RESUMEN

We discuss the dynamical robustness of biological networks represented by directed graphs, such as neural networks and gene regulatory networks. The theoretical results indicate that networks with low indegree variance and high outdegree variance are dynamically robust. We propose a machine learning method that gives equilibrium states to input-output networks with a recurrent hidden layer. We verify the theory by using the learned networks having various indegree and outdegree distributions. We also show that the basin of attraction of an equilibrium state is narrow when networks are dynamically robust.

Asunto(s)

RESUMEN

Although outdegree distributions of gene regulatory networks have scale-free characteristics similar to other biological networks, indegree distributions have single-scale characteristics with significantly lower variance than that of outdegree distributions. In this study, we mathematically explain that such asymmetric characteristics arise from dynamical robustness, which is the property of maintaining an equilibrium state of gene expressions against inevitable perturbations to the networks, such as gene dysfunction and mutation of promoters. We reveal that the expression of a single gene is robust to a perturbation for a large number of inputs and a small number of outputs. Applying these results to the networks, we also show that an equilibrium state of the networks is robust if the variance of the indegree distribution is low (i.e., single-scale characteristics) and that of the outdegree distribution is high (i.e., scale-free characteristics). These asymmetric characteristics are conserved across a wide range of species, from bacteria to humans.

Asunto(s)

RESUMEN

To estimate gene regulatory networks, it is important that we know the number of connections, or sparseness of the networks. It can be expected that the robustness to perturbations is one of the factors determining the sparseness. We reconstruct a semi-quantitative model of gene networks from gene expression data in embryonic development and detect the optimal sparseness against perturbations. The dense networks are robust to connection-removal perturbation, whereas the sparse networks are robust to misexpression perturbation. We show that there is an optimal sparseness that serves as a trade-off between these perturbations, in agreement with the optimal result of validation for testing data. These results suggest that the robustness to the two types of perturbations determines the sparseness of gene networks.

Asunto(s)

RESUMEN

The delayed feedback control (DFC) is applied to stabilize unstable quasi-periodic orbits (QPOs) in discrete-time systems. The feedback input is given by the difference between the current state and a time-delayed state in the DFC. However, there is an inevitable time-delay mismatch in QPOs. To evaluate the influence of the time-delay mismatch on the DFC, we propose a phase reduction method for QPOs and construct a phase response curve (PRC) from unstable QPOs directly. Using the PRC, we estimate the rotation number of QPO stabilized by the DFC. We show that the orbit of the DFC is consistent with the unstable QPO perturbed by a small state difference resulting from the time-delay mismatch, implying that the DFC can certainly stabilize the unstable QPO.

RESUMEN

We propose a tetrahedral Gray code that facilitates visualization of genome information on the surfaces of a tetrahedron, where the relative abundance of each [Formula: see text]-mer in the genomic sequence is represented by a color of the corresponding cell of a triangular lattice. For biological significance, the code is designed such that the [Formula: see text]-mers corresponding to any adjacent pair of cells differ from each other by only one nucleotide. We present a simple procedure to draw such a pattern on the development surfaces of a tetrahedron. The thus constructed tetrahedral Gray code can demonstrate evolutionary conservation and variation of the genome information of many organisms at a glance. We also apply the tetrahedral Gray code to the honey bee (Apis mellifera) genome to analyze its methylation structure. The results indicate that the honey bee genome exhibits CpG overrepresentation in spite of its methylation ability and that two conserved motifs, CTCGAG and CGCGCG, in the unmethylated regions are responsible for the overrepresentation of CpG.

Asunto(s)

RESUMEN

Several cis-acting elements play critical roles in maintaining circadian expression of clock and clock-controlled genes. Using in silico analysis, we identified 10 sequence motifs that are correlated with the circadian phases of gene expression in the cartilage. One of these motifs, an E-box-like clock-related element (EL-box; GGCACGAGGC), can mediate BMAL1/CLOCK-induced transcription, which is typically regulated through an E-box or E'-box. Expression of EL-box-containing genes, including Ank, Dbp, and Nr1d1 (Rev-erbα), was induced by BMAL1/CLOCK or BMAL1/NPAS2. Compared with the E-box, the EL-box elements had distinct responsiveness to DEC1, DEC2, and HES1: suppressive actions of DEC1 and DEC2 on the EL-box were less potent than those on the E-box. HES1, which is known to bind to the N-box (CACNAG), suppressed enhancer activity of the EL-box, but not the E-box. In the Dbp promoter, an EL-box worked cooperatively with a noncanonical (NC) E-box to mediate BMAL1/CLOCK actions. These findings suggest that in addition to known clock elements, the EL-box element may contribute to circadian regulation of clock and clock-controlled genes.

Asunto(s)

RESUMEN

MOTIVATION: How to find motifs from genome-scale functional sequences, such as all the promoters in a genome, is a challenging problem. Word-based methods count the occurrences of oligomers to detect excessively represented ones. This approach is known to be fast and accurate compared with other methods. However, two problems have hampered the application of such methods to large-scale data. One is the computational cost necessary for clustering similar oligomers, and the other is the bias in the frequency of fixed-length oligomers, which complicates the detection of significant words. RESULTS: We introduce a method that uses a DNA Gray code and equiprobable oligomers, which solve the clustering problem and the oligomer bias, respectively. Our method can analyze 18 000 sequences of ~1 kbp long in 30 s. We also show that the accuracy of our method is superior to that of a leading method, especially for large-scale data and small fractions of motif-containing sequences. AVAILABILITY: The online and stand-alone versions of the application, named Hegma, are available at our website: http://www.genome.ist.i.kyoto-u.ac.jp/~ichinose/hegma/ CONTACT: ichinose@i.kyoto-u.ac.jp; o.gotoh@i.kyoto-u.ac.jp

Asunto(s)

RESUMEN

This paper is an attempt to understand how knowledge and events are represented and processed in the brain. An important point is the question of what carries information in the brain - the mean firing rate or the timing of spikes? The idea we want to pursue is that, contrary to the traditional view, the brain might use higher order statistics, which means in essence that timing of spikes plays a critical role in encoding, representing, and processing knowledge and events in the brain.A recently revealed salient nature of cortical pyramidal cells, i.e., the high variability of inter-spike intervals suggests that a cortical neuron may function effectively as a coincidence detector. At the same time, non-classical experimental phenomena of task-related, short time-scaled dynamical modulations of temporal correlations between neurons suggest a non-classical view on the dynamics working in the brain. In response to contexts or external events, a group of neurons, a dynamical cell assembly, spontaneously organizes, linked temporarily by coincident timing of incident spikes, showing correlated firing with each other. This is an emergent property of neuronal populations in the cortex.We make a theoretical exploration on issues as (1) the description of such emergent dynamics of dynamical cell assemblies based on the working hypothesis that a cortica neuron functions effectively as a coincidence detector, and (2) the principle of spatio-temporal coding based on the hypothetical emergent dynamics. Note that the conventional rate coding hypothesis does not give satisfactory answers to fundamental questions on the representation and processing of knowledge or events in the brain, e.g., the questions of cross-modular integration of information or the binding problem, and representation of hierarchical knowledge etc.The first goal is to give a non-encyclopedic review on (1) the temporal structure of spike sequences, focusing on the question of the basic code in the brain; (2) the paradigms on representation of knowledge and events proposed from a theoretical or experimental basis. The classical paradigms of Hebb and Barlow with their experimental and theoretical critiques, and more recently proposed experiment-based paradigms are reviewed. Also a review is given on (3) the experimentally observed spatio-temporal structure of spike dynamics.The second goal is to give a description of the dynamical cell assembly - the central concept in this paper. Aside from the question of physiological basis, we make a theoretical study, under a working hypothesis that a cortical neuron functions effectively as a coincidence detector, on the emergent dynamics of cell assemblies, and also examine how the observed experimental data could be explained within this theoretical setting.We also try to give the principle of spatio-temporal coding based on the dynamical cell assembly framework. A key concept is the internal mechanism of "dialogue" among neuronal pools in the brain. This provides a dynamical foundation of bi-directional interactions for the linkage of distant modules to create integrated information. We present a simple model in order to illustrate the working principle of coincidence detector systems. Relations with other temporal coding paradigms are also discussed. Copyright 1996 Elsevier Science Ltd.