Estimation of Synaptic Activity during Neuronal Oscillations

In the study of brain connectivity, an accessible and convenient way to unveil local functional structures is to infer the time trace of synaptic conductances received by a neuron by using exclusively information about its membrane potential (or voltage). Mathematically speaking, it constitutes a challenging inverse problem: it consists in inferring time-dependent parameters (synaptic conductances) departing from the solutions of a dynamical system that models the neuron’s membrane voltage. Several solutions have been proposed to perform these estimations when the neuron fluctuates mildly within the subthreshold regime, but very few methods exist for the spiking regime as large amplitude oscillations (revealing the activation of complex nonlinear dynamics) hinder the adaptability of subthreshold-based computational strategies (mostly linear). In a previous work, we presented a mathematical proof-of-concept that exploits the analytical knowledge of the period function of the model. Inspired by the relevance of the period function, in this paper we generalize it by providing a computational strategy that can potentially adapt to a variety of models as well as to experimental data. We base our proposal on the frequency versus synaptic conductance curve (f−gsyn), derived from an analytical study of a base model, to infer the actual synaptic conductance from the interspike intervals of the recorded voltage trace. Our results show that, when the conductances do not change abruptly on a time-scale smaller than the mean interspike interval, the time course of the synaptic conductances is well estimated. When no base model can be cast to the data, our strategy can be applied provided that a suitable f−gsyn table can be experimentally constructed. Altogether, this work opens new avenues to unveil local brain connectivity in spiking (nonlinear) regimes.

Automatic parameter estimation of multicompartmental neuron models via minimization of trace error with control adjustment

We describe a new technique to fit conductance-based neuron models to intracellular voltage traces from isolated biological neurons. The biological neurons are recorded in current-clamp with pink (1/ f) noise injected to perturb the activity of the neuron. The new algorithm finds a set of parameters that allows a multicompartmental model neuron to match the recorded voltage trace. Attempting to match a recorded voltage trace directly has a well-known problem: mismatch in the timing of action potentials between biological and model neuron is inevitable and results in poor phenomenological match between the model and data. Our approach avoids this by applying a weak control adjustment to the model to promote alignment during the fitting procedure. This approach is closely related to the control theoretic concept of a Luenberger observer. We tested this approach on synthetic data and on data recorded from an anterior gastric receptor neuron from the stomatogastric ganglion of the crab Cancer borealis. To test the flexibility of this approach, the synthetic data were constructed with conductance models that were different from the ones used in the fitting model. For both synthetic and biological data, the resultant models had good spike-timing accuracy.

Measurement and Analysis of Postsynaptic Potentials Using a Novel Voltage-Deconvolution Method

Accurate measurement of postsynaptic potential amplitudes is a central requirement for the quantification of synaptic strength, dynamics of short-term and long-term plasticity, and vesicle-release statistics. However, the intracellular voltage is a filtered version of the underlying synaptic signal and so a method of accounting for the distortion caused by overlapping postsynaptic potentials must be used. Here a voltage-deconvolution technique is demonstrated that defilters the entire voltage trace to reveal an underlying signal of well-separated synaptic events. These isolated events can be cropped out and reconvolved to yield a set of isolated postsynaptic potentials from which voltage amplitudes may be measured directly—greatly simplifying this common task. The method also has the significant advantage of providing a higher temporal resolution of the dynamics of the underlying synaptic signal. The versatility of the method is demonstrated by a variety of experimental examples, including excitatory and inhibitory connections to neurons with passive membranes and those with activated voltage-gated currents. The deconvolved current-clamp voltage has many features in common with voltage-clamp current measurements. These similarities are analyzed using cable theory and a multicompartment cell reconstruction, as well as direct comparison to voltage-clamp experiments.

Thermal Decomposition of Li(NTO)·2H2O and Na(NTO)·H2O (NTO = Anion of 3-Nitro-1,2,4-triazol-5-one): Kinetics Derived from T-jump/FTIR Spectroscopy

A "snapshot" simulation of the surface reaction zone is captured by a thin film of material heated rapidly to temperatures characteristic of the burning surface by using the T-jump/FTIR spectroscopy. The time-to-exotherm (tx) kinetics method derived from the control voltage trace of the Pt filament can be introduced to resolve the kinetics of an energetic material owing to its high sensitivity to the thermochemical reactions. The kinetic parameters of the two title compounds are determined under different pressures. The results show that Li(NTO)·2H2O and Na(NTO)·H2O (NTO = anion of 3-nitro-1,2,4-triazol-5-one) exhibit weak pressure dependence, their decomposition is dominated by the condensed phase chemistry irrespective of the pressure in the 0.1-1.1 MPa range. The values of Ea determined here are smaller than those given by a traditional non-isothermal differential scanning colorimetry (DSC) method, which might be resembled as the surface of explosion more closely and enabled the pyrolysis surface to be incorporated into models of steady and possibly unsteady combustion. The kinetics can also be successfully used to understand the behavior of the energetic material in practical combustion problems.

Resolving the electrode fall spaces of electric arcs

The measurement of the cathode and anode fall in potential in arc discharges between metal electrodes in gases at atmospheric pressure has presented considerable difficulties because of the small extent of the fall spaces. For the same reason there are no satisfactory observations of the thickness of these spaces. Early mirror oscillograms of te voltage of arcs of decreasing length indicated the existence of a minimum voltage, necessary to maintain an arc, and its value was taken to be equal to the sum of cathode and anode falls in potential. Attempts to determine these individually either by using different substances for the electrodes or by a moving probe have met with only limited success. In order to separate the electrode falls in a single experiment, a high speed cathode ray oscilloscope is used. The arc having been first established, its anode is driven towards the stationary cathode while the variation of arc voltage with time is recorded as the arc length is reduced to zero. Oscillograms show two discontinuities in the voltage trace which correspond to the anode and cathode falls. From the duration of the steps, and the known velocity of approach of the anode, approximate values of the thickness of the fall spaces are determined. Arcs between electrodes of tin, copper, graphite, and tungsten are investigated in argon, nitrogen and air, mostly at atmospheric, but also at reduced, gas pressures. At one atmosphere the cathode falls observed are between 11 and 15 V for currents of 10 A and above, whereas the anode falls lie in the range of 2 to 5 V. Fluctuations in arc voltage are found to originate mainly at the cathode. The cathode fall for tin in argon is constant below 30 A but slowly increasing at larger currents. The anode fall for graphite is independent of current up to 60 A. The thickness of the anode fall space in metal vapour arcs is of the order 10 -2 to 10 -4 cm depending on the gas. The thickness of the cathode fall space does not exceed 4 x 10 -6 cm, a value consistent with the excitation theory of vapour arcs.