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1.  Nonlinear properties of medial entorhinal cortex neurons reveal frequency selectivity during multi-sinusoidal stimulation 
The neurons in layer II of the medial entorhinal cortex are part of the grid cell network involved in the representation of space. Many of these neurons are likely to be stellate cells with specific oscillatory and firing properties important for their function. A fundamental understanding of the nonlinear basis of these oscillatory properties is critical for the development of theories of grid cell firing. In order to evaluate the behavior of stellate neurons, measurements of their quadratic responses were used to estimate a second order Volterra kernel. This paper uses an operator theory, termed quadratic sinusoidal analysis (QSA), which quantitatively determines that the quadratic response accounts for a major part of the nonlinearity observed at membrane potential levels characteristic of normal synaptic events. Practically, neurons were probed with multi-sinusoidal stimulations to determine a Hermitian operator that captures the quadratic function in the frequency domain. We have shown that the frequency content of the stimulation plays an important role in the characteristics of the nonlinear response, which can distort the linear response as well. Stimulations with enhanced low frequency amplitudes evoked a different nonlinear response than broadband profiles. The nonlinear analysis was also applied to spike frequencies and it was shown that the nonlinear response of subthreshold membrane potential at resonance frequencies near the threshold is similar to the nonlinear response of spike trains.
doi:10.3389/fncel.2014.00239
PMCID: PMC4137241  PMID: 25191226
entorhinal cortex; stellate neurons; grid cells; quadratic sinusoidal analysis; frequency domain; nonlinear oscillations; resonance
2.  Optical dissection of odor information processing in vivo using GCaMPs expressed in specified cell types of the olfactory bulb 
Understanding central processing requires precise monitoring of neural activity across populations of identified neurons in the intact brain. Here we used recently-optimized variants of the genetically-encoded calcium sensor GCaMP (GCaMP3 and GCaMPG5G) to image activity among genetically- and anatomically-defined neuronal populations in the olfactory bulb (OB), including two types of GABA-ergic interneurons (periglomerular (PG) and short axon (SA) cells) and OB output neurons (mitral/tufted (MT) cells) projecting to piriform cortex. We first established that changes in neuronal spiking can be accurately related to GCaMP fluorescence changes via a simple quantitative relationship over a large dynamic range. We next used in vivo two-photon imaging from individual neurons and epifluorescence signals reflecting population-level activity to investigate the spatiotemporal representation of odorants across these neuron types in anesthetized and awake mice. Under anesthesia, individual PG and SA cells showed temporally simple responses and little spontaneous activity, while MT cells were spontaneously active and showed diverse temporal responses. At the population level, response patterns of PG, SA and MT cells were surprisingly similar to those imaged from sensory inputs, with shared odorant-specific topography across the dorsal OB and inhalation-coupled temporal dynamics. During wakefulness, PG and SA cell responses increased in magnitude but remained temporally simple while those of MT cells changed to complex spatiotemporal patterns reflecting restricted excitation and widespread inhibition. These results point to multiple circuit elements with distinct roles in transforming odor representations in the OB and provide a framework for further dissecting early olfactory processing using optical and genetic tools.
doi:10.1523/JNEUROSCI.4824-12.2013
PMCID: PMC3690468  PMID: 23516293
3.  GenNet: A Platform for Hybrid Network Experiments 
We describe General Network (GenNet), a software plugin for the real time experimental interface (RTXI) dynamic clamp system that allows for straightforward and flexible implementation of hybrid network experiments. This extension to RTXI allows for hybrid networks that contain an arbitrary number of simulated and real neurons, significantly improving upon previous solutions that were limited, particularly by the number of cells supported. The benefits of this system include the ability to rapidly and easily set up and perform scalable experiments with hybrid networks and the ability to scan through ranges of parameters. We present instructions for installing, running and using GenNet for hybrid network experiments and provide several example uses of the system.
doi:10.3389/fninf.2011.00011
PMCID: PMC3146038  PMID: 21845179
RTXI; dynamic clamp; simulation; real-time Linux; computational neuroscience
4.  Spike Resonance Properties in Hippocampal O-LM cells are Dependent on Refractory Dynamics 
The Journal of Neuroscience  2012;32(11):3637-3651.
During a wide variety of behaviors, hippocampal field potentials show significant power in the theta (4–12 Hz) frequency range and individual neurons commonly phase-lock with the 4–12 Hz field potential. The underlying cellular and network mechanisms that generate the theta rhythm, however, are poorly understood. Oriens-lacunosum moleculare (O-LM) interneurons have been implicated as crucial contributors to generating theta in local hippocampal circuits because of their unique axonal projections, slow synaptic kinetics and the fact that spikes are phase locked to theta field potentials in vivo. We performed experiments in brain slice preparations from Long-Evans rats to investigate the ability of O-LM cells to generate phase-locked spike output in response to artificial synaptic inputs. We find that O-LM cells do not respond with any preference in spike output at theta frequencies when injected with broadband artificial synaptic inputs. However, when presented with frequency-modulated inputs, O-LM spike output shows the ability to phase-lock well to theta-modulated inputs, despite their strong low-pass profiles of subthreshold membrane impedance. This result was dependent on spike refractory dynamics and could be controlled by real-time manipulation of the post-spike afterhyperpolarization. Finally, we show that the ability of O-LM cells to phase-lock well to theta-rich inputs is independent of the h-current, a membrane mechanism often implicated in the generation of theta frequency activity.
doi:10.1523/JNEUROSCI.1361-11.2012
PMCID: PMC3316126  PMID: 22423087
Oriens-Lacunosum Moleculare; interneuron; hippocampus; theta; h-current; dynamic clamp; after-hyperpolarization; resonance; refractory
5.  Membrane Properties and the Balance between Excitation and Inhibition Control Gamma-Frequency Oscillations Arising from Feedback Inhibition 
PLoS Computational Biology  2012;8(1):e1002354.
Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30–80 Hz gamma rhythm in which network oscillations arise through ‘stochastic synchrony’ capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.
Author Summary
The gamma rhythm is a prominent, 30–80-Hz EEG signal that is associated with cognition. Several classes of computational models have been posited to explain the gamma rhythm mechanistically. We study a particular class in which the gamma rhythm arises from delayed negative feedback. Our study is unique in that we calibrate the model from direct measurements. We also test the model's most critical predictions directly in experiments that take advantage of cutting-edge computer technologies able to simulate ion channels in real time. Our major findings are that a large amount of “background” synaptic input to neurons is necessary to promote the gamma rhythm; that inhibitory neurons are specially tuned to keep the gamma rhythm stable; that noise has a strong effect on network frequency; and that incoming sensory input can be represented with sensitivity that depends on the strength of excitatory-excitatory synapses and the number of neurons receiving the input. Overall, our results support the hypothesis that the gamma rhythm reflects the presence of delayed feedback that controls overall cortical activity on a cycle-by-cycle basis. Furthermore, its frequency range mainly reflects the timescale of synaptic inhibition, the degree of background activity, and noise levels in the network.
doi:10.1371/journal.pcbi.1002354
PMCID: PMC3261914  PMID: 22275859
6.  Dynamic Clamp: Alteration of Response Properties and Creation of Virtual Realities in Neurophysiology 
doi:10.1523/JNEUROSCI.5954-09.2010
PMCID: PMC2837935  PMID: 20164323
Conductance; Noise; Control; Feedback; Action Potential; Patch Clamp

Results 1-6 (6)