Analysis of a neural oscillator

Although the Matsuoka neural oscillator, which was originally proposed as a model of central pattern generators, has widely been used for various robots performing rhythmic movements, its characteristics are not clearly explained even now. This article shows two closed-form relations that express the frequency and amplitude of the generated oscillation as functions of the parameters of the model. Although they are derived based on a rough linear approximation, they accord with the result obtained by a simulation considerably. The obtained relations also give us some nontrivial predictions about the properties of the oscillator.     

Multiple modes in a coral species abundance distribution

Species abundance distributions are an important measure of biodiversity and community structure. These distributions are affected by sampling, and alternative species-abundance models often make similar predictions for small sample sizes. Very large samples reveal the relative abundances of rare species, and thus provide information about species relative abundances that small samples cannot. Here, we present the species-abundance distribution for a sample of > 40,000 coral colonies at a single site, exceeding existing samples of coral local assemblages by over an order of magnitude. This abundance distribution is multimodal when examined on a logarithmic scale. Four different model selection procedures all indicate that the underlying community abundance distribution has at least three modes. We show that the multiple modes are not caused by mixtures of species with different habitat preferences. However, spatial aggregation partially explains our results. We inspect published work on species abundance distributions, and suggest that multimodality may be a common feature of large samples.     

Optimal open-loop desynchronization of neural oscillator populations

Deep brain stimulation (DBS) is an increasingly used medical treatment for various neurological disorders. While its mechanisms are not fully understood, experimental evidence suggests that through application of periodic electrical stimulation DBS may act to desynchronize pathologically synchronized populations of neurons resulting desirable changes to a larger brain circuit. However, the underlying mathematical mechanisms by which periodic stimulation can engender desynchronization in a coupled population of neurons is not well understood. In this work, a reduced phase-amplitude reduction framework is used to characterize the desynchronizing influence of periodic stimulation on a population of coupled oscillators. Subsequently, optimal control theory allows for the design of periodic, open-loop stimuli with the capacity to destabilize completely synchronized solutions while simultaneously stabilizing rotating block solutions. This framework exploits system nonlinearities in order to strategically modify unstable Floquet exponents. In the limit of weak neural coupling, it is shown that this method only requires information about the phase response curves of the individual neurons. The effects of noise and heterogeneity are also considered and numerical results are presented. This framework could ultimately be used to inform the design of more efficient deep brain stimulation waveforms for the treatment of neurological disease.

     

Spike-time reliability of layered neural oscillator networks

We study the reliability of layered networks of coupled “type I” neural oscillators in response to fluctuating input signals. Reliability means that a signal elicits essentially identical responses upon repeated presentations, regardless of the network’s initial condition. We study reliability on two distinct scales: neuronal reliability, which concerns the repeatability of spike times of individual neurons embedded within a network, and pooled-response reliability, which concerns the repeatability of total synaptic outputs from a subpopulation of the neurons in a network. We find that neuronal reliability depends strongly both on the overall architecture of a network, such as whether it is arranged into one or two layers, and on the strengths of the synaptic connections. Specifically, for the type of single-neuron dynamics and coupling considered, single-layer networks are found to be very reliable, while two-layer networks lose their reliability with the introduction of even a small amount of feedback. As expected, pooled responses for large enough populations become more reliable, even when individual neurons are not. We also study the effects of noise on reliability, and find that noise that affects all neurons similarly has much greater impact on reliability than noise that affects each neuron differently. Qualitative explanations are proposed for the phenomena observed.

Resonant hopping of a robot controlled by an artificial neural oscillator

The bouncing gaits of terrestrial animals (hopping, running, trotting) can be modeled as a hybrid dynamic system, with spring-mass dynamics during stance and ballistic motion during the aerial phase. We used a simple hopping robot controlled by an artificial neural oscillator to test the ability of the neural oscillator to adaptively drive this hybrid dynamic system. The robot had a single joint, actuated by an artificial pneumatic muscle in series with a tendon spring. We examined how the oscillator-robot system responded to variation in two neural control parameters: descending neural drive and neuromuscular gain. We also tested the ability of the oscillator-robot system to adapt to variations in mechanical properties by changing the series and parallel spring stiffnesses. Across a 100-fold variation in both supraspinal gain and muscle gain, hopping frequency changed by less than 10%. The neural oscillator consistently drove the system at the resonant half-period for the stance phase, and adapted to a new resonant half-period when the muscle series and parallel stiffnesses were altered. Passive cycling of elastic energy in the tendon accounted for 70-79% of the mechanical work done during each hop cycle. Our results demonstrate that hopping dynamics were largely determined by the intrinsic properties of the mechanical system, not the specific choice of neural oscillator parameters. The findings provide the first evidence that an artificial neural oscillator will drive a hybrid dynamic system at partial resonance.     

Multiple modes of cytoplasmic dynein regulation

In performing its multiple cellular functions, the cytoplasmic dynein motor is subject to complex regulation involving allosteric mechanisms within the dynein complex, as well as numerous extramolecular interactions controlling subcellular targeting and motor activity. Recent work has distinguished high- and low-load regulatory modes for cytoplasmic dynein, which, combined with a diversity of targeting mechanisms, accounts for a very broad range of functions.     

Multiple photopigments entrain the Mammalian circadian oscillator

Circadian rhythms are entrained to the natural day:night cycle. Melanopsin expressed in retinal ganglion cells partially accounts for circadian photoentrainment. Dkhissi-Benyahya et al. demonstrate that medium wavelength opsin (MW-opsin) also plays an important role in the process. Furthermore, they develop a model explaining wavelength-dependent photoentrainment by melanopsin and MW-opsin.     

A new model for simple neural nets and its application in the design of a neural oscillator

The results of a previous theoretical study of a class of systems are applied for the design of neural nets which try to simulate biological behavior. Besides the models for single aperiodic and periodic neurons, a “neural oscillator” is developed which consists of two cross-excited neurons. Its response is similar to the firing pattern of certain biological neural oscillators, like the flying system of the locust. Also, by proper change of its parameters, it can be made highly irregular, providing a deterministic model for the spontaneous neural activity.     

Cyclic modes in neural net models

Neural network models with possible cross-coupling from every neuron to every other neuron are condisered. The all-or-none law is assumed for firing of neurons. A network is shown to have a set of latent cyclic modes. If the net is stimulated briefly, it will subsequently either return to quiescence or settle into periodic activity in one of its cyclic modes. Realization of cyclic modes and analysis of nets are discussed. A learning rule for adjustment of synaptic strengths is presented.     

Cyclic modes in artificial neural nets

Artificial neural nets constructed of dicrete populations of 200–1000 formal neurons have been studied through computer simulation. Among the basic assumptions of operation of these nets are the following: a) Each neuron fires at times which are integral multiples of the synaptic delay . b) It produces the appropriate PSP's after . c) All the neurons have the same refractory period and d) temporal summation occurs without decrement, for a period less than the synaptic delay. The nets were specified by a number of parameters: fraction of inhibitory neurons in the population, average number of connections to each cell, threshold for cell firing. These parameters did not determine the detailed microscopical structures of nets which was established separately on a random basis.For the range of the parameters considered in this study it was found that neural nets are capable of supporting self-maintaining activity in the form of cycling modes, characterized by a fixed period. The period of the cycles can be altered by a steady, non-cycling external input to the net. Evidence is presented that the cycling modes depend upon the statistical parameters of the net and the stimulus characteristics rather than on the detailed structure of the net. These results suggest that non-structured nerve nets may respond in specific manner to specific stimuli.

Glossary

Parameters of Neural Net Model Synaptic delay - A Total number of neurons in the netlet - h Fraction of inhibitory neurons in the netlet (in % of total number of neurons) - ⁺ Average number of axon branches emanating from anexcitatory neuron - ^– Average number of axon branches emanating from an inhibitory neuron - k ⁺ Average EPSP produced by an excitatory neuron in arbitrary units of amplitude - k ^– Average IPSP produced by an inhibitory neuron in arbitrary units of amplitude - Firing threshold of neurons in the netlet - The minimum number of ESPS's necessary to trigger a neuron in the absence of inhibitory inputs - The minimum number of ESPS's necessary to trigger a neuron in the presence of inhibitory inputs. Dynamic Parameters of the Model n An integer giving the number of elapsed synaptic delays (i.e. elapsed time) - _n The activity; i.e. the fraction of active neurons in the netlet at t=n (the actual number of active cells is given by _nA) - _n={ⁱ_n} State vector of single netlet at time n This research has been supported by NIH grants NS-8012 and NS-8498, and NSF grant GB-30498. Computation assistance was provoded by the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources grant RR-3.     

Dynamics of a hybrid system of a brain neural network and an artificial nonlinear oscillator

In the brain, many functional modules interact with each other to execute complex information processing. Understanding the nature of these interactions is necessary for understanding how the brain functions. In this study, to mimic interacting modules in the brain, we constructed a hybrid system mutually coupling a hippocampal CA3 network as an actual brain module and a radial isochron clock (RIC) simulated by a personal computer as an artificial module. Return map analysis of the CA3-RIC system's dynamics showed the mutual entrainment and complex dynamics dependent on the coupling modes. The phase response curve of CA3 was modeled regarding the CA3 as a nonlinear oscillator. Using the phase response curves of CA3 and RIC, we reconstructed return maps of the hybrid system's dynamics. Although the reconstructed return maps almost agreed with the experimental data, there were deviations dependent on the coupling mode. In particular, we noted that the deviation was smaller under the bidirectional coupling conditions than during the one-way coupling from RIC to CA3. These results suggest that brain modules may flexibly change their dynamical properties through interaction with other modules.     

Multiple modes of ribosomal RNA transcription in vitro

The rate of rRNA synthesis from E. coli DNA in vitro can exhibit an unusual temperature dependence. Instead of the typical sigmoid curve, at least five to six pronounced peaks of rRNA synthesis are detectable over a 30° range in temperature. rRNA synthesis from preformed initiation complexes exhibits a similar pattern and shows that the number of polymerases able to initiate rRNA synthesis increases with each successive peak. These results are interpreted in terms of a model which proposes that the rRNA cistrons are served by multiple promoter sites (subpromoters) whose activation energies form a graded series. Thus the number of polymerases initiating rRNA synthesis could be controlled by regulating the number of active subpromoters.     

Protein 8-class secondary structure prediction using conditional neural fields

Compared with the protein 3-class secondary structure (SS) prediction, the 8-class prediction gains less attention and is also much more challenging, especially for proteins with few sequence homologs. This paper presents a new probabilistic method for 8-class SS prediction using conditional neural fields (CNFs), a recently invented probabilistic graphical model. This CNF method not only models the complex relationship between sequence features and SS, but also exploits the interdependency among SS types of adjacent residues. In addition to sequence profiles, our method also makes use of non-evolutionary information for SS prediction. Tested on the CB513 and RS126 data sets, our method achieves Q8 accuracy of 64.9 and 64.7%, respectively, which are much better than the SSpro8 web server (51.0 and 48.0%, respectively). Our method can also be used to predict other structure properties (e.g. solvent accessibility) of a protein or the SS of RNA.     

A theoretical basis for conditional probability analyses of neural discharge activity

A theory has been developed which allows the estimation of the probability density of a discharge, given that an arbitrary condition is fulfilled. It is shown that the common methods for the evaluation of a post-stimulus time (PST) histogram and a hazard function can be considered as special applications of this theory. Whereas the usual hazard function shows how the probability of a discharge depends on the time elapsed since the last discharge, generalized hazard functions proposed in the present paper allow to reveal also the influence of the last but one discharge, the last but two discharge, and so on. In contrast to the usual method for the estimation of a hazard function, the applicability of the procedures proposed here is not restricted to stationary discharge activity. Some elementary applications are illustrated by analysing simulated discharge activity mimicing the response of a single auditory-nerve fiber to a high-intensity tone burst.     

Genetic dissection of neural circuitry regulating behavioral state using conditional transgenics

Conditional transgenic animals are useful tools that can be used to determine the detailed anatomic and molecular bases of sleep–wake regulation. This short review highlights some of the most recent molecular biological technologies for “systems-level” sleep research in freely behaving animals. These technical advances include a wide range of approaches from conditional deletion of genes based on the Cre/loxP technology to RNA interference to the in vivo reversible manipulation (silencing and activation) of neurons by tetracycline-controlled tetanus neurotoxin or the expression of genetically modified receptor-channel complexes. In combination with these advanced genetic techniques, adeno-associated viral vectors (AAVs) represent a versatile gene delivery system for stereotaxic-based brain microinjections and regionally restricted transduction of neuronal cell populations.

     

Fast and robust image segmentation by small-world neural oscillator networks

Inspired by the temporal correlation theory of brain functions, researchers have presented a number of neural oscillator networks to implement visual scene segmentation problems. Recently, it is shown that many biological neural networks are typical small-world networks. In this paper, we propose and investigate two small-world models derived from the well-known LEGION (locally excitatory and globally inhibitory oscillator network) model. To form a small-world network, we add a proper proportion of unidirectional shortcuts (random long-range connections) to the original LEGION model. With local connections and shortcuts, the neural oscillators can not only communicate with neighbors but also exchange phase information with remote partners. Model 1 introduces excitatory shortcuts to enhance the synchronization within an oscillator group representing the same object. Model 2 goes further to replace the global inhibitor with a sparse set of inhibitory shortcuts. Simulation results indicate that the proposed small-world models could achieve synchronization faster than the original LEGION model and are more likely to bind disconnected image regions belonging together. In addition, we argue that these two models are more biologically plausible.     

Multiple binding modes for Hoechst 33258 to DNA

Two binding modes for the bisbenzimidazole Hoechst 33258 to native DNA at physiological conditions have been distinguished. Type 1 binding, which dominated at low dye/phosphate ratios (D/P less than 0.05) or low dye concentrations, had a high quantum yield of fluorescence with maximum emission at 460 nm. Binding of the dye at type 2 sites (0.05 less than D/P less than 0.4) lead to quenching of fluorescence from type 1 bound dye, presumably by nonradiative energy transfer. Fluorescence quantum yield of type 2 bound dye was low (phi = 0.05-0.1) and it peaked around 490 nm. At D/P greater than 0.4, the dye/DNA complex precipitated. This was caused by an additional dye-DNA interaction that was strongly cooperative. The anomalous dispersion of the refractive index of the complex changed abruptly around D/P = 0.4, indicating that the precipitating dye-DNA interaction involved strong electronic interaction between dye molecules. Hoechst 33258 precipitated polynucleotides irrespective of strandedness and base composition when dye concentration was raised above 1 X 10(-5) M. In the presence of 25% ethanol, type 2 binding to DNA did not occur, whereas the binding constant for type 1 binding (kappa = 2 X 10(3) M-1) was about two orders of magnitude smaller than in physiological buffer. DNA was not precipitated by high concentrations of Hoechst 33258 in 25% ethanol.