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PubMed2004

A proposal for using the ensemble approach to understand genetic regulatory networks.

Understanding the genetic regulatory network comprising genes, RNA, proteins and the network connections and dynamical control rules among them, is a major task of contemporary systems biology. I focus here on the use of the ensemble approach to find one or more well-defined ensembles of model networks whose statistical features match those of real cells and organisms. Such ensembles should help explain and predict features of real cells and organisms. More precisely, an ensemble of model networks is defined by constraints on the "wiring diagram" of regulatory interactions, and the "rules" governing the dynamical behavior of regulated components of the network. The ensemble consists of all networks consistent with those constraints. Here I discuss ensembles of random Boolean networks, scale free Boolean networks, "medusa" Boolean networks, continuous variable networks, and others. For each ensemble, M statistical features, such as the size distribution of avalanches in gene activity changes unleashed by transiently altering the activity of a single gene, the distribution in distances between gene activities on different cell types, and others, are measured. This creates an M-dimensional space, where each ensemble corresponds to a cluster of points or distributions. Using current and future experimental techniques, such as gene arrays, these M properties are to be measured for real cells and organisms, again yielding a cluster of points or distributions in the M-dimensional space. The procedure then finds ensembles close to those of real cells and organisms, and hill climbs to attempt to match the observed M features. Thus obtains one or more ensembles that should predict and explain many features of the regulatory networks in cells and organisms.

Cell Differentiation↗

PubMed1999

Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map.

We discuss a method by which the dynamics of a network of neurons, coupled by mutual inhibition, can be reduced to a one-dimensional map. This network consists of a pair of neurons, one of which is an endogenous burster, and the other excitable but not bursting in the absence of phasic input. The latter cell has more than one slow process. The reduction uses the standard separation of slow/fast processes; it also uses information about how the dynamics on the slow manifold evolve after a finite amount of slow time. From this reduction we obtain a one-dimensional map dependent on the parameters of the original biophysical equations. In some parameter regimes, one can deduce that the original equations have solutions in which the active phase of the originally excitable cell is constant from burst to burst, while in other parameter regimes it is not. The existence or absence of this kind of regulation corresponds to qualitatively different dynamics in the one-dimensional map. The computations associated with the reduction and the analysis of the dynamics includes the use of coordinates that parameterize by time along trajectories, and "singular Poincaré maps" that combine information about flows along a slow manifold with information about jumps between branches of the slow manifold.

Animals↗

PubMed2005

Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation.

The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation. Earlier work by Coolen and Sherrington on a parallel dynamics far from saturation is extended here to account for finite stochastic noise due to a Hebbian and a sequential learning rule. Phase diagrams are obtained with stationary states and quasiperiodic nonstationary solutions. The relevant dependence of these diagrams and of the quasiperiodic solutions on the stochastic noise and on initial inputs for the overlaps is explicitly discussed.

Algorithms↗

PubMed2005

Effect of prior cognitive state on resting state networks measured with functional connectivity.

To address the extent to which functional connectivity measures an absolute brain state, we observed the effect of prior performance of a language task on resting-state networks in regions associated with language. Six subjects were imaged during rest before and after a block-design language task. Connectivity maps were generated for each of four language regions (identified from analysis of the language activation portion of the study) in each subject for both rest periods. Conjunction analysis demonstrated distinct networks of voxels for each seed region, indicating separate functional subnetworks associated with the different regions. In a comparison of rest before and after the activation task widespread and significant changes were observed in all individuals, suggesting that the measured resting state network reflects a dynamic image of the current brain state. At the group level, an extended network was observed that was largely persistent over time. Even at the group level an increase in connectivity was observed between left and right middle frontal gyri, and between posterior cingulate cortex and medial frontal cortex in the rest after the language task. These results suggest that functional connectivity may be a powerful measure of cognitive state, sensitive to differences between controls and patients together with the particular cognitive processing occurring during the rest state.

Brain Mapping↗

PubMed2000

Mean field theory for asymmetric neural networks.

The computation of mean firing rates and correlations is intractable for large neural networks. For symmetric networks one can derive mean field approximations using the Taylor series expansion of the free energy as proposed by Plefka. In asymmetric networks, the concept of free energy is absent. Therefore, it is not immediately obvious how to extend this method to asymmetric networks. In this paper we extend Plefka's approach to asymmetric networks and in fact to arbitrary probability distributions. The method is based on an information geometric argument. The method is illustrated for asymmetric neural networks with sequential dynamics. We compare our approximate analytical results with Monte Carlo simulations for a network of 100 neurons. It is shown that the quality of the approximation for asymmetric networks is as good as for symmetric networks.

Models, Neurological↗

PubMed2002

Highly clustered scale-free networks.

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power-law distribution of degree, linear preferential attachment of new links, and a negative correlation between the age of a node and its link attachment rate. Notably, the degree distribution is conserved even though only the most recently grown part of the network is considered. As the network grows, the clustering reaches an asymptotic value larger than that for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors, coauthorship in science, and word synonyms. These highly clustered scale-free networks indicate that memory effects are crucial for a correct description of the dynamics of growing networks.

Journal Article↗

PubMed2002

Dynamical response of an excitatory-inhibitory neural network to external stimulation: an application to image segmentation.

Neural network models comprising elements that have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamical behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the building block of larger networks, is subjected to external stimulation. The response shows transition between various types of dynamics, depending upon the magnitude of the stimulus. The corresponding network model, obtained by coupling such pairs over a local neighborhood in a two-dimensional plane, can achieve a satisfactory segmentation of an image into "object" and "background." Results for synthetic and "real-life" images are given.

Journal Article↗

PubMed2024

Regulating IL-2 Immune Signaling Function Via A Core Allosteric Structural Network.

Human interleukin-2 (IL-2) is a crucial cytokine for T cell regulation, with therapeutic potential in cancer and autoimmune diseases. However, IL-2's pleiotropic effects across different immune cell types often lead to toxicity and limited efficacy. Previous efforts to enhance IL-2's therapeutic profile have focused on modifying its receptor binding sites. Yet, the underlying dynamics and intramolecular networks contributing to IL-2 receptor recognition remain unexplored. This study presents a detailed characterization of IL-2 dynamics compared to two engineered IL-2 mutants, "superkines" S15 and S1, which exhibit biased signaling towards effector T cells. Using NMR spectroscopy and molecular dynamics simulations, we demonstrate significant variations in core dynamic pathways and conformational exchange rates across these three IL-2 variants. We identify distinct allosteric networks and minor state conformations in the superkines, despite their structural similarity to wild-type IL-2. Furthermore, we rationally design a mutation (L56A) in the S1 superkine's core network, which partially reverts its dynamics, receptor binding affinity, and T cell signaling behavior towards that of wild-type IL-2. Our results reveal that IL-2 superkine core dynamics play a critical role in their enhanced receptor binding and function, suggesting that modulating IL-2 dynamics and core allostery represents an untapped approach for designing immunotherapies with improved immune cell selectivity profiles.

Interleukin-2↗

PubMed2002

Genexp--a genetic network simulation environment.

UNLABELLED: An environment for simulation of dynamics of genetic regulatory networks is presented. The model is based on the recurrent neural network principle and allows to interactively simulate various genetic regulatory interactions under different features of the system. The results are displayed graphically. AVAILABILITY: http://proteom.biomed.cas.cz/genexp

Computer Simulation↗

PubMed2000

Combinatorial explosion in model gene networks.

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics. (c) 2000 American Institute of Physics.

Journal Article↗

PubMed2006

Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics.

Nearly all neuronal information processing and interneuronal communication in the brain involves action potentials, or spikes, which drive the short-term synaptic dynamics of neurons, but also their long-term dynamics, via synaptic plasticity. In many brain structures, action potential activity is considered to be sparse. This sparseness of activity has been exploited to reduce the computational cost of large-scale network simulations, through the development of event-driven simulation schemes. However, existing event-driven simulations schemes use extremely simplified neuronal models. Here, we implement and evaluate critically an event-driven algorithm (ED-LUT) that uses precalculated look-up tables to characterize synaptic and neuronal dynamics. This approach enables the use of more complex (and realistic) neuronal models or data in representing the neurons, while retaining the advantage of high-speed simulation. We demonstrate the method's application for neurons containing exponential synaptic conductances, thereby implementing shunting inhibition, a phenomenon that is critical to cellular computation. We also introduce an improved two-stage event-queue algorithm, which allows the simulations to scale efficiently to highly connected networks with arbitrary propagation delays. Finally, the scheme readily accommodates implementation of synaptic plasticity mechanisms that depend on spike timing, enabling future simulations to explore issues of long-term learning and adaptation in large-scale networks.

Action Potentials↗

PubMed2000

A signal-flow-graph approach to on-line gradient calculation.

A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple one-input, one-output transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both on-line and batch-backward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and time-variant, dynamic system represented by an SFG, in particular any feedforward, time-delay, or recurrent neural network. In this work, we use discrete-time notation, but the same theory holds for the continuous-time case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both off-line and on-line. On-line learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion.

Algorithms↗

PubMed1999

Spatio-temporal analysis of electric brain activity during semantic and phonological word processing.

There is an ongoing debate in cognitive neuroscience about the time course and the functional independence of the different processes involved in encoding written language material. New data indicate very fast and highly parallel language analysis networks in the brain. Here we demonstrate a methodological approach to study the temporal dynamics of this network by searching for time periods where different task demands emphasize different aspects of the network. Multi-channel event related potentials (ERPs) were recorded during a semantic and a phonological reading task from 14 healthy subjects. Signals were analyzed exclusively on the basis of the spatial configuration of the electric potential distributions (ERP maps), since differences in these spatial patterns directly reflect changes in the configuration of the active sources in the brain. This analysis did not reveal any differences of the evoked brain electric fields between the two tasks up to 280 ms post-stimulus. The ERP maps then differed for a brief period between 280 and 380 ms, before they were similar again. The analysis of the maps using a global linear localization procedure revealed a network of areas, active in both tasks, that mainly involved the left postero-temporal and left antero-temporal regions. The left posterior activation was found already around 100 ms post-stimulus, indicating that language-specific functions appear early in time. We therefore conclude that phonological and semantic processing are essentially performed in both tasks and that only late decision-related processes influence the relative strength of activity of the different modules in the complex language network.

Adult↗

PubMed1998

Continuous attractors and oculomotor control.

A recurrent neural network can possess multiple stable states, a property that many brain theories have implicated in learning and memory. There is good evidence for such multistability in the brainstem neural network that controls eye position. Because the stable states are arranged in a continuous dynamical attractor, the network can store a memory of eye position with analog neural encoding. Continuous attractors in model networks depend on precisely tuned positive feedback, and their robust maintenance requires mechanisms of synaptic plasticity. These ideas may have wider scope than just the oculomotor system. More generally, the internal models postulated by theories of biological motor control may be recurrent networks with continuous attractors.

Journal Article↗

PubMed1978

Self-stimulation in the rat: quantitative characteristics of the reward pathway.

Quantitative characteristics of the neural pathway that carries the reinforcing signal in electrical self-stimulation of the brain were established by finding which combinations of stimulation parameters give the same performance in a runway. The reward for each run was a train of evenly spaced monophasic cathodal pulses from a monopolar electrode. With train duration and pulse frequency held constant, the required current was a hyperbolic function of pulse duration, with chronaxie c approximately 1.5 msec. With pulse duration held constant, the required strength of the train (the charge delivered per second) was a hyperbolic function of train duration, with chronaxie C approximately 500 msec. To a first approximation, the values of c and C were independent of the choice either of train duration and pulse frequency or of pulse duration, respectively. Hence, the current intensity required by any choice of train duration, pulse frequency, and pulse duration dependent on only two basic parameters, c and C, and one quantity, Qi, the required impulse charge. These may reflect, respectively, current integration by directly excited neurons; temporal integration of neural activity by synaptic processes in a neural network; and the peak of the impulse response of the network, assuming that the network has linear dynamics and that the reward depends on the peak of the output of the network.

Animals↗

PubMed2000

Learning-induced synchronization of a globally coupled excitable map system.

We propose a pulse-coupled neural network model in which one-dimensional excitable maps connected in a time-delayed network serve as the neural processing units. Although the individual processing unit has simple dynamical properties, the network exhibits collective chaos in the active states. Introducing a Hebbian learning algorithm for synaptic connections enhances the synchronization of excitation timing of the units within a subpopulation. The synchronizing clusters approximately exhibit a power-law size distribution, suggesting a hierarchy of synchronization. After applying a stationary signal to a subpopulation of the units with learning, the network then reproduces the signal. The learnable time range is much longer than the inherent time scale of the processing units, i.e., the synaptic delay time. Also, the network can reproduce periodic signals with time resolution finer than the delay time. Our present network model can be considered as a temporal association device which operates in chaotic states.

Animals↗

PubMed2006

Recurrent neural network as a linear attractor for pattern association.

We propose a linear attractor network based on the observation that similar patterns form a pipeline in the state space, which can be used for pattern association. To model the pipeline in the state space, we present a learning algorithm using a recurrent neural network. A least-squares estimation approach utilizing the interdependency between neurons defines the dynamics of the network. The region of convergence around the line of attraction is defined based on the statistical characteristics of the input patterns. Performance of the learning algorithm is evaluated by conducting several experiments in benchmark problems, and it is observed that the new technique is suitable for multiple-valued pattern association.

Letter↗

PubMed2006

Dynamic analysis of optimality in myocardial energy metabolism under normal and ischemic conditions.

To better understand the dynamic regulation of optimality in metabolic networks under perturbed conditions, we reconstruct the energetic-metabolic network in mammalian myocardia using dynamic flux balance analysis (DFBA). Additionally, we modified the optimal objective from the maximization of ATP production to the minimal fluctuation of the profile of metabolite concentration under ischemic conditions, extending the hypothesis of original minimization of metabolic adjustment to create a composite modeling approach called M-DFBA. The simulation results are more consistent with experimental data than are those of the DFBA model, particularly the retentive predominant contribution of fatty acid to oxidative ATP synthesis, the exact mechanism of which has not been elucidated and seems to be unpredictable by the DFBA model. These results suggest that the systemic states of metabolic networks do not always remain optimal, but may become suboptimal when a transient perturbation occurs. This finding supports the relevance of our hypothesis and could contribute to the further exploration of the underlying mechanism of dynamic regulation in metabolic networks.

Computer Simulation↗