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We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.
The response of the sensorimotor cortical slice to repetitive, single-site afferent drive is mapped using both evoked potential and metabolic mapping [2-deoxyglucose (2DG)] methods. Systematic changes (increases or decreases) in the evoked potential occur during repetitive 3-5 Hz stimulation. These resemble the changes in SI neuron response observed in the in vivo studies of the preceding companion article; they occur rapidly, recover within 1 min and are reproducible if stimulus parameters remain unchanged. Place, timing, and intensity of repetitive stimulation influence the amplitude and form of the response alterations observed at a given cortical locus. The neuron populations that exhibit different response modifications to the same repetitive stimulus are distributed nonrandomly in the slice: neurons occupying column-shaped aggregates undergo a common response alteration (either an increase or decrease) during repetitive stimulation, with sharp boundaries separating neighboring aggregates distinguishable on the basis of their dynamic behaviors. The distribution of stimulus-evoked 2DG uptake in the slice is "columnar," the dimensions of the 2DG columns corresponding to those mapped with neurophysiological methods. Taken together, the findings support the concept that repetitive stimulation causes the intrinsic network of somatosensory cortex to modify dynamically the network's response to extrinsic excitatory drive so that the local differences in the pattern of extrinsic excitatory drive to neighboring cortical columns are enhanced.
We study the condensation phenomenon in a zero-range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase transition between a condensed phase and an uncondensed phase, and the phase diagram is obtained analytically. As for the dynamical property, we find that the relaxation dynamics depends on the global structure of underlying networks. The relaxation time follows the power law tau approximately Lz with the network size L in the condensed phase. The dynamic exponent z is found to take a different value depending on whether underlying networks have a tree structure or not.
Years of careful experimental analysis have revealed that signaling molecules are organized into complex networks of biochemical reactions exquisitely regulated in time and space to provide a cell with high-fidelity information about an extremely noisy and volatile environment. A new view of signaling networks as systems consisting of multiple complex elements interacting in a multifarious fashion is emerging, a view that conflicts with the single-gene or protein-centric approach common in biological research. The postgenomic era has brought about a different, network-centric methodology of analysis, suddenly forcing researchers toward the opposite extreme of complexity, where the networks being explored are, to a certain extent, intractable and uninterpretable. Both the cartoons of simple pathways and the very large "hair-ball" diagrams of large intracellular networks are also representations of static worlds, superficially devoid of dynamics and chemistry. These representations are often viewed as being analogous to stably linked computer and neural networks rather than dynamically changing networks of chemical interactions, where the notions of concentration, compartmentalization, and diffusion may be the primary determinants of connectivity. Arguably, the systems biology approach, relying on computational modeling coupled with various experimental techniques and methodologies, will be an essential component of analysis of the behavior of signal transduction pathways. Combining the dynamical view of rapidly evolving responses and the structural view arising from high-throughput analyses of the interacting species will be the best approach toward efforts toward greater understanding of intracellular signaling processes.
In this work I investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. I perform extensive simulations for the calculation of the mean squared displacement, the network coverage, and the survival probability on a network with a concentration c of static traps. It is shown that the random walkers remain close to their origin, but cover a large part of the network at the same time. This behavior is markedly different than usual random walk processes in the literature. For the trapping problem I numerically compute Phi(n,c) , the survival probability of mobile species at time n , as a function of the concentration of trap nodes, c . Comparison of these results to the Rosenstock approximation indicate that this is an adequate description for networks with 2 3 the behavior is more complicated and one needs to employ a truncated cumulant expansion.
Considerable progress has been made in identifying the molecular composition of complex signaling networks controlling cell proliferation, differentiation, and survival. However, to discover general building principles and predict the dynamic behavior of signaling networks, it is necessary to develop quantitative models based on experimental observations. Here we report a mathematical model of the core module of the Janus family of kinases (JAK)-signal transducer and activator of transcription (STAT) signaling pathway based on time-resolved measurements of receptor and STAT5 phosphorylation. Applying the fitted model, we can determine the quantitative behavior of STAT5 populations not accessible to experimental measurement. By in silico investigations, we identify the parameters of nuclear shuttling as the most sensitive to perturbations and verify experimentally the model prediction that inhibition of nuclear export results in a reduced transcriptional yield. The model reveals that STAT5 undergoes rapid nucleocytoplasmic cycles, continuously coupling receptor activation and target gene transcription, thereby forming a remote sensor between nucleus and receptor. Thus, dynamic modeling of signaling pathways can promote functional understanding at the systems level.
Oscillatory attractor neural networks can perform temporal segmentation, i.e., separate the joint inputs they receive, through the formation of staggered oscillations. This property, which may be basic to many perceptual functions, is investigated here in the context of a symmetric dynamic system. The fully segmented mode is one type of limit cycle that this system can develop. It can be sustained for only a limited number n of oscillators. This limitation to a small number of segments is a basic phenomenon in such systems. Within our model we can explain it in terms of the limited range of narrow subharmonic solutions of the single nonlinear oscillator. Moreover, this point of view allows us to understand the dominance of three leading amplitudes in solutions of partial segmentation, which are obtained for high n. The latter are also abundant when we replace the common input with a graded one, allowing for different inputs to different oscillators. Switching to an input with fluctuating components, we obtain segmentation dominance for small systems and quite irregular waveforms for large systems.
This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works.
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In continuation of earlier computer simulation studies 15 of the feedback inhibition exercised by the Golgi cells of the cerebellum, an attempt is made at modeling the behavior of Purkinje and basket cells under somewhat more complex functional circumstances. The simulation study is based on a realistic network model (with respect to numerical and metrical parameters, and consisting of more than 3 X 10(4) units) of the cat cerebellar cortex, derived from a recent quantitative histological and stereological analysis 9-12. As an input two identical pairs of foci of incoming mossy fiber activity are applied, separated from one another both spatially and temporally. The stimulation results showed that the assumption of a rigidly preaddressed wiring in the parallel fiber--Purkinje cell synaptic system (i.e. that parallel fibers would systematically select for contact Purkinje cells standing in register) would hardly be realistic because such a solution would offer no advantage whatever over a randomly connected synaptic system. The results would favor the contention that dendritic geometry of the Purkinje cells has a crucial significance in the sense of the concepts developed by W. Rall. The stimulation gives some important hints for the ways in which the specific inhibitory interneuron systems (Golgi and basket cells) add refinement to the operations of the network, particularly in securing integration of the influences of parallel fibers thrown into action by mossy input to spatially and temporally separated foci, especially at the level of Purkinje cells positioned in interfocal areas. Reducing the length of the parallel fibers to one-half of what was suggested by the stereological studies causes a serious breakdown of interfocal neighborhood interactions.
A hydrophilic semi-interpenetrating polymer network of polyvinyl alcohol (PVA), poly(ethylene glycol) (PEG) and crosslinked polyacrylamide (PAM) chains has been synthesized and its potential for controlled release of macromolecular drugs has been assessed by taking insulin as a representative drug. The semi-IPN was characterized by IR studies and network parameters such as the average molecular weight between crosslinks (Mc), crosslink density (q), and number of elastically effective chains (Ve) were evaluated. The effect of chemical architecture of the IPN was investigated on the percent loading of insulin and its subsequent release from the loaded device. Other parameters such as the thickness of the gel, molecular weight of PEG and pH and temperature of the release medium were also studied for their possible impact on the release of insulin. The whole release data was analyzed by Ficks power law and the influence of various factors on the plausible mechanism of insulin release was investigated.
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Surface layers (S-layers), which form the outermost layers of many Bacteria and Archaea, consist of protein molecules arranged in two-dimensional crystalline arrays. Bacillus anthracis, a gram-positive, spore-forming bacterium, responsible for anthrax, synthesizes two abundant surface proteins: Sap and EA1. Regulatory studies showed that EA1 and Sap appear sequentially at the surface of the parental strain. Sap and EA1 can form arrays. The structural parameters of S-layers from mutant strains (EA1(-) and Sap(-)) were determined by computer image processing of electron micrographs of negatively stained regular S-layer fragments or deflated whole bacteria. Sap and EA1 projection maps were calculated on a p1 symmetry basis. The unit cell parameters of EA1 were a = 69 A, b = 83 A, and gamma = 106 degrees, while those of Sap were a = 184 A, b = 81 A, and gamma = 84 degrees. Freeze-etching experiments and the analysis of the peripheral regions of the cell suggested that the two S-layers have different settings. We characterized the settings of each network at different growth phases. Our data indicated that the scattered emergence of EA1 destabilizes the Sap S-layer.
BACKGROUND: The problem of estimating the parameters of dynamic models of complex biological systems from time series data is becoming increasingly important. METHODS AND RESULTS: Particular consideration is given to metabolic systems that are formulated as Generalized Mass Action (GMA) models. The estimation problem is posed as a global optimization task, for which novel techniques can be applied to determine the best set of parameter values given the measured responses of the biological system. The challenge is that this task is nonconvex. Nonetheless, deterministic optimization techniques can be used to find a global solution that best reconciles the model parameters and measurements. Specifically, the paper employs branch-and-bound principles to identify the best set of model parameters from observed time course data and illustrates this method with an existing model of the fermentation pathway in Saccharomyces cerevisiae. This is a relatively simple yet representative system with five dependent states and a total of 19 unknown parameters of which the values are to be determined. CONCLUSION: The efficacy of the branch-and-reduce algorithm is illustrated by the S. cerevisiae example. The method described in this paper is likely to be widely applicable in the dynamic modeling of metabolic networks.
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The evolution of sex determination mechanisms is known to be relatively rapid, though recent evidence indicates that certain parts of the mechanism may be more highly conserved. These characteristics establish the sex determination mechanism as a good candidate for the theoretical study of gene network evolution, particularly of networks involved in development. We investigate the short-term evolutionary potential of the sex determination mechanism in Drosophila melanogaster with the aid of a synchronous logical model. We introduce general theoretical concepts such as a network-specific form of mutation, and a notion of functional equivalence between networks. We apply this theoretical framework to the sex determination mechanism and compare it to a population of random networks, enabling us to find features both general to sex determination networks, and particular to the Drosophila network. In general, sex determination networks exist within large sets of functionally equivalent networks all of which satisfy the sex determination task. These large sets are in turn composed of subsets which are mutationally related, suggesting a high degree of flexibility is available without compromising the core functionality. Two particular characteristics of the Drosophila network are found: (a) a parsimonious use of gene interactions, and (b) the network structure can produce a relatively large number of dynamical pattern variations through single network mutations.
To elucidate the hidden dynamics of extracellular-signal-regulated kinase (ERK) signalling networks, we developed a simulation model of ERK signalling networks by constraining in silico dynamics based on in vivo dynamics in PC12 cells. We predicted and validated that transient ERK activation depends on rapid increases of epidermal growth factor and nerve growth factor (NGF) but not on their final concentrations, whereas sustained ERK activation depends on the final concentration of NGF but not on the temporal rate of increase. These ERK dynamics depend on Ras and Rap1 dynamics, the inactivation processes of which are growth-factor-dependent and -independent, respectively. Therefore, the Ras and Rap1 systems capture the temporal rate and concentration of growth factors, and encode these distinct physical properties into transient and sustained ERK activation, respectively.