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PubMedDate not supplied

Coordinated motor activity in simulated spinal networks emerges from simple biologically plausible rules of connectivity.

The spinal motor circuits of the Xenopus embryo have been simulated in a 400-neuron network. To explore the consequences of differing patterns of synaptic connectivity within the network for the generation of the motor rhythm, a system of biologically plausible rules was devised to control synapse formation by three parameters. Each neuron had an intrinsic probability of synapse formation (P(soma), specified by a space constant lambda) that was a monotonically decreasing function of its soma location in the rostro-caudal axis of the simulated network. The neurons had rostral and caudal going axons of specified length (L(axon)) associated with a probability of synapse formation (P(axon)). The final probability of synapse formation was the product of P(soma) and P(axon). Realistic coordinated activity only occurred when L(axon) and the probabilities of interconnection were sufficiently high. Increasing the values of the three network parameters reduced the burst duration, cycle period, and rostro-caudal delay and increased the reliability with which the network functioned as measured by the coefficient of variance of these parameters. Whereas both L(axon) and P(axon) had powerful and consistent effects on network output, the effects of lambda on burst duration and rostro-caudal delay were more variable and depended on the values of the other two parameters. This network model can reproduce the rostro-caudal coordination of swimming without using coupled oscillator theory. The changes in network connectivity and resulting changes in activity explored by the model mimic the development of the motor pattern for swimming in the real embryo.

Animals↗
PubMed2003

Organization of neural networks in the neocortex.

Implanted semimicroelectrodes were used in conscious cats to record spike discharges from groups of close-lying neurons, i.e., multineuron activity, in the deep layers of the frontal and motor areas of the cortex at different levels of food motivation. Spike activity was extracted from 4-7 neurons and interneuronal interactions were studied by cross-correlation analysis between neighboring neurons in each zone (local networks) and between neurons in two zones (distributed networks) with analysis epochs of 0-100 msec. The results showed that neurons in local networks can be divided into two subgroups: neurons with high-amplitude spikes and a predominance of output (divergent) connections and neurons with low-amplitude spikes and a predominance of input (convergent) connections. Local networks are based on powerful monosynaptic connections (with delays of up to 2 msec) between large and small neurons. Most connections in distributed networks were between small neurons in local networks of the frontal cortex and large neurons in local networks in the motor cortex. Food deprivation for 24 h mainly affected late (with delays of 2-100 msec) cross-correlation interneuronal relationships in both local and distributed networks.

Animals↗
PubMed1999

Size and form in efficient transportation networks.

Many biological processes, from cellular metabolism to population dynamics, are characterized by allometric scaling (power-law) relationships between size and rate. An outstanding question is whether typical allometric scaling relationships--the power-law dependence of a biological rate on body mass--can be understood by considering the general features of branching networks serving a particular volume. Distributed networks in nature stem from the need for effective connectivity, and occur both in biological systems such as cardiovascular and respiratory networks and plant vascular and root systems, and in inanimate systems such as the drainage network of river basins. Here we derive a general relationship between size and flow rates in arbitrary networks with local connectivity. Our theory accounts in a general way for the quarter-power allometric scaling of living organisms, recently derived under specific assumptions for particular network geometries. It also predicts scaling relations applicable to all efficient transportation networks, which we verify from observational data on the river drainage basins. Allometric scaling is therefore shown to originate from the general features of networks irrespective of dynamical or geometric assumptions.

Biological Transport↗
PubMed2004

Genomic analysis of regulatory network dynamics reveals large topological changes.

Network analysis has been applied widely, providing a unifying language to describe disparate systems ranging from social interactions to power grids. It has recently been used in molecular biology, but so far the resulting networks have only been analysed statically. Here we present the dynamics of a biological network on a genomic scale, by integrating transcriptional regulatory information and gene-expression data for multiple conditions in Saccharomyces cerevisiae. We develop an approach for the statistical analysis of network dynamics, called SANDY, combining well-known global topological measures, local motifs and newly derived statistics. We uncover large changes in underlying network architecture that are unexpected given current viewpoints and random simulations. In response to diverse stimuli, transcription factors alter their interactions to varying degrees, thereby rewiring the network. A few transcription factors serve as permanent hubs, but most act transiently only during certain conditions. By studying sub-network structures, we show that environmental responses facilitate fast signal propagation (for example, with short regulatory cascades), whereas the cell cycle and sporulation direct temporal progression through multiple stages (for example, with highly inter-connected transcription factors). Indeed, to drive the latter processes forward, phase-specific transcription factors inter-regulate serially, and ubiquitously active transcription factors layer above them in a two-tiered hierarchy. We anticipate that many of the concepts presented here--particularly the large-scale topological changes and hub transience--will apply to other biological networks, including complex sub-systems in higher eukaryotes.

Algorithms↗
PubMed2007

Reversible stress softening of actin networks.

The mechanical properties of cells play an essential role in numerous physiological processes. Organized networks of semiflexible actin filaments determine cell stiffness and transmit force during mechanotransduction, cytokinesis, cell motility and other cellular shape changes. Although numerous actin-binding proteins have been identified that organize networks, the mechanical properties of actin networks with physiological architectures and concentrations have been difficult to measure quantitatively. Studies of mechanical properties in vitro have found that crosslinked networks of actin filaments formed in solution exhibit stress stiffening arising from the entropic elasticity of individual filaments or crosslinkers resisting extension. Here we report reversible stress-softening behaviour in actin networks reconstituted in vitro that suggests a critical role for filaments resisting compression. Using a modified atomic force microscope to probe dendritic actin networks (like those formed in the lamellipodia of motile cells), we observe stress stiffening followed by a regime of reversible stress softening at higher loads. This softening behaviour can be explained by elastic buckling of individual filaments under compression that avoids catastrophic fracture of the network. The observation of both stress stiffening and softening suggests a complex interplay between entropic and enthalpic elasticity in determining the mechanical properties of actin networks.

Actins↗
PubMed2005

Reverse engineering of regulatory networks in human B cells.

Cellular phenotypes are determined by the differential activity of networks linking coregulated genes. Available methods for the reverse engineering of such networks from genome-wide expression profiles have been successful only in the analysis of lower eukaryotes with simple genomes. Using a new method called ARACNe (algorithm for the reconstruction of accurate cellular networks), we report the reconstruction of regulatory networks from expression profiles of human B cells. The results are suggestive a hierarchical, scale-free network, where a few highly interconnected genes (hubs) account for most of the interactions. Validation of the network against available data led to the identification of MYC as a major hub, which controls a network comprising known target genes as well as new ones, which were biochemically validated. The newly identified MYC targets include some major hubs. This approach can be generally useful for the analysis of normal and pathologic networks in mammalian cells.

Algorithms↗
PubMed2005

Adaptive evolution of bacterial metabolic networks by horizontal gene transfer.

Numerous studies have considered the emergence of metabolic pathways, but the modes of recent evolution of metabolic networks are poorly understood. Here, we integrate comparative genomics with flux balance analysis to examine (i) the contribution of different genetic mechanisms to network growth in bacteria, (ii) the selective forces driving network evolution and (iii) the integration of new nodes into the network. Most changes to the metabolic network of Escherichia coli in the past 100 million years are due to horizontal gene transfer, with little contribution from gene duplicates. Networks grow by acquiring genes involved in the transport and catalysis of external nutrients, driven by adaptations to changing environments. Accordingly, horizontally transferred genes are integrated at the periphery of the network, whereas central parts remain evolutionarily stable. Genes encoding physiologically coupled reactions are often transferred together, frequently in operons. Thus, bacterial metabolic networks evolve by direct uptake of peripheral reactions in response to changed environments.

Adaptation, Physiological↗
PubMed2026

Targeting cortico-striatal-amygdalar networks via theta-band frontoparietal synchronization in opioid use disorder: a randomized tACS-fMRI Trial.

Theta-band oscillation is integral to fronto-parietal connectivity in the executive control network and its top-down regulation on subcortical areas. External frontoparietal synchronization using theta-frequency transcranial alternating current (tACS) is a technology to potentially engage this network. In this pre-registered, triple-blind, sham-controlled trial (NCT03907644), we tested this intervention targeting the right frontoparietal network in people with opioid use disorder (OUD) to measure network engagement and behavioral outcomes. Sixty male participants with OUD were randomized to receive 20 min of active or sham 6 Hz tACS (HD electrodes over F4 and P4). Structural, resting-state, task-based fMRI drug cue reactivity, and repeated cue-induced craving assessments were collected immediately before and after stimulation. Pre-registered outcome measures were analyzed using time × group interaction models to examine (1) modulation of drug cue-related brain activity, (2) changes in craving, (3) alterations in functional connectivity, and (4) relationship between electric field, neural responses, and craving behavior. (1) A significant Time × Group interaction revealed decreased post-stimulation opioid cue-related activity in the active group relative to sham, involving key nodes in reward processing (ventral striatum, amygdala and ventral tegmental area) (FWE corrected α = 0.05) (2) subjective craving did not differ significantly between groups (3) Group by time generalized psychophysiological interaction analyses showed increased right frontoparietal network engagement (β = 2.63, p= 0.0308) following stimulation, and increased top-down inhibitory regulation of frontoparietal network on right ventral striatum (β = 1.99, p= 0.037) and left medial amygdala (β = 1.97, p= 0.039) (4) Electric field strength in the right frontal/parietal node predicted frontoparietal network engagement in the active group (r = 0.43, p= 0.02). Together, these findings demonstrate that theta-band frontoparietal tACS can modulate activity and task-dependent coupling within cortical-subcortical circuits in OUD, supporting network-targeted neuromodulation as a potential intervention for addiction.

Humans↗
PubMed2004

The yeast coexpression network has a small-world, scale-free architecture and can be explained by a simple model.

We investigated the gene coexpression network in Saccharomyces cerevisiae, in which genes are linked when they are coregulated. This network is shown to have a scale-free, small-world architecture. Such architecture is typical of biological networks in which the nodes are connected when they are involved in the same biological process. Current models for the evolution of intracellular networks do not adequately reproduce the features that we observe in the network. We therefore derive a new model for its evolution based on the observation that there is a positive correlation between the sequence similarity of paralogues and their probability of coexpression or sharing of transcription factor binding sites (TFBSs). The simple, neutralist's model consists of (1) coduplication of genes with their TFBSs, (2) deletion and duplication of individual TFBSs and (3) gene loss. A network is constructed by connecting genes that share multiple TFBSs. Our model reproduces the scale-free, small-world architecture of the coregulation network and the homology relations between coregulated genes without the need for selection either at the level of the network structure or at the level of gene regulation.

Binding Sites↗
PubMed2002

Spontaneous network activity of cerebellar granule neurons: impairment by in vivo chronic cannabinoid administration.

Synchronized activity of neuronal networks has been proposed to be essential for cerebellar function. To examine the occurrence and organization of spontaneous neuronal activity in the cerebellum in vivo, we imaged mouse cerebellar slices loaded with the intracellular Ca2+ concentration indicator, fura-2. Recordings were then analysed statistically to identify correlated network activity. Ca2+ imaging revealed consistent spontaneous correlated network activity of granule cells (GC), which often occurred in clusters of coactivated GC. The number of spontaneously active GC, their activation frequency and correlation, were controlled by glutamate and GABA ionotropic receptors. These findings indicate that distinctive patterns of correlated activity between GC networks may be relevant for cerebellar circuit function. Cannabinoid antagonist-precipitated delta9-tetrahydrocannabinol (THC) withdrawal impaired motor coordination. Given that the cerebellum has been suggested recently to be a main substrate for cannabinoid withdrawal, we used imaging of spontaneous network activity to examine whether GC, which contain CB1 cannabinoid receptors, respond to chronic THC treatment and withdrawal. Acute administration of THC had no effect on patterns of spontaneous GC network activity. In contrast, chronic THC administration severely impaired GC activity and network coordination. Incubation of cerebellar slices, from chronically THC-treated mice, with the cannabinoid antagonist, SR141716A increased the number and network correlation of active GC. These data provide physiological evidence of the involvement of cerebellar circuits in the adaptive changes occurring during chronic THC exposure and withdrawal.

Animals↗
PubMedDate not supplied

Phenotypic and dynamical transitions in model genetic networks. I. Emergence of patterns and genotype-phenotype relationships.

Genotype-phenotype interactions during the evolution of form in multicellular organisms is a complex problem but one that can be aided by computational approaches. We present here a framework within which developmental patterns and their underlying genetic networks can be simulated. Gene networks were chosen to reflect realistic regulatory circuits, including positive and negative feedback control, and the exchange of a subset of gene products between cells, or within a syncytium. Some of these networks generate stable spatial patterns of a subset of their molecular constituents, and can be assigned to categories (e.g., "emergent" or "hierarchic") based on the topology of molecular circuitry. These categories roughly correspond to what has been discussed in the literature as "self-organizing" and "programmed" processes of development. The capability of such networks to form patterns of repeating stripes was studied in network ensembles in which parameters of gene-gene interaction were caused to vary in a manner analogous to genetic mutation. The evolution under mutational change of individual representative networks of each category was also simulated. We have found that patterns with few stripes (< or =3) are most likely to originate in the form of a hierarchic network, whereas those with greater numbers of stripes (> or =4) originate most readily as emergent networks. However, regardless of how many stripes it contains, once a pattern is established, there appears to be an evolutionary tendency for emergent mechanisms to be replaced by hierarchic mechanisms. These results have potential significance for the understanding of genotype-phenotype relationships in the evolution of metazoan form.

Biological Evolution↗
PubMed2006

Evolutionary changes of metabolic networks and their biosynthetic capacities.

The metabolic networks of different species show a large variety in their structural design. In this work, the evolution of functional properties of metabolism in relation with metabolic network structure is investigated. The metabolism of ancestral species is inferred from the metabolism of contemporary species using a Bayesian network model for metabolism evolution. Subsequently, these networks are analysed with the recently developed method of network expansion. This method allows for a structural analysis of metabolic networks as well as a quantification of network functions in terms of their synthesising capacities when they are provided with certain external resources. The evolutionary dynamics of one particular network function: the metabolic expansion of glucose is investigated.

Adaptation, Physiological↗
PubMed2005

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent.

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.

Journal Article↗
PubMed2004

Dynamical basis of intentions and expectations in a simple neuronal network.

Selection of behavioral responses to external stimuli is strongly influenced by internal states, such as intentions and expectations. These internal states are often attributed to higher-order brain functions. Yet here we show that even in the simple feeding network of Aplysia, external stimuli do not directly specify which motor output is expressed; instead, the motor output is specified by the state of the network at the moment of stimulation. The history-dependence of this network state manifests itself in the same way as do intentions and expectations in the behavior of higher animals. Remarkably, we find that activity-dependent plasticity of a synapse within the network itself, rather than some higher-order network, mediates one important aspect of the change in the network state. Through this mechanism, changes in the network state become an automatic consequence of the generation of behavior. Altogether, our findings suggest that intentions and expectations may emerge within behavior-generating networks themselves from the plasticity of the very processes that generate the behavior.

Animals↗
PubMed2004

Design of a directed molecular network.

An ability to rationally design complex networks from the bottom up can offer valuable quantitative model systems for use in gaining a deeper appreciation for the principles governing the self-organization and functional characteristics of complex systems. We report herein the de novo design, graph prediction, experimental analysis, and characterization of simple self-organized, nonlinear molecular networks. Our approach makes use of the sequence-dependent auto- and cross-catalytic functional characteristics of template-directed peptide fragment condensation reactions in neutral aqueous solutions. Starting with an array of 81 sequence similar 32-residue coiled-coil peptides, we estimated the relative stability difference between all plausible A(2)B-type coiled-coil ensembles and used this information to predict the auto- and cross-catalysis pathways and the resulting plausible network motif and connectivities. Similar to most complex systems, the generated graph displays clustered nodes with an overall hierarchical architecture. To test the validity of the design principles used, nine nodes composing a main segment of the graph were experimentally analyzed for their capacity in establishing the predicted network connectivity. The resulting self-organized chemical network is shown to display 25 directed edges in good agreement with the graph analysis estimations. Moreover, we show that by varying the system parameters (presence or absence of certain substrates or templates), its operating network motif can be altered, even to the extremes of turning pathways on or off. We suggest that this approach can be expanded for the construction of large-scale networks, offering a means to study and to understand better the emergent, collective behaviors of networks.

Amino Acid Sequence↗
PubMed2005

Conserved modular design of an oxygen sensory/signaling network with species-specific output.

Principles of modular design are evident in signaling networks that detect and integrate a given signal and, depending on the organism in which the network module is present, transduce this signal to affect different metabolic or developmental pathways. Here we report a global transcriptional analysis of an oxygen sensory/signaling network in Caulobacter crescentus consisting of the sensor histidine kinase FixL, its cognate response regulator FixJ, the transcriptional regulator FixK, and the kinase inhibitor FixT. It is known that in rhizobial bacteria these proteins form a network that regulates transcription of genes required for symbiotic nitrogen fixation, anaerobic and microaerobic respiration, and hydrogen metabolism under hypoxic conditions. We have identified a positive feedback loop in this network and present evidence that the negative feedback regulator, FixT, acts to inhibit FixL by mimicking a response regulator. Overall, the core circuit topology of the Fix network is conserved between the rhizobia and C. crescentus, a free-living aerobe that cannot fix nitrogen, respire anaerobically, or metabolize hydrogen. In C. crescentus, the Fix network is required for normal cellular growth during hypoxia and controls expression of genes encoding four distinct aerobic respiratory terminal oxidases and multiple carbon and nitrogen metabolic enzymes. Thus, the Fix network is a conserved sensory/signaling module whose transcriptional output has been adapted to the unique physiologies of C. crescentus and the nitrogen-fixing rhizobia.

Amino Acid Sequence↗
PubMed2006

Highly designable phenotypes and mutational buffers emerge from a systematic mapping between network topology and dynamic output.

Deciphering the design principles for regulatory networks is fundamental to an understanding of biological systems. We have explored the mapping from the space of network topologies to the space of dynamical phenotypes for small networks. Using exhaustive enumeration of a simple model of three- and four-node networks, we demonstrate that certain dynamical phenotypes can be generated by an atypically broad spectrum of network topologies. Such dynamical outputs are highly designable, much like certain protein structures can be designed by an unusually broad spectrum of sequences. The network topologies that encode a highly designable dynamical phenotype possess two classes of connections: a fully conserved core of dedicated connections that encodes the stable dynamical phenotype and a partially conserved set of variable connections that controls the transient dynamical flow. By comparing the topologies and dynamics of the three- and four-node network ensembles, we observe a large number of instances of the phenomenon of "mutational buffering," whereby addition of a fourth node suppresses phenotypic variation amongst a set of three-node networks.

Biophysical Phenomena↗
PubMed2006

Modularity and community structure in networks.

Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as "modularity" over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.

Journal Article↗