Orientation hypercolumns of the visual cortex: Ring model

A hypercolumn of the visual cortex is a functional unit formed of neighboring columns whose neurons respond to a stimulus of particular orientation. The function of the hypercolumn is to amplify the orientation tuning of visually evoked responses. According to the conventional simple model of a hypercolumn, neuronal populations with different orientation preferences are distributed on a ring. Every population is described by a firing rate (FR) model. To determine the limitations of the FR-ring model, it was compared with a more detailed ring model, which takes into account the distribution of neurons of each population according to their voltage values. In the case of leaky integrate-and-fire neurons, every neuronal population is described by the Fokker-Planck equation (FPE). The mapping of parameters was obtained. The simulations revealed differences in the behavior of the two models. The FPE-based model reacts faster to a change in stimulus orientation. The FPE ring model gives a steady-state solution in the form of waves of activity traveling on the ring, whereas the FR ring model presents amplitude instability for the same parameter set. The FPE ring model reproduces the characteristic effects of the FR ring model: virtual rotation and symmetry breaking.     

Neuronal population activity and functional imaging.

Human functional brain imaging detects blood flow changes that are thought to reflect the activity of neuronal populations and, thus, the responses of neurons that carry behaviourally relevant information. Since this relationship is poorly understood, we explored the link between the activity of single neurons and their neuronal population. The functional imaging results were in good agreement with levels of population activation predicted from the known effects of sensory stimulation, learning and attention on single cortical neurons. However, the nature of the relationship between population activation and single neuron firing was very surprising. Population activation was strongly influenced by those neurons firing at low rates and so was very sensitive to the baseline or 'spontaneous' firing rate. When neural representations were sparse and neurons were tuned to several stimulus dimensions, population activation was hardly influenced by the few neurons whose firing was most strongly modulated by the task or stimulus. Measures of population activation could miss changes in information processing given simultaneous changes in neurons' baseline firing, response modulation or tuning width. Factors that can modulate baseline firing, such as attention, may have a particularly large influence on population activation. The results have implications for the interpretation of functional imaging signals and for cross-calibration between different methods for measuring neuronal activity.     

A variant of the integrate-and-fire model to simulate the adaptive neural firing pattern

The integrate-and-fire (IF) based modeling technique has been long employed to study the neural firing activities. This paper introduces a variant of the IF model in order to simulate the adaptive neural firing pattern. An inductor branch is integrated into the IF model to track the variance of the external stimulus, and subsequently control the decrease of the instantaneous firing rate in response to the sustained stimulation. Simulation results demonstrated that the proposed model was able to reproduce the adaptive neural firing pattern. Besides, the inductor branch might adjust the decay rate of the adaptive firing curve and the prominent firing rate upon the onset of the adaptation. The proposed model is characterized by its structure simplicity and simulation efficiency, which would be helpful for the analysis and prediction of the adaptive firing responses of the sensory neurons.     

Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data

The Ornstein-Uhlenbeck process has been proposed as a model for the spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the first passage of the process to a constant boundary, or threshold. While the Laplace transform of the first-passage time distribution is available, the probability distribution function has not been obtained in any tractable form. We address the problem of estimating the parameters of the process when the only available data from a neuron are the interspike intervals, or the times between firings. In particular, we give an algorithm for computing maximum likelihood estimates and their corresponding confidence regions for the three identifiable (of the five model) parameters by numerically inverting the Laplace transform. A comparison of the two-parameter algorithm (where the time constant tau is known a priori) to the three-parameter algorithm shows that significantly more data is required in the latter case to achieve comparable parameter resolution as measured by 95% confidence intervals widths. The computational methods described here are a efficient alternative to other well known estimation techniques for leaky integrate-and-fire models. Moreover, it could serve as a template for performing parameter inference on more complex integrate-and-fire neuronal models.     

Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity

Structural inhomogeneities in synaptic efficacies have a strong impact on population response dynamics of cortical networks and are believed to play an important role in their functioning. However, little is known about how such inhomogeneities could evolve by means of synaptic plasticity. Here we present an adaptive model of a balanced neuronal network that combines two different types of plasticity, STDP and synaptic scaling. The plasticity rules yield both long-tailed distributions of synaptic weights and firing rates. Simultaneously, a highly connected subnetwork of driver neurons with strong synapses emerges. Coincident spiking activity of several driver cells can evoke population bursts and driver cells have similar dynamical properties as leader neurons found experimentally. Our model allows us to observe the delicate interplay between structural and dynamical properties of the emergent inhomogeneities. It is simple, robust to parameter changes and able to explain a multitude of different experimental findings in one basic network.     

A zonal model of cortical functions

A model of cortical functions is developed with the object of simulating the observed behavior of individual neurons organized in unit circuits and functional systems of the cerebellum, the cerebrum and the hippocampal formation. The neuronal model is capable of representing refractory and potentiated states, as well as the firing and lowest resting states. The unit circuits of each system consist of all common types of cells with known synaptic connections. In the cerebral system these unit circuits are interconnected to form columns as well as zones. A new discrete neural network equation, which takes account of interactions with the extracellular field, is proposed to simulate electrical activity in these circuits. A coherent theory of cortical activity and functions is derived that accounts for many of the observed phenomena, including those associated with the development of long-term potentiation and sequential memory. Three appendices are devoted to the theory of extracellular interactions, the derivation of non-linear network equations, and a computer program to simulate learning in the cortex.     

Global rhythmic activities in hippocampal neural fields and neural coding

Global oscillations of the neural field represent some of the most interesting expressions of the hippocampal activity, being related also to learning and memory. To study oscillatory activities of the CA3 field in theta range, a model of this sub-field of Hippocampus has been formulated. The model describes the firing activity of CA3 neuronal populations within the frame of a kinetic theory of neural systems and it has been used for computer simulations. The results show that the propagation of activities induced in the neural field by hippocampal afferents occurs only in narrow time windows confined by inhibitory barrages, whose time-course follows the theta rhythm. Moreover, during each period of a theta wave, the entire CA3 field bears a firing activity with peculiar space-time patterns, a sort of specific imprint, which can induce effects with similar patterns on brain regions driven by the hippocampal formation. The simulation has also demonstrated the ability of medial septum to influence the global activity of the CA3 pyramidal population through the control of the population of inhibitory interneurons. At last, the possible involvement of global population oscillations in neural coding has been discussed.     

Hippocampal ripple oscillations (200 Hz) in mechanisms of memory consolidation

A current status of knowledge about high-frequency (140-200 Hz) ripple oscillations in the CA1 hippocampal subfield is summarized and considered in the context of two-stage model of the hippocampal memory processing. A large body of evidence suggests highly-selective recruitment of pyramidal cells and interneurons in the generation of the oscillatory pattern after co-operative sharp-wave-related discharge of CA3 pyramidal neurons. We also discuss a role of transmission via gap junctions in the mechanisms of ripple oscillations as well as their adaptive aminergic (histaminergic) modulation. Patterns of neuronal firing in the hippocampus observed during ripple oscillations reproduce space-dependant neuronal activity from the previous waking period. Together with a data about efficacy of high-frequency stimulation for induction of synaptic modification it points out a role for ripples in the formation of long-term memory. Focal ultra fast ripples (up to 500 Hz) have been shown to participate in the development of temporal lobe epilepsy.     

Is photomorphogenic shade avoidance adaptive? Perspectives from population biology

Photomorphogenic shade avoidance responses provide an ideal model system for integrating genetic, physiological and population biology approaches to the study of adaptive plasticity. The adaptive plasticity hypothesis predicts that shade avoidance phenotypes induced by low ratios of red to far-red light (R:FR) will have high relative fitness in dense stands, but will suffer a fitness disadvantage at low density. Experiments with transgenic and mutant plants in which photomorphogenic genes are disabled, as well as phenotype manipulation by means of altered R:FR, strongly support the shade avoidance hypothesis. The observation of photomorphogenic ecotypes in different selective environments also suggests that the shade avoidance response has undergone adaptive evolution. Quantitative genetic variation in R:FR sensitivity has been detected in wild populations, indicating that the evolutionary potential exists for response to natural selection. However, evolutionary response may be constrained by genetic correlations among developmentally linked traits. Therefore it cannot be assumed that an observed suite of photomorphogenic responses represents an adaptive optimum for every trait.     

Computer simulation for studying calcium dependent abnormalities in firing mechanism of molluscan neurones

Computer modelling technique is proposed to assist in physiological research on invertebrate neuronal membranes. The firing mechanism of a single patch of invertebrate neuronal membrane has been studied in dependence on maximum Ca++ conductance. The calculations are based on modification of Hodgkin-Huxley's data completed by a straight line approximation between experimental points of the kinetic parameters of Ca++ current and early transient potassium current. The time course of conductance changes is assumed to be proportional to m2h for Ca++ current. Three distinct potassium currents are involved into the model, viz. transient potassium current, delayed potassium current and Ca++-dependent potassium current. The modified Euler method run on a digital computer has been used for numerical integration of kinetic equations. Significant effects of Ca++ conductance on spike broadening, plateau development and spike afterhyperpolarization are represented. In the range of small Ca++ conductance an infinite spontaneous activity can be triggered by a short (suprathreshold) current pulse which may be considered a model of pacemaker activity. Plateau development resulting from potassium blocking or decreasing potassium equilibrium is facilitated by Ca++ conductance in the range of greater Ca++ conductance. The effects of voltage sensitivity of the coupling coefficient describing the current of Ca++-dependent K+ channels were studied and compared to the voltage independent case. The coupling coefficient seems to be a crucial factor in broadening the range of Ca++ conductance responsible for pacemaker activity. For greater values of Ca++ conductance, a decrease of the coupling coefficient leads to a transition from prolonged bursting to interruption of burst activity by burst-afterhyperpolarization. The blocking effect of 4-aminopyridine on fast outward current has been studied by the model which has a practical significance considering that aminopyridine is known as a convulsive agent. We suppose that it is reasonable to study the convulsive effects of aminopyridine by the model based on the kinetics of the isolated neuronal membrane. The model may help in understanding the ionic background underlying abnormal network activity during epileptic discharges of mammalian neurones.     

The adaptive evolution of plasticity: phytochrome-mediated shade avoidance responses

Many plants display a characteristic suite of developmental"shade avoidance" responses, such as stem elongation and acceleratedreproduction, to the low ratio of red to far-red wavelengths(R:FR) reflected or transmitted from green vegetation. ThisR:FR cue of crowding and vegetation shade is perceived by thephytochrome family of photoreceptors. Phytochrome-mediated responsesprovide an ideal system for investigating the adaptive evolutionof phenotypic plasticity in natural environments. The molecularand developmental mechanisms underlying shade avoidance responsesare well studied, and testable ecological hypotheses exist fortheir adaptive significance. Experimental manipulation of phenotypesdemonstrates that shade avoidance responses may be adaptive,resulting in phenotypes with high relative fitness in the environmentsthat induce those phenotypes. The adaptive value of shade avoidancedepends upon the competitive environment, resource availability,and the reliability of the R:FR cue for predicting the selectiveenvironment experienced by an induced phenotype. Comparativestudies and a reciprocal transplant experiment with Impatienscapensis provide evidence of adaptive divergence in shade avoidanceresponses between woodland and clearing habitats, which mayresult from population differences in the frequency of selectionon shade avoidance traits, as well as differences in the reliabilityof the R:FR cue. Recent rapid progress in elucidating phytochromesignaling pathways in the genetic model Arabidopsis thalianaand other species now provides the opportunity for studyinghow selection on shade avoidance traits in natural environmentsacts upon the molecular mechanisms underlying natural phenotypicvariation.     

Neuronal models for sleep-wake regulation and synaptic reorganization in the sleeping hippocampus

In this article, we discuss mathematical models that address the control of sleep-wake behavior in the infant and adult rodent and a model that addresses changes in single-cell firing patterns in the hippocampus across wake and rapid eye movement (REM) sleep states. Each of the models describes the dynamics of experimentally identified neuronal components--either the firing activity of wake-and sleep-promoting neuronal populations or the spiking activity of hippocampal pyramidal neurons. Our discussion of each model illustrates how a mathematical model that describes the temporal dynamics of the modeled neuronal components can reveal specifics about proposed neuronal mechanisms that underlie sleep-wake regulation or sleep-specific firing patterns. For example, the dynamics of the models developed for sleep-wake regulation in the infant rodent lend insight into the involved brain-stem neuronal populations and the evolution of the network during maturation. The results of the model for sleep-wake regulation in the adult rodent suggest distinct properties of the involved neuronal populations and their interactions that account for long-lasting and brief waking bouts. The dynamics of the model for sleep-specific hippocampal neural activity proposes neural mechanisms to account for observed activity changes that can invoke synaptic reorganization associated with learning and memory consolidation.     

Timing over Tuning: Overcoming the Shortcomings of a Line Attractor during a Working Memory Task

How the brain stores information about a sensory stimulus in working memory is not completely known. Clues about the mechanisms responsible for working memory can be gleaned by recording from neurons during the performance of a delayed response task. I focus on the data recorded during such an experiment, a classic tactile discrimination task. I describe how the observed variability in the firing rate during a trial suggests that the type of attractor that is responsible for holding the stimulus information is not a fixed-point type attractor. I propose an alternate mechanism to a line attractor that allows the network to hold the value of an analog stimulus variable for the duration of the delay period, but rather than maintain a constant level of activity, the cells'' firing rate varies throughout the delay period. I describe how my proposed mechanism offers a substantial advantage over a line attractor: The tuning requirements of cell to cell connections are greatly eased from that of a line attractor. To accommodate a change in the length of the delay period, I show that the network can be altered by changing a single parameter - the timing of an executive signal that originates outside of the network. To demonstrate the mechanism, as well as the tuning benefits, I use a well known model of propagation in neuronal networks.     

Dynamic behavior analysis of fractional-order Hindmarsh–Rose neuronal model

Previous experimental work has shown that the firing rate of multiple time-scales of adaptation for single rat neocortical pyramidal neurons is consistent with fractional-order differentiation, and the fractional-order neuronal models depict the firing rate of neurons more verifiably than other models do. For this reason, the dynamic characteristics of the fractional-order Hindmarsh–Rose (HR) neuronal model were here investigated. The results showed several obvious differences in dynamic characteristic between the fractional-order HR neuronal model and an integer-ordered model. First, the fractional-order HR neuronal model displayed different firing modes (chaotic firing and periodic firing) as the fractional order changed when other parameters remained the same as in the integer-order model. However, only one firing mode is displayed in integer-order models with the same parameters. The fractional order is the key to determining the firing mode. Second, the Hopf bifurcation point of this fractional-order model, from the resting state to periodic firing, was found to be larger than that of the integer-order model. Third, for the state of periodically firing of fractional-order and integer-order HR neuron model, the firing frequency of the fractional-order neuronal model was greater than that of the integer-order model, and when the fractional order of the model decreased, the firing frequency increased.     

Management of synchronized network activity by highly active neurons

Increasing evidence supports the idea that spontaneous brain activity may have an important functional role. Cultured neuronal networks provide a suitable model system to search for the mechanisms by which neuronal spontaneous activity is maintained and regulated. This activity is marked by synchronized bursting events (SBEs)--short time windows (hundreds of milliseconds) of rapid neuronal firing separated by long quiescent periods (seconds). However, there exists a special subset of rapidly firing neurons whose activity also persists between SBEs. It has been proposed that these highly active (HA) neurons play an important role in the management (i.e. establishment, maintenance and regulation) of the synchronized network activity. Here, we studied the dynamical properties and the functional role of HA neurons in homogeneous and engineered networks, during early network development, upon recovery from chemical inhibition and in response to electrical stimulations. We found that their sequences of inter-spike intervals (ISI) exhibit long time correlations and a unimodal distribution. During the network's development and under intense inhibition, the observed activity follows a transition period during which mostly HA neurons are active. Studying networks with engineered geometry, we found that HA neurons are precursors (the first to fire) of the spontaneous SBEs and are more responsive to electrical stimulations.     

A Spike-Timing Pattern Based Neural Network Model for the Study of Memory Dynamics

It is well accepted that the brain''s computation relies on spatiotemporal activity of neural networks. In particular, there is growing evidence of the importance of continuously and precisely timed spiking activity. Therefore, it is important to characterize memory states in terms of spike-timing patterns that give both reliable memory of firing activities and precise memory of firing timings. The relationship between memory states and spike-timing patterns has been studied empirically with large-scale recording of neuron population in recent years. Here, by using a recurrent neural network model with dynamics at two time scales, we construct a dynamical memory network model which embeds both fast neural and synaptic variation and slow learning dynamics. A state vector is proposed to describe memory states in terms of spike-timing patterns of neural population, and a distance measure of state vector is defined to study several important phenomena of memory dynamics: partial memory recall, learning efficiency, learning with correlated stimuli. We show that the distance measure can capture the timing difference of memory states. In addition, we examine the influence of network topology on learning ability, and show that local connections can increase the network''s ability to embed more memory states. Together theses results suggest that the proposed system based on spike-timing patterns gives a productive model for the study of detailed learning and memory dynamics.     

Internally generated preactivation of single neurons in human medial frontal cortex predicts volition

Understanding how self-initiated behavior is encoded by neuronal circuits in the human brain remains elusive. We recorded the activity of 1019 neurons while twelve subjects performed self-initiated finger movement. We report progressive neuronal recruitment over ～1500 ms before subjects report making the decision to move. We observed progressive increase or decrease in neuronal firing rate, particularly in the supplementary motor area (SMA), as the reported time of decision was approached. A population of 256 SMA neurons is sufficient to predict in single trials the impending decision to move with accuracy greater than 80% already 700 ms prior to subjects' awareness. Furthermore, we predict, with a precision of a few hundred ms, the actual time point of this voluntary decision to move. We implement a computational model whereby volition emerges once a change in internally generated firing rate of neuronal assemblies crosses a threshold.     

Low-frequency neuronal oscillations as operant processing of integrative mechanisms of conditioning and plasticity

It was found that neuronal activity of the rabbit somatosensory cortex could be operantly conditioned according to the given algorithm of biofeedback control of nociceptive stimulation leading to rising or lowering of firing rate of multiunit activity, or to changes of range of units interspike intervals, or neuronal firing patterns for conditional stimulus, which become operants. Neuronal interactions of its population with feedback and systems of cardiovascular and pain regulation lead to appearance of wave patterns, combining elements to integrative activity by conditioning. Low-frequency oscillations of neuronal assemblies within range of 0.02-0.8 Hz act as operant processing in mechanisms of system plasticity and conditioning.     

Interplay of Intrinsic and Synaptic Conductances in the Generation of High-Frequency Oscillations in Interneuronal Networks with Irregular Spiking

High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.