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PubMed2004

A graph grammar approach to artificial life.

We present the high-level language of relational growth grammars (RGGs) as a formalism designed for the specification of ALife models. RGGs can be seen as an extension of the well-known parametric Lindenmayer systems and contain rule-based, procedural, and object-oriented features. They are defined as rewriting systems operating on graphs with the edges coming from a set of user-defined relations, whereas the nodes can be associated with objects. We demonstrate their ability to represent genes, regulatory networks of metabolites, and morphologically structured organisms, as well as developmental aspects of these entities, in a common formal framework. Mutation, crossing over, selection, and the dynamics of a network of gene regulation can all be represented with simple graph rewriting rules. This is demonstrated in some detail on the classical example of Dawkins' biomorphs and the ABC model of flower morphogenesis: other applications are briefly sketched. An interactive program was implemented, enabling the execution of the formalism and the visualization of the results.

Algorithms↗
PubMedDate not supplied

[Changes in synaptic potentials and axonal delays as factors causing epileptic instability of neuronal networks].

Synaptic weights, axonal delays and excitability thresholds are three basic parameters influencing the function of neuronal network as a dynamic system. Changes of the general level of the signal flow, without changes in relation between excitatory and inhibitory connections can cause pathologic oscillations in the network. The conductivity in neuronal nets depends on electrochemical processes and may be influenced by the pH-status, ion concentrations, among other parameters. Also different pathological processes can change it. Even slight changes of axonal delays, as shown above, can cause in certain situations unstable, epileptic oscillations of the net.

Action Potentials↗
PubMed1996

Propagation of synchronous spiking activity in feedforward neural networks.

'Synfire' activity has been proposed as a model for the experimentally observed accurate spike patterns in cortical activity. We investigated the structural and dynamical aspects of this theory. To quantify the degree of synchrony in neural activity, we introduced the concept of 'pulse packets'. This enabled us to derive a novel neural transmission function which was used to assess the role of the single neuron dynamics and to characterize the stability conditions for propagating synfire activity. Thus, we could demonstrate that the cortical network is able to sustain synchronous spiking activity using local feedforward (synfire) connections. This new approach opens the way for a quantitative description of neural network dynamics, and enables us to test the synfire hypothesis on physiological data.

Action Potentials↗
PubMed2002

Ingeneue: a versatile tool for reconstituting genetic networks, with examples from the segment polarity network.

Here we describe a software tool for synthesizing molecular genetic data into models of genetic networks. Our software program Ingeneue, written in Java, lets the user quickly turn a map of a genetic network into a dynamical model consisting of a set of ordinary differential equations. We developed Ingeneue as part of an ongoing effort to explore the design and evolvability of genetic networks. Ingeneue has three principal advantages over other available mathematical software: it automates instantiation of the same network model in each cell in a 2-D sheet of cells; it constructs model equations from pre-made building blocks corresponding to common biochemical processes; and it automates searches through parameter space, sensitivity analyses, and other common tasks. Here we discuss the structure of the software and some of the issues we have dealt with. We conclude with some examples of results we have achieved with Ingeneue for the Drosophila segment polarity network.

Animals↗
PubMed2004

Pacemaker neurons and neuronal networks: an integrative view.

Rhythmically active neuronal networks give rise to rhythmic motor activities but also to seemingly non-rhythmic behaviors such as sleep, arousal, addiction, memory and cognition. Many of these networks contain pacemaker neurons. The ability of these neurons to generate bursts of activity intrinsically lies in voltage- and time-dependent ion fluxes resulting from a dynamic interplay among ion channels, second messenger pathways and intracellular Ca2+ concentrations, and is influenced by neuromodulators and synaptic inputs. This complex intrinsic and extrinsic modulation of pacemaker activity exerts a dynamic effect on network activity. The nonlinearity of bursting activity might enable pacemaker neurons to facilitate the onset of excitatory states or to synchronize neuronal ensembles--an interactive process that is intimately regulated by synaptic and modulatory processes.

Action Potentials↗
PubMed2005

Identification of dynamical correlations within the myosin motor domain by the normal mode analysis of an elastic network model.

In order to systematically analyze functionally relevant dynamical correlations within macromolecular complexes, we have developed computational methods based on the normal mode analysis of an elastic network model. First, we define two types of dynamical correlations (fluctuation-based and density-based), which are computed by summing up contributions from all low-frequency normal modes up to a given cutoff. Then we use them to select dynamically important "hinge residues" whose elastic distortion affects the fluctuations of a large number of residues. Second, in order to clarify long-range dynamical correlations, we decompose the dynamical correlations to individual normal modes to identify the most relevant modes. We have applied these methods to the analysis of the motor domain of Dictyostelium myosin and have obtained the following three interesting results that shed light on its mechanism of force generation: first, we find the hinge residues are distributed over several key inter-subdomain joints (including the nucleotide-binding pocket, the relay helix, the SH1 helix, the strut between the upper 50 kDa and the lower 50 kDa subdomains), which is consistent with their hypothesized roles in modulating functionally relevant inter-subdomain conformational changes; second, a single mode 7 (for structure 1VOM) is found to dominate the fluctuation-based correlations between the converter/strut and the nucleotide-binding pocket, revealing a surprising simplicity for their intriguing roles in the force generation mechanism; finally, we find a negative density-based correlation between the strut and the nucleotide-binding pocket, which is consistent with the hypothesized signaling pathway that links the actin-binding site's opening/closing with the nucleotide-binding pocket's closing/opening.

Animals↗
PubMed2003

A natural class of robust networks.

As biological studies shift from molecular description to system analysis we need to identify the design principles of large intracellular networks. In particular, without knowing the molecular details, we want to determine how cells reliably perform essential intracellular tasks. Recent analyses of signaling pathways and regulatory transcription networks have revealed a common network architecture, termed scale-free topology. Although the structural properties of such networks have been thoroughly studied, their dynamical properties remain largely unexplored. We present a prototype for the study of dynamical systems to predict the functional robustness of intracellular networks against variations of their internal parameters. We demonstrate that the dynamical robustness of these complex networks is a direct consequence of their scale-free topology. By contrast, networks with homogeneous random topologies require fine-tuning of their internal parameters to sustain stable dynamical activity. Considering the ubiquity of scale-free networks in nature, we hypothesize that this topology is not only the result of aggregation processes such as preferential attachment; it may also be the result of evolutionary selective processes.

Biophysical Phenomena↗
PubMed2005

An adaptive tissue characterization network for model-free visualization of dynamic contrast-enhanced magnetic resonance image data.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has become an important source of information to aid cancer diagnosis. Nevertheless, due to the multi-temporal nature of the three-dimensional volume data obtained from DCE-MRI, evaluation of the image data is a challenging task and tools are required to support the human expert. We investigate an approach for automatic localization and characterization of suspicious lesions in DCE-MRI data. It applies an artificial neural network (ANN) architecture which combines unsupervised and supervised techniques for voxel-by-voxel classification of temporal kinetic signals. The algorithm is easy to implement, allows for fast training and application even for huge data sets and can be directly used to augment the display of DCE-MRI data. To demonstrate that the system provides a reasonable assessment of kinetic signals, the outcome is compared with the results obtained from the model-based three-time-points (3TP) technique which represents a clinical standard protocol for analysing breast cancer lesions. The evaluation based on the DCE-MRI data of 12 cases indicates that, although the ANN is trained with imprecisely labeled data, the approach leads to an outcome conforming with 3TP without presupposing an explicit model of the underlying physiological process.

Algorithms↗
PubMedDate not supplied

Neural dynamics of psychotherapy: what modeling might tell us about us.

A neural network theory is proposed for some of the effects of verbal psychotherapy in individuals who are not seriously disturbed but seeking to function more effectively. The network theories are built on a combination of the supervised ARTMAP network and competitive attractor dynamics. The modeling exercise leads to some guidelines for psychotherapists that involve both cognitive and emotional reinforcement in a climate closer to skill learning than to medical treatment.

Humans↗
PubMed2003

Functional imaging and pain: behavior, perception, and modulation.

Time-dependent increases of local metabolic or blood flow rates have been described in spinal cord and brain during acute and chronic pain states in experimental animals, in parallel with changes of different behavioral endpoints of pain and hyperalgesia. In healthy human volunteers, pain intensity-related hemodynamic changes have been identified in a widespread, bilateral brain system including parietal, insular, cingulate, and frontal cortical areas, as well as thalamus, amygdala, and midbrain. Specific patterns of activity may characterize hyperalgesic states and some chronic pain conditions. Forebrain nociceptive systems are under inhibitory control by endogenous opioids and can be affected by acute administration of mu-opioid receptor agonists. Anticipation of pain may in itself induce changes in brain nociceptive networks. Moreover, pain-related cortical activity can be modulated by hypnotic suggestions, focusing or diverting attention, and placebo. These findings begin to disclose the spatio-temporal dynamics of brain networks underlying pain perception and modulation.

Animals↗
PubMed2007

Least-squares methods for identifying biochemical regulatory networks from noisy measurements.

BACKGROUND: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. RESULTS: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-kappaB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. CONCLUSION: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks.

Algorithms↗
PubMed2002

Dynamic instabilities induced by asymmetric influence: prisoners' dilemma game in small-world networks.

A two-dimensional small-world-type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node, with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium-type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, its recovery requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long-range connections.

Behavior↗
PubMed2004

Dynamical mean-field approximation to small-world networks of spiking neurons: from local to global and/or from regular to random couplings.

By extending a dynamical mean-field approximation previously proposed by the author [Phys. Rev. E 67, 041903 (2003)]], we have developed a semianalytical theory which takes into account a wide range of couplings in a small-world network. Our network consists of noisy N -unit FitzHugh-Nagumo neurons with couplings whose average coordination number Z may change from local ( Z<<N ) to global couplings ( Z=N-1 ) and/or whose concentration of random couplings p is allowed to vary from regular ( p=0 ) to completely random (p=1) . We have taken into account three kinds of spatial correlations: the on-site correlation, the correlation for a coupled pair, and that for a pair without direct couplings. The original 2N -dimensional stochastic differential equations are transformed to 13-dimensional deterministic differential equations expressed in terms of means, variances, and covariances of state variables. The synchronization ratio and the firing-time precision for an applied single spike have been discussed as functions of Z and p . Our calculations have shown that with increasing p , the synchronization is worse because of increased heterogeneous couplings, although the average network distance becomes shorter. Results calculated by our theory are in good agreement with those by direct simulations.

Journal Article↗
PubMed2004

Evolutionary optimization with data collocation for reverse engineering of biological networks.

MOTIVATION: Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. RESULTS: We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Algorithms↗
PubMed1997

Autocatalytic networks with intermediates. I: Irreversible reactions.

A class of autocatalytic reaction networks based on template-dependent replication and specific catalysis is considered. Trimolecular "elementary steps" of simple replicator dynamics are resolved into two consecutive irreversible reactions. The extreme cases, competition for common resources and hypercycle-like cooperative feedback, were analyzed in some detail. Although the dynamics of the extended networks resembles corresponding replicator dynamics in general, there are significant differences. Most notably, the interior fixed points in the cooperative model turned out to be asymptotically stable for an arbitrary number of species, whereas simple replicator dynamic predicts an asymptotically stable periodic orbit fixed for four species and fewer and a stable periodic orbit for all other cases.

Bioreactors↗
PubMed1994

Psychiatry and the new dynamics.

Self-organizing and self-tuning neural networks are conceptualized as nonlinear dynamical systems. It is shown that biological psychiatry can be encompassed within this nonlinear dynamical framework, where it becomes coherent with trends in cognitive science. A state space representation that is a hyperspace with an energy topology and a fractal dimension is utilized. The state space representation provides a unifying framework for the classification of mental disorders. Clinical phenomena in schizophrenia can be explained in terms of nonlinear dynamics. The framework is also productive of psychiatric research. These results motivate the development of a nonlinear dynamical psychiatry.

Autistic Disorder↗
PubMed1996

Gamma-aminobutyric acid type B receptor-dependent burst-firing in thalamic neurons: a dynamic clamp study.

Synchronized network responses in thalamus depend on phasic inhibition originating in the thalamic reticular nucleus (nRt) and are mediated by the neurotransmitter gamma-aminobutyric acid (GABA). A suggested role for intra-nRt connectivity in inhibitory phasing remains controversial. Recently, functional GABA type B (GABAB) receptors were demonstrated on nRt cells, and the slow time course of the GABAB synaptic response seems ideally suited to deinactivate low-threshold calcium channels. This promotes burst firing, a characteristic feature of synchronized responses. Here we investigate GABAB-mediated rebound burst firing in thalamic cells. Whole-cell current-clamp recordings were obtained from nRt cells and somatosensory thalamocortical relay cells in rat brain slices. Synthetic GABAB inhibitory postsynaptic potentials, generated by a hybrid computerneuron synapse (dynamic clamp), triggered rebound low-threshold calcium spikes in both cell types when peak inhibitory postsynaptic potential hyperpolarization was greater than -92 mV. The threshold inhibitory postsynaptic potential conductance for rebound burst generation was comparable in nRt (7 nS) and thalamocortical (5 nS) cells. However, burst onset in nRt (1 s) was considerably delayed compared with thalamocortical (0.6 s) cells. Thus, GABAB inhibitory postsynaptic potentials can elicit low-threshold calcium spikes in both relay and nRt neurons, but the resultant oscillation frequency would be faster for thalamocortical-nRt networks (3 Hz) than for nRt-nRt networks (1-2 Hz). We conclude, therefore, that fast (> 2 Hz) GABAB-dependent thalamic oscillations are maintained primarily by reciprocal connections between excitatory and inhibitory cells. These findings further indicate that when oscillatory neural networks contain both recurrent and reciprocal inhibition, then distinct population frequencies may result when one or the other type of inhibition is favored.

Animals↗
PubMed2006

Organization of the state space of a simple recurrent network before and after training on recursive linguistic structures.

Recurrent neural networks are often employed in the cognitive science community to process symbol sequences that represent various natural language structures. The aim is to study possible neural mechanisms of language processing and aid in development of artificial language processing systems. We used data sets containing recursive linguistic structures and trained the Elman simple recurrent network (SRN) for the next-symbol prediction task. Concentrating on neuron activation clusters in the recurrent layer of SRN we investigate the network state space organization before and after training. Given a SRN and a training stream, we construct predictive models, called neural prediction machines, that directly employ the state space dynamics of the network. We demonstrate two important properties of representations of recursive symbol series in the SRN. First, the clusters of recurrent activations emerging before training are meaningful and correspond to Markov prediction contexts. We show that prediction states that naturally arise in the SRN initialized with small random weights approximately correspond to states of Variable Memory Length Markov Models (VLMM) based on individual symbols (i.e. words). Second, we demonstrate that during training, the SRN reorganizes its state space according to word categories and their grammatical subcategories, and the next-symbol prediction is again based on the VLMM strategy. However, after training, the prediction is based on word categories and their grammatical subcategories rather than individual words. Our conclusion holds for small depths of recursions that are comparable to human performances. The methods of SRN training and analysis of its state space introduced in this paper are of a general nature and can be used for investigation of processing of any other symbol time series by means of SRN.

Artificial Intelligence↗