
@article {166888,
	title = {Laplacian Dynamics and Kron Reduction in Species-Reaction Graphs of Chemical Reaction Networks},
	journal = {Bulletin of Mathematical Biology},
	volume = {88},
	year = {2026},
	month = {05},
	abstract = {<p class="rtejustify">We present a new method for deriving the dynamics of chemical reaction networks using the Laplacian matrix of the corresponding species{\textendash}reaction graph, in contrast to previous works that use the Laplacian of the graph of complexes. Species-reaction graphs are bipartite graphs that contain two sets of vertices, one representing species and the other representing reactions, connected by directed edges that indicate relationships between them. Our approach starts by assigning appropriate edge weights to this bipartite graph, which are then used to compute the weighted graph Laplacian. This Laplacian reformulation of the system of differential equations governing the network dynamics emphasizes the flow of information throughout the chemical reaction network considered as causal network. As an application of this framework, we introduce a novel model reduction technique based on the Kron reduction of the weighted Laplacian matrix associated with the species-reaction graphs. Our systematic approach involves identifying nodes for deletion while preserving the bipartite structure, followed by constructing the Kron-reduced model. To demonstrate the effectiveness of our method, we apply it to a complex biochemical network, showing how model simplification facilitates analysis and interpretation of these systems.</p>
},
	keywords = {Biochemical Network, Biochemical Reaction Network, Chemical Reaction Network Dynamics, Complex Networks, Graph Theory, Reaction Kinetics, Reaction Mechanisms},
	doi = {10.1007/s11538-026-01651-1},
	url = {https://link.springer.com/article/10.1007/s11538-026-01651-1},
	author = {Gasparyan, Manvel and Bhalla, Upinder and Radulescu, Ovidiu and Rao, Shodhan}
}
@article {150949,
	title = {Mathematical basis and toolchain for hierarchical optimization of biochemical networks.},
	journal = {PLoS Comput Biol},
	volume = {20},
	year = {2024},
	month = {2024 Dec 02},
	pages = {e1012624},
	abstract = {<p>Biological signalling systems are complex, and efforts to build mechanistic models must confront a huge parameter space, indirect and sparse data, and frequently encounter multiscale and multiphysics phenomena. We present HOSS, a framework for Hierarchical Optimization of Systems Simulations, to address such problems. HOSS operates by breaking down extensive systems models into individual pathway blocks organized in a nested hierarchy. At the first level, dependencies are solely on signalling inputs, and subsequent levels rely only on the preceding ones. We demonstrate that each independent pathway in every level can be efficiently optimized. Once optimized, its parameters are held constant while the pathway serves as input for succeeding levels. We develop an algorithmic approach to identify the necessary nested hierarchies for the application of HOSS in any given biochemical network. Furthermore, we devise two parallelizable variants that generate numerous model instances using stochastic scrambling of parameters during initial and intermediate stages of optimization. Our results indicate that these variants produce superior models and offer an estimate of solution degeneracy. Additionally, we showcase the effectiveness of the optimization methods for both abstracted, event-based simulations and ODE-based models.</p>
},
	issn = {1553-7358},
	doi = {10.1371/journal.pcbi.1012624},
	author = {Viswan, Nisha Ann and Tribut, Alexandre and Gasparyan, Manvel and Radulescu, Ovidiu and Bhalla, Upinder S}
}
