Effects of Ih and TASK-like shunting current on dendritic impedance in layer 5 pyramidal-tract neurons

Pyramidal neurons in neocortex have complex input-output relationships that depend on their morphologies, ion channel distributions, and the nature of their inputs, but which cannot be replicated by simple integrate-and-fire models. The impedance properties of their dendritic arbors, such as resonance and phase shift, shape neuronal responses to synaptic inputs and provide intraneuronal functional maps reflecting their intrinsic dynamics and excitability. Experimental studies of dendritic impedance have shown that neocortical pyramidal tract neurons exhibit distance-dependent changes in resonance and impedance phase with respect to the soma. We therefore investigated how well several biophysically-detailed multi-compartment models of neocortical layer 5 pyramidal tract neurons reproduce the location-dependent impedance profiles observed experimentally. Each model tested here exhibited location-dependent impedance profiles, but most captured either the observed impedance amplitude or phase, not both. The only model that captured features from both incorporates HCN channels and a shunting current, like that produced by Twik-related acid-sensitive K+ (TASK) channels. TASK-like channel activity in this model was dependent on local peak HCN channel conductance (Ih). We found that while this shunting current alone is insufficient to produce resonance or realistic phase response, it modulates all features of dendritic impedance, including resonance frequencies, resonance strength, synchronous frequencies, and total inductive phase. We also explored how the interaction of Ih and a TASK-like shunting current shape synaptic potentials and produce degeneracy in dendritic impedance profiles, wherein different combinations of Ih and shunting current can produce the same impedance profile.

Interfacing gene circuits with microelectronics through engineered population dynamics

While there has been impressive progress connecting bacterial behavior with electrodes, an attractive observation to facilitate advances in synthetic biology is that the growth of a bacterial colony can be determined from impedance changes over time. Here, we interface synthetic biology with microelectronics through engineered population dynamics that regulate the accumulation of charged metabolites. We demonstrate electrical detection of the bacterial response to heavy metals via a population control circuit. We then implement this approach to a synchronized genetic oscillator where we obtain an oscillatory impedance profile from engineered bacteria. We lastly miniaturize an array of electrodes to form “bacterial integrated circuits” and demonstrate its applicability as an interface with genetic circuits. This approach paves the way for new advances in synthetic biology, analytical chemistry, and microelectronic technologies.

Estimating broad trend of acoustic impedance profile from observed seismic reflection data using first principles only

Estimation of broad features or the low-frequency part of acoustic impedance from conventional reflection data is an essential yet challenging step for quantitative interpretation of seismic data due to its band-limited nature. A missing low-frequency part leads to non-uniqueness in the solution as well as placing restrictions in recovering the absolute impedance values. The current industry practice fills this gap by assuming either an initial impedance model or statistical restrictions on such a model. Doing away with such assumptions but using only first principles (Zoeppritz's equations) and homogeneous layered earth model, we have formulated a set of linear equations that are then solved for an unknown reflection co-efficient using singular value decomposition (SVD) approach with time sampled seismic trace as the input data. The present work demonstrates the effectiveness of reconstructing a broad and smooth impedance profile from first principles and even from acquired seismic reflection data. It also illustrates the method's success with real data, while determining in one go the unknown scale factor linking the true and the relative seismic amplitudes, and the smallest singular value to be retained in the solution from only the knowledge of the average value of the acoustic impedance over the depth range in question. Thus, the salient feature of this work is the ability to reconstruct an approximate impedance profile from field data without the aid of an initial model or statistical assumption on the reflectivity series. This approximate impedance profile can serve as a reliable initial input for more refined inversion or geologic interpretation.

Resonance modulation, annihilation and generation of antiresonance and antiphasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics

Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slaved to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decrease with the input frequency. In contrast, for f ≪ 1 the dynamics is quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.

Feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band-limited reflection data

Because seismic reflection data are band limited, acoustic impedance profiles derived from them are nonunique. The conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients. By making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers, we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data. Drawing only on first principles, the Zoeppritz equation in this case, the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data. The local layer-cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness, provided that the objective is to reconstruct a smooth version of the impedance profile that includes only its crude structures. Tests on synthetic data generated from elementary models and from measured logs of acoustic impedance demonstrated the efficacy of the method, even when a significant amount of noise was added to the data. The emergence of consistent estimates of impedance, approximating the original impedance, from synthetic data generated for several frequency bands has inspired our confidence in the method. The other attractive outputs of the method are as follows: (1) an accurate estimate of the impedance mean, (2) an accurate reconstruction of the direct-current (DC) frequency of the reflectivity, and (3) an acceptable reconstruction of the broad outline of the original impedance profile. These outputs can serve as constraints for either more refined inversions or geologic interpretations. Beginning from the restriction of band-limited data, we have devised a method that neither requires a starting input model nor imposes mathematical constraints on the earth reflectivity and still yielded significant and relevant geologic information.