critical nodes and capturing dynamic transitions, paving the way for more effective pharmacological target selection and biomarker development. By addressing key shortcomings of conventional models, this innovative integration of quantum graph concepts and differential modelling offers approach to understanding and analysing biological systems.
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