Exact solutions for signal propagation along an excitable transmission line.

A simple transmission line composed of pulse-coupled units is presented. The model captures the basic properties of excitable media with, in particular, the robust transmission of information via traveling wave solutions. For rectified linear units with a cut-off threshold, the model is exactly solvable and analytical results on propagation are presented. The ability to convey a nontrivial message is studied in detail.

Threshold curve for the excitability of bidimensional spiking neurons.

We shed light on the threshold for spike initiation in two-dimensional neuron models. A threshold criterion that depends on both the membrane voltage and the recovery variable is proposed. This approach provides a simple and unified framework that accounts for numerous voltage threshold properties including adaptation, variability, and time-dependent dynamics. In addition, neural features such as accommodation, inhibition-induced spike, and postinhibitory (-excitatory) facilitation are the direct consequences of the existence of a threshold curve. Implications for neural modeling are also discussed.

Cyclic negative feedback systems: what is the chance of oscillation?

Many biological oscillators have a cyclic structure consisting of negative feedback loops. In this paper, we analyze the impact that the addition of a positive or a negative self-feedback loop has on the oscillatory behavior of the three negative feedback oscillators proposed by Tsai et al. (Science 231:126-129, 2008) where, in contrast with numerous oscillator models, the interactions between elements occur via the modulation of the degradation rates. Through analytical and computational studies we show that an additional self-feedback affects the oscillatory behavior. In the high-cooperativity limit, i.e., for large Hill coefficients, we derive exact analytical conditions for oscillations and show that the relative location between the dissociation constants of the Hill functions and the ratio of kinetic parameters determines the possibility of oscillatory activities. We compute analytically the probability of oscillations for the three models and show that the smallest domain of periodic behavior is obtained for the negative-plus-negative feedback system whereas the additional positive self-feedback loop does not modify significantly the chance to oscillate. We numerically investigate to what extent the properties obtained in the sharp situation applied in the smooth case. Results suggest that a switch-like coupling behavior, a time-scale separation, and a repressilator-type architecture with an even number of elements facilitate the emergence of sustained oscillations in biological systems. An additional positive self-feedback loop produces robustness and adaptability whereas an additional negative self-feedback loop reduces the chance to oscillate.

Screening of chemicals for human bioaccumulative potential with a physiologically based toxicokinetic model.

Human bioaccumulative potential is an important element in the risk assessment of chemicals. Due to the high number of synthetic chemicals, there exists the need to develop prioritisation strategies. The purpose of this study was to develop a predictive tool for human bioaccumulation risk assessment that incorporates not only the chemical properties of the compounds, but also the processes that tend to decrease the concentration of the compound such as metabolisation. We used a generic physiologically based toxicokinetic model that based on in vitro human liver metabolism data, minimal renal excretion and a constant exposure was able to assess the bioaccumulative potential of a chemical. The approach has been analysed using literature data on well-known bioaccumulative compounds and liver metabolism data from the ECVAM database and a subset of the ToxCast phase I chemical library-in total 94 compounds covering pharmaceuticals, plant protection products and industrial chemicals. Our results provide further evidence that partitioning properties do not allow for a reliable screening criteria for human chemical hazard. Our model, based on a 100% intestinal absorption assumption, suggests that metabolic clearance, plasma protein-binding properties and renal excretion are the main factors in determining whether bioaccumulation will occur and its amount. It is essential that in vitro metabolic clearance tests with metabolic competent cell lines as well as plasma protein-binding assays be performed for suspected bioaccumulative compounds.

On the performance of voltage stepping for the simulation of adaptive, nonlinear integrate-and-fire neuronal networks.

In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez (2009) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.

Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation.

The quadratic integrate-and-fire (QIF) model with adaptation is commonly used as an elementary neuronal model that reproduces the main characteristics of real neurons. In this paper, we introduce a QIF neuron with a nonlinear adaptive current. This model reproduces the neuron-computational features of real neurons and is analytically tractable. It is shown that under a constant current input chaotic firing is possible. In contrast to previous study the neuron is not sinusoidally forced. We show that the spike-triggered adaptation is a key parameter to understand how chaos is generated.

Structuring process and closure principle in spatial and temporal reproduction tasks.

The goal of the experiment reported was to replicate the previous Sarrazin's (2000) study in order to verify, with an adequate methodological procedure, whether or not the closure principle applied in spatial and temporal reproduction tasks. The hypothesis defended was that the closure of the pattern is an intrinsic property of the structuring process in spatial memory. The stimuli consisted of eight visually presented dots that appeared sequentially with inter-dot distances corresponding to inter-dot durations. After a learning phase, participants reproduced the spatial (space condition) or temporal (time condition) characteristics of the target 60 times in succession. We analyzed the variance level for both element location and Inter-Element-Interval (IEI) on spatial and temporal responses. Two main results emerge from this experiment: (1) the critical dependency of the closure principle to the nature (spatial or temporal) of the response, (2) the importance to consider both locations and intervals as complementary information. These results are discussed in the light of physical system, in particular in term of compensation phenomenon and we proposed a mathematical model that replicates the qualitative feature of variance for both space and time conditions.

Event-driven simulations of nonlinear integrate-and-fire neurons.

Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

A model of contextual effect on reproduced extents in recall tasks: the issue of the imputed motion hypothesis.

In this article the fundamental question of space and time dependencies in the reproduction of spatial or temporal extents is studied. The functional dependence of spatial responses on the temporal context and the corresponding dependence of temporal responses on spatial context are reported as the tau and kappa effects, respectively. A common explanation suggested that the participant imputes motion to discontinuous displays. Using a mathematical model we explore the imputed velocity hypothesis and provide a globally fit model that addresses the question of sequences modelling. Our model accounts for observed data in the tau experiment. The accuracy of the model is improved introducing a new hypothesis based on small velocity variations. On the other hand, results show that the imputed velocity hypothesis fails to reproduce the kappa effect. This result definitively shows that both effects are not symmetric.

Pulse propagation in discrete excitatory networks of integrate-and-fire neurons.

We study the propagation of solitary waves in a discrete excitatory network of integrate-and-fire neurons. We show the existence and the stability of a fast wave and a family of slow waves. Fast waves are similar to those already described in continuum networks. Stable slow waves have not been previously reported in purely excitatory networks and their propagation is particular to the discrete nature of the network. The robustness of our results is studied in the presence of noise.

Bifurcation properties of the average activity of interconnected neural populations.

The relevant scale for the study of the electrical activity of neural networks is a problem of mathematical and biological interest. From a continuous model of the cortex activity we derive a simple model of an interconnected pair of excitatory and inhibitory neural populations that describes the activity of a homogeneous network. Our model depends on three parameters that stand for the scale variability of the network. A bifurcation analysis reveals a great variety of patterns that arise from the interplay of excitatory and inhibitory populations provided by synaptic interactions. We emphasize the differences between the dynamical regimes when considering a moderate and a high inhibitory scale. We discuss the consequences on a propagating activity.

McKean caricature of the FitzHugh-Nagumo model: traveling pulses in a discrete diffusive medium.

This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by the McKean caricature of the FitzHugh-Nagumo model. In the limit of a weak coupling strength, we construct the traveling wave solutions and obtain the critical coupling constant below which propagation failure occurs. We report the existence of two different pulse traveling waves with different propagation speeds. Analytical results on the wave speed are obtained. Earlier results on propagation in the bistable medium are found as a limiting regime of our analysis.

Piecewise linear differential equations and integrate-and-fire neurons: insights from two-dimensional membrane models.

We derive and study two-dimensional generalizations of integrate-and-fire models which can be found from a piecewise linear idealization of the FitzHugh-Nagumo or Morris-Lecar model. These models give rise to new properties not present in one-dimensional integrate-and-fire models. A detailed analytical study of the models is presented. In particular, (i) for the piecewise linear FitzHugh-Nagumo model, we determine analytically the bistability regime between stationary solutions and oscillations, that is, typical for class-II models. (ii) In the piecewise Morris-Lecar model, we find a noncanonical class-I transition from a stationary state to oscillations with logarithmic dependence similar to that found for leaky integrate-and-fire models. (iii) Furthermore, we establish a relation to the recently proposed resonate-and-fire model and show that a short input current pulse can trigger several spikes.

Wave propagation in discrete media.

We have considered infinite systems of nonlinear ODEs on the one-dimensional integer lattice which describes the activity in an excitatorily coupled network of excitable cells. For an ideal nonlinearity, we calculated the speed of propagation of an activity and derived the condition for its existence. We also studied the existence and stability of the traveling wave solution and gave, in the simplest case, its explicit expression. We established that some unstable traveling waves lead to propagation with an enlarging profile defined by a front velocity and a wake velocity. We generalized some results to inhomogeneous medium and network with long range connections.