Other methods are necessary. The most fine-scaled approach to epistasis is the geometric theory of gene interaction [44]. Once graph G (N,E) is built and the edge costs are computed and associated with their corresponding edges, path queries in the graph can then be computed. To compute all the pathways, from the initial starting node (0000 in our trials), a search expansion is performed by adding each connected node as a child to the current node in a search tree representation. Since backward edges are possible, a mechanism to detect cycles is included by making sure that expanded nodes do not appear twice in a pathway. When a cycle is detected, the last node of the cycle is not expanded. The overall expansion continues until all the search tree branches reach the target node 1111. The final search tree will represent all possible pathways. In addition to the search tree, we use a priority queue Q that maintains ranked all the current leaves of the search tree to be expanded. We use a Dijkstra-like cost-to-come sorting function in Q, which represents the accumulated costs of the pathways since the source node. The priority queue ranks all ASP2215 web available leaf nodes to be expanded and the node with lowest cost is always expanded first. This guarantees that each node is reached in the order of appearance in the shortest path from the source node to it. This guarantees that the shortest cycles are always found first. Since cycle determination is important in our research, all identified cycles are stored and saved for later analysis. Although our experiments involved searches with different graphs (single or multiple drugs), searches with either forward orbackward edges and searches with different starting nodes (1111 for backwards pathways), the described search method was the same and handled well all situations. The used notation in our figures shows backward edges in red and forward edges in green.Degree of AdditivityThe degree of additivity, roughly how close a landscape is to being a completely additive landscape, can be measured in different ways. We used the qualitative measure of additivity which ranges from 0 to 1 for fitness landscapes. For a formal definition: The set Bp consist of all double mutants such that both corresponding single mutations are beneficial. The set B(Bp consists of all double mutants in Bp which are more fit than at least one of the corresponding single mutants. DBD . The 18325633 qualitative measure of additivity is the ratio DBp D DBD 1 for an additive landscapes. For random fitness DBp D landscapes, the measure is expected to be close to zero in this setting. Indeed, using standard arguments in the Orr-Gillespie approach, the wild-type has very high fitness also in the new environment, in comparison with a randomly GSK2140944 generated genotype. By definition, fitness is uncorrelated for a random fitness landscape, so that double mutants combining beneficial mutations are expected to be no more fit than randomly generated genotypes. It follows that the qualitative measure is close to zero, and a more precise estimate is that it should be less than 3 for random landscapes in this context. The derivation of this result will be published elsewhere. The conclusion depends on an analysis of TEM data from the record of clinically found mutants. For the 15 TEM-85 landscapes, the qualitative measure applies for 9 out of the 15 landscapes. The result is 0, 0, 0, 1/3, 5/6, 1, 1, 1, 1. The mean value is 0.57. This result deviates consi.Other methods are necessary. The most fine-scaled approach to epistasis is the geometric theory of gene interaction [44]. Once graph G (N,E) is built and the edge costs are computed and associated with their corresponding edges, path queries in the graph can then be computed. To compute all the pathways, from the initial starting node (0000 in our trials), a search expansion is performed by adding each connected node as a child to the current node in a search tree representation. Since backward edges are possible, a mechanism to detect cycles is included by making sure that expanded nodes do not appear twice in a pathway. When a cycle is detected, the last node of the cycle is not expanded. The overall expansion continues until all the search tree branches reach the target node 1111. The final search tree will represent all possible pathways. In addition to the search tree, we use a priority queue Q that maintains ranked all the current leaves of the search tree to be expanded. We use a Dijkstra-like cost-to-come sorting function in Q, which represents the accumulated costs of the pathways since the source node. The priority queue ranks all available leaf nodes to be expanded and the node with lowest cost is always expanded first. This guarantees that each node is reached in the order of appearance in the shortest path from the source node to it. This guarantees that the shortest cycles are always found first. Since cycle determination is important in our research, all identified cycles are stored and saved for later analysis. Although our experiments involved searches with different graphs (single or multiple drugs), searches with either forward orbackward edges and searches with different starting nodes (1111 for backwards pathways), the described search method was the same and handled well all situations. The used notation in our figures shows backward edges in red and forward edges in green.Degree of AdditivityThe degree of additivity, roughly how close a landscape is to being a completely additive landscape, can be measured in different ways. We used the qualitative measure of additivity which ranges from 0 to 1 for fitness landscapes. For a formal definition: The set Bp consist of all double mutants such that both corresponding single mutations are beneficial. The set B(Bp consists of all double mutants in Bp which are more fit than at least one of the corresponding single mutants. DBD . The 18325633 qualitative measure of additivity is the ratio DBp D DBD 1 for an additive landscapes. For random fitness DBp D landscapes, the measure is expected to be close to zero in this setting. Indeed, using standard arguments in the Orr-Gillespie approach, the wild-type has very high fitness also in the new environment, in comparison with a randomly generated genotype. By definition, fitness is uncorrelated for a random fitness landscape, so that double mutants combining beneficial mutations are expected to be no more fit than randomly generated genotypes. It follows that the qualitative measure is close to zero, and a more precise estimate is that it should be less than 3 for random landscapes in this context. The derivation of this result will be published elsewhere. The conclusion depends on an analysis of TEM data from the record of clinically found mutants. For the 15 TEM-85 landscapes, the qualitative measure applies for 9 out of the 15 landscapes. The result is 0, 0, 0, 1/3, 5/6, 1, 1, 1, 1. The mean value is 0.57. This result deviates consi.