Efficient fitting of conductance-based model neurons from somatic current clamp

Estimating biologically realistic model neurons from electrophysiological data is a key issue in neuroscience that is central to understanding neuronal function and network behavior. However, directly fitting detailed Hodgkin?CHuxley type model neurons to somatic membrane potential data is a notoriously difficult optimization problem that can require hours/days of supercomputing time. Here we extend an efficient technique that indirectly matches neuronal currents derived from somatic membrane potential data to two-compartment model neurons with passive dendrites. In consequence, this approach can fit semi-realistic detailed model neurons in a few minutes. For validation, fits are obtained to model-derived data for various thalamo-cortical neuron types, including fast/regular spiking and bursting neurons. A key aspect of the validation is sensitivity testing to perturbations arising in experimental data, including sampling rates, inadequately estimated membrane dynamics/channel kinetics and intrinsic noise. We find that maximal conductance estimates and the resulting membrane potential fits diverge smoothly and monotonically from near-perfect matches when unperturbed. Curiously, some perturbations have little effect on the error because they are compensated by the fitted maximal conductances. Therefore, the extended current-based technique applies well under moderately inaccurate model assumptions, as required for application to experimental data. Furthermore, the accompanying perturbation analysis gives insights into neuronal homeostasis, whereby tuning intrinsic neuronal properties can compensate changes from development or neurodegeneration.     

Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.     

Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods

Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.     

Towards an artificial brain

Three components of a brain model operating on neuromolecular computing principles are described. The first component comprises neurons whose input-output behavior is controlled by significant internal dynamics. Models of discrete enzymatic neurons, reaction-diffusion neurons operating on the basis of the cyclic nucleotide cascade, and neurons controlled by cytoskeletal dynamics are described. The second component of the model is an evolutionary learning algorithm which is used to mold the behavior of enzyme-driven neurons or small networks of these neurons for specific function, usually pattern recognition or target seeking tasks. The evolutionary learning algorithm may be interpreted either as representing the mechanism of variation and natural selection acting on a phylogenetic time scale, or as a conceivable ontogenetic adaptation mechanism. The third component of the model is a memory manipulation scheme, called the reference neuron scheme. In principle it is capable of orchestrating a repertoire of enzyme-driven neurons for coherent function. The existing implementations, however, utilize simple neurons without internal dynamics. Spatial navigation and simple game playing (using tic-tac-toe) provide the task environments that have been used to study the properties of the reference neuron model. A memory-based evolutionary learning algorithm has been developed that can assign credit to the individual neurons in a network. It has been run on standard benchmark tasks, and appears to be quite effective both for conventional neural nets and for networks of discrete enzymatic neurons. The models have the character of artificial worlds in that they map the hierarchy of processes in the brain (at the molecular, neuronal, and network levels), provide a task environment, and use this relatively self-contained setup to develop and evaluate learning and adaptation algorithms.     

Estimating parameters and predicting membrane voltages with conductance-based neuron models

Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin–Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.     

Functional organization and structure of the serotonergic neuronal network of terrestrial snail

The extension of knowledge how the brain works requires permanent improvement of methods of recording of neuronal activity and increase in the number of neurons recorded simultaneously to better understand the collective work of neuronal networks and assemblies. Conventional methods allow simultaneous intracellular recording up to 2-5 neurons and their membrane potentials, currents or monosynaptic connections or observation of spiking of neuronal groups with subsequent discrimination of individual spikes with loss of details of the dynamics of membrane potential. We recorded activity of a compact group of serotonergic neurons (up to 56 simultaneously) in the ganglion of a terrestrial mollusk using the method of optical recording of membrane potential that allowed to record individual action potentials in details with action potential parameters and to reveal morphology of the neurons rcorded. We demonstrated clear clustering in the group in relation with the dynamics of action potentials and phasic or tonic components in the neuronal responses to external electrophysiological and tactile stimuli. Also, we showed that identified neuron Pd2 could induce activation of a significant number of neurons in the group whereas neuron Pd4 did not induce any activation. However, its activation is delayed with regard to activation of the reacting group of neurons. Our data strongly support the concept of possible delegation of the integrative function by the network to a single neuron.     

Brain signal predictions from multi-scale networks using a linearized framework

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies (≲ 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models (≳ 10⁶ neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials (‘spikes’) or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin.Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for.The work also constitutes a major advance in computational efficiency of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework.     

Non-Linear Neuronal Responses as an Emergent Property of Afferent Networks: A Case Study of the Locust Lobula Giant Movement Detector

In principle it appears advantageous for single neurons to perform non-linear operations. Indeed it has been reported that some neurons show signatures of such operations in their electrophysiological response. A particular case in point is the Lobula Giant Movement Detector (LGMD) neuron of the locust, which is reported to locally perform a functional multiplication. Given the wide ramifications of this suggestion with respect to our understanding of neuronal computations, it is essential that this interpretation of the LGMD as a local multiplication unit is thoroughly tested. Here we evaluate an alternative model that tests the hypothesis that the non-linear responses of the LGMD neuron emerge from the interactions of many neurons in the opto-motor processing structure of the locust. We show, by exposing our model to standard LGMD stimulation protocols, that the properties of the LGMD that were seen as a hallmark of local non-linear operations can be explained as emerging from the dynamics of the pre-synaptic network. Moreover, we demonstrate that these properties strongly depend on the details of the synaptic projections from the medulla to the LGMD. From these observations we deduce a number of testable predictions. To assess the real-time properties of our model we applied it to a high-speed robot. These robot results show that our model of the locust opto-motor system is able to reliably stabilize the movement trajectory of the robot and can robustly support collision avoidance. In addition, these behavioural experiments suggest that the emergent non-linear responses of the LGMD neuron enhance the system''s collision detection acuity. We show how all reported properties of this neuron are consistently reproduced by this alternative model, and how they emerge from the overall opto-motor processing structure of the locust. Hence, our results propose an alternative view on neuronal computation that emphasizes the network properties as opposed to the local transformations that can be performed by single neurons.     

Transient Responses to Rapid Changes in Mean and Variance in Spiking Models

The mean input and variance of the total synaptic input to a neuron can vary independently, suggesting two distinct information channels. Here we examine the impact of rapidly varying signals, delivered via these two information conduits, on the temporal dynamics of neuronal firing rate responses. We examine the responses of model neurons to step functions in either the mean or the variance of the input current. Our results show that the temporal dynamics governing response onset depends on the choice of model. Specifically, the existence of a hard threshold introduces an instantaneous component into the response onset of a leaky-integrate-and-fire model that is not present in other models studied here. Other response features, for example a decaying oscillatory approach to a new steady-state firing rate, appear to be more universal among neuronal models. The decay time constant of this approach is a power-law function of noise magnitude over a wide range of input parameters. Understanding how specific model properties underlie these response features is important for understanding how neurons will respond to rapidly varying signals, as the temporal dynamics of the response onset and response decay to new steady-state determine what range of signal frequencies a population of neurons can respond to and faithfully encode.     

Reliable circuits from irregular neurons: A dynamical approach to understanding central pattern generators

Central pattern generating neurons from the lobster stomatogastric ganglion were analyzed using new nonlinear methods. The LP neuron was found to have only four or five degrees of freedom in the isolated condition and displayed chaotic behavior. We show that this chaotic behavior could be regularized by periodic pulses of negative current injected into the neuron or by coupling it to another neuron via inhibitory connections. We used both a modified Hindmarsh-Rose model to simulate the neurons behavior phenomenologically and a more realistic conductance-based model so that the modeling could be linked to the experimental observations. Both models were able to capture the dynamics of the neuron behavior better than previous models. We used the Hindmarsh-Rose model as the basis for building electronic neurons which could then be integrated into the biological circuitry. Such neurons were able to rescue patterns which had been disabled by removing key biological neurons from the circuit.     

Dynamical features of higher-order correlation events: impact on cortical cells

Cortical neurons receive signals from thousands of other neurons. The statistical properties of the input spike trains substantially shape the output response properties of each neuron. Experimental and theoretical investigations have mostly focused on the second order statistical features of the input spike trains (mean firing rates and pairwise correlations). Little is known of how higher order correlations affect the integration and firing behavior of a cell independently of the second order statistics. To address this issue, we simulated the dynamics of a population of 5000 neurons, controlling both their second order and higher-order correlation properties to reflect physiological data. We then used these ensemble dynamics as the input stage to morphologically reconstructed cortical cells (layer 5 pyramidal, layer 4 spiny stellate cell), and to an integrate and fire neuron. Our results show that changes done solely to the higher-order correlation properties of the network’s dynamics significantly affect the response properties of a target neuron, both in terms of output rate and spike timing. Moreover, the neuronal morphology and voltage dependent mechanisms of the target neuron considerably modulate the quantitative aspects of these effects. Finally, we show how these results affect sparseness of neuronal representations, tuning properties, and feature selectivity of cortical cells. An erratum to this article can be found at     

Ion concentration dynamics as a mechanism for neuronal bursting

We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.     

Dynamic interactions between orexin and dynorphin may delay onset of functional orexin effects: a modeling study

Orexin (also known as hypocretin) neurons play a key role in regulating sleep-wake behavior, but the links between orexin neuron electrophysiology and function have not been explored. Orexin neurons are wake-active, and spiking activity in orexin neurons may anticipate transitions to wakefulness by several seconds. However, it is suggested that while the orexin system is necessary to maintain sustained wake bouts, orexin has little effect on brief wake bouts. In vitro experiments investigating the actions of orexin and dynorphin, a colocalized neuropeptide, on orexin neurons indicate that the dynamics of desensitization to dynorphin may represent a mechanism for modulating local network activity and resolving the apparent discrepancy between the onset of firing in orexin neurons and the onset of functional orexin effects. To investigate the role of dynorphin on orexin neuron activity, a Hodgkin-Huxley-type model orexin neuron was developed in which baseline electrophysiology, orexin/dynorphin action, and dynorphin desensitization were closely tied to experimental data. In this model framework, model orexin neuron responses to orexin/dynorphin action were calibrated by simulating the physiologic effects of static orexin and dynorphin bath application on orexin neurons. Then behavior in a small network of model orexin neurons was simulated with pure orexin, pure dynorphin, or combined orexin and dynorphin coupling based on the mechanisms established in the static case. It was found that the dynamics of desensitization to dynorphin can mediate a clear shift from a network in which firing is suppressed by dynorphin-mediated inhibition to a network of neurons with high firing rates sustained by orexin-mediated excitation. The findings suggest that dynamic interactions between orexin and dynorphin at transitions from sleep to wake may delay onset of functional orexin effects.     

A Model Study of Cellular Short-Term Memory Produced by Slowly Inactivating Potassium Conductances

We analyzed the cellular short-term memory effects induced by a slowly inactivating potassium (Ks) conductance using a biophysical model of a neuron. We first described latency-to-first-spike and temporal changes in firing frequency as a function of parameters of the model, injected current and prior history of the neuron (deinactivation level) under current clamp. This provided a complete set of properties describing the Ks conductance in a neuron. We then showed that the action of the Ks conductance is not generally appropriate for controlling latency-to-first-spike under random synaptic stimulation. However, reliable latencies were found when neuronal population computation was used. Ks inactivation was found to control the rate of convergence to steady-state discharge behavior and to allow frequency to increase at variable rates in sets of synaptically connected neurons. These results suggest that inactivation of the Ks conductance can have a reliable influence on the behavior of neuronal populations under real physiological conditions.     

Neuronal Mechanisms Encoding Global-to-Fine Information in Inferior-Temporal Cortex

Sugase et al. found that global information is represented at the initial transient firing of a single face-responsive neuron in inferior-temporal (IT) cortex, and that finer information is represented at the subsequent sustained firing. A feed-forward model and an attractor network are conceivable models to reproduce this dynamics. The attractor network, specifically an associative memory model, is employed to elucidate the neuronal mechanisms producing the dynamics. The results obtained by computer simulations show that a state of neuronal population initially approaches to a mean state of similar memory patterns, and that it finally converges to a memory pattern. This dynamics qualitatively coincides with that of face-responsive neurons. The dynamics of a single neuron in the model also coincides with that of a single face-responsive neuron. Furthermore, we propose two physiological experiments and predict the results from our model. Both predicted results are not explainable by the feed-forward model. Therefore, if the results obtained by actual physiological experiments coincide with our predicted results, the attractor network might be the neuronal mechanisms producing the dynamics of face-responsive neurons.     

Mutualistic networks: moving closer to a predictive theory

Plant–animal mutualistic networks sustain terrestrial biodiversity and human food security. Global environmental changes threaten these networks, underscoring the urgency for developing a predictive theory on how networks respond to perturbations. Here, I synthesise theoretical advances towards predicting network structure, dynamics, interaction strengths and responses to perturbations. I find that mathematical models incorporating biological mechanisms of mutualistic interactions provide better predictions of network dynamics. Those mechanisms include trait matching, adaptive foraging, and the dynamic consumption and production of both resources and services provided by mutualisms. Models incorporating species traits better predict the potential structure of networks (fundamental niche), while theory based on the dynamics of species abundances, rewards, foraging preferences and reproductive services can predict the extremely dynamic realised structures of networks, and may successfully predict network responses to perturbations. From a theoretician's standpoint, model development must more realistically represent empirical data on interaction strengths, population dynamics and how these vary with perturbations from global change. From an empiricist's standpoint, theory needs to make specific predictions that can be tested by observation or experiments. Developing models using short‐term empirical data allows models to make longer term predictions of community dynamics. As more longer term data become available, rigorous tests of model predictions will improve.     

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.     

Microfluidics for in vivo imaging of neuronal and behavioral activity in Caenorhabditis elegans

The nematode C. elegans is an excellent model organism for studying behavior at the neuronal level. Because of the organism's small size, it is challenging to deliver stimuli to C. elegans and monitor neuronal activity in a controlled environment. To address this problem, we developed two microfluidic chips, the 'behavior' chip and the 'olfactory' chip for imaging of neuronal and behavioral responses in C. elegans. We used the behavior chip to correlate the activity of AVA command interneurons with the worm locomotion pattern. We used the olfactory chip to record responses from ASH sensory neurons exposed to high-osmotic-strength stimulus. Observation of neuronal responses in these devices revealed previously unknown properties of AVA and ASH neurons. The use of these chips can be extended to correlate the activity of sensory neurons, interneurons and motor neurons with the worm's behavior.     

Non-zero mean alpha oscillations revealed with computational model and empirical data

Ongoing oscillations and evoked responses are two main types of neuronal activity obtained with diverse electrophysiological recordings (EEG/MEG/iEEG/LFP). Although typically studied separately, they might in fact be closely related. One possibility to unite them is to demonstrate that neuronal oscillations have non-zero mean which predicts that stimulus- or task-triggered amplitude modulation of oscillations can contribute to the generation of evoked responses. We validated this mechanism using computational modelling and analysis of a large EEG data set. With a biophysical model, we indeed demonstrated that intracellular currents in the neuron are asymmetric and, consequently, the mean of alpha oscillations is non-zero. To understand the effect that neuronal currents exert on oscillatory mean, we varied several biophysical and morphological properties of neurons in the network, such as voltage-gated channel densities, length of dendrites, and intensity of incoming stimuli. For a very large range of model parameters, we observed evidence for non-zero mean of oscillations. Complimentary, we analysed empirical rest EEG recordings of 90 participants (50 young, 40 elderly) and, with spatio-spectral decomposition, detected at least one spatially-filtred oscillatory component of non-zero mean alpha oscillations in 93% of participants. In order to explain a complex relationship between the dynamics of amplitude-envelope and corresponding baseline shifts, we performed additional simulations with simple oscillators coupled with different time delays. We demonstrated that the extent of spatial synchronisation may obscure macroscopic estimation of alpha rhythm modulation while leaving baseline shifts unchanged. Overall, our results predict that amplitude modulation of neural oscillations should at least partially explain the generation of evoked responses. Therefore, inference about changes in evoked responses with respect to cognitive conditions, age or neuropathologies should be constructed while taking into account oscillatory neuronal dynamics.