23 research outputs found
Computing paths and cycles in biological interaction graphs
<p>Abstract</p> <p>Background</p> <p>Interaction graphs (signed directed graphs) provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops) and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments.</p> <p>Results</p> <p>We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible) this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops.</p> <p>Conclusion</p> <p>The calculation of shortest positive/negative paths and cycles in interaction graphs is an important method for network analysis in Systems Biology. This contribution draws the attention of the community to this important computational problem and provides a number of new algorithms, partially specifically tailored for biological interaction graphs. All algorithms have been implemented in the <it>CellNetAnalyzer </it>framework which can be downloaded for academic use at <url>http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html</url>.</p
Optimality-preserving Reduction of Chemical Reaction Networks
Across many disciplines, chemical reaction networks (CRNs) are an established
population model defined as a system of coupled nonlinear ordinary differential
equations. In many applications, for example, in systems biology and
epidemiology, CRN parameters such as the kinetic reaction rates can be used as
control inputs to steer the system toward a given target. Unfortunately, the
resulting optimal control problem is nonlinear, therefore, computationally very
challenging. We address this issue by introducing an optimality-preserving
reduction algorithm for CRNs. The algorithm partitions the original state
variables into a reduced set of macro-variables for which one can define a
reduced optimal control problem from which one can exactly recover the solution
of the original control problem. Notably, the reduction algorithm runs with
polynomial time complexity in the size of the CRN. We use this result to reduce
reachability and control problems of large-scale protein-interaction networks
and vaccination models with hundreds of thousands of state variables
Biological Networks
Networks of coordinated interactions among biological entities govern a myriad of biological functions that span a wide range of both length and time scalesâfrom ecosystems to individual cells and from years to milliseconds. For these networks, the concept âthe whole is greater than the sum of its partsâ applies as a norm rather than an exception. Meanwhile, continued advances in molecular biology and high-throughput technology have enabled a broad and systematic interrogation of whole-cell networks, allowing the investigation of biological processes and functions at unprecedented breadth and resolutionâeven down to the single-cell level. The explosion of biological data, especially molecular-level intracellular data, necessitates new paradigms for unraveling the complexity of biological networks and for understanding how biological functions emerge from such networks. These paradigms introduce new challenges related to the analysis of networks in which quantitative approaches such as machine learning and mathematical modeling play an indispensable role. The Special Issue on âBiological Networksâ showcases advances in the development and application of in silico network modeling and analysis of biological systems
Recent advances in petri nets and concurrency
CEUR Workshop Proceeding