Mónica Suárez Korsnes ^1* Håkon André Ramberg ² Kristin Austlid Taskén ³ Reinert Korsnes ⁴

• ¹ Department of Clinical and Molecular Medicine, Norwegian University of Science and Technology, Trondheim, Norway
• ² Oslo University Hospital, Oslo, Nordland, Norway
• ³ University of Oslo, Oslo, Oslo, Norway
• ⁴ Korsnes Biocomputing (KoBio), Trondheim, Sør-Trøndelag, Norway

Cancer cell clustering is a critical factor in metastasis, with cells often believed to migrate in groups as they establish themselves in new environments. This study presents preliminary findings from an in vitro experiment, suggesting that co-culturing cells provides an effective method for observing this phenomenon, even though the cells are grown as monolayers. We introduce a novel single-cell tracking approach based on graph theory to identify clusters in PC3 cells cultivated in both monoculture and co-culture with PC12 cells, using 66-hour time-lapse recordings. The initial step consists of defining 'linked' pairs of PC3 cells, laying the foundation for the application of graph theory. We propose two alternative definitions for cell pairings. The first method, Method 1, defines cells as 'linked' at a given time t if they are close together within a defined time period before and after t. A second potential alternative method, Method 2, pairs cells if there is an overlap between the convex hulls of their respective tracks during this time period. Pairing cells enables the application of graph theory for subsequent analysis. This framework represents a cell as a vertex (node) and a relation between two cells as an edge. An interconnected set of high-degree nodes (nodes with many connections or edges) forms a subgraph, or backbone, that defines a patch (cluster) of cells. All nodes connected to this backbone are part of the subgraph. The backbone of high-degree nodes functions as a partition (or cut) of the initial graph. Two consecutive clusters in the video are considered to share the same identity if the following cluster contains at least p = 75 % of the cells from the preceding cluster, and the mean positions of their cells are within △r = 75 µm. PC3 cells grown in co-culture appear to form persistent clusters exceeding 10 cells after 40 to 50 h incubation following seeding.In contrast, PC3 cells cultured alone (mono-culture) did not exhibit this behaviour. This approach is experimental and require further validation with a broader dataset.