Modulating the gain of the input-output function of neurons is critical for processing of stimuli and network dynamics. Previous gain control mechanisms have suggested that voltage fluctuations play a key role in determining neuronal gain in vivo. Here we show that, under increased membrane conductance, voltage fluctuations restore Na+ current and reduce spike frequency adaptation in rat hippocampal CA1 pyramidal neurons in vitro. As a consequence, membrane voltage fluctuations produce a leftward shift in the f-I relationship without a change in gain, relative to an increase in conductance alone. Furthermore, we show that these changes have important implications for the integration of inhibitory inputs. Due to the ability to restore Na+ current, hyperpolarizing membrane voltage fluctuations mediated by GABAA-like inputs can increase firing rate in a high conductance state. Finally, our data show that the effects on gain and synaptic integration are mediated by voltage fluctuations within a physiologically relevant range of frequencies (10–40 Hz).

We consider the mechanisms by which coherent activity arises in the hippocampus and entorhinal cortex, two brain areas that are associated with episodic memory in humans and similar forms of memory in animal models. Our approach relies upon techniques from the theory of coupled oscillators. We show that such techniques can yield accurate predictions of the behavior of synaptically coupled neurons. Future work will expand upon these techniques to include real-world complications that better mimic the in vivo state.

Summary

Gain modulation is an important feature of neural activity. Previous work has focused on the ability of background synaptic noise to modulate the slope (i.e. gain) of the frequency current (f-I) relationship in neurons. To date, demonstrations of gain control that are independent of synaptic noise have been limited. We investigated the effects of increasing somatic conductance in the form of tonic inhibition on the initial and steady-state f-I relationship of CA1 pyramidal cells. We find that increasing membrane conductance reduces the gain of the steady-state f-I relationship through a graded increase in the magnitude of spike frequency-adaptation. Increased adaptation arises through a conductance-induced depolarization of spike voltage threshold. Thus, by increasing the magnitude of spike frequency adaptation, added conductance can reduce the gain of the steady-state f-I relationship in the absence of random background membrane fluctuations.

Data from neurons in vivo have shown that spike output can often sustain episodes of high variability. Theoretical studies have indicated that the high conductance state of neurons brought on by synaptic activity can contribute to an increase in the variability of spike output by decreasing the integration time scale of the neuron. In the present work, we were interested in understanding how background synaptic conductance activity alters the interspike interval (ISI) variability of layer III pyramidal cells of the medial entorhinal cortex. We compared ISI variability in pyramidal cells as a result of synaptic current- or conductance-mediated membrane fluctuations. We found that the effects of background synaptic conductance activity on ISI variability depend on the neuron type. In pyramidal cells lacking spike frequency adaptation, the variability increased in relation to a comparable synaptic current stimulus. In contrast, in pyramidal cells displaying spike frequency adaptation, the synaptic conductance stimulus produced lower ISI variability. To understand this result we constructed a phenomenological model that reproduced the basic properties of these neurons under control and increased leak conductance. We found that leak can change the properties of the neuron by acting as a bifurcation parameter that reduces the afterdepolarization (ADP) and decreases the slope (gain) of the frequency-current relationship, particularly for transient stimuli. A lower gain with the added leak causes a reduction in ISI variability. We conclude that the ability of a high conductance state to increase ISI variability cannot be generalized and can depend on the spike ADP dynamics expressed by the neuron.

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.

How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity.

Author Summary

Individual oscillators, such as pendulum-based clocks and fireflies, can spontaneously organize into a coherent, synchronized entity with a common frequency. Neurons can oscillate under some circumstances, and can synchronize their firing both within and across brain regions. Synchronized assemblies of neurons are thought to underlie cognitive functions such as recognition, recall, perception and attention. Pathological synchrony can lead to epilepsy, tremor and other dynamical diseases, and synchronization is altered in most mental disorders. Biological neurons synchronize despite conduction delays, heterogeneous circuit composition, and noise. In biological experiments, we built simple networks in which two living neurons could interact via a computer in real time. The computer precisely controlled the nature of the connectivity and the length of the communication delays. We characterized the synchronization tendencies of individual, isolated oscillators by measuring how much a single input delivered by the computer transiently shortened or lengthened the cycle period of the oscillation. We then used this information to correctly predict the strong dependence of the coordination pattern of the firing of the component neurons on the length of the communication delays. Upon this foundation, we can begin to build a theory of the basic principles of synchronization in more complex brain circuits.