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Metabolomic networks in plants: Transitions from pattern recognition to biological interpretation.

Nowadays techniques for non-targeted metabolite profiling allow for the generation of huge amounts of relevant data essential for the construction of dynamic metabolomic networks. Thus, metabolomics, besides transcriptomics or proteomics, provides a major tool for the characterization of postgenomic processes. In this work, we introduce comparative correlation analysis as a complementary approach to characterize the physiological states of various organs of diverse plant species with focus on specific participation of metabolites in different reaction networks. The correlations observed are induced by diminutive fluctuations in environmental conditions, which propagate through the system and induce specific patterns depending on the genomic background. In order to examine this hypothesis, numeric examples of such fluctuations are computed and compared with experimentally obtained metabolite data.

Algorithms↗

Individual differences in brain dynamics across a social cognition network induced by cortico-cerebellar tDCS in adults with autism spectrum disorder (ASD).

Autism spectrum disorder (ASD) is a neurodevelopmental condition with core diagnostic domains of social communication impairments, restricted interests and repetitive behaviors. Idiosyncratic brain organization is a potential hallmark of ASD. Previous transcranial direct current stimulation (tDCS) studies often targeted dorsolateral prefrontal cortex, with changes oin brain dynamics averaged across the cohort. We utilized a magnetoencephalographic (MEG) array to characterize individual differences in brain dynamics induced by cortico-cerebellar tDCS across nodes of a social cognition network. A randomized, sham-controlled, double-blind, within-subject clinical trial was conducted in a cohort of 24 young adults with ASD or high autistic traits. Two separate sessions of computerized social learning activities were combined with verum/sham tDCS, with anodal electrode over right temporoparietal junction (TPJ) and cathode on right deltoid. Following stimulation, theta- and alpha-band activity were evaluated within nodes of a social cognition network: bilateral TPJ, fusiform, medial prefrontal cortex and Crus I/II of cerebellum. Idiosyncratic participant-specific up- and down-regulation of theta- and alpha-band activity occurred across the network. Activity in right Crus I/II, a region inundated by the stimulation current, strongly correlated with the change of activity summed across all cerebral cortical nodes in theta- but not alpha-band. Intrinsic theta-band activity is believed to mediate input/output relationships in cerebellar cortex and to drive synaptic plasticity. These results suggest that theta-band stimulation of cerebellar cortex might be an effective therapy for individuals on the autism spectrum who present with cerebellar hyperactivity.

Humans↗

Interpreting spatial and temporal neural activity through a recurrent neural network brain-machine interface.

We propose the use of optimized brain-machine interface (BMI) models for interpreting the spatial and temporal neural activity generated in motor tasks. In this study, a nonlinear dynamical neural network is trained to predict the hand position of primates from neural recordings in a reaching task paradigm. We first develop a method to reveal the role attributed by the model to the sampled motor, premotor, and parietal cortices in generating hand movements. Next, using the trained model weights, we derive a temporal sensitivity measure to asses how the model utilized the sampled cortices and neurons in real-time during BMI testing.

Algorithms↗

Structure and dynamics of the hydrogen-bond network around (R,R)-pterocarpans with biological activity in aqueous solution.

Molecular dynamics simulations were carried out in the presence of 2380 water molecules (TIP3P) to explore the conformational preferences of 3,9-dimethoxy-4-prenylpterocarpan (bitucarpin A) and 3,9-dihydroxy-4,8-diprenylpterocarpan (erybraedin C) and the H-bond network around them, using the empirical general AMBER force field (GAFF). Specific angle and torsional parameters have been improved in order to match the geometries of the minimum energy structures obtained from an earlier DFT/ab initio study in vacuo, taking into account a few configurations [Alagona, G.; Ghio, C.; Monti, S. Phys. Chem. Chem. Phys. 2004, 6, 2849-2857]. RESP partial charges were assigned to reproduce the electrostatic potential determined at the HF/6-31G level of theory. The analysis of trajectories allowed the conformations of bitucarpin and erybraedin as well as the distribution of water molecules around them to be elucidated. During one of the simulations only, the scaffold of erybraedin undergoes interconversion from its most stable Ht conformation to the Ot one and vice versa. Radial distribution functions, coordination numbers, and angular distributions put forward the extent of solvent structure and the hydrogen bonding behavior of their various (methoxy, hydroxyl, or ethereal) oxygen atoms. The distribution of solvent molecules in the first and second solvation shells as well as the residence times for the different solute-solvent interacting sites have been considered.

Hydrogen Bonding↗

Dynamics and plasticity in developing neuronal networks in vitro.

When dissociated cortical tissue is brought into culture, neurons readily grow out by forming axonal and dendritic arborizations and synaptic connections. These developing neuronal networks in vitro display spontaneous firing activity from about the end of the first week in vitro. When cultured on multielectrode arrays firing activity can be recorded from many neurons simultaneously over long periods of time. These experimental approaches provide valuable data for studying firing dynamics in neuronal networks in relation to an ongoing development of neurons and synaptic connectivity in the network. This chapter summarizes recent findings on the characteristics and developmental changes in the spontaneous firing dynamics. These changes include long-lasting transient periods of increased firing at individual sites on a time scale of days to weeks, and an age-specific repetitive pattern of synchronous network firing (network bursts) on a time scale of seconds. Especially the spatio-temporal organization of firing within network bursts showed great stability over many hours. In addition, a progressive day-to-day evolution was observed, with an initial broadening of the burst firing rate profile during the 3rd week in vitro (WIV) and a pattern of abrupt onset and precise spike timing from the 5th WIV onwards. These developmental changes are discussed in the light of structural changes in the network and activity-dependent plasticity mechanisms. Preliminary findings are presented on the pattern of spike sequences within network burst, as well as the effect of external stimulation on the spatio-temporal organization within network bursts.

Animals↗

Mathematical modelling of dynamics and control in metabolic networks. III. Linear reaction sequences.

Kinetics of linear sequences of enzymatic reactions converting a single substrate into a single product are examined with emphasis on obtaining the relationship between the individual kinetic parameters and overall dynamic behavior. Chains of reactions exhibiting irreversible Michaelis-Menten kinetics are examined via scaling, linearization and modal analysis. The modal analysis gives the conditions under which the quasi-steady state assumption is applicable for one reaction relative to another in such a reaction sequence. The linearized description permits characterization of the transient response in terms of temporal moments. The moments provide useful physical insight and also provide a basis for systematic model reduction.

Enzymes↗

Reverse engineering gene networks: integrating genetic perturbations with dynamical modeling.

While the fundamental building blocks of biology are being tabulated by the various genome projects, microarray technology is setting the stage for the task of deducing the connectivity of large-scale gene networks. We show how the perturbation of carefully chosen genes in a microarray experiment can be used in conjunction with a reverse engineering algorithm to reveal the architecture of an underlying gene regulatory network. Our iterative scheme identifies the network topology by analyzing the steady-state changes in gene expression resulting from the systematic perturbation of a particular node in the network. We highlight the validity of our reverse engineering approach through the successful deduction of the topology of a linear in numero gene network and a recently reported model for the segmentation polarity network in Drosophila melanogaster. Our method may prove useful in identifying and validating specific drug targets and in deconvolving the effects of chemical compounds.

Algorithms↗

On redundancy in neural architecture: dynamics of a simple module-based neural network and initial-state independence.

This article discusses the relationship between redundancy in neural architecture and activity (cell output or internal state) dynamics with a simple module-based neural network. In the network, a single neural cell with self-feedback is employed as a module sub-network, and all module sub-networks are connected via inter-module connections. In general, the activity dynamics of a single neural cell with positive self-feedback may have two minima in its energy surface, and the minimum the cell state converges to depends on the initial states. However, in the module-based network with all the same intra-module connections, an independence from initial states becomes conspicuous as the number of modules increases due to the architectural redundancy. Simulation and analytical studies on the network dynamics illustrate that the cell states always converge to a global minimum irrelevantly of the initial cell-states, and they never go to a local minimum when a sufficient number of modules are employed.

Journal Article↗

A model for a network of phosphorylation-dephosphorylation cycles displaying the dynamics of dominoes and clocks.

We consider a model for a network of phosphorylation-dephosphorylation cycles coupled through forward and backward regulatory interactions, such that a protein phosphorylated in a given cycle activates the phosphorylation of a protein by a kinase in the next cycle as well as the dephosphorylation of a protein by a phosphatase in a preceding cycle. The network is cyclically organized in such a way that the protein phosphorylated in the last cycle activates the kinase in the first cycle. We study the dynamics of the network in the presence of both forward and backward coupling, in conditions where a threshold exists in each cycle in the amount of protein phosphorylated as a function of the ratio of kinase to phosphatase maximum rates. We show that this system can display sustained (limit-cycle) oscillations in which each cycle in the pathway is successively turned on and off, in a sequence resembling the fall of a series of dominoes. The model thus provides an example of a biochemical system displaying the dynamics of dominoes and clocks (Murray & Kirschner, 1989). It also shows that a continuum of clock waveforms exists of which the fall of dominoes represents a limit. When the cycles in the network are linked through only forward (positive) coupling, bistability is observed, while in the presence of only backward (negative) coupling, the system can display multistability or oscillations, depending on the number of cycles in the network. Inhibition or activation of any kinase or phosphatase in the network immediately stops the oscillations by bringing the system into a stable steady state; oscillations resume when the initial value of the kinase or phosphatase rate is restored. The progression of the system on the limit cycle can thus be temporarily halted as long as an inhibitor is present, much as when a domino is held in place. These results suggest that the eukaryotic cell cycle, governed by a network of phosphorylation-dephosphorylation reactions in which the negative control of cyclin-dependent kinases plays a prominent role, behaves as a limit-cycle oscillator impeded in the presence of inhibitors. We contrast the case where the sequence of domino-like transitions constitutes the clock with the case where the sequence of transitions is passively coupled to a biochemical oscillator operating as an independent clock.

Animals↗

Predicting internal protein dynamics from structures using coupled networks of hindered rotators.

Internal motions in proteins, such as oscillations of internuclear vectors u(N(i)H(i) (N)) of amide bonds about their equilibrium position, can be characterized by a local order parameter. This dynamic parameter can be determined experimentally by measuring the longitudinal and transverse relaxation rates of (15)N(i) nuclei by suitable NMR methods. In this paper, it is shown that local variations of order parameters S(ii) (2) can be predicted from the knowledge of the structure. To this effect, the diffusive motion of the internuclear vector u(N(i)H(i) (N)) is described in a potential that takes into account the deviations of the angles theta(ij) between u(N(i)H(i) (N)) and neighboring vectors u(N(j)H(j) (N)) from their average value and similarly of deviations of the angles subtended between u(N(i)H(i) (N)) and u(X(j)Y(j)), where X(j) and Y(j) are heavy atoms in the vicinity of the u(N(i)H(i) (N)) vector under investigation. It is shown how the concept of vicinity can be defined by a simple cutoff threshold, i.e., by neglecting vectors u(X(j)Y(j)) with distances d(N(i),X(j))>7.5 A. The local order parameters S(ii) (2) can be predicted from the structure using a limited set of coordinates of heavy atoms. The inclusion of a larger number of heavy atoms does not improve the predictions. Applications to calmodulin, calbindin, and interleukin 4 illustrate the success and limitations of the predictions.

Algorithms↗

Slow filament dynamics and viscoelasticity in entangled and active actin networks.

This paper deals with correlations between the viscoelastic impedance of entangled actin networks and the slow conformational dynamics and diffusive motions of single filaments. The single filament dynamics is visualized and analysed by analysing the Brownian motion of attached colloidal beads, which enables independent measurements of characteristic viscoelastic response times such as the entanglement and reptation times. We further studied the frequency-dependent viscoelastic impedance of active actin-heavy-meromyosin II networks by magnetic-tweezers microrheometry to gain insight into the effect of such highly dynamic and force-generating crosslinkers (exhibiting bond lifetimes of less than 1 s) on the rheological properties. We show that at high frequencies (higher than 1 Hz) the viscoelastic loss modulus is slightly increased relative to the entangled network (associated with an increase in the energy dissipated during mechanical excitations), while at low frequencies the plateau of the impedance spectrum becomes more pronounced as a consequence of the cross-linking of the network and the suppression of the terminal regime. Our data provide evidence that the myosin motor protein may play a role as softener of the actin cortex, enabling the adaptive reduction of the yield stress of cells and thus facilitating cellular deformations.

Actin Cytoskeleton↗

Experiments in artificial psychology: conditioning of asynchronous neural network models.

An asynchronous model for the dynamics of neural networks admits learning behaviors characteristic of classical and operant conditioning provided that appropriate plasticity algorithms are chosen. Stimulus generalization and discrimination can also be observed. Studies of such psychological phenomena are carried out by computer simulation of networks with designated sensory, association, and motor neurons, and the results are compared to those for live subjects. Various prescriptions for plasticity are investigated, including those corresponding to reward, punishment, and unlearning routines. These are characterized by their effect on network stability as quantified by a newly proposed stability measure.

Animals↗

Classification of rhythmic patterns in the stomatogastric ganglion.

A large class of neural pattern generators change their rhythmic output under the influence of neuromodulators. We present a method for identifying the variety of rhythmic patterns generated by small neural networks. The technique provides a tool for investigating the biological mechanisms responsible for pattern generation and pattern switching. Discrete methods based on transition graphs are applied to dynamic biological networks to generate sets of possible rhythmic behaviours. A measure is introduced onto the set of rhythms to quantify their differences and organize the set according to clusters of similar rhythms. Each cluster represents a different operational mode of the network. Examples are drawn from the stomatogastric ganglion, a well studied network that controls the muscles in the foregut of crustaceans. Classes of rhythms are found that correspond to experimentally observed patterns, and other classes of rhythms are found that have not yet been observed. Predictions are made for the rhythmic output of the stomatogastric ganglion under specific manipulations of parameters in the biological network.

Animals↗

Response of complex networks to stimuli.

We consider the response of complex systems to stimuli and argue for the importance of both sensitivity, the possibility of large response to small stimuli, and robustness, the possibility of small response to large stimuli. Using a dynamic attractor network model for switching of patterns of behavior, we show that the scale-free topologies often found in nature enable more sensitive response to specific changes than do random networks. This property may be essential in networks where appropriate response to environmental change is critical and may, in such systems, be more important than features, such as connectivity, often used to characterize network topologies. Phenomenologically observed exponents for functional scale-free networks fall in a range corresponding to the onset of particularly high sensitivities, while still retaining robustness.

Biology↗

Locally activated neural networks and stable neural controller design for nonlinear dynamic systems.

A stable neural control scheme using a locally activated neural network has been proposed for a class of nonlinear dynamic systems. The locally activated neural network, for a given input, essentially selects a small subset of the network hidden nodes for output computation using the CMAC-like content addressing mechanism. This network aims to maintain local representations of the system dynamics. Thus, the global control performance in the concerned state space is achieved by the cooperation of many local control efforts and furthermore, real-time control can be facilitated because only a small sized network is involved to control and learn at any given time. The proposed control scheme is composed of two stages: (1) prediction error based learning in which the network attempts to learn the nonlinear basis functions of the plant inverse dynamics by a modified backpropagation learning rule; and (2) tracking error based learning in which the network weights are further fine-tuned using the basis set obtained in (1). This basis set spans the locally partitioned vector space of the system inverse dynamics when the prediction error based learning is achieved within a prescribed error tolerance. For uniform stability, the sliding mode control is introduced as a safety mechanism when the network has not sufficiently learned the plant dynamics yet. With suitable assumptions on the controlled plant, global stability and tracking error convergence proof has been given. Finally, the proposed control scheme is verified with computer simulation.

Adaptation, Physiological↗

Self-organizing network services with evolutionary adaptation.

This paper proposes a novel framework for developing adaptive and scalable network services. In the proposed framework, a network service is implemented as a group of autonomous agents that interact in the network environment. Agents in the proposed framework are autonomous and capable of simple behaviors (e.g., replication, migration, and death). In this paper, an evolutionary adaptation mechanism is designed using genetic algorithms (GAs) for agents to evolve their behaviors and improve their fitness values (e.g., response time to a service request) to the environment. The proposed framework is evaluated through simulations, and the simulation results demonstrate the ability of autonomous agents to adapt to the network environment. The proposed framework may be suitable for disseminating network services in dynamic and large-scale networks where a large number of data and services need to be replicated, moved, and deleted in a decentralized manner.

Algorithms↗

Hardware prototypes of a Boolean neural network and the simulated annealing optimization method.

Boolean Neural Network is a neural network that operates with binary weight values of "1" and "0". Otherwise it is formally analogous to the Multilayer Perceptron (MLP). Simulated Annealing is a stochastic optimization methods that is suitable for performing nonlinear multivariable optimization tasks. Training a Boolean Neural Network is a well-suited problem to this algorithm. However, the Simulated Annealing method is computationally heavy, which makes the training procedure slow. The training speed can be improved by using custom designed hardware for the whole system including the optimization method and the neural network. Hardware prototypes of a Boolean Neural Network and the Simulated Annealing optimization method have been designed using discrete components. The Boolean Neural Network implementation is basically a dynamically configurable feedforward network of Boolean logic gates of two inputs. The Simulated Annealing implementation is a general purpose hardware tool for multivariable optimization tasks. Here it is applied to do supervised training of the Boolean Neural Network hardware.

Algorithms↗