Democratization in a passive dendritic tree : an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius

A Measurement of Newton's Gravitational Constant

A precision measurement of the gravitational constant $G$ has been made using a beam balance. Special attention has been given to determining the calibration, the effect of a possible nonlinearity of the balance and the zero-point variation of the balance. The equipment, the measurements and the analysis are described in detail. The value obtained for G is 6.674252(109)(54) 10^{-11} m3 kg-1 s-2. The relative statistical and systematic uncertainties of this result are 16.3 10^{-6} and 8.1 10^{-6}, respectively.Comment: 26 pages, 20 figures, Accepted for publication by Phys. Rev.

A low-voltage activated, transient calcium current is responsible for the time-dependent depolarizing inward rectification of rat neocortical neurons in vitro

Intracellular recordings were obtained from rat neocortical neurons in vitro. The current-voltage-relationship of the neuronal membrane was investigated using current- and single-electrode-voltage-clamp techniques. Within the potential range up to 25 mV positive to the resting membrane potential (RMP: –75 to –80 mV) the steady state slope resistance increased with depolarization (i.e. steady state inward rectification in depolarizing direction). Replacement of extracellular NaCl with an equimolar amount of choline chloride resulted in the conversion of the steady state inward rectification to an outward rectification, suggesting the presence of a voltage-dependent, persistent sodium current which generated the steady state inward rectification of these neurons. Intracellularly injected outward current pulses with just subthreshold intensities elicited a transient depolarizing potential which invariably triggered the first action potential upon an increase in current strength. Single-electrode-voltage-clamp measurements reveled that this depolarizing potential was produced by a transient calcium current activated at membrane potentials 15–20 mV positive to the RMP and that this current was responsible for the time-dependent increase in the magnitude of the inward rectification in depolarizing direction in rat neocortical neurons. It may be that, together with the persistent sodium current, this calcium current regulates the excitability of these neurons via the adjustment of the action potential threshold

Conserved properties of dendritic trees in four cortical interneuron subtypes

Dendritic trees influence synaptic integration and neuronal excitability, yet appear to develop in rather arbitrary patterns. Using electron microscopy and serial reconstructions, we analyzed the dendritic trees of four morphologically distinct neocortical interneuron subtypes to reveal two underlying organizational principles common to all. First, cross-sectional areas at any given point within a dendrite were proportional to the summed length of all dendritic segments distal to that point. Consistent with this observation, total cross-sectional area was almost perfectly conserved at bifurcation points. Second, dendritic cross-sections became progressively more elliptical at more proximal, larger diameter, dendritic locations. Finally, computer simulations revealed that these conserved morphological features limit distance dependent filtering of somatic EPSPs and facilitate distribution of somatic depolarization into all dendritic compartments. Because these features were shared by all interneurons studied, they may represent common organizational principles underlying the otherwise diverse morphology of dendritic trees

Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances ($\approx$10~$\mu m$) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig

What we talk about when we talk about capacitance measured with the voltage-clamp step method

Capacitance is a fundamental neuronal property. One common way to measure capacitance is to deliver a small voltage-clamp step that is long enough for the clamp current to come to steady state, and then to divide the integrated transient charge by the voltage-clamp step size. In an isopotential neuron, this method is known to measure the total cell capacitance. However, in a cell that is not isopotential, this measures only a fraction of the total capacitance. This has generally been thought of as measuring the capacitance of the “well-clamped” part of the membrane, but the exact meaning of this has been unclear. Here, we show that the capacitance measured in this way is a weighted sum of the total capacitance, where the weight for a given small patch of membrane is determined by the voltage deflection at that patch, as a fraction of the voltage-clamp step size. This quantifies precisely what it means to measure the capacitance of the “well-clamped” part of the neuron. Furthermore, it reveals that the voltage-clamp step method measures a well-defined quantity, one that may be more useful than the total cell capacitance for normalizing conductances measured in voltage-clamp in nonisopotential cells

Efficient Long-Range Entanglement using Dynamic Circuits

Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by non-unitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: CNOT gate teleportation between up to 101 qubits by feeding forward 99 mid-circuit measurement outcomes, and the preparation of Greenberger-Horne-Zeilinger (GHZ) states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices.Comment: 7 pages, 3 figures (main text) + 11 pages, 6 figures (appendix

Electron impact excitation cross sections for allowed transitions in atoms

We present a semiempirical Gaunt factor for widely used Van Regemorter formula [Astrophys. J. 136, 906 (1962)] for the case of allowed transitions in atoms with the LS coupling scheme. Cross sections calculated using this Gaunt factor agree with measured cross sections to within the experimental error.Comment: RevTeX, 3 pages, 10 PS figures, 2 PS tables, submitted to Phys. Rev.