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Mathematical modelling of dynamics and control in metabolic networks. IV. Local stability analysis of single biochemical control loops.

The objective of the study presented herein is to describe the dynamic behavior of a single biochemical control loop, a simple system but an important element of metabolic networks. This loop is a self-regulated sequence of reactions that converts an initial substrate (S) into a final product (P). It consists of three basic elements: (1) a regulated reaction, where the concentration of P controls the flux (I) into the system. This element serves as the control element in the feedback circuit. (2) a sequence of unregulated reactions that leads to the formation of P. This process is to be regulated so that the production rate of P meets a desired target. (3) a process (R) that removes P from the loop to another part of the metabolic network. A mathematical description is formulated that consists of two differential equations and two unspecified functions that represent the reaction rates of I and R. This description is scaled to clarify functional dependence and to attempt a separation of genetic and process determined parameters. The global dynamic behavior of the model is assessed qualitatively by examining the occurrence of static and dynamic bifurcations, multiple steady states or sustained oscillations respectively, via local stability analysis. General criteria for both types of bifurcations are developed without specifying the functional form of I and R, but explicitly accounting for the kinetic properties of the reaction chain. A particularly simple criterion is found for static bifurcations which can appear only for loops with positive feedback, i.e. when the regulated reaction is activated by P. This criterion only contains the properties of I and R. The criteria for dynamic bifurcations, which occur when the feedback interaction is inhibitory, are more complex. These depend strongly on the properties of the reaction chain, and oscillations are favored if the dynamic operator describing the reaction sequence is of high order or if it contains time delays.

Feedback↗

Synaptic organizations and dynamical properties of weakly connected neural oscillators. II. Learning phase information.

This is the second of two articles devoted to analyzing the relationship between synaptic organizations (anatomy) and dynamical properties (function) of networks of neural oscillators near multiple supercritical Andronov-Hopf bifurcation points. Here we analyze learning processes in such networks. Regarding learning dynamics, we assume (1) learning is local (i.e. synaptic modification depends on pre- and postsynaptic neurons but not on others), (2) synapses modify slowly relative to characteristic neuron response times, (3) in the absence of either pre- or postsynaptic activity, the synapse weakens (forgets). Our major goal is to analyze all synaptic organizations of oscillatory neural networks that can memorize and retrieve phase information or time delays. We show that such network have the following attributes: (1) the rate of synaptic plasticity connected with learning is determined locally by the presynaptic neurons, (2) the excitatory neurons must be long-axon relay neurons capable of forming distant connections with other excitatory and inhibitory neurons, (3) if inhibitory neurons have long axons, then the network can learn, passively forget and actively unlearn information by adjusting synaptic plasticity rates.

Learning↗

Loop motions of triosephosphate isomerase observed with elastic networks.

The internal dynamics of triosephosphate isomerase have been investigated with elastic networks, with and without a substrate bound. The slowest modes of motion involve large domain motions but also a loop motion that conforms to the changes observed between the crystal structures and . Our computations confirm that the different motions of this loop are important in several of the computed slowest modes. We have shown that elastic network computations on this protein system can combine atoms for the functional parts of the structure with coarse-grained (cg) representations of the remainder of the structure in several different ways. Similar loop motions are seen with elastic network models for atomistic and mixed cg models. The loop motions are reproduced with an overlap of 0.75-0.79 by combining the four slowest modes of motion for the free and complex forms of the enzyme.

Anisotropy↗

Learning first-pass structural attachment preferences with dynamic grammars and recursive neural networks.

One of the central problems in the study of human language processing is ambiguity resolution: how do people resolve the extremely pervasive ambiguity of the language they encounter? One possible answer to this question is suggested by experience-based models, which claim that people typically resolve ambiguities in a way which has been successful in the past. In order to determine the course of action that has been "successful in the past" when faced with some ambiguity, it is necessary to generalize over past experience. In this paper, we will present a computational experience-based model, which learns to generalize over linguistic experience from exposure to syntactic structures in a corpus. The model is a hybrid system, which uses symbolic grammars to build and represent syntactic structures, and neural networks to rank these structures on the basis of its experience. We use a dynamic grammar, which provides a very tight correspondence between grammatical derivations and incremental processing, and recursive neural networks, which are able to deal with the complex hierarchical structures produced by the grammar. We demonstrate that the model reproduces a number of the structural preferences found in the experimental psycholinguistics literature, and also performs well on unrestricted text.

Choice Behavior↗

Jackson and the frontal executive hierarchy.

Executive actions are represented and hierarchically organized in the cortex of the frontal lobe. The representation and coordination of an action or series of actions have the same anatomical substrate: an executive neuronal network (cognit) in forntal cortex. That network interacts structurally and dynamically with perceptual networks of posterior cortex at the highest levels of the perception-action cycle.

Brain Injuries↗

Application of recurrent neural network to predict bacterial growth in dynamic conditions.

A combination of a factorial design and two central composite designs was used to assess quantitatively the effects of acid pH (5.6-7.0) or alkaline pH (7.0-9.5) and NaCl (0-8%) variations on the growth of Listeria monocytogenes in a meat broth, at 20 degrees C and lower temperature 10 degrees C. Two principal phenomena were observed when bacteria were submitted to abrupt change of pH and a(w) during growth, whatever the growth temperature: (i) large environmental variations induced a lag phase following the fluctuation, and (ii) the growth continued with a generation time value different from that observed before the change or that associated to the new environment. A dynamic model, based on recurrent neural network (RNN), was developed to describe the growth of L. monocytogenes as a function of temperature and fluctuating conditions of acid pH, alkaline pH and concentration of NaCl. The results showed that the neural network model can be used to represent the complex effects of environmental variable conditions on the microorganism behaviour.

Hydrogen-Ion Concentration↗

Large-scale profiling of Rab GTPase trafficking networks: the membrome.

Rab GTPases and SNARE fusion proteins direct cargo trafficking through the exocytic and endocytic pathways of eukaryotic cells. We have used steady state mRNA expression profiling and computational hierarchical clustering methods to generate a global overview of the distribution of Rabs, SNAREs, and coat machinery components, as well as their respective adaptors, effectors, and regulators in 79 human and 61 mouse nonredundant tissues. We now show that this systems biology approach can be used to define building blocks for membrane trafficking based on Rab-centric protein activity hubs. These Rab-regulated hubs provide a framework for an integrated coding system, the membrome network, which regulates the dynamics of the specialized membrane architecture of differentiated cells. The distribution of Rab-regulated hubs illustrates a number of facets that guides the overall organization of subcellular compartments of cells and tissues through the activity of dynamic protein interaction networks. An interactive website for exploring datasets comprising components of the Rab-regulated hubs that define the membrome of different cell and organ systems in both human and mouse is available at http://www.membrome.org/.

Animals↗

A neural network model of foraging decisions made under predation risk.

This article develops the cognitive-emotional forager (CEF) model, a novel application of a neural network to dynamical processes in foraging behavior. The CEF is based on a neural network known as the gated dipole, introduced by Grossberg, which is capable of representing short-term affective reactions in a manner similar to Solomon and Corbit's (1974) opponent process theory. The model incorporates a trade-off between approach toward food and avoidance of predation under varying levels of motivation induced by hunger. The results of simulations in a simple patch selection paradigm, using a lifetime fitness criterion for comparison, indicate that the CEF model is capable of nearly optimal foraging and outperforms a run-of-luck rule-of-thumb model. Models such as the one presented here can illuminate the underlying cognitive and motivational components of animal decision making.

Animals↗

Body area network--a key infrastructure element for patient-centered telemedicine.

The Body Area Network (BAN) extends the range of existing wireless network technologies by an ultra-low range, ultra-low power network solution optimised for long-term or continuous healthcare applications. It enables wireless radio communication between several miniaturised, intelligent Body Sensor (or actor) Units (BSU) and a single Body Central Unit (BCU) worn at the human body. A separate wireless transmission link from the BCU to a network access point--using different technology--provides for online access to BAN components via usual network infrastructure. The BAN network protocol maintains dynamic ad-hoc network configuration scenarios and co-existence of multiple networks.BAN is expected to become a basic infrastructure element for electronic health services: By integrating patient-attached sensors and mobile actor units, distributed information and data processing systems, the range of medical workflow can be extended to include applications like wireless multi-parameter patient monitoring and therapy support. Beyond clinical use and professional disease management environments, private personal health assistance scenarios (without financial reimbursement by health agencies / insurance companies) enable a wide range of applications and services in future pervasive computing and networking environments.

Artificial Intelligence↗

Complex dynamics in simple Hopfield neural networks.

A class of simple Hopfield neural networks with a parameter is investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated; the bifurcation plot and several important phase portraits are presented as well. By virtue of a recent result of horseshoe theory in dynamical systems, we present rigorous computer-assisted verifications for chaotic behavior in the simple Hopfield neural networks for certain parameters and give a brief discussion on the robustness of the chaotic behavior. Quantitative descriptions of the complexity of these neural networks are also given in terms of topological entropy.

Algorithms↗

Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus.

Cells that produce intrinsic theta oscillations often contain the hyperpolarization-activated current I(h). In this article, we use models and dynamic clamp experiments to investigate the synchronization properties of two such cells (stellate cells of the entorhinal cortex and O-LM cells of the hippocampus) in networks with fast-spiking (FS) interneurons. The model we use for stellate cells and O-LM cells is the same, but the stellate cells are excitatory and the O-LM cells are inhibitory, with inhibitory postsynaptic potential considerably longer than those from FS interneurons. We use spike time response curve methods (STRC), expanding that technique to three-cell networks and giving two different ways in which the analysis of the three-cell network reduces to that of a two-cell network. We show that adding FS cells to a network of stellate cells can desynchronize the stellate cells, while adding them to a network of O-LM cells can synchronize the O-LM cells. These synchronization and desynchronization properties critically depend on I(h). The analysis of the deterministic system allows us to understand some effects of noise on the phase relationships in the stellate networks. The dynamic clamp experiments use biophysical stellate cells and in silico FS cells, with connections that mimic excitation or inhibition, the latter with decay times associated with FS cells or O-LM cells. The results obtained in the dynamic clamp experiments are in a good agreement with the analytical framework.

Action Potentials↗

The effect of intact talin and talin tail fragment on actin filament dynamics and structure depends on pH and ionic strength.

We employed quasi-elastic light scattering and electron microscopy to investigate the influence of intact talin and talin tail fragment on actin filament dynamics and network structure. Using these methods, we confirm previous reports that intact talin induces cross-linking as well as filament shortening on actin networks. We now show that the effect of intact talin as well as talin tail fragment on actin networks is controlled by pH and ionic strength. At pH 7.5, actin filament dynamics in the presence of intact talin and talin tail fragment are characterized by a rapid decay of the dynamic structure factor and by a square root power law for the stretched exponential decay which is in contrast with the theory for pure actin solutions. At pH 6 and low ionic strength, intact talin cross-links actin filaments more tightly than talin tail fragment. Talin head fragment showed no effect on actin networks, indicating that the actin binding sites reside probably exclusively within the tail domain.

Actins↗

Classification of signal-time curves from dynamic MR mammography by neural networks.

The aim of this study was to test the performance of artificial neural networks for the classification of signal-time curves obtained from breast masses by dynamic MRI. Signal-time courses from 105 parenchyma, 162 malignant, and 102 benign tissue regions were examined. The latter two groups were histopathologically verified. Four neural networks corresponding to different temporal resolutions of the signal-time curves were tested. The resolution ranges from 28 measurements with a temporal spacing of 23s to just 3 measurements taken 1.8, 3, and 10 minutes after contrast medium administration. Discrimination between malignant and benign lesions is best if 28 measurement points are used (sensitivity: 84%, specificity: 81%). The use of three measurement points results in 78% sensitivity and 76% specificity. These results correspond to values obtained by human experts who visually evaluated signal-time curves without considering additional morphologic information. All examined networks yielded poor results for the subclassification of the benign lesions into fibroadenomas and benign proliferative changes. Neural networks can computationally fast distinguish between malignant and benign lesions even when only a few post-contrast measurements are made. More precise specification of the type of the benign lesion will require incorporation of additional morphological or pharmacokinetic information.

Adult↗

Dynamics of rumor spreading in complex networks.

We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allows us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer-to-peer communication networks, and social spreading phenomena.

Journal Article↗

Oscillations and irregular emission in networks of linear spiking neurons.

The dynamics of a network of randomly connected inhibitory linear integrate and fire (LIF) neurons (with a floor for the depolarization), in the presence of stochastic external afferent input, is considered in various parameter regimes of the neurons and of the network. Applying a technique recently introduced by Brunel and Hakim, we classify the regimes in which such a network has stable stationary states and in which spike emission rates oscillate. In the vicinity of the bifurcation line, the oscillation frequency and its amplitude are computed and compared with simulations. As for leaky IF neurons, the space of parameters can be compacted into two. Yet despite significant technical differences between the two models, related to both the different dynamics of the depolarization as well as to the different boundary conditions, the qualitative behavior is rather similar. The significance of LIF neurons and of the differences with leaky IF neurons is discussed.

Action Potentials↗

Neural networks through the hourglass.

The effect of the synaptic plasticity on the dynamics of a large neural network is studied. Our approach is analytic but inspired by the data, both simulated and experimental. We explain formation of the small strongly connected assemblies within a dynamical network following Hebb's rule. Also, we find the conditions for the synchrony effect in the stochastic network in the absence of large synchronized input.

Models, Neurological↗

Dynamic muscle force predictions from EMG: an artificial neural network approach.

EMG signals of dynamically contracting muscle have never been used to predict experimentally known muscle forces across subjects. Here, we use an artificial neural network (ANN) approach to first derive an EMG-force relationship from a subset of experimentally determined EMGs and muscle forces; second, we use this relationship to predict individual muscle forces for different contractile conditions and in subjects whose EMG and force data were not used in the derivation of the EMG-force relationship; and third, we validate the predicted muscle forces against the known forces recorded in vivo. EMG and muscle forces were recorded from the cat soleus for a variety of locomotor conditions giving a data base from three subjects, four locomotor conditions, and 8-16 steps per subject and condition. Considering the conceptual differences in the tasks investigated (e.g. slow walking vs. trotting), the intra-subject results obtained here are superior to those published previously, even though the approach did not require a muscle model or the instantaneous contractile conditions as input for the force predictions. The inter-subject results are the first of this kind to be presented in the literature and they typically gave cross-correlation coefficients between actual and predicted forces of >0.90 and root mean square errors of <15%, thus they were considered excellent. From the results of this study, it was concluded that ANNs represent a powerful tool to capture the essential features of EMG-force relationships of dynamically contracting muscle, and that ANNs might be used widely to predict muscle forces based on EMG signals.

Algorithms↗

Object selection based on oscillatory correlation.

One of the classical topics in neural networks is winner-take-all (WTA), which has been widely used in unsupervised (competitive) learning, cortical processing, and attentional control. Owing to global connectivity, WTA networks, however, do not encode spatial relations in the input, and thus cannot support sensory and perceptual processing where spatial relations are important. We propose a new architecture that maintains spatial relations between input features. This selection network builds on Locally Excitatory Globally Inhibitory Oscillator Networks (LEGION) dynamics and slow inhibition. In an input scene with many objects (patterns), the network selects the largest object. This system can be easily adjusted to select several largest objects, which then alternate in time. We analyze the speed of selection, and further show that a two-stage selection network gains efficiency by combining selection with parallel removal of noisy regions. The network is applied to select the most salient object in gray-level images. As a special case, the selection network without local excitation gives rise to a new form of oscillatory WTA.

Journal Article↗