The mechanoelectrical transducer (MET) is a crucial component of mammalian auditory system. The gating mechanism of the MET channel remains a puzzling issue, though there are many speculations, due to the lack of essential molecular building blocks. To understand the working principle of mammalian MET, we propose a molecular level prototype which constitutes a charged blocker, a realistic ion channel and its surrounding membrane. To validate the proposed prototype, we make use of a well-established ion channel theory, the Poisson-Nernst-Planck equations, for three-dimensional (3D) numerical simulations. A wide variety of model parameters, including bulk ion concentration, applied external voltage, blocker charge and blocker displacement, are explored to understand the basic function of the proposed MET prototype. We show that our prototype prediction of channel open probability in response to blocker relative displacement is in a remarkable accordance with experimental observation of rat cochlea outer hair cells. Our results appear to suggest that tip links which connect hair bundles gate MET channels.
Mechanoelectrical transducer; Gating mechanism; Poisson-Nernst-Planck model; Ion channel
Lateral inhibition of cells surrounding an excited area is a key property of sensory systems, sharpening the preferential tuning of individual cells in the presence of closely related input signals. In the olfactory pathway, a dendrodendritic synaptic microcircuit between mitral and granule cells in the olfactory bulb has been proposed to mediate this type of interaction through granule cell inhibition of surrounding mitral cells. However, it is becoming evident that odor inputs result in broad activation of the olfactory bulb with interactions that go beyond neighboring cells. Using a realistic modeling approach we show how backpropagating action potentials in the long lateral dendrites of mitral cells, together with granule cell actions on mitral cells within narrow columns forming glomerular units, can provide a mechanism to activate strong local inhibition between arbitrarily distant mitral cells. The simulations predict a new role for the dendrodendritic synapses in the multicolumnar organization of the granule cells. This new paradigm gives insight into the functional significance of the patterns of connectivity revealed by recent viral tracing studies. Together they suggest a functional wiring of the olfactory bulb that could greatly expand the computational roles of the mitral–granule cell network.
Olfactory processing; Modeling; Mitral cells; Granule cells
The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron’s response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.
System identification; Olfactory sensory neurons; White noise analysis; I/O modeling
Ankle control is critical to both standing balance and efficient walking. This hypothesis presented in this paper is that a Flat Interface Nerve Electrode (FINE) placed around the sciatic nerve with a fixed number of contacts at predetermined locations and without a priori knowledge of the nerve’s underlying neuroanatomy can selectively control each ankle motion. Models of the human sciatic nerve surrounded by a FINE of varying size were created and used to calculate the probability of selective activation of axons within any arbitrarily designated, contiguous group of fascicles. Simulations support the hypothesis and suggest that currently available implantable technology cannot selectively recruit each target plantar flexor individually but can restore plantar flexion or dorsiflexion from a site on the sciatic nerve without spillover to antagonists. Successful activation of individual ankle muscles in 90% of the population can be achieved by utilizing bipolar stimulation and/or by using a cuff with at least 20 contacts.
sciatic nerve; Flat Interface Nerve Electrode (FINE); Functional Electrical Stimulation (FES); three dimensional Finite Element Method (3D FEM); selective stimulation
Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. Central pattern generators, such as those of the crustacean stomatogastric ganglion (STG), are able to robustly maintain their functionality over a wide range of burst periods. Previous experimental work involving extracellular recordings of the pyloric pattern of the STG has demonstrated that as the burst period varies, the inter-neuronal delays are altered proportionally, resulting in burst phases that are roughly invariant. The question whether spike delays within bursts are also proportional to pyloric period has not been explored in detail. The mechanism by which the pyloric neurons accomplish phase maintenance is currently not obvious. Previous studies suggest that the co-regulation of certain ion channel properties may play a role in governing neuronal activity. Here, we observed in long-term recordings of the pyloric rhythm that spike delays can vary proportionally with burst period, so that spike phase is maintained. We then used a conductance-based model neuron to determine whether co-varying ionic membrane conductances results in neural output that emulates the experimentally observed phenomenon of spike phase maintenance. Next, we utilized a model neuron database to determine whether conductance correlations exist in model neuron populations with highly maintained spike phases. We found that co-varying certain conductances, including the sodium and transient calcium conductance pair, causes the model neuron to maintain a specific spike phase pattern. Results indicate a possible relationship between conductance co-regulation and phase maintenance in STG neurons.
stomatogastric system; pyloric neural network; model neuron database; conductance-based model; phase maintenance
Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies. Two candidate mechanisms of synchronized firing include direct coupling and shared noisy inputs. In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, recent experimental work indicates that direct electrical or synaptic coupling is weak, but shared synaptic input in the absence of modulated stimuli is strong. However, previous modeling efforts have not accounted for this aspect of firing in the parasol cell population. Here we develop a new model that incorporates the effects of common noise, and apply it to analyze the light responses and synchronized firing of a large, densely-sampled network of over 250 simultaneously recorded parasol cells. We use a generalized linear model in which the spike rate in each cell is determined by the linear combination of the spatio-temporally filtered visual input, the temporally filtered prior spikes of that cell, and unobserved sources representing common noise. The model accurately captures the statistical structure of the spike trains and the encoding of the visual stimulus, without the direct coupling assumption present in previous modeling work. Finally, we examined the problem of decoding the visual stimulus from the spike train given the estimated parameters. The common-noise model produces Bayesian decoding performance as accurate as that of a model with direct coupling, but with significantly more robustness to spike timing perturbations.
Retina; Generalized linear model; State-space model; Multielectrode; Recording; Random-effects model
State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in state-space models with non-Gaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way, we point out connections to some related standard statistical methods, including spline smoothing and isotonic regression. Finally, we note that the computational methods reviewed here do not in fact depend on the state-space setting at all; instead, the key property we are exploiting involves the bandedness of certain matrices. We close by discussing some applications of this more general point of view, including Markov chain Monte Carlo methods for neural decoding and efficient estimation of spatially-varying firing rates.
Deep brain stimulation (DBS) and lesioning are two surgical techniques used in the treatment of advanced Parkinson’s disease (PD) in patients whose symptoms are not well controlled by drugs, or who experience dyskinesias as a side effect of medications. Although these treatments have been widely practiced, the mechanisms behind DBS and lesioning are still not well understood. The subthalamic nucleus (STN) and globus pallidus pars interna (GPi) are two common targets for both DBS and lesioning. Previous studies have indicated that DBS not only affects local cells within the target, but also passing axons within neighboring regions. Using a computational model of the basal ganglia-thalamic network, we studied the relative contributions of activation and silencing of local cells (LCs) and fibers of passage (FOPs) to changes in the accuracy of information transmission through the thalamus (thalamic fidelity), which is correlated with the effectiveness of DBS. Activation of both LCs and FOPs during STN and GPi-DBS were beneficial to the outcome of stimulation. During STN and GPi lesioning, effects of silencing LCs and FOPs were different between the two types of lesioning. For STN lesioning, silencing GPi FOPs mainly contributed to its effectiveness, while silencing only STN LCs did not improve thalamic fidelity. In contrast, silencing both GPi LCs and GPe FOPs during GPi lesioning contributed to improvements in thalamic fidelity. Thus, two distinct mechanisms produced comparable improvements in thalamic function: driving the output of the basal ganglia to produce tonic inhibition and silencing the output of the basal ganglia to produce tonic disinhibition. These results show the importance of considering effects of activating or silencing fibers passing close to the nucleus when deciding upon a target location for DBS or lesioning.
dynamics; firing; latency; bistability; A-type current
Calmodulin (CaM) is a major Ca2+ binding protein involved in two opposing processes of synaptic plasticity of CA1 pyramidal neurons: long-term potentiation (LTP) and depression (LTD). The N- and C-terminal lobes of CaM bind to its target separately but cooperatively and introduce complex dynamics that cannot be well understood by experimental measurement. Using a detailed stochastic model constructed upon experimental data, we have studied the interaction between CaM and Ca2+-CaM-dependent protein kinase II (CaMKII), a key enzyme underlying LTP. The model suggests that the accelerated binding of one lobe of CaM to CaMKII, when the opposing lobe is already bound to CaMKII, is a critical determinant of the cooperative interaction between Ca2+, CaM, and CaMKII. The model indicates that the target-bound Ca2+ free N-lobe has an extended lifetime and may regulate the Ca2+ response of CaMKII during LTP induction. The model also reveals multiple kinetic pathways which have not been previously predicted for CaM-dissociation from CaMKII.
Calmodulin; CaMKII; Synaptic plasticity; Gillespie algorithm; Particle swarm theory
We used a particle-based Monte Carlo simulation to dissect the regulatory mechanism of molecular translocation of CaMKII, a key regulator of neuronal synaptic function. Geometry was based upon measurements from EM reconstructions of dendrites in CA1 hippocampal pyramidal neurons. Three types of simulations were performed to investigate the effects of geometry and other mechanisms that control CaMKII translocation in and out of dendritic spines. First, the diffusional escape rate of CaMKII from model spines of varied morphologies was examined. Second, a postsynaptic density (PSD) was added to study the impact of binding sites on this escape rate. Third, translocation of CaMKII from dendrites and trapping in spines was investigated using a simulated dendrite. Based on diffusion alone, a spine of average dimensions had the ability to retain CaMKII for duration of ~4 s. However, binding sites mimicking those in the PSD controlled the residence time of CaMKII in a highly nonlinear manner. In addition, we observed that F-actin at the spine head/neck junction had a significant impact on CaMKII trapping in dendritic spines. We discuss these results in the context of possible mechanisms that may explain the experimental results that have shown extended accumulation of CaMKII in dendritic spines during synaptic plasticity and LTP induction.
CaMKII; Diffusion; Translocation; Narrow escape problem
This paper proposes that the network dynamics of the mammalian visual cortex are highly structured and strongly shaped by temporally localized barrages of excitatory and inhibitory firing we call ‘multiple-firing events’ (MFEs). Our proposal is based on careful study of a network of spiking neurons built to reflect the coarse physiology of a small patch of layer 2/3 of V1. When appropriately benchmarked this network is capable of reproducing the qualitative features of a range of phenomena observed in the real visual cortex, including spontaneous background patterns, orientation-specific responses, surround suppression and gamma-band oscillations. Detailed investigation into the relevant regimes reveals causal relationships among dynamical events driven by a strong competition between the excitatory and inhibitory populations. It suggests that along with firing rates, MFE characteristics can be a powerful signature of a regime. Testable predictions based on model observations and dynamical analysis are proposed.
Electronic supplementary material
The online version of this article (doi:10.1007/s10827-013-0445-9) contains supplementary material, which is available to authorized users.
Visual cortex; Cascade; Dynamical systems
Multineuronal recordings have revealed that neurons in primary visual cortex (V1) exhibit coordinated fluctuations of spiking activity in the absence and in the presence of visual stimulation. From the perspective of understanding a single cell’s spiking activity relative to a behavior or stimulus, these network flutuations are typically considered to be noise. We show that these events are highly correlated with another commonly recorded signal, the local field potential (LFP), and are also likely related to global network state phenomena which have been observed in a number of neural systems. Moreover, we show that attributing a component of cell firing to these network fluctuations via explicit modeling of the LFP improves the recovery of cell properties. This suggests that the impact of network fluctuations may be estimated using the LFP, and that a portion of this network activity is unrelated to the stimulus and instead reflects ongoing cortical activity. Thus, the LFP acts as an easily accessible bridge between the network state and the spiking activity.
Local field potential; correlation; network state; spontaneous activity; multielectrode array; decoding; population coding
What is the role of higher-order spike correlations for neuronal information processing? Common data analysis methods to address this question are devised for the application to spike recordings from multiple single neurons. Here, we present a new method which evaluates the subthreshold membrane potential fluctuations of one neuron, and infers higher-order correlations among the neurons that constitute its presynaptic population. This has two important advantages: Very large populations of up to several thousands of neurons can be studied, and the spike sorting is obsolete. Moreover, this new approach truly emphasizes the functional aspects of higher-order statistics, since we infer exactly those correlations which are seen by a neuron. Our approach is to represent the subthreshold membrane potential fluctuations as presynaptic activity filtered with a fixed kernel, as it would be the case for a leaky integrator neuron model. This allows us to adapt the recently proposed method CuBIC (cumulant based inference of higher-order correlations from the population spike count; Staude et al., J Comput Neurosci 29(1–2):327–350, 2010c) with which the maximal order of correlation can be inferred. By numerical simulation we show that our new method is reasonably sensitive to weak higher-order correlations, and that only short stretches of membrane potential are required for their reliable inference. Finally, we demonstrate its remarkable robustness against violations of the simplifying assumptions made for its construction, and discuss how it can be employed to analyze in vivo intracellular recordings of membrane potentials.
Shot noise process; Intracellular recording; Subthreshold activity; Presynaptic population; Correlated neuronal groups
The spatial variation of the extracellular action potentials (EAP) of a single neuron contains information about the size and location of the dominant current source of its action potential generator, which is typically in the vicinity of the soma. Using this dependence in reverse in a three-component realistic probe + brain + source model, we solved the inverse problem of characterizing the equivalent current source of an isolated neuron from the EAP data sampled by an extracellular probe at multiple independent recording locations. We used a dipole for the model source because there is extensive evidence it accurately captures the spatial roll-off of the EAP amplitude, and because, as we show, dipole localization, beyond a minimum cell-probe distance, is a more accurate alternative to approaches based on monopole source models. Dipole characterization is separable into a linear dipole moment optimization where the dipole location is fixed, and a second, nonlinear, global optimization of the source location. We solved the linear optimization on a discrete grid via the lead fields of the probe, which can be calculated for any realistic probe + brain model by the finite element method. The global source location was optimized by means of Tikhonov regularization that jointly minimizes model error and dipole size. The particular strategy chosen reflects the fact that the dipole model is used in the near field, in contrast to the typical prior applications of dipole models to EKG and EEG source analysis. We applied dipole localization to data collected with stepped tetrodes whose detailed geometry was measured via scanning electron microscopy. The optimal dipole could account for 96% of the power in the spatial variation of the EAP amplitude. Among various model error contributions to the residual, we address especially the error in probe geometry, and the extent to which it biases estimates of dipole parameters. This dipole characterization method can be applied to any recording technique that has the capabilities of taking multiple independent measurements of the same single units.
Multisite recording; Inverse problem; Passive conductor model; Lead field theory; Finite element method (FEM)
A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the “inputs” and “outputs”, respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The “scaling-up” issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.
Multi-input multi-output neuronal systems; Pre-frontal cortex; Dynamic modeling; Nonlinear modeling; Principal Dynamic Modes; Volterra modeling
Although associational/commissural (A/C) and perforant path (PP) inputs to CA3b pyramidal cells play a central role in hippocampal mnemonic functions, the active and passive processes that shape A/C and PP AMPA and NMDA receptor-mediated unitary EPSP/EPSC (AMPA and NMDA uEPSP/uEPSC) have not been fully characterized yet. Here we find no differences in somatic amplitude between A/C and PP for either AMPA or NMDA uEPSPs. However, larger AMPA uEPSCs were evoked from proximal than from distal A/C or PP. Given the space-clamp constraints in CA3 pyramidal cells, these voltage clamp data suggest that the location-independence of A/C and PP AMPA uEPSP amplitudes is achieved in part through the activation of voltage dependent conductances at or near the soma. Moreover, similarity in uEPSC amplitudes for distal A/C and PP points to the additional participation of unclamped active conductances. Indeed, the pharmacological blockade of voltage-dependent conductances eliminates the location-independence of these inputs. In contrast, the location-independence of A/C and PP NMDA uEPSP/uEPSC amplitudes is maintained across all conditions indicating that propagation is not affected by active membrane processes. The location-independence for A/C uEPSP amplitudes may be relevant in the recruitment of CA3 pyramidal cells by other CA3 pyramidal cells. These data also suggest that PP excitation represents a significant input to CA3 pyramidal cells. Implication of the passive data on local synaptic properties is further investigated in the companion paper with a detailed computational model.
AMPA receptor; NMDA receptor; Hippocampus
Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.
Visual adaptation; Primary visual cortex; Population coding; Fisher Information; Cortical circuit; Computational model; Short-term synaptic depression; Spike-frequency adaptation
Optogenetics offers an unprecedented ability to spatially target neuronal stimulations. This study investigated via simulation, for the first time, how the spatial pattern of excitation affects the response of channelrhodopsin-2 (ChR2) expressing neurons. First we described a methodology for modeling ChR2 in the NEURON simulation platform. Then, we compared four most commonly considered illumination strategies (somatic, dendritic, axonal and whole cell) in a paradigmatic model of a cortical layer V pyramidal cell. We show that the spatial pattern of illumination has an important impact on the efficiency of stimulation and the kinetics of the spiking output. Whole cell illumination synchronizes the depolarization of the dendritic tree and the soma and evokes spiking characteristics with a distinct pattern including an increased bursting rate and enhanced back propagation of action potentials (bAPs). This type of illumination is the most efficient as a given irradiance threshold was achievable with only 6 % of ChR2 density needed in the case of somatic illumination. Targeting only the axon initial segment requires a high ChR2 density to achieve a given threshold irradiance and a prolonged illumination does not yield sustained spiking. We also show that patterned illumination can be used to modulate the bAPs and hence spatially modulate the direction and amplitude of spike time dependent plasticity protocols. We further found the irradiance threshold to increase in proportion to the demyelination level of an axon, suggesting that measurements of the irradiance threshold (for example relative to the soma) could be used to remotely probe a loss of neural myelin sheath, which is a hallmark of several neurodegenerative diseases.
Optogenetics; Channelrhodopsin; Neural stimulation
The role of cortical feedback in the thalamocortical processing loop has been extensively investigated over the last decades. With an exception of several cases, these searches focused on the cortical feedback exerted onto thalamo-cortical relay (TC) cells of the dorsal lateral geniculate nucleus (LGN). In a previous, physiological study, we showed in the cat visual system that cessation of cortical input, despite decrease of spontaneous activity of TC cells, increased spontaneous firing of their recurrent inhibitory interneurons located in the perigeniculate nucleus (PGN). To identify mechanisms underlying such functional changes we conducted a modeling study in NEURON on several networks of point neurons with varied model parameters, such as membrane properties, synaptic weights and axonal delays. We considered six network topologies of the retino-geniculo-cortical system. All models were robust against changes of axonal delays except for the delay between the LGN feed-forward interneuron and the TC cell. The best representation of physiological results was obtained with models containing reciprocally connected PGN cells driven by the cortex and with relatively slow decay of intracellular calcium. This strongly indicates that the thalamic reticular nucleus plays an essential role in the cortical influence over thalamo-cortical relay cells while the thalamic feed-forward interneurons are not essential in this process. Further, we suggest that the dependence of the activity of PGN cells on the rate of calcium removal can be one of the key factors determining individual cell response to elimination of cortical input.
Electronic supplementary material
The online version of this article (doi:10.1007/s10827-012-0430-8) contains supplementary material, which is available to authorized users.
Lateral geniculate nucleus; Perigeniculate nucleus; Cortical feedback; Calcium; Modeling