A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex.

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.

The Touch and Zap method for in vivo whole-cell patch recording of intrinsic and visual responses of cortical neurons and glial cells.

Whole-cell patch recording is an essential tool for quantitatively establishing the biophysics of brain function, particularly in vivo. This method is of particular interest for studying the functional roles of cortical glial cells in the intact brain, which cannot be assessed with extracellular recordings. Nevertheless, a reasonable success rate remains a challenge because of stability, recording duration and electrical quality constraints, particularly for voltage clamp, dynamic clamp or conductance measurements. To address this, we describe "Touch and Zap", an alternative method for whole-cell patch clamp recordings, with the goal of being simpler, quicker and more gentle to brain tissue than previous approaches. Under current clamp mode with a continuous train of hyperpolarizing current pulses, seal formation is initiated immediately upon cell contact, thus the "Touch". By maintaining the current injection, whole-cell access is spontaneously achieved within seconds from the cell-attached configuration by a self-limited membrane electroporation, or "Zap", as seal resistance increases. We present examples of intrinsic and visual responses of neurons and putative glial cells obtained with the revised method from cat and rat cortices in vivo. Recording parameters and biophysical properties obtained with the Touch and Zap method compare favourably with those obtained with the traditional blind patch approach, demonstrating that the revised approach does not compromise the recorded cell. We find that the method is particularly well-suited for whole-cell patch recordings of cortical glial cells in vivo, targeting a wider population of this cell type than the standard method, with better access resistance. Overall, the gentler Touch and Zap method is promising for studying quantitative functional properties in the intact brain with minimal perturbation of the cell's intrinsic properties and local network. Because the Touch and Zap method is performed semi-automatically, this approach is more reproducible and less dependent on experimenter technique.

Firing clamp: a novel method for single-trial estimation of excitatory and inhibitory synaptic neuronal conductances.

Understanding non-stationary neuronal activity as seen in vivo requires estimation of both excitatory and inhibitory synaptic conductances from a single trial of recording. For this purpose, we propose a new intracellular recording method, called "firing clamp." Synaptic conductances are estimated from the characteristics of artificially evoked probe spikes, namely the spike amplitude and the mean subthreshold potential, which are sensitive to both excitatory and inhibitory synaptic input signals. The probe spikes, timed at a fixed rate, are evoked in the dynamic-clamp mode by injected meander-like current steps, with the step duration depending on neuronal membrane voltage. We test the method with perforated-patch recordings from isolated cells stimulated by external application or synaptic release of transmitter, and validate the method with simulations of a biophysically-detailed neuron model. The results are compared with the conductance estimates based on conventional current-clamp recordings.

Complementary theta resonance filtering by two spatially segregated mechanisms in CA1 hippocampal pyramidal neurons.

Synaptic input to a neuron may undergo various filtering steps, both locally and during transmission to the soma. Using simultaneous whole-cell recordings from soma and apical dendrites from rat CA1 hippocampal pyramidal cells, and biophysically detailed modeling, we found two complementary resonance (bandpass) filters of subthreshold voltage signals. Both filters favor signals in the theta (3-12 Hz) frequency range, but have opposite location, direction, and voltage dependencies: (1) dendritic H-resonance, caused by h/HCN-channels, filters signals propagating from soma to dendrite when the membrane potential is close to rest; and (2) somatic M-resonance, caused by M/Kv7/KCNQ and persistent Na(+) (NaP) channels, filters signals propagating from dendrite to soma when the membrane potential approaches spike threshold. Hippocampal pyramidal cells participate in theta network oscillations during behavior, and we suggest that that these dual, polarized theta resonance mechanisms may convey voltage-dependent tuning of theta-mediated neural coding in the entorhinal/hippocampal system during locomotion, spatial navigation, memory, and sleep.

Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels.

Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency-a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in "hot spots" of dendrites, spines or axons.

Efficient evaluation of neuron populations receiving colored-noise current based on a refractory density method.

The expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential, for the case of colored noise. We propose this approximation in order to extend the recently proposed white noise model [A. V. Chizhov and L. J. Graham, Phys. Rev. E 75, 011924 (2007)] to the case of colored noise, applying a refractory density approach to conductance-based neurons. The uncoupled neurons of a single population receive a common input and are dispersed by the noise. Within the framework of the model the effect of noise is expressed by the so-called hazard function, which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term. To derive the hazard function we solve the Kolmogorov-Fokker-Planck equation for a mean voltage-driven neuron fluctuating due to colored noisy current. We show that a sum of both a self-similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case. We demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate-and-fire and detailed conductance-based neurons in response to an injected current step.

Impact of synaptic noise and conductance state on spontaneous cortical firing.

Cortical neurons in-vivo operate in a continuum of overall conductance states, depending on the average level of background synaptic input throughout the dendritic tree. We compare how variability, or fluctuations, in this input affects the statistics of the resulting 'spontaneous' or 'background' firing activity, between two extremes of the mean input corresponding to a low-conductance (LC) and a high-conductance (HC) state. In the HC state, we show that both firing rate and regularity increase with increasing variability. In the LC state, firing rate also increases with input variability, but in contrast to the HC state, firing regularity first decreases and then increases with an increase in the variability. At high levels of input variability, firing regularity in both states converge to similar values.

Population model of hippocampal pyramidal neurons, linking a refractory density approach to conductance-based neurons.

We propose a macroscopic approach toward realistic simulations of the population activity of hippocampal pyramidal neurons, based on the known refractory density equation with a different hazard function and on a different single-neuron threshold model. The threshold model is a conductance-based model taking into account adaptation-providing currents, which is reduced by omitting the fast sodium current and instead using an explicit threshold criterion for action potential events. Compared to the full pyramidal neuron model, the threshold model well approximates spike-time moments, postspike refractory states, and postsynaptic current integration. The dynamics of a neural population continuum are described by a set of one-dimensional partial differential equations in terms of the distributions of the refractory density (where the refractory state is defined by the time elapsed since the last action potential), the membrane potential, and the gating variables of the voltage-dependent channels, across the entire population. As the source term in the density equation, the probability density of firing, or hazard function, is derived from the Fokker-Planck (FP) equation, assuming that a single neuron is governed by a deterministic average-across-population input and a noise term. A self-similar solution of the FP equation in the subthreshold regime is obtained. Responses of the ensemble to stimulation by a current step and oscillating current are simulated and compared with individual neuron simulations. An example of interictal-like activity of a population of all-to-all connected excitatory neurons is presented.

A method of combined single-cell electrophysiology and electroporation.

This paper describes a method of extracellular recording and subsequent electroporation with the same electrode in single retinal ganglion cells in vitro. We demonstrate anatomical identification of neurons whose receptive fields were measured quantitatively. We discuss how this simple method should also be applicable for the delivery of a variety of intracellular agents, including gene delivery, to physiologically characterized neurons, both in vitro and in vivo.

Contrasting effects of the persistent Na+ current on neuronal excitability and spike timing.

The persistent Na+ current, INaP, is known to amplify subthreshold oscillations and synaptic potentials, but its impact on action potential generation remains enigmatic. Using computational modeling, whole-cell recording, and dynamic clamp of CA1 hippocampal pyramidal cells in brain slices, we examined how INaP changes the transduction of excitatory current into action potentials. Model simulations predicted that INaP increases afterhyperpolarizations, and, although it increases excitability by reducing rheobase, INaP also reduces the gain in discharge frequency in response to depolarizing current (f/I gain). These predictions were experimentally confirmed by using dynamic clamp, thus circumventing the longstanding problem that INaP cannot be selectively blocked. Furthermore, we found that INaP increased firing regularity in response to sustained depolarization, although it decreased spike time precision in response to single evoked EPSPs. Finally, model simulations demonstrated that I(NaP) increased the relative refractory period and decreased interspike-interval variability under conditions resembling an active network in vivo.

Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning.

This intracellular study investigates synaptic mechanisms of orientation and direction selectivity in cat area 17. Visually evoked inhibition was analyzed in 88 cells by detecting spike suppression, hyperpolarization, and reduction of trial-to-trial variability of membrane potential. In 25 of these cells, inhibition visibility was enhanced by depolarization and spike inactivation and by direct measurement of synaptic conductances. We conclude that excitatory and inhibitory inputs share the tuning preference of spiking output in 60% of cases, whereas inhibition is tuned to a different orientation in 40% of cases. For this latter type of cells, conductance measurements showed that excitation shared either the preference of the spiking output or that of the inhibition. This diversity of input combinations may reflect inhomogeneities in functional intracortical connectivity regulated by correlation-based activity-dependent processes.