Cis-regulatory module detection using constraint programming

We propose a method for finding CRMs in a set of co-regulated genes. Each CRM consists of a set of binding sites of transcription factors. We wish to find CRMs involving the same transcription factors in multiple sequences. Finding such a combination of transcription factors is inherently a combinatorial problem. We solve this problem by combining the principles of itemset mining and constraint programming. The constraints involve the putative binding sites of transcription factors, the number of sequences in which they co-occur and the proximity of the binding sites. Genomic background sequences are used to assess the significance of the modules. We experimentally validate our approach and compare it with state-of-the-art techniques

Algorithms for Approximate Subtropical Matrix Factorization

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for finding patterns from the data. Rather than using the standard algebra -- and the summation of the rank-1 components to build the approximation of the original matrix -- we use the subtropical algebra, which is an algebra over the nonnegative real values with the summation replaced by the maximum operator. Subtropical matrix factorizations allow "winner-takes-it-all" interpretations of the rank-1 components, revealing different structure than the normal (nonnegative) factorizations. We study the complexity and sparsity of the factorizations, and present a framework for finding low-rank subtropical factorizations. We present two specific algorithms, called Capricorn and Cancer, that are part of our framework. They can be used with data that has been corrupted with different types of noise, and with different error metrics, including the sum-of-absolute differences, Frobenius norm, and Jensen--Shannon divergence. Our experiments show that the algorithms perform well on data that has subtropical structure, and that they can find factorizations that are both sparse and easy to interpret.Comment: 40 pages, 9 figures. For the associated source code, see http://people.mpi-inf.mpg.de/~pmiettin/tropical

Digital clocks: simple Boolean models can quantitatively describe circadian systems

Copyright © 2012 The Royal Society This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day-night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate that the ability of logic models to provide a computationally efficient representation of system behaviour could greatly facilitate the reverse-engineering of large-scale biochemical networks

Fuzzy multi-criteria decision making for carbon dioxide geological storage in Turkey

The problem of choosing the best location for CO2 storage is a crucial and challenging multi-criteria decision problem for some companies. This study compares the performance of three fuzzy-based multi-criteria decision making (MCDM) methods, including Fuzzy TOPSIS, Fuzzy ELECTRE I and Fuzzy VIKOR for solving the carbon dioxide geological storage location selection problem in Turkey. The results show that MCDM approach is a useful tool for decision makers in the selection of potential sites for CO2 geological storage