Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.     

Resonance modulation,annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics

Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slave to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decreases with the input frequency. In contrast, for f ? 1 the dynamics are quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.     

Genetic evaluation of ovulatory disorders in Austrian Fleckvieh cows: a comparison between linear models and survival analysis

The objective of this study was to compare linear models and survival analysis for genetic evaluation of ovulatory disorders, which included veterinary treatments of silent heat/anestrus and cystic ovaries. Data of 23 450 daughters of 274 Austrian Fleckvieh sires were analyzed. For linear model analyses, ovulatory disorders were defined as a binary response (presence or absence) in the time periods from calving to 150 days after calving and from calving to 300 days after calving. For survival analysis, ovulatory disorders were defined either as the number of days from calving to the day of the first treatment for an ovulatory disorder (uncensored record) or from calving to the day of culling, or the last day of the period under investigation (until 150 or 300 days after calving; censored record). Estimates of heritability were very similar (0.016 to 0.020) across methods and periods. Correlations between sire estimated breeding value from linear model and survival analysis were 0.98, whereas correlations between different time periods were somewhat lower (0.95 and 0.96). The results showed that the length of time period had a larger effect on genetic evaluation than methodology.     

FPNA: interaction between FPGA and neural computation

Neural networks are usually considered as naturally parallel computing models. But the number of operators and the complex connection graph of standard neural models can not be directly handled by digital hardware devices. More particularly, several works show that programmable digital hardware is a real opportunity for flexible hardware implementations of neural networks. And yet many area and topology problems arise when standard neural models are implemented onto programmable circuits such as FPGAs, so that the fast FPGA technology improvements can not be fully exploited. Therefore neural network hardware implementations need to reconcile simple hardware topologies with complex neural architectures. The theoretical and practical framework developed, allows this combination thanks to some principles of configurable hardware that are applied to neural computation: Field Programmable Neural Arrays (FPNA) lead to powerful neural architectures that are easy to map onto FPGAs, thanks to a simplified topology and an original data exchange scheme. This paper shows how FPGAs have led to the definition of the FPNA computation paradigm. Then it shows how FPNAs contribute to current and future FPGA-based neural implementations by solving the general problems that are raised by the implementation of complex neural networks onto FPGAs.     

Coherency and connectivity in oscillating neural networks: linear partialization analysis

 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. Received: 20 October 1995 / Accepted in revised form: 20 May 1996     

A note on mathematical models for the interaction of neural elements

By introducing a plausible model for the initiation of axonal impulses the output is obtained as a function of the input incoming impulses. If the temporal aspects of the excitatory process resulting from the afferent impulses are sufficiently rapid one obtains the discontinuous or microscopic model of McCulloch-Pitts. If these are sufficiently slow a continuous model, such as Rashevsky’s one or two factor theory, is a natural model. But the linear relation between the strength of excitation of one axon and excitatory factor of the next will not in general hold. However, under conditions which are not too restrictive the linear relation with threshold can be considered as satisfactory approximation over a fairly wide range of values. This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

Quercetin and DNA in solution: analysis of the dynamics of their interaction with a linear dichroism study

Flow-Linear Dichroism (LD) spectra on quercetin-DNA solutions (buffer-ethanol 30%) showed evidence that the flavonol can intercalate the biopolymer. There is no electrostatic component in the formation of the quercetin-DNA complex. The DNA concentration and the planarity of the chromophore are limiting factors in the interaction. There are no induced LD signals for concentrations of the biopolymer less than 7.8 × 10⁻³M phosphate. The interaction is most probably of a hydrophobic nature between the most hydrophobic segment of the quercetin (benzopyran-4-one) and the intercalation site, which allows the chromophore to penetrate the DNA helix and to arrange its planar structure more or less parallel to the adjacent planes of the nitrogenous bases. A comparison between the planar and hydrophobic flavonol quercetin, and the non-planar and hydrophilic flavanone dihydroquercetin, showed that the interaction of the latter with DNA was strongly limited. The notable biological activity of the quercetin compared to the ‘weaker’ activity of the dihydroquercetin could also be derived from the different planarity (and probably hydrophobicity) of the two flavonoids. The very low concentration of the quercetin-DNA complex was efficiently shown by the high sensitivity of the LD technique, whereas it could not be resolved by isotropic UV-Vis and induced circular dichroism spectra. The hypothesis of a frame shift mutagenicity activity of quercetin (Science 1977; 197: 577–578) is highly improbable. In fact, the affinity of quercetin for DNA, which emerges from this study, is very low compared with that of a typical intercalator agent (Q. Rev. Biophys. I 1992; 25: 51–170)     

Mosaic analysis with oep mutant reveals a repressive interaction between floor-plate and non-floor-plate mutant cells in the zebrafish neural tube

The floor plate is located at the ventral midline of the neural tube in vertebrates. Floor-plate development is severely impaired in zebrafish one-eyed pinhead (oep) mutants. oep encodes a membrane-bound protein with an epiblast growth factor (EGF) motif and functions autonomously in floor-plate precursors. To understand the cell behavior and cell-cell interaction during floor-plate development, the distribution and gene expression of wild-type and oep mutant cells in genetic mosaics were examined. When mutant shield cells were transplanted into a wild-type host, an ectopic neural tube with a floor plate was induced. However, the floor plate of the secondary axis was consistently devoid of mutant cells while its notochord was composed entirely of mutant cells. This indicates that oep shield cells adopt only a notochord fate in a wild-type environment. In reciprocal transplants (wild to oep), however, grafted shield cells frequently contributed to part of the floor-plate region of the secondary neural tube and expressed floor-plate markers. Careful examination of serial sections revealed that a mutant neural cell, when located next to the wild-type cells at the ventral midline, inhibited floor-plate differentiation of the adjacent wild-type cells. This inhibition was effective over an area only one- or two-cells wide along the anteroposterior axis. As the cells located at the ventral midline of the oep neural tube are thought to possess a neural character, similar to those located on either side of the floor plate in a wild-type embryo, this inhibition may play an important role during normal development in restricting the floor-plate region into the ventral-most midline by antagonizing homeogenetic signals from the floor-plate cells.     

Fine mapping and interaction analysis of a linear rabies virus neutralizing epitope

A novel human antibody AR16, targeting the G5 linear epitope of rabies virus glycoprotein (RVG) was shown to have promising antivirus potency. Using AR16, the minimal binding region within G5 was identified as HDFR (residues 261–264), with key residues HDF (residues 261–263) identified by alanine replacement scanning. The key HDF was highly conserved within phylogroup I Lyssaviruses but not those in phylogroup II. Using computer-aided docking and interaction models, not only the key residues (Asp30, Asp31, Tyr32, Trp53, Asn54, Glu99, Ile101, and Trp166) of AR16 that participated in the interaction with G5 were identified, the van der Waals forces that mediated the epitope–antibody interaction were also revealed. Seven out of eight presumed key residues (Asp30, Asp31, Tyr32, Trp53, Asn54, Glu99, and Ile101) were located at the variable regions of AR16 heavy chains. A novel mAb cocktail containing AR16 and CR57, has the potential to recognize non-overlapping, non-competing epitopes, and neutralize a broad range of rabies virus.     

A model of the interaction between autoregulation and neural activation in the brain

In this paper a model is proposed that predicts the response of the cerebral vasculature to changes in arterial blood pressure, arterial CO2 concentration and neural stimulation. Cerebral blood flow (CBF) is assumed to be controlled through changes in arterial compliance, and hence arterial resistance and volume, through three feedback mechanisms, which act in a linear additive manner, based on CBF, arterial CO2 and neural stimulus. Together with arterial, capillary and venous compartments, a tissue compartment is included, which contributes partly to the initial rise found in the deoxyhaemoglobin response to neural activation. Dynamic simulations of the model under different conditions show that there is significant interaction between the autoregulation and activation processes, and that the level of autoregulation has a strong influence on the CBF and deoxyhaemoglobin responses to neural activation. Overshoot in the deoxyhaemoglobin response is eliminated completely in the absence of this regulation. The feedback mechanism time constants significantly affect the CBF and deoxyhaemoglobin responses. Changes in arterial blood pressure (ABP) are found to have a strong influence on the neural activation response, with the amplitude of the response decreasing significantly at high baseline ABP. Dynamic changes in ABP also have a significant and potentially confounding impact on the measured deoxyhaemoglobin response to neural activation.     

On the relationship between two models of neural entrainment

A comparison is established between the two models of neural entrainment proposed by Nagumo and Sato (1972) and by Torras (1986). Both are formulated in terms of a transition equation whose solutions of period m correspond to the different (m:r)-entrainment patterns. The existence of a transformation relating both transition equations implies the equivalence between stable entrainment for the former model and unstable entrainment for the latter one. However, there is no counterpart for the stable entrainment arising in Torras' model.     

Use of AMMI and linear regression models to analyze genotype-environment interaction in durum wheat

Summary The joint durum wheat (Triticum turgidum L var durum) breeding program of the International Maize and Wheat Improvement Center (CIMMYT) and the International Center for Agricultural Research in the Dry Areas (ICARDA) for the Mediterranean region employs extensive multilocation testing. Multilocation testing produces significant genotype-environment (GE) interaction that reduces the accuracy for estimating yield and selecting appropriate germ plasm. The sum of squares (SS) of GE interaction was partitioned by linear regression techniques into joint, genotypic, and environmental regressions, and by Additive Main effects and the Multiplicative Interactions (AMMI) model into five significant Interaction Principal Component Axes (IPCA). The AMMI model was more effective in partitioning the interaction SS than the linear regression technique. The SS contained in the AMMI model was 6 times higher than the SS for all three regressions. Postdictive assessment recommended the use of the first five IPCA axes, while predictive assessment AMMI1 (main effects plus IPCA1). After elimination of random variation, AMMI1 estimates for genotypic yields within sites were more precise than unadjusted means. This increased precision was equivalent to increasing the number of replications by a factor of 3.7.     

Indistinguishability and identifiability analysis of linear compartmental models.

Two compartmental model structures are said to be indistinguishable if they have the same input-output properties. In cases in which available a priori information is not sufficient to specify a unique compartmental model structure, indistinguishable model structures may have to be generated and their attributes examined for relevance. An algorithm is developed that, for a given compartmental model, investigates the complete set of models with the same number of compartments and the same input-output structure as the original model, applies geometrical rules necessary for indistinguishable models, and test models meeting the geometrical criteria for equality of transfer functions. Identifiability is also checked in the algorithm. The software consists of three programs. Program 1 determines the number of locally identifiable parameters. Program 2 applies several geometrical rules that eliminate many (generally most) of the candidate models. Program 3 checks the equality between system transfer functions of the original model and models being tested. Ranks of Jacobian matrices and submatrices and other criteria are used to check patterns of moment invariants and local identifiability. Structural controllability and structural observability are checked throughout the programs. The approach was successfully used to corroborate results from examples investigated by others.     

A method of analysis of the models of neural nets

Taking into account Caianiello's work of 1961 a model of a neuron quite similar to his is proposed and studied. For this model, where a temporal summation and a period of refractoriness are assumed, a mathematical approach and a simulation on computer were realized. Particular types of nets were used, namely: nets with topological structures, and fully random nets. The difference between the two types is that the first type has a two-dimensional square structure and depends on the rules of the formation of connection between the neurons, while the second type is realized by means of the probability distribution function governing the formation of the structure of the net.These types of neural nets are analysed by means of a method which permits to obtain various parameters which characterize their behaviour in time and space in terms of the trajectory of the system. Many experiments are also reported; the statistical analyses, made on them, show the great importance and influence of refractoriness on the behaviour of neural networks.In the last part of the work an interesting case is reported, in which the reaction of the net to a disturbance shows that a kind of adaptation takes place, although the structure of the net stays unchanged.On leave of absence from the Lithuanian Academy of Sciences, Vilnius, Lithuanian S.S.R.