A Constrained, Force-Directed Layout Algorithm for Biological Pathways

Abstract

Abstract. We present a new elegant algorithm for layout of biological signaling pathways. It uses a force-directed layout scheme, taking into account directional and regional constraints enforced by different molecular interaction types and subcellular locations in a cell. The algorithm has been successfully implemented as part of a pathway integration and analysis toolkit named Patika, and results with respect to computational complexity and quality of the layout have been found satisfactory.

Cerebral: Visualizing Multiple Experimental Conditions on a Graph with Biological Context

“…The straightforward approaches do not adequately support layers and groups [16]. Several attempts have been made to extend force-directed placement to accommodate grouping, for example Fruchterman and Reingold [17] use repulsive walls to contain nodes within an external boundary and Genc and Dogrusoz [18] use mobile internal walls to separate the graph into compartments. However, these methods suffer from fragility.…”

Statistical Challenges in Biological Networks

“…Force layout techniques [see Di Battista et al (1999, chap. 10) for a general exposition and for a constrained version suitable for biological pathways, see Genc and Dogrusoz (2004)] view the network as a physical system, whose edges are connected by springs, with attractive forces applied to adjacent vertices and repulsive forces to all pairs of vertices. These algorithms seek two-dimensional layouts in which adjacent vertices are placed close to each other exhibiting small edge lengths, while vertices remain well separated.…”

A Compound Graph Layout Algorithm for Biological Pathways

“…algorithm CompoundLayout() (1) call Initialization() (2) set phase to 1 (3) if layout type is incremental then (4) increment phase to 3 (5) while phase ≤ 3 do (6) set step to 1, error to 0 (7) while (step < maxIterCount(phase) and error > errorThreshold(phase)) or !allTreesGrown do (8) call ApplySpringForces() (9) call ApplyRepulsionForces() (10) if phase = 1 then (11) call ApplyGravitationForces() (12) call ApplyRelativityForces() (13) call CalcNodePositionsAndSizes() (14) call UpdateCompartmentBounds() (15) if phase = 2 and !allTreesGrown and step % growStep = 0 then (16) call GrowTreesOneLevel() (17) increment step by 1 (18) increment phase by 1 A quick analysis reveals that the running time of layout is O(k · n 2 ) where n is the total number of nodes in the compound pathway, and k is the number of iterations required to reach an energy minimal state.…”

“…A layout algorithm for signaling pathways was proposed and implemented within Patika earlier [9]. However neither this algorithm nor any of the previously proposed ones address advanced pathway representations including nested drawings, intergraph relations, and application-specific constraints such as compartmental constraints at the same time.…”