Detecting and Estimating Signals in Noisy Cable Structures, I: Neuronal Noise Sources

In recent theoretical approaches addressing the problem of neural coding, tools from statistical estimation and information theory have been applied to quantify the ability of neurons to transmit information through their spike outputs. These techniques, though fairly general, ignore the specific nature of neuronal processing in terms of its known biophysical properties. However, a systematic study of processing at various stages in a biophysically faithful model of a single neuron can identify the role of each stage in information transfer. Toward this end, we carry out a theoretical analysis of the information loss of a synaptic signal propagating along a linear, one-dimensional, weakly active cable due to neuronal noise sources along the way, using both a signal reconstruction and a signal detection paradigm. Here we begin such an analysis by quantitatively characterizing three sources of membrane noise: (1) thermal noise due to the passive membrane resistance, (2) noise due to stochastic openings and closings of voltage-gated membrane channels (Na^+ and K^+), and (3) noise due to random, background synaptic activity. Using analytical expressions for the power spectral densities of these noise sources, we compare their magnitudes in the case of a patch of membrane from a cortical pyramidal cell and explore their dependence on different biophysical parameters

Extracting synaptic conductances from single membrane potential traces

In awake animals, the activity of the cerebral cortex is highly complex, with neurons firing irregularly with apparent Poisson statistics. One way to characterize this complexity is to take advantage of the high interconnectivity of cerebral cortex and use intracellular recordings of cortical neurons, which contain information about the activity of thousands of other cortical neurons. Identifying the membrane potential (Vm) to a stochastic process enables the extraction of important statistical signatures of this complex synaptic activity. Typically, one estimates the total synaptic conductances (excitatory and inhibitory) but this type of estimation requires at least two Vm levels and therefore cannot be applied to single Vm traces. We propose here a method to extract excitatory and inhibitory conductances (mean and variance) from single Vm traces. This "VmT method" estimates conductance parameters using maximum likelihood criteria, under the assumption are that synaptic conductances are described by Gaussian stochastic processes and are integrated by a passive leaky membrane. The method is illustrated using models and is tested on guinea-pig visual cortex neurons in vitro using dynamic-clamp experiments. The VmT method holds promises for extracting conductances from single-trial measurements, which has a high potential for in vivo applications.Comment: Neuroscience (in press

The role of ongoing dendritic oscillations in single-neuron dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as temporally local, near-instantaneous mappings from the current input of the cell to its current output, brought about by somatic summation of dendritic contributions that are generated in spatially localized functional compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations, and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought

Detecting and Estimating Signals in Noisy Cable Structures, II: Information Theoretical Analysis

This is the second in a series of articles that seek to recast classical single-neuron biophysics in information-theoretical terms. Classical cable theory focuses on analyzing the voltage or current attenuation of a synaptic signal as it propagates from its dendritic input location to the spike initiation zone. On the other hand, we are interested in analyzing the amount of information lost about the signal in this process due to the presence of various noise sources distributed throughout the neuronal membrane. We use a stochastic version of the linear one-dimensional cable equation to derive closed-form expressions for the second-order moments of the fluctuations of the membrane potential associated with different membrane current noise sources: thermal noise, noise due to the random opening and closing of sodium and potassium channels, and noise due to the presence of “spontaneous” synaptic input. We consider two different scenarios. In the signal estimation paradigm, the time course of the membrane potential at a location on the cable is used to reconstruct the detailed time course of a random, band-limited current injected some distance away. Estimation performance is characterized in terms of the coding fraction and the mutual information. In the signal detection paradigm, the membrane potential is used to determine whether a distant synaptic event occurred within a given observation interval. In the light of our analytical results, we speculate that the length of weakly active apical dendrites might be limited by the information loss due to the accumulated noise between distal synaptic input sites and the soma and that the presence of dendritic nonlinearities probably serves to increase dendritic information transfer

Non-stationary filtered shot noise processes and applications to neuronal membranes

Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In particular, they can model the membrane potential Vm of neurons driven by stochastic input, where these filtered processes are able to capture the non-stationary characteristics of Vm fluctuations in response to pre-synaptic input with variable rate. In this paper, we apply the general framework of Poisson Point Processes transformations to analyse these systems in the general case of variable input rate. We obtain exact analytic expressions, and very accurate approximations, for the joint cumulants of filtered shot noise processes with multiplicative noise. These general results are then applied to a model of neuronal membranes subject to conductance shot noise with continuously variable rate of pre-synaptic spikes. We propose very effective approximations for the time evolution of Vm distribution and simple method to estimate the pre-synaptic rate from a small number of Vm traces. This work opens the perspective of obtaining analytic access to important statistical properties of conductance-based neuronal models such as the the first passage time.Comment: 18 pages, 13 figure

Inferring connection proximity in networks of electrically coupled cells by subthreshold frequency response analysis

Electrical synapses continuously transfer signals bi-directionally from one cell to another, directly or indirectly via intermediate cells. Electrical synapses are common in many brain structures such as the inferior olive, the subcoeruleus nucleus and the neocortex, between neurons and between glial cells. In the cortex, interneurons have been shown to be electrically coupled and proposed to participate in large, continuous cortical syncytia, as opposed to smaller spatial domains of electrically coupled cells. However, to explore the significance of these findings it is imperative to map the electrical synaptic microcircuits, in analogy with in vitro studies on monosynaptic and disynaptic chemical coupling. Since "walking” from cell to cell over large distances with a glass pipette is challenging, microinjection of (fluorescent) dyes diffusing through gap-junctions remains so far the only method available to decipher such microcircuits even though technical limitations exist. Based on circuit theory, we derive analytical descriptions of the AC electrical coupling in networks of isopotential cells. We then suggest an operative electrophysiological protocol to distinguish between direct electrical connections and connections involving one or more intermediate cells. This method allows inferring the number of intermediate cells, generalizing the conventional coupling coefficient, which provides limited information. We validate our method through computer simulations, theoretical and numerical methods and electrophysiological paired recording

Somatosensory neurons integrate the geometry of skin deformation and mechanotransduction channels to shape touch sensing.

Touch sensation hinges on force transfer across the skin and activation of mechanosensitive ion channels along the somatosensory neurons that invade the skin. This skin-nerve sensory system demands a quantitative model that spans the application of mechanical loads to channel activation. Unlike prior models of the dynamic responses of touch receptor neurons in Caenorhabditis elegans (Eastwood et al., 2015), which substituted a single effective channel for the ensemble along the TRNs, this study integrates body mechanics and the spatial recruitment of the various channels. We demonstrate that this model captures mechanical properties of the worm's body and accurately reproduces neural responses to simple stimuli. It also captures responses to complex stimuli featuring non-trivial spatial patterns, like extended or multiple contacts that could not be addressed otherwise. We illustrate the importance of these effects with new experiments revealing that skin-neuron composites respond to pre-indentation with increased currents rather than adapting to persistent stimulation

Signalling properties at single synapses and within the interneuronal network in the CA1 region of the rodent hippocampus

Understanding how the complexity of connections among the neurons in the brain is established and modified in an experience- and activity-dependent way is a challenging task of Neuroscience. Although in the last decades many progresses have been made in characterising the basic mechanisms of synaptic transmission, a full comprehension of how information is transferred and processed by neurons has not been fully achieved. In the present study, theoretical tools and patch clamp experiments were used to further investigate synaptic transmission, focusing on quantal transmission at single synapses and on different types of signalling at the level of a particular interneuronal network in the CA1 area of the rodent hippocampus. The simultaneous release of more than one vesicle from an individual presynaptic active zone is a typical mechanism that can affect the strength and reliability of synaptic transmission. At many central synapses, however, release caused by a single presynaptic action potential is limited to one vesicle (univesicular release). The likelihood of multivesicular release at a particular synapse has been tied to release probability (Pr), and whether it can occur at Schaffer collateral\u2013CA1 synapses, at which Pr ranges widely, is controversial. In contrast with previous findings, proofs of multivesicular release at this synapse have been recently obtained at late developmental stages; however, in the case of newborn hippocampus, it is still difficult to find strong evidence in one direction or another. In order to address this point, in the first part of this study a simple and general stochastic model of synaptic release has been developed and analytically solved. The model solution gives analytical mathematical expressions relating basic quantal parameters with average values of quantities that can be measured experimentally. Comparison of these quantities with the experimental measures allows to determine the most probable values of the quantal parameters and to discriminate the univesicular from the multivesicular mode of glutamate release. The model has been validated with data previously collected at glutamatergic CA3-CA1 synapses in the hippocampus from newborn (P1-P5 old) rats. The results strongly support a multivesicular type of release process requiring a variable pool of immediately releasable vesicles. Moreover, computing quantities that are functions of the model parameters, the mean amplitude of the synaptic response to the release of a single vesicle (Q) was estimated to be 5-10 pA, in very good agreement with experimental findings. In addition, a multivesicular type of release was supported by various experimental evidences: a high variability of the amplitude of successes, with a coefficient of variation ranging from 0.12 to 0.73; an average potency ratio a2/a1 between the second and first response to a pair of stimuli bigger than 1; and changes in the potency of the synaptic response to the first stimulus when the release probability was modified by increasing or decreasing the extracellular calcium concentration. This work indicates that at glutamatergic CA3-CA1 synapses of the neonatal rat hippocampus a single action potential may induce the release of more than one vesicle from the same release site. In a more systemic approach to the analysis of communication between neurons, it is interesting to investigate more complex, network interactions. GABAergic interneurons constitute a heterogeneous group of cells which exert a powerful control on network excitability and are responsible for the oscillatory behaviour crucial for information processing in the brain. They have been differently classified according to their morphological, neurochemical and physiological characteristics. In the second part of this study, whole cell patch clamp recordings were used to further characterize, in transgenic mice expressing EGFP in a subpopulation of GABAergic interneurons containing somatostatin (GIN mice), the functional properties of EGFPpositive cells in stratum oriens of the CA1 region of the hippocampus, in slice cultures obtained from P8 old animals. These cells showed passive and active membrane properties similar to those found in stratum oriens interneurons projecting to stratum lacunosum-moleculare. Moreover, they exhibited different firing patterns which were maintained upon membrane depolarization: irregular (48%), regular (30%) and clustered (22%). Paired recordings from EGFP-positive cells often revealed electrical coupling (47% of the cases), which was abolished by carbenoxolone (200 mM). On average, the coupling coefficient was 0.21 \ub1 0.07. When electrical coupling was particularly strong it acted as a powerful low-pass filter, thus contributing to alter the output of individual cells. The dynamic interaction between cells with various firing patterns may differently control GABAergic signalling, leading, as suggested by simulation data, to a wide range of interneuronal communication. In additional paired recordings of a presynaptic EGFP positive interneuron and a postsynaptic principal cell, trains of action potentials in interneurons rarely evoked GABAergic postsynaptic currents (3/45 pairs) with small amplitude and slow kinetics, and that at 20 Hz exhibited short-term depression. In contrast, excitatory connections between principal cells and EGFP-positive interneurons were found more often (17/55 pairs) and exhibited a frequency and use-dependent facilitation, particularly in the gamma band. In conclusion, it appears that EGFP-positive interneurons in stratum oriens of GIN mice constitute a heterogeneous population of cells interconnected via electrical synapses, exhibiting particular features in their chemical and electrical synaptic signalling. Moreover, the dynamic interaction between these interneurons may differentially affect target cells and neuronal communication within the hippocampal network

Expression of truncated Kir6.2 promotes insertion of functionally inverted ATP-sensitive K+ channels

ATP-sensitive K+ (KATP) channels couple cellular metabolism to electrical activity in many cell types. Wild-type KATP channels are comprised of four pore forming (Kir6.x) and four regulatory (sulfonylurea receptor, SURx) subunits that each contain RKR endoplasmic reticulum retention sequences that serve to properly translocate the channel to the plasma membrane. Truncated Kir6.x variants lacking RKR sequences facilitate plasma membrane expression of functional Kir6.x in the absence of SURx; however, the effects of channel truncation on plasma membrane orientation have not been explored. To investigate the role of truncation on plasma membrane orientation of ATP sensitive K+ channels, three truncated variants of Kir6.2 were used (Kir6.2ΔC26, 6xHis-Kir6.2ΔC26, and 6xHis-EGFP-Kir6.2ΔC26). Oocyte expression of Kir6.2ΔC26 shows the presence of a population of inverted inserted channels in the plasma membrane, which is not present when co-expressed with SUR1. Immunocytochemical staining of intact and permeabilized HEK293 cells revealed that the N-terminus of 6xHis-Kir6.2ΔC26 was accessible on both sides of the plasma membrane at roughly equivalent ratios, whereas the N-terminus of 6xHis-EGFP-Kir6.2Δ26 was only accessible on the intracellular face. In HEK293 cells, whole-cell electrophysiological recordings showed a ca. 50% reduction in K+ current upon addition of ATP to the extracellular solution for 6xHis-Kir6.2ΔC26, though sensitivity to extracellular ATP was not observed in 6xHis-EGFP-Kir6.2ΔC26. Importantly, the population of channels that is inverted exhibited similar function to properly inserted channels within the plasma membrane. Taken together, these data suggest that in the absence of SURx, inverted channels can be formed from truncated Kir6.x subunits that are functionally active which may provide a new model for testing pharmacological modulators of Kir6.x, but also indicates the need for added caution when using truncated Kir6.2 mutants. © 2021, The Author(s).Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]