Controllability Analysis of Intercellular Protein-Protein Interaction Networks.

Understanding how control is organized across interacting cells is an important challenge in computational and systems biology, especially in diseases involving disrupted communication among different cell types. Although network controllability analysis has been widely applied to intracellular biological networks, much less attention has been given to cell-cell interaction networks. A major difficulty is that the underlying protein-protein interaction networks are often undirected, which limits the direct use of maximum-matching-based structural controllability methods. Here, we introduce Minimum Driver Orientation (MDO), a framework that assigns directions to undirected protein-protein interactions so that the number of driver nodes is minimized. We further show theoretically that connected graphs contain no critical nodes under MDO and that quasi-critical nodes constitute a distinct structural control category. We then applied MDO to oligodendrocyte-macrophage (OM) and oligodendrocyte-T-cell (OT) interaction networks relevant to multiple sclerosis (MS). MDO suggested distinct control-node localization patterns in the 2 systems: the OM network showed a more bridge- and macrophage-associated pattern, whereas the OT network showed a more cell-type-specific pattern involving oligodendrocyte and T-cell proteins. Comparisons with random, degree-based, and ligand-receptor-informed orientation schemes showed that the smaller driver-node fractions obtained by MDO were specific to the MDO optimization and were not reproduced by simple orientation rules. Functional annotation and MS-associated protein overlap analyses were interpreted as exploratory biological assessments rather than direct validation of disease mechanisms. Overall, MDO provides a useful computational framework for analyzing maximum-matching-based controllability in undirected intercellular interaction networks.