MOTIVATION: Interpretation of high-throughput gene expression profiling requires a knowledge of the design principles underlying the networks that sustain cellular machinery. Recently a novel approach based on the study of network topologies has been proposed. This methodology has proven to be useful for the analysis of a variety of biological systems, including metabolic networks, networks of protein-protein interactions, and gene networks that can be derived from gene expression data. In the present paper, we focus on several important issues related to the topology of gene expression networks that have not yet been fully studied. RESULTS: The networks derived from gene expression profiles for both time series experiments in yeast and perturbation experiments in cell lines are studied. We demonstrate that independent from the experimental organism (yeast versus cell lines) and the type of experiment (time courses versus perturbations) the extracted networks have similar topological characteristics suggesting together with the results of other common principles of the structural organization of biological networks. A novel computational model of network growth that reproduces the basic design principles of the observed networks is presented. Advantage of the model is that it provides a general mechanism to generate networks with different types of topology by a variation of a few parameters. We investigate the robustness of the network structure to random damages and to deliberate removal of the most important parts of the system and show a surprising tolerance of gene expression networks to both kinds of disturbance.

MOTIVATION: Cluster analysis of genome-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and samples. In the present paper, we focus on several important issues related to clustering algorithms that have not yet been fully studied. RESULTS: We describe a simple and robust algorithm for the clustering of temporal gene expression profiles that is based on the simulated annealing procedure. In general, this algorithm guarantees to eventually find the globally optimal distribution of genes over clusters. We introduce an iterative scheme that serves to evaluate quantitatively the optimal number of clusters for each specific data set. The scheme is based on standard approaches used in regular statistical tests. The basic idea is to organize the search of the optimal number of clusters simultaneously with the optimization of the distribution of genes over clusters. The efficiency of the proposed algorithm has been evaluated by means of a reverse engineering experiment, that is, a situation in which the correct distribution of genes over clusters is known a priori. The employment of this statistically rigorous test has shown that our algorithm places greater than 90% genes into correct clusters. Finally, the algorithm has been tested on real gene expression data (expression changes during yeast cell cycle) for which the fundamental patterns of gene expression and the assignment of genes to clusters are well understood from numerous previous studies.

MOTIVATION: Local multiple sequence alignment is a basic tool for extracting functionally important regions shared by a family of protein sequences. We present an effectively polynomial-time algorithm for rigorously solving the local multiple alignment problem. RESULTS: The algorithm is based on the dead-end elimination procedure that makes it possible to avoid an exhaustive search. In the framework of the sum-of-pairs scoring system, certain rejection criteria are derived in order to eliminate those sequence segments and segment pairs that can be mathematically shown to be inconsistent (dead-ending) with the globally optimal alignment. Iterative application of the elimination criteria results in a rapid reduction of combinatorial possibilities without considering them explicitly. In the vast majority of cases, the procedure converges to a unique globally optimal solution. In contrast to the exhaustive search, whose computational complexity is combinatorial, the algorithm is computationally feasible because the number of operations required to eliminate the dead-ending segments and segment pairs grows quadratically and cubically, respectively, with the total number of sequence elements. The method is illustrated on a set of protein families for which the globally optimal alignments are well recognized. AVAILABILITY: The source code of the program implementing the algorithm is available upon request from the authors. CONTACT: [email protected].

The neuronal population vector is a measure of the combined directional tendency of the ensemble of directionally tuned cells in the motor cortex. It has been found experimentally that a trajectory of limb movement can be predicted by adding together population vectors, tip-to-tail, calculated for successive instants of time to construct a neural trajectory. In the present paper we consider a model of the dynamic evolution of the population vector. The simulated annealing algorithm was used to adjust the connection strengths of a feedback neural network so that it would generate a given trajectory by a sequence of population vectors. This was repeated for different trajectories. Resulting sets of connection strengths reveal a common feature regardless of the type of trajectories generated by the network: namely, the mean connection strength was negatively correlated with the angle between the preferred directions of neuronal pair involved in the connection. The results are discussed in the light of recent experimental findings concerning neuronal connectivity within the motor cortex.