Stochastic self-tuning hybrid algorithm for reaction-diffusion systems.

Many biochemical phenomena involve reactants with vastly different concentrations, some of which are amenable to continuum-level descriptions, while the others are not. We present a hybrid self-tuning algorithm to model such systems. The method combines microscopic (Brownian) dynamics for diffusion with mesoscopic (Gillespie-type) methods for reactions and remains efficient in a wide range of regimes and scenarios with large variations of concentrations. Its accuracy, robustness, and versatility are balanced by redefining propensities and optimizing the mesh size and time step. We use a bimolecular reaction to demonstrate the potential of our method in a broad spectrum of scenarios: from almost completely reaction-dominated systems to cases where reactions rarely occur or take place very slowly. The simulation results show that the number of particles present in the system does not degrade the performance of our method. This makes it an accurate and computationally efficient tool to model complex multireaction systems.

Simulating human sleep spindle MEG and EEG from ion channel and circuit level dynamics.

BACKGROUND: Although they form a unitary phenomenon, the relationship between extracranial M/EEG and transmembrane ion flows is understood only as a general principle rather than as a well-articulated and quantified causal chain. METHOD: We present an integrated multiscale model, consisting of a neural simulation of thalamus and cortex during stage N2 sleep and a biophysical model projecting cortical current densities to M/EEG fields. Sleep spindles were generated through the interactions of local and distant network connections and intrinsic currents within thalamocortical circuits. 32,652 cortical neurons were mapped onto the cortical surface reconstructed from subjects' MRI, interconnected based on geodesic distances, and scaled-up to current dipole densities based on laminar recordings in humans. MRIs were used to generate a quasi-static electromagnetic model enabling simulated cortical activity to be projected to the M/EEG sensors. RESULTS: The simulated M/EEG spindles were similar in amplitude and topography to empirical examples in the same subjects. Simulated spindles with more core-dominant activity were more MEG weighted. COMPARISON WITH EXISTING METHODS: Previous models lacked either spindle-generating thalamic neural dynamics or whole head biophysical modeling; the framework presented here is the first to simultaneously capture these disparate scales. CONCLUSIONS: This multiscale model provides a platform for the principled quantitative integration of existing information relevant to the generation of sleep spindles, and allows the implications of future findings to be explored. It provides a proof of principle for a methodological framework allowing large-scale integrative brain oscillations to be understood in terms of their underlying channels and synapses.

Monitoring Spiking Activity of Many Individual Neurons in Invertebrate Ganglia.

Optical recording with fast voltage sensitive dyes makes it possible, in suitable preparations, to simultaneously monitor the action potentials of large numbers of individual neurons. Here we describe methods for doing this, including considerations of different dyes and imaging systems, methods for correlating the optical signals with their source neurons, procedures for getting good signals, and the use of Independent Component Analysis for spike-sorting raw optical data into single neuron traces. These combined tools represent a powerful approach for large-scale recording of neural networks with high temporal and spatial resolution.

Disruption of mGluR5 in parvalbumin-positive interneurons induces core features of neurodevelopmental disorders.

Alterations in glutamatergic transmission onto developing GABAergic systems, in particular onto parvalbumin-positive (Pv(+)) fast-spiking interneurons, have been proposed as underlying causes of several neurodevelopmental disorders, including schizophrenia and autism. Excitatory glutamatergic transmission, through ionotropic and metabotropic glutamate receptors, is necessary for the correct postnatal development of the Pv(+) GABAergic network. We generated mutant mice in which the metabotropic glutamate receptor 5 (mGluR5) was specifically ablated from Pv(+) interneurons postnatally, and investigated the consequences of such a manipulation at the cellular, network and systems levels. Deletion of mGluR5 from Pv(+) interneurons resulted in reduced numbers of Pv(+) neurons and decreased inhibitory currents, as well as alterations in event-related potentials and brain oscillatory activity. These cellular and sensory changes translated into domain-specific memory deficits and increased compulsive-like behaviors, abnormal sensorimotor gating and altered responsiveness to stimulant agents. Our findings suggest a fundamental role for mGluR5 in the development of Pv(+) neurons and show that alterations in this system can produce broad-spectrum alterations in brain network activity and behavior that are relevant to neurodevelopmental disorders.

Biophysical Neural Spiking, Bursting, and Excitability Dynamics in Reconfigurable Analog VLSI.

We study a range of neural dynamics under variations in biophysical parameters underlying extended Morris-Lecar and Hodgkin-Huxley models in three gating variables. The extended models are implemented in NeuroDyn, a four neuron, twelve synapse continuous-time analog VLSI programmable neural emulation platform with generalized channel kinetics and biophysical membrane dynamics. The dynamics exhibit a wide range of time scales extending beyond 100 ms neglected in typical silicon models of tonic spiking neurons. Circuit simulations and measurements show transition from tonic spiking to tonic bursting dynamics through variation of a single conductance parameter governing calcium recovery. We similarly demonstrate transition from graded to all-or-none neural excitability in the onset of spiking dynamics through the variation of channel kinetic parameters governing the speed of potassium activation. Other combinations of variations in conductance and channel kinetic parameters give rise to phasic spiking and spike frequency adaptation dynamics. The NeuroDyn chip consumes 1.29 mW and occupies 3 mm × 3 mm in 0.5 µm CMOS, supporting emerging developments in neuromorphic silicon-neuron interfaces.

Probabilistic reversal learning is impaired in Parkinson's disease.

In many everyday settings, the relationship between our choices and their potentially rewarding outcomes is probabilistic and dynamic. In addition, the difficulty of the choices can vary widely. Although a large body of theoretical and empirical evidence suggests that dopamine mediates rewarded learning, the influence of dopamine in probabilistic and dynamic rewarded learning remains unclear. We adapted a probabilistic rewarded learning task originally used to study firing rates of dopamine cells in primate substantia nigra pars compacta [Morris G, Nevet A, Arkadir D, Vaadia E, Bergman H (2006) Midbrain dopamine neurons encode decisions for future action. Nat Neurosci 9:1057-1063] for use as a reversal learning task with humans. We sought to investigate how the dopamine depletion in Parkinson's disease (PD) affects probabilistic reward learning and adaptation to a reversal in reward contingencies. Over the course of 256 trials subjects learned to choose the more favorable from among pairs of images with small or large differences in reward probabilities. During a subsequent otherwise identical reversal phase, the reward probability contingencies for the stimuli were reversed. Seventeen PD patients of mild to moderate severity were studied off of their dopaminergic medications and compared to 15 age-matched controls. Compared to controls, PD patients had distinct pre- and post-reversal deficiencies depending upon the difficulty of the choices they had to learn. The patients also exhibited compromised adaptability to the reversal. A computational model of the subjects' trial-by-trial choices demonstrated that the adaptability was sensitive to the gain with which patients weighted pre-reversal feedback. Collectively, the results implicate the nigral dopaminergic system in learning to make choices in environments with probabilistic and dynamic reward contingencies.

Motion detection and prediction through spike-timing dependent plasticity.

We describe a possible mechanism for the formation of direction- and velocity-selective cells in visual cortex through spike-timing dependent learning. We contrast the case where only feedforward excitation and inhibition signals are provided to visual neurons with the case where both feedforward and feedback signals are provided. In the feedforward-only case, neurons become selective for a broad range of velocities centered around the training velocity. However, we show that direction selectivity in this case is strongly dependent on delayed feedforward inhibition and in contrast to experimental results, becomes dramatically weaker when inhibition is reduced. When feedback connections are introduced, direction selectivity becomes much more robust due to predictive delays encoded in recurrent activity. Direction selectivity persists in the face of decreasing inhibition in a manner similar to experimental findings. The model predicts that direction-selective cells should exhibit anticipatory activity due to recurrent excitation and suggests a pivotal role for spike-timing dependent plasticity in shaping cortical circuits for visual motion detection and prediction.

Potassium model for slow (2-3 Hz) in vivo neocortical paroxysmal oscillations.

In slow neocortical paroxysmal oscillations, the de- and hyperpolarizing envelopes in neocortical neurons are large compared with slow sleep oscillations. Increased local synchrony of membrane potential oscillations during seizure is reflected in larger electroencephalographic oscillations and the appearance of spike- or polyspike-wave complex recruitment at 2- to 3-Hz frequencies. The oscillatory mechanisms underlying this paroxysmal activity were investigated in computational models of cortical networks. The extracellular K(+) concentration ([K(+)](o)) was continuously computed based on neuronal K(+) currents and K(+) pumps as well as glial buffering. An increase of [K(+)](o) triggered a transition from normal awake-like oscillations to 2- to 3-Hz seizure-like activity. In this mode, the cells fired periodic bursts and nearby neurons oscillated highly synchronously; in some cells depolarization led to spike inactivation lasting 50-100 ms. A [K(+)](o) increase, sufficient to produce oscillations could result from excessive firing (e.g., induced by external stimulation) or inability of K(+) regulatory system (e.g., when glial buffering was blocked). A combination of currents including high-threshold Ca(2+), persistent Na(+) and hyperpolarization-activated depolarizing (I(h)) currents was sufficient to maintain 2- to 3-Hz activity. In a network model that included lateral K(+) diffusion between cells, increase of [K(+)](o) in a small region was generally sufficient to maintain paroxysmal oscillations in the whole network. Slow changes of [K(+)](o) modulated the frequency of bursting and, in some case, led to fast oscillations in the 10- to 15-Hz frequency range, similar to the fast runs observed during seizures in vivo. These results suggest that modifications of the intrinsic currents mediated by increase of [K(+)](o) can explain the range of neocortical paroxysmal oscillations in vivo.

Rapid temporal modulation of synchrony by competition in cortical interneuron networks.

The synchrony of neurons in extrastriate visual cortex is modulated by selective attention even when there are only small changes in firing rate (Fries, Reynolds, Rorie, & Desimone, 2001). We used Hodgkin-Huxley type models of cortical neurons to investigate the mechanism by which the degree of synchrony can be modulated independently of changes in firing rates. The synchrony of local networks of model cortical interneurons interacting through GABA(A) synapses was modulated on a fast timescale by selectively activating a fraction of the interneurons. The activated interneurons became rapidly synchronized and suppressed the activity of the other neurons in the network but only if the network was in a restricted range of balanced synaptic background activity. During stronger background activity, the network did not synchronize, and for weaker background activity, the network synchronized but did not return to an asynchronous state after synchronizing. The inhibitory output of the network blocked the activity of pyramidal neurons during asynchronous network activity, and during synchronous network activity, it enhanced the impact of the stimulus-related activity of pyramidal cells on receiving cortical areas (Salinas & Sejnowski, 2001). Synchrony by competition provides a mechanism for controlling synchrony with minor alterations in rate, which could be useful for information processing. Because traditional methods such as cross-correlation and the spike field coherence require several hundred milliseconds of recordings and cannot measure rapid changes in the degree of synchrony, we introduced a new method to detect rapid changes in the degree of coincidence and precision of spike timing.

Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity.

In vivo, in vitro and computational studies were used to investigate the impact of the synaptic background activity observed in neocortical neurons in vivo. We simulated background activity in vitro using two stochastic Ornstein-Uhlenbeck processes describing glutamatergic and GABAergic synaptic conductances, which were injected into a cell in real time using the dynamic clamp technique. With parameters chosen to mimic in vivo conditions, layer 5 rat prefrontal cortex cells recorded in vitro were depolarized by about 15 mV, their membrane fluctuated with a S.D. of about 4 mV, their input resistances decreased five-fold, their spontaneous firing had a high coefficient of variation and an average firing rate of about 5-10 Hz. Brief changes in the variance of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synaptic conductance fluctuations induced time-locked spiking without significantly changing the average membrane potential of the cell. These transients mimicked increases in the correlation of excitatory inputs. Background activity was highly effective in modulating the firing-rate/current curve of the cell: the variance of the simulated gamma-aminobutyric acid (GABA) and AMPA conductances individually set the input/output gain, the mean excitatory and inhibitory conductances set the working point, and the mean inhibitory conductance controlled the input resistance. An average ratio of inhibitory to excitatory mean conductances close to 4 was optimal in generating membrane potential fluctuations with high coefficients of variation. We conclude that background synaptic activity can dynamically modulate the input/output properties of individual neocortical neurons in vivo.

Interactions between membrane conductances underlying thalamocortical slow-wave oscillations.

Neurons of the central nervous system display a broad spectrum of intrinsic electrophysiological properties that are absent in the traditional "integrate-and-fire" model. A network of neurons with these properties interacting through synaptic receptors with many time scales can produce complex patterns of activity that cannot be intuitively predicted. Computational methods, tightly linked to experimental data, provide insights into the dynamics of neural networks. We review this approach for the case of bursting neurons of the thalamus, with a focus on thalamic and thalamocortical slow-wave oscillations. At the single-cell level, intrinsic bursting or oscillations can be explained by interactions between calcium- and voltage-dependent channels. At the network level, the genesis of oscillations, their initiation, propagation, termination, and large-scale synchrony can be explained by interactions between neurons with a variety of intrinsic cellular properties through different types of synaptic receptors. These interactions can be altered by neuromodulators, which can dramatically shift the large-scale behavior of the network, and can also be disrupted in many ways, resulting in pathological patterns of activity, such as seizures. We suggest a coherent framework that accounts for a large body of experimental data at the ion-channel, single-cell, and network levels. This framework suggests physiological roles for the highly synchronized oscillations of slow-wave sleep.

Variability of quantal synaptic currents in thalamocortical neurons.

Broad amplitude variability and skewed distributions are characteristic features of quantal synaptic currents (minis) at central synapses. The relative contributions of the various underlying sources are still debated. Through computational models of thalamocortical neurons, we separated intra- from extra-synaptic sources. Our simulations indicate that the external factors of local input resistance and dendritic filtering generate equally small amounts of negatively skewed synaptic variability. The ability of these two factors to reduce positive skew increased as their contribution to variability increased, which in control trials for morphological, biophysical, and experimental parameters never exceeded 10% of the range. With these dendritic factors ruled out, we tested multiple release models, which led to distributions with clearly non-physiological multiple peaks. We conclude that intra-synaptic organization is the primary determinant of synaptic variability in thalamocortical neurons and, due to extra-synaptic mechanisms, is more potent than the data suggested. Thalamortical neurons, especially in rodents, constitute a remarkably favorable system for molecular genetic studies of synaptic variability and its functional consequence.

A new correlation-based measure of spike timing reliability.

We introduce a new correlation-based measure of spike timing reliability. Unlike other measures, it does not require the definition of a posteriori "events". It relies on only one parameter, which relates to the timescale of spike timing precision. We test the measure on surrogate data sets with varying amounts of spike time jitter, and missing or additional spikes, and compare it with a widely used histogram-based measure. The measure is efficient and faithful in characterizing spike timing reliability and produces smaller errors in the reliability estimate than the histogram-based measure based on the same number of trials.

Information transfer in entrained cortical neurons.

Cortical interneurons connected by gap junctions can provide a synchronized inhibitory drive that can entrain pyramidal cells. This was studied in a single-compartment Hodgkin-Huxley-type model neuron that was entrained by periodic inhibitory inputs with low jitter in the input spike times (i.e. high precision), and a variable but large number of presynaptic spikes on each cycle. During entrainment the Shannon entropy of the output spike times was reduced sharply compared with its value outside entrainment. Surprisingly, however, the information transfer as measured by the mutual information between the number of inhibitory inputs in a cycle and the phase lag of the subsequent output spike was significantly increased during entrainment. This increase was due to the reduced contribution of the internal correlations to the output variability. These theoretical predictions were supported by experimental recordings from the rat neocortex and hippocampus in vitro.

Dynamic brain sources of visual evoked responses.

It has been long debated whether averaged electrical responses recorded from the scalp result from stimulus-evoked brain events or stimulus-induced changes in ongoing brain dynamics. In a human visual selective attention task, we show that nontarget event-related potentials were mainly generated by partial stimulus-induced phase resetting of multiple electroencephalographic processes. Independent component analysis applied to the single-trial data identified at least eight classes of contributing components, including those producing central and lateral posterior alpha, left and right mu, and frontal midline theta rhythms. Scalp topographies of these components were consistent with their generation in compact cortical domains.

Face recognition by independent component analysis.

A number of current face recognition algorithms use face representations found by unsupervised statistical methods. Typically these methods find a set of basis images and represent faces as a linear combination of those images. Principal component analysis (PCA) is a popular example of such methods. The basis images found by PCA depend only on pairwise relationships between pixels in the image database. In a task such as face recognition, in which important information may be contained in the high-order relationships among pixels, it seems reasonable to expect that better basis images may be found by methods sensitive to these high-order statistics. Independent component analysis (ICA), a generalization of PCA, is one such method. We used a version of ICA derived from the principle of optimal information transfer through sigmoidal neurons. ICA was performed on face images in the FERET database under two different architectures, one which treated the images as random variables and the pixels as outcomes, and a second which treated the pixels as random variables and the images as outcomes. The first architecture found spatially local basis images for the faces. The second architecture produced a factorial face code. Both ICA representations were superior to representations based on PCA for recognizing faces across days and changes in expression. A classifier that combined the two ICA representations gave the best performance.

Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.

To investigate the basis of the fluctuating activity present in neocortical neurons in vivo, we have combined computational models with whole-cell recordings using the dynamic-clamp technique. A simplified 'point-conductance' model was used to represent the currents generated by thousands of stochastically releasing synapses. Synaptic activity was represented by two independent fast glutamatergic and GABAergic conductances described by stochastic random-walk processes. An advantage of this approach is that all the model parameters can be determined from voltage-clamp experiments. We show that the point-conductance model captures the amplitude and spectral characteristics of the synaptic conductances during background activity. To determine if it can recreate in vivo-like activity, we injected this point-conductance model into a single-compartment model, or in rat prefrontal cortical neurons in vitro using dynamic clamp. This procedure successfully recreated several properties of neurons intracellularly recorded in vivo, such as a depolarized membrane potential, the presence of high-amplitude membrane potential fluctuations, a low-input resistance and irregular spontaneous firing activity. In addition, the point-conductance model could simulate the enhancement of responsiveness due to background activity. We conclude that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and GABAergic conductances varying stochastically.

Computational approaches to motor control.

New concepts and computational models that integrate behavioral and neurophysiological observations have addressed several of the most fundamental long-standing problems in motor control. These problems include the selection of particular trajectories among the large number of possibilities, the solution of inverse kinematics and dynamics problems, motor adaptation and the learning of sequential behaviors.

Gain modulation in the central nervous system: where behavior, neurophysiology, and computation meet.

Gain modulation is a nonlinear way in which neurons combine information from two (or more) sources, which may be of sensory, motor, or cognitive origin. Gain modulation is revealed when one input, the modulatory one, affects the gain or the sensitivity of the neuron to the other input, without modifying its selectivity or receptive field properties. This type of modulatory interaction is important for two reasons. First, it is an extremely widespread integration mechanism; it is found in a plethora of cortical areas and in some subcortical structures as well, and as a consequence it seems to play an important role in a striking variety of functions, including eye and limb movements, navigation, spatial perception, attentional processing, and object recognition. Second, there is a theoretical foundation indicating that gain-modulated neurons may serve as a basis for a general class of computations, namely, coordinate transformations and the generation of invariant responses, which indeed may underlie all the brain functions just mentioned. This article describes the relationships between computational models, the physiological properties of a variety of gain-modulated neurons, and some of the behavioral consequences of damage to gain-modulated neural representations.