Computing knot polynomials for long chains can be a very time consuming process. The same applies to the topological analysis of all chromosomes embedded in a cell. Below, we list typical computational costs of determining entanglement types in single chromosomes or full cells as well as the costs for constructing the chromosome matrix fingerprint. When the relaxation method is used, times are naturally longer.
The time needed to identify all knots in terms of their type and chirality for all chromosomes of cell 2 [1] is 66 minutes.
The average time needed to calculate a knotting fingerprint (matrix encoding the knotting types of all subchains in a given chromosome) is 2,5 minutes (138 seconds) based on 20 chromosomes from cell 2 under the following conditions: 1 closure - out of the center of mass (for the random closure method, 10 tries, it would be around 10 times slower).
The average time needed to detect links between two chromosomes based on 1520 pairs [2] equals 0.53s.
The average time needed to detect links for each pair of chromosomes inside a cell based on 8 cells [2] is equal to 100.25s (cell 1: 114.5s, c2: 64s, c3: 87s, c4: 115s, c5: 72.5s, c6: 218.5s. c7: 64.5s, c8: 66.5s).
The average time needed to calculate whGLN and max|GLN| between two chromosomes based on 1520 pairs [2] is equal to 1.01s.
The average time needed to calculate whGLN and max|GLN| for each pair of chromosomes embedded in the cell based on 8 cells [2] is 191.81s (cell 1: 223.5s, c2: 187.5s, c3: 189.5s, c4: 187.5s, c5: 186.5s, c6: 187s. c7: 187.5s, c8: 185.5s).
The average time needed to perform a relaxation using a molecular dynamics simulation and to subsequently detemine knotting fingerprints for a single chromosome (eg. chromosome x from cell 2 [1]) is about 5 minutes.
