Synaptic inhibition and excitation estimated via the time constant of membrane potential fluctuations

When recording the membrane potential, V, of a neuron it is desirable to be able to extract the synaptic input. Critically, the synaptic input is stochastic and nonreproducible so one is therefore often restricted to single-trial data. Here, we introduce means of estimating the inhibition and excitation and their confidence limits from single sweep trials. The estimates are based on the mean membrane potential, V̄, and the membrane time constant, τ. The time constant provides the total conductance ( G = capacitance/τ) and is extracted from the autocorrelation of V. The synaptic conductances can then be inferred from V̄ when approximating the neuron as a single compartment. We further employ a stochastic model to establish limits of confidence. The method is verified on models and experimental data, where the synaptic input is manipulated pharmacologically or estimated by an alternative method. The method gives best results if the synaptic input is large compared with other conductances, the intrinsic conductances have little or no time dependence or are comparably small, the ligand-gated kinetics is faster than the membrane time constant, and the majority of synaptic contacts are electrotonically close to soma (recording site). Although our data are in current clamp, the method also works in V-clamp recordings, with some minor adaptations. All custom made procedures are provided in Matlab.

Potassium conductance dynamics confer robust spike-time precision in a neuromorphic model of the auditory brain stem

A fundamental question in neuroscience is how neurons perform precise operations despite inherent variability. This question also applies to neuromorphic engineering, where low-power microchips emulate the brain using large populations of diverse silicon neurons. Biological neurons in the auditory pathway display precise spike timing, critical for sound localization and interpretation of complex waveforms such as speech, even though they are a heterogeneous population. Silicon neurons are also heterogeneous, due to a key design constraint in neuromorphic engineering: smaller transistors offer lower power consumption and more neurons per unit area of silicon, but also more variability between transistors and thus between silicon neurons. Utilizing this variability in a neuromorphic model of the auditory brain stem with 1,080 silicon neurons, we found that a low-voltage-activated potassium conductance ( gKL) enables precise spike timing via two mechanisms: statically reducing the resting membrane time constant and dynamically suppressing late synaptic inputs. The relative contribution of these two mechanisms is unknown because blocking gKL in vitro eliminates dynamic adaptation but also lengthens the membrane time constant. We replaced gKL with a static leak in silico to recover the short membrane time constant and found that silicon neurons could mimic the spike-time precision of their biological counterparts, but only over a narrow range of stimulus intensities and biophysical parameters. The dynamics of gKL were required for precise spike timing robust to stimulus variation across a heterogeneous population of silicon neurons, thus explaining how neural and neuromorphic systems may perform precise operations despite inherent variability.

Dynamics of Deterministic and Stochastic Paired Excitatory—Inhibitory Delayed Feedback

We examine the effects of paired delayed excitatory and inhibitory feedback on a single integrate—and—fire neuron with reversal potentials embedded within a feedback network. These effects are studied using bifurcation theory and numerical analysis. The feedback occurs through modulation of the excitatory and inhibitory conductances by the previous firing history of the neuron; as a consequence, the feedback also modifies the membrane time constant. Such paired feedback is ubiquitous in the nervous system. We assume that the feedback dynamics are slower than the membrane time constant, which leads to a rate model formulation. Our article provides an extensive analysis of the possible dynamical behaviors of such simple yet realistic neural loops as a function of the balance between positive and negative feedback, with and without noise, and offers insight into the potential behaviors such loops can exhibit in response to time-varying external inputs. With excitatory feedback, the system can be quiescent, can be periodically firing, or can exhibit bistability between these two states. With inhibitory feedback, quiescence, oscillatory firing rates, and bistability between constant and oscillatory firing-rate solutions are possible. The general case of paired feedback exhibits a blend of the behaviors seen in the extreme cases and can produce chaotic firing. We further derive a condition for a dynamically balanced paired feedback in which there is neither bistability nor oscillations. We also show how a biophysically plausible smoothing of the firing function by noise can modify the existence and stability of fixed points and oscillations of the system. We take advantage in our mathematical analysis of the existence of an invariant manifold, which reduces the dimensionality of the dynamics, and prove the stability of this manifold. The novel computational challenges involved in analyzing such dynamics with and without noise are also described. Our results demonstrate that a paired delayed feedback loop can act as a sophisticated computational unit, capable of switching between a variety of behaviors depending on the input current, the relative strengths and asymmetry of the two parallel feedback pathways, and the delay distributions and noise level.