Evaluating automated parameter constraining procedures of neuron models by experimental and surrogate data

Evaluation and comparison of methods for neuronal parameter optimization using the Neuroptimus software framework

Finding optimal parameters for detailed neuronal models is a ubiquitous challenge in neuroscientific research. In recent years, manual model tuning has been gradually replaced by automated parameter search using a variety of different tools and methods. However, using most of these software tools and choosing the most appropriate algorithm for a given optimization task require substantial technical expertise, which prevents the majority of researchers from using these methods effectively. To address these issues, we developed a generic platform (called Neuroptimus) that allows users to set up neural parameter optimization tasks via a graphical interface, and to solve these tasks using a wide selection of state-of-the-art parameter search methods implemented by five different Python packages. Neuroptimus also offers several features to support more advanced usage, including the ability to run most algorithms in parallel, which allows it to take advantage of high-performance computing architectures. We used the common interface provided by Neuroptimus to conduct a detailed comparison of more than twenty different algorithms (and implementations) on six distinct benchmarks that represent typical scenarios in neuronal parameter search. We quantified the performance of the algorithms in terms of the best solutions found and in terms of convergence speed. We identified several algorithms, including covariance matrix adaptation evolution strategy and particle swarm optimization, that consistently, without any fine-tuning, found good solutions in all of our use cases. By contrast, some other algorithms including all local search methods provided good solutions only for the simplest use cases, and failed completely on more complex problems. We also demonstrate the versatility of Neuroptimus by applying it to an additional use case that involves tuning the parameters of a subcellular model of biochemical pathways. Finally, we created an online database that allows uploading, querying and analyzing the results of optimization runs performed by Neuroptimus, which enables all researchers to update and extend the current benchmarking study. The tools and analysis we provide should aid members of the neuroscience community to apply parameter search methods more effectively in their research.

Setting a double-capacitive neuron coupled with Josephson junction and piezoelectric source

Perception of voice means acoustic electric conversion in the auditory system, and changes of external magnetic field can affect the neural activities by taming the channel current via some field components including memristor and Josephson junction. Combination of two capacitors via an electric component is effective to describe the physical property of artificial cell membrane, which is often used to reproduce the characteristic of electric activities in cell membrane. Involvement of two capacitive variables for two capacitors in the neural circuit can discern the effect of field diversity in the media in two sides of the cell membrane in theoretical way. A Josephson junction is used to couple a piezoelectric neural circuit composed of two capacitors, one inductor and one nonlinear resistor. Field energy is mainly kept in the capacitive and inductive components, and it is obtained and converted into dimensionless energy function. The Hamilton energy function in an equivalent auditory neuron is verified by using the Helmholtz theorem. Noisy excitation on the neural circuit can be detected via the Josephson junction channel and similar stochastic resonance is detected by regulating the noise intensity, as a result, the average energy reaches a peak value under stochastic resonance. An adaptive law controls the bifurcation parameter, which is relative to the membrane property, and energy shift controls the mode selection during continuous growth of the bifurcation parameter. That is, external energy injection derived from acoustic wave or magnetic field will control the energy level, and then suitable firing patterns are controlled effectively.

A Multimodal Fitting Approach to Construct Single-Neuron Models With Patch Clamp and High-Density Microelectrode Arrays

In computational neuroscience, multicompartment models are among the most biophysically realistic representations of single neurons. Constructing such models usually involves the use of the patch-clamp technique to record somatic voltage signals under different experimental conditions. The experimental data are then used to fit the many parameters of the model. While patching of the soma is currently the gold-standard approach to build multicompartment models, several studies have also evidenced a richness of dynamics in dendritic and axonal sections. Recording from the soma alone makes it hard to observe and correctly parameterize the activity of nonsomatic compartments. In order to provide a richer set of data as input to multicompartment models, we here investigate the combination of somatic patch-clamp recordings with recordings of high-density microelectrode arrays (HD-MEAs). HD-MEAs enable the observation of extracellular potentials and neural activity of neuronal compartments at subcellular resolution. In this work, we introduce a novel framework to combine patch-clamp and HD-MEA data to construct multicompartment models. We first validate our method on a ground-truth model with known parameters and show that the use of features extracted from extracellular signals, in addition to intracellular ones, yields models enabling better fits than using intracellular features alone. We also demonstrate our procedure using experimental data by constructing cell models from in vitro cell cultures. The proposed multimodal fitting procedure has the potential to augment the modeling efforts of the computational neuroscience community and provide the field with neuronal models that are more realistic and can be better validated.

Optimal control methods for nonlinear parameter estimation in biophysical neuron models

Functional forms of biophysically-realistic neuron models are constrained by neurobiological and anatomical considerations, such as cell morphologies and the presence of known ion channels. Despite these constraints, neuron models still contain unknown static parameters which must be inferred from experiment. This inference task is most readily cast into the framework of state-space models, which systematically takes into account partial observability and measurement noise. Inferring only dynamical state variables such as membrane voltages is a well-studied problem, and has been approached with a wide range of techniques beginning with the well-known Kalman filter. Inferring both states and fixed parameters, on the other hand, is less straightforward. Here, we develop a method for joint parameter and state inference that combines traditional state space modeling with chaotic synchronization and optimal control. Our methods are tailored particularly to situations with considerable measurement noise, sparse observability, very nonlinear or chaotic dynamics, and highly uninformed priors. We illustrate our approach both in a canonical chaotic model and in a phenomenological neuron model, showing that many unknown parameters can be uncovered reliably and accurately from short and noisy observed time traces. Our method holds promise for estimation in larger-scale systems, given ongoing improvements in calcium reporters and genetically-encoded voltage indicators.

Systems neuroscience aims to understand how individual neurons and neural networks process external stimuli into behavioral responses. Underlying this characterization are mathematical models intimately shaped by experimental observations. But neural systems are high-dimensional and contain highly nonlinear interactions, so developing accurate models remains a challenge given current experimental capabilities. In practice, this means that the dynamical equations characterizing neural activity have many unknown parameters, and these parameters must be inferred from data. This inference problem is nontrivial owing to model nonlinearity, system and measurement noise, and the sparsity of observations from electrode recordings. Here, we present a novel method for inferring model parameters of neural systems. Our technique combines ideas from control theory and optimization, and amounts to using data to “control” estimates toward the best fit. Our method compares well in accuracy against other state-of-the-art inference methods, both in phenomenological chaotic systems and biophysical neuron models. Our work shows that many unknown model parameters of interest can be inferred from voltage measurements, despite signaling noise, instrument noise, and low observability.

Computational Concepts for Reconstructing and Simulating Brain Tissue

It has previously been shown that it is possible to derive a new class of biophysically detailed brain tissue models when one computationally analyzes and exploits the interdependencies or the multi-modal and multi-scale organization of the brain. These reconstructions, sometimes referred to as digital twins, enable a spectrum of scientific investigations. Building such models has become possible because of increase in quantitative data but also advances in computational capabilities, algorithmic and methodological innovations. This chapter presents the computational science concepts that provide the foundation to the data-driven approach to reconstructing and simulating brain tissue as developed by the EPFL Blue Brain Project, which was originally applied to neocortical microcircuitry and extended to other brain regions. Accordingly, the chapter covers aspects such as a knowledge graph-based data organization and the importance of the concept of a dataset release. We illustrate algorithmic advances in finding suitable parameters for electrical models of neurons or how spatial constraints can be exploited for predicting synaptic connections. Furthermore, we explain how in silico experimentation with such models necessitates specific addressing schemes or requires strategies for an efficient simulation. The entire data-driven approach relies on the systematic validation of the model. We conclude by discussing complementary strategies that not only enable judging the fidelity of the model but also form the basis for its systematic refinements.

Cell type-specific mechanisms of information transfer in data-driven biophysical models of hippocampal CA3 principal neurons

The transformation of synaptic input into action potential output is a fundamental single-cell computation resulting from the complex interaction of distinct cellular morphology and the unique expression profile of ion channels that define the cellular phenotype. Experimental studies aimed at uncovering the mechanisms of the transfer function have led to important insights, yet are limited in scope by technical feasibility, making biophysical simulations an attractive complementary approach to push the boundaries in our understanding of cellular computation. Here we take a data-driven approach by utilizing high-resolution morphological reconstructions and patch-clamp electrophysiology data together with a multi-objective optimization algorithm to build two populations of biophysically detailed models of murine hippocampal CA3 pyramidal neurons based on the two principal cell types that comprise this region. We evaluated the performance of these models and find that our approach quantitatively matches the cell type-specific firing phenotypes and recapitulate the intrinsic population-level variability in the data. Moreover, we confirm that the conductance values found by the optimization algorithm are consistent with differentially expressed ion channel genes in single-cell transcriptomic data for the two cell types. We then use these models to investigate the cell type-specific biophysical properties involved in the generation of complex-spiking output driven by synaptic input through an information-theoretic treatment of their respective transfer functions. Our simulations identify a host of cell type-specific biophysical mechanisms that define the morpho-functional phenotype to shape the cellular transfer function and place these findings in the context of a role for bursting in CA3 recurrent network synchronization dynamics.

The hippocampus is comprised of numerous types of neurons, which constitute the cellular substrate for its rich repertoire of network dynamics. Among these are sharp waves, sequential activations of ensembles of neurons that have been shown to be crucially involved in learning and memory. In the CA3 area of the hippocampus, two types of excitatory cells, thorny and a-thorny neurons, are preferentially active during distinct phases of a sharp wave, suggesting a differential role for these cell types in phenomena such as memory consolidation. Using a strictly data-driven approach, we built biophysically realistic models of both thorny and a-thorny cells and used them to investigate the integrative differences between these two cell types. We found that both neuron classes have the capability of integrating incoming synaptic inputs in a supralinear fashion, although only a-thorny cells respond with bursts of action potentials to spatially and temporally clustered synaptic inputs. Additionally, by using a computational approach based on information theory, we show that, owing to this propensity for bursting, a-thorny cells can encode more information in their spiking output than their thorny counterpart. These results shed new light on the computational capabilities of two types of excitatory neurons and suggest that thorny and a-thorny cells may play distinct roles in the generation of hippocampal network synchronization.

Integrating single-cell transcriptomics and microcircuit computer modeling

Biophysically realistic computer modeling of neuronal microcircuitry has served as a testing ground for hypotheses related to the structure and function of different brain microcircuits. Recent advances in single-cell transcriptomics provide snapshots of a neuron's molecular state and have demonstrated that cell-specific genetic markers engineer the electrophysiological properties of a neuron. Integrating these molecular details with biophysical modeling can allow unprecedented mechanistic insights. In this opinion review, we consider systems biology-based strategies involving statistical deconvolution and gene ontology to integrate the two approaches. We foresee that this integration will infer the nonlinear interactions between the transcriptomically detailed neurons in different brain states. For an initial assessment of these integrative strategies, we recommend testing them on a penetrant phenotype such as epilepsy or a basic organism model such as Caenorhabditis elegans.

Nonlinear effects of intrinsic dynamics on temporal encoding in a model of avian auditory cortex

Neurons exhibit diverse intrinsic dynamics, which govern how they integrate synaptic inputs to produce spikes. Intrinsic dynamics are often plastic during development and learning, but the effects of these changes on stimulus encoding properties are not well known. To examine this relationship, we simulated auditory responses to zebra finch song using a linear-dynamical cascade model, which combines a linear spectrotemporal receptive field with a dynamical, conductance-based neuron model, then used generalized linear models to estimate encoding properties from the resulting spike trains. We focused on the effects of a low-threshold potassium current (K_LT) that is present in a subset of cells in the zebra finch caudal mesopallium and is affected by early auditory experience. We found that K_LT affects both spike adaptation and the temporal filtering properties of the receptive field. The direction of the effects depended on the temporal modulation tuning of the linear (input) stage of the cascade model, indicating a strongly nonlinear relationship. These results suggest that small changes in intrinsic dynamics in tandem with differences in synaptic connectivity can have dramatic effects on the tuning of auditory neurons.

Experience-dependent developmental plasticity involves changes not only to synaptic connections, but to voltage-gated currents as well. Using biophysical models, it is straightforward to predict the effects of this intrinsic plasticity on the firing patterns of individual neurons, but it remains difficult to understand the consequences for sensory coding. We investigated this in the context of the zebra finch auditory cortex, where early exposure to a complex acoustic environment causes increased expression of a low-threshold potassium current. We simulated responses to song using a detailed biophysical model and then characterized encoding properties using generalized linear models. This analysis revealed that this potassium current has strong, nonlinear effects on how the model encodes the song’s temporal structure, and that the sign of these effects depend on the temporal tuning of the synaptic inputs. This nonlinearity gives intrinsic plasticity broad scope as a mechanism for developmental learning in the auditory system.

Homogeneous and Narrow Bandwidth of Spike Initiation in Rat L1 Cortical Interneurons

The cortical layer 1 (L1) contains a population of GABAergic interneurons, considered a key component of information integration, processing, and relaying in neocortical networks. In fact, L1 interneurons combine top–down information with feed-forward sensory inputs in layer 2/3 and 5 pyramidal cells (PCs), while filtering their incoming signals. Despite the importance of L1 for network emerging phenomena, little is known on the dynamics of the spike initiation and the encoding properties of its neurons. Using acute brain tissue slices from the rat neocortex, combined with the analysis of an existing database of model neurons, we investigated the dynamical transfer properties of these cells by sampling an entire population of known “electrical classes” and comparing experiments and model predictions. We found the bandwidth of spike initiation to be significantly narrower than in L2/3 and 5 PCs, with values below 100 cycle/s, but without significant heterogeneity in the cell response properties across distinct electrical types. The upper limit of the neuronal bandwidth was significantly correlated to the mean firing rate, as anticipated from theoretical studies but not reported for PCs. At high spectral frequencies, the magnitude of the neuronal response attenuated as a power-law, with an exponent significantly smaller than what was reported for pyramidal neurons and reminiscent of the dynamics of a “leaky” integrate-and-fire model of spike initiation. Finally, most of our in vitro results matched quantitatively the numerical simulations of the models as a further contribution to independently validate the models against novel experimental data.

Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.

A biophysical modelling platform of the cochlear nucleus and other auditory circuits: From channels to networks

Models of the auditory brainstem have been an invaluable tool for testing hypotheses about auditory information processing and for highlighting the most important gaps in the experimental literature. Due to the complexity of the auditory brainstem, and indeed most brain circuits, the dynamic behavior of the system may be difficult to predict without a detailed, biologically realistic computational model. Despite the sensitivity of models to their exact construction and parameters, most prior models of the cochlear nucleus have incorporated only a small subset of the known biological properties. This confounds the interpretation of modelling results and also limits the potential future uses of these models, which require a large effort to develop. To address these issues, we have developed a general purpose, biophysically detailed model of the cochlear nucleus for use both in testing hypotheses about cochlear nucleus function and also as an input to models of downstream auditory nuclei. The model implements conductance-based Hodgkin-Huxley representations of cells using a Python-based interface to the NEURON simulator. Our model incorporates most of the quantitatively characterized intrinsic cell properties, synaptic properties, and connectivity available in the literature, and also aims to reproduce the known response properties of the canonical cochlear nucleus cell types. Although we currently lack the empirical data to completely constrain this model, our intent is for the model to continue to incorporate new experimental results as they become available.

Synaptic Activation of a Detailed Purkinje Cell Model Predicts Voltage-Dependent Control of Burst-Pause Responses in Active Dendrites

The dendritic processing in cerebellar Purkinje cells (PCs), which integrate synaptic inputs coming from hundreds of thousands granule cells and molecular layer interneurons, is still unclear. Here we have tested a leading hypothesis maintaining that the significant PC output code is represented by burst-pause responses (BPRs), by simulating PC responses in a biophysically detailed model that allowed to systematically explore a broad range of input patterns. BPRs were generated by input bursts and were more prominent in Zebrin positive than Zebrin negative (Z+ and Z-) PCs. Different combinations of parallel fiber and molecular layer interneuron synapses explained type I, II and III responses observed in vivo. BPRs were generated intrinsically by Ca-dependent K channel activation in the somato-dendritic compartment and the pause was reinforced by molecular layer interneuron inhibition. BPRs faithfully reported the duration and intensity of synaptic inputs, such that synaptic conductance tuned the number of spikes and release probability tuned their regularity in the millisecond range. Interestingly, the burst and pause of BPRs depended on the stimulated dendritic zone reflecting the different input conductance and local engagement of voltage-dependent channels. Multiple local inputs combined their actions generating complex spatio-temporal patterns of dendritic activity and BPRs. Thus, local control of intrinsic dendritic mechanisms by synaptic inputs emerges as a fundamental PC property in activity regimens characterized by bursting inputs from granular and molecular layer neurons.

Single Neuron Optimization as a Basis for Accurate Biophysical Modeling: The Case of Cerebellar Granule Cells

In realistic neuronal modeling, once the ionic channel complement has been defined, the maximum ionic conductance (G_i-max) values need to be tuned in order to match the firing pattern revealed by electrophysiological recordings. Recently, selection/mutation genetic algorithms have been proposed to efficiently and automatically tune these parameters. Nonetheless, since similar firing patterns can be achieved through different combinations of G_i-max values, it is not clear how well these algorithms approximate the corresponding properties of real cells. Here we have evaluated the issue by exploiting a unique opportunity offered by the cerebellar granule cell (GrC), which is electrotonically compact and has therefore allowed the direct experimental measurement of ionic currents. Previous models were constructed using empirical tuning of G_i-max values to match the original data set. Here, by using repetitive discharge patterns as a template, the optimization procedure yielded models that closely approximated the experimental G_i-max values. These models, in addition to repetitive firing, captured additional features, including inward rectification, near-threshold oscillations, and resonance, which were not used as features. Thus, parameter optimization using genetic algorithms provided an efficient modeling strategy for reconstructing the biophysical properties of neurons and for the subsequent reconstruction of large-scale neuronal network models.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons

Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.

Electrical activity of ON and OFF retinal ganglion cells: a modelling study

OBJECTIVE

Retinal ganglion cells (RGCs) demonstrate a large range of variation in their ionic channel properties and morphologies. Cell-specific properties are responsible for the unique way RGCs process synaptic inputs, as well as artificial electrical signals such as that from a visual prosthesis. A cell-specific computational modelling approach allows us to examine the functional significance of regional membrane channel expression and cell morphology.

APPROACH

In this study, an existing RGC ionic model was extended by including a hyperpolarization activated non-selective cationic current as well as a T-type calcium current identified in recent experimental findings. Biophysically-defined model parameters were simultaneously optimized against multiple experimental recordings from ON and OFF RGCs.

MAIN RESULTS

With well-defined cell-specific model parameters and the incorporation of detailed cell morphologies, these models were able to closely reconstruct and predict ON and OFF RGC response properties recorded experimentally.

SIGNIFICANCE

The resulting models were used to study the contribution of different ion channel properties and spatial structure of neurons to RGC activation. The techniques of this study are generally applicable to other excitable cell models, increasing the utility of theoretical models in accurately predicting the response of real biological neurons.

Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization

The Purkinje cell (PC) is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN). In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1), we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS) and Ranvier nodes (RNs), proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.

Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells

Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.

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.

A flexible, interactive software tool for fitting the parameters of neuronal models

The construction of biologically relevant neuronal models as well as model-based analysis of experimental data often requires the simultaneous fitting of multiple model parameters, so that the behavior of the model in a certain paradigm matches (as closely as possible) the corresponding output of a real neuron according to some predefined criterion. Although the task of model optimization is often computationally hard, and the quality of the results depends heavily on technical issues such as the appropriate choice (and implementation) of cost functions and optimization algorithms, no existing program provides access to the best available methods while also guiding the user through the process effectively. Our software, called Optimizer, implements a modular and extensible framework for the optimization of neuronal models, and also features a graphical interface which makes it easy for even non-expert users to handle many commonly occurring scenarios. Meanwhile, educated users can extend the capabilities of the program and customize it according to their needs with relatively little effort. Optimizer has been developed in Python, takes advantage of open-source Python modules for nonlinear optimization, and interfaces directly with the NEURON simulator to run the models. Other simulators are supported through an external interface. We have tested the program on several different types of problems of varying complexity, using different model classes. As targets, we used simulated traces from the same or a more complex model class, as well as experimental data. We successfully used Optimizer to determine passive parameters and conductance densities in compartmental models, and to fit simple (adaptive exponential integrate-and-fire) neuronal models to complex biological data. Our detailed comparisons show that Optimizer can handle a wider range of problems, and delivers equally good or better performance than any other existing neuronal model fitting tool.

Automatic parameter estimation of multicompartmental neuron models via minimization of trace error with control adjustment

We describe a new technique to fit conductance-based neuron models to intracellular voltage traces from isolated biological neurons. The biological neurons are recorded in current-clamp with pink (1/f) noise injected to perturb the activity of the neuron. The new algorithm finds a set of parameters that allows a multicompartmental model neuron to match the recorded voltage trace. Attempting to match a recorded voltage trace directly has a well-known problem: mismatch in the timing of action potentials between biological and model neuron is inevitable and results in poor phenomenological match between the model and data. Our approach avoids this by applying a weak control adjustment to the model to promote alignment during the fitting procedure. This approach is closely related to the control theoretic concept of a Luenberger observer. We tested this approach on synthetic data and on data recorded from an anterior gastric receptor neuron from the stomatogastric ganglion of the crab Cancer borealis. To test the flexibility of this approach, the synthetic data were constructed with conductance models that were different from the ones used in the fitting model. For both synthetic and biological data, the resultant models had good spike-timing accuracy.

A quantitative description of dendritic conductances and its application to dendritic excitation in layer 5 pyramidal neurons

Postsynaptic integration is a complex function of passive membrane properties and nonlinear activation of voltage-gated channels. Some cortical neurons express many voltage-gated channels, with each displaying heterogeneous dendritic conductance gradients. This complexity has hindered the construction of experimentally based mechanistic models of cortical neurons. Here we show that it is possible to overcome this obstacle. We recorded the membrane potential from the soma and apical dendrite of layer 5 (L5) pyramidal neurons of the rat somatosensory cortex. A combined experimental and numerical parameter peeling procedure was implemented to optimize a detailed ionic mechanism for the generation and propagation of dendritic spikes in neocortical L5 pyramidal neurons. In the optimized model, the density of voltage-gated Ca(2+) channels decreased linearly from the soma, and leveled at the distal apical dendrite. The density of the small-conductance Ca(2+)-activated channel decreased along the apical dendrite, whereas the density of the large-conductance Ca(2+)-gated K(+) channel was uniform throughout the apical dendrite. The model predicted an ionic mechanism for the generation of a dendritic spike, the interaction of this spike with the backpropagating action potential, the mechanism responsible for the ability of the proximal apical dendrite to control the coupling between the axon and the dendrite, and the generation of NMDA spikes in the distal apical tuft. Moreover, in addition to faithfully predicting many experimental results recorded from the apical dendrite of L5 pyramidal neurons, the model validates a new methodology for mechanistic modeling of neurons in the CNS.

Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms

Cortical information processing originates from the exchange of action potentials between many cell types. To capture the essence of these interactions, it is of critical importance to build mathematical models that reflect the characteristic features of spike generation in individual neurons. We propose a framework to automatically extract such features from current-clamp experiments, in particular the passive properties of a neuron (i.e., membrane time constant, reversal potential, and capacitance), the spike-triggered adaptation currents, as well as the dynamics of the action potential threshold. The stochastic model that results from our maximum likelihood approach accurately predicts the spike times, the subthreshold voltage, the firing patterns, and the type of frequency-current curve. Extracting the model parameters for three cortical cell types revealed that cell types show highly significant differences in the time course of the spike-triggered currents and moving threshold, that is, in their adaptation and refractory properties but not in their passive properties. In particular, GABAergic fast-spiking neurons mediate weak adaptation through spike-triggered currents only, whereas regular spiking excitatory neurons mediate adaptation with both moving threshold and spike-triggered currents. GABAergic nonfast-spiking neurons combine the two distinct adaptation mechanisms with reduced strength. Differences between cell types are large enough to enable automatic classification of neurons into three different classes. Parameter extraction is performed for individual neurons so that we find not only the mean parameter values for each neuron type but also the spread of parameters within a group of neurons, which will be useful for future large-scale computer simulations.

Multiscale exploration of mouse brain microstructures using the knife-edge scanning microscope brain atlas

Connectomics is the study of the full connection matrix of the brain. Recent advances in high-throughput, high-resolution 3D microscopy methods have enabled the imaging of whole small animal brains at a sub-micrometer resolution, potentially opening the road to full-blown connectomics research. One of the first such instruments to achieve whole-brain-scale imaging at sub-micrometer resolution is the Knife-Edge Scanning Microscope (KESM). KESM whole-brain data sets now include Golgi (neuronal circuits), Nissl (soma distribution), and India ink (vascular networks). KESM data can contribute greatly to connectomics research, since they fill the gap between lower resolution, large volume imaging methods (such as diffusion MRI) and higher resolution, small volume methods (e.g., serial sectioning electron microscopy). Furthermore, KESM data are by their nature multiscale, ranging from the subcellular to the whole organ scale. Due to this, visualization alone is a huge challenge, before we even start worrying about quantitative connectivity analysis. To solve this issue, we developed a web-based neuroinformatics framework for efficient visualization and analysis of the multiscale KESM data sets. In this paper, we will first provide an overview of KESM, then discuss in detail the KESM data sets and the web-based neuroinformatics framework, which is called the KESM brain atlas (KESMBA). Finally, we will discuss the relevance of the KESMBA to connectomics research, and identify challenges and future directions.

Intrinsic morphological diversity of thick-tufted layer 5 pyramidal neurons ensures robust and invariant properties of in silico synaptic connections

The morphology of neocortical pyramidal neurons is not only highly characteristic but also displays an intrinsic diversity that renders each neuron morphologically unique. We investigated the significance of this intrinsic morphological diversity in in silico networks composed of thick-tufted layer 5 (TTL5) pyramidal neurons, by comparing the in silico and in vitro properties of TTL5 synaptic connections. The synaptic locations of in silico connections were determined by placing 3D reconstructed TTL5 neurons randomly in a volume equivalent to that of layer 5 in the juvenile rat somatosensory cortex and using a 'collision-detection' algorithm to identify the incidental loci of axo-dendritic overlap. The activation time of the modelled synapses and their biophysical properties were characterized based on experimental measurements. We found that the anatomical loci of synapses and the physiological properties of the somatically recorded EPSPs closely matched those recorded experimentally without the need for any fine-tuning. Furthermore, perturbations to both the physiological or anatomical parameters of the model did not alter the average physiological properties of the population of modelled synaptic connections. This microcircuit-level robust behaviour was due to the intrinsic diversity of the morphology of pyramidal neurons in the microcircuit. We conclude that synaptic transmission in a network of TTL5 neurons is highly invariant across microcircuits suggesting that intrinsic diversity is a mechanism to ensure the same average synaptic properties in different animals of the same species. Finally, we show that the average physiological properties of the TTL5 microcircuit are surprisingly robust to anatomical and physiological perturbations also partly due to the intrinsic diversity of pyramidal neuron morphology.

An Ultrascalable Solution to Large-scale Neural Tissue Simulation

Neural tissue simulation extends requirements and constraints of previous neuronal and neural circuit simulation methods, creating a tissue coordinate system. We have developed a novel tissue volume decomposition, and a hybrid branched cable equation solver. The decomposition divides the simulation into regular tissue blocks and distributes them on a parallel multithreaded machine. The solver computes neurons that have been divided arbitrarily across blocks. We demonstrate thread, strong, and weak scaling of our approach on a machine with more than 4000 nodes and up to four threads per node. Scaling synapses to physiological numbers had little effect on performance, since our decomposition approach generates synapses that are almost always computed locally. The largest simulation included in our scaling results comprised 1 million neurons, 1 billion compartments, and 10 billion conductance-based synapses and gap junctions. We discuss the implications of our ultrascalable Neural Tissue Simulator, and with our results estimate requirements for a simulation at the scale of a human brain.

Optimizing brain networks topologies using multi-objective evolutionary computation

The analysis of brain network topological features has served to better understand these networks and reveal particular characteristics of their functional behavior. The distribution of brain network motifs is particularly useful for detecting and describing differences between brain networks and random and computationally optimized artificial networks. In this paper we use a multi-objective evolutionary optimization approach to generate optimized artificial networks that have a number of topological features resembling brain networks. The Pareto set approximation of the optimized networks is used to extract network descriptors that are compared to brain and random network descriptors. To analyze the networks, the clustering coefficient, the average path length, the modularity and the betweenness centrality are computed. We argue that the topological complexity of a brain network can be estimated using the number of evaluations needed by an optimization algorithm to output artificial networks of similar complexity. For the analyzed network examples, our results indicate that while original brain networks have a reduced structural motif number and a high functional motif number, they are not optimal with respect to these two topological features. We also investigate the correlation between the structural and functional motif numbers, the average path length and the clustering coefficient in random, optimized and brain networks.

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-Huxley 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.

Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.

A possible approach to understanding the neuronal bases of the computational properties of the nervous system consists of modelling its basic building blocks, neurons and synapses, and then simulating their collective activity emerging in large networks. In developing such models, a satisfactory description level must be chosen as a compromise between simplicity and faithfulness in reproducing experimental data. Deterministic neuron models – i.e., models that upon repeated simulation with fixed parameter values provide the same results – are usually made up of ordinary differential equations and allow for relatively fast simulation times. By contrast, they do not describe accurately the underlying stochastic response properties arising from the microscopical correlate of neuronal excitability. Stochastic models are usually based on mathematical descriptions of individual ion channels, or on an effective macroscopic account of their random opening and closing. In this contribution we describe a general method to transform any deterministic neuron model into its effective stochastic version that accurately replicates the statistical properties of ion channels random kinetics.

Response properties of visual neurons in the turtle nucleus isthmi

The optic tectum holds a central position in the tectofugal pathway of non-mammalian species and is reciprocally connected with the nucleus isthmi. Here, we recorded from individual nucleus isthmi pars parvocellularis (Ipc) neurons in the turtle eye-attached whole-brain preparation in response to a range of computer-generated visual stimuli. Ipc neurons responded to a variety of moving or flashing stimuli as long as those stimuli were small. When mapped with a moving spot, the excitatory receptive field was of circular Gaussian shape with an average half-width of less than 3°. We found no evidence for directional sensitivity. For moving spots of varying sizes, the measured Ipc response-size profile was reproduced by the linear Difference-of-Gaussian model, which is consistent with the superposition of a narrow excitatory center and an inhibitory surround. Intracellular Ipc recordings revealed a strong inhibitory connection from the nucleus isthmi pars magnocellularis (Imc), which has the anatomical feature to provide a broad inhibitory projection. The recorded Ipc response properties, together with the modulatory role of the Ipc in tectal visual processing, suggest that the columns of Ipc axon terminals in turtle optic tectum bias tectal visual responses to small dark changing features in visual scenes.

The use of automated parameter searches to improve ion channel kinetics for neural modeling

The voltage and time dependence of ion channels can be regulated, notably by phosphorylation, interaction with phospholipids, and binding to auxiliary subunits. Many parameter variation studies have set conductance densities free while leaving kinetic channel properties fixed as the experimental constraints on the latter are usually better than on the former. Because individual cells can tightly regulate their ion channel properties, we suggest that kinetic parameters may be profitably set free during model optimization in order to both improve matches to data and refine kinetic parameters. To this end, we analyzed the parameter optimization of reduced models of three electrophysiologically characterized and morphologically reconstructed globus pallidus neurons. We performed two automated searches with different types of free parameters. First, conductance density parameters were set free. Even the best resulting models exhibited unavoidable problems which were due to limitations in our channel kinetics. We next set channel kinetics free for the optimized density matches and obtained significantly improved model performance. Some kinetic parameters consistently shifted to similar new values in multiple runs across three models, suggesting the possibility for tailored improvements to channel models. These results suggest that optimized channel kinetics can improve model matches to experimental voltage traces, particularly for channels characterized under different experimental conditions than recorded data to be matched by a model. The resulting shifts in channel kinetics from the original template provide valuable guidance for future experimental efforts to determine the detailed kinetics of channel isoforms and possible modulated states in particular types of neurons.

Encoding the fine-structured mechanism of action potential dynamics with qualitative motifs

This work presents a neuroinformatic method for deriving mechanistic descriptions of fine-structured neural activity. This is a new development in the computer-assisted analysis of dynamics in conductance-based models, which is illustrated using single compartment models of an action potential. A sequence of abstract, qualitative motifs is inferred from this analysis, forming a template that is independent of the specific equations from which they were abstracted. The template encodes the assumptions behind the model reduction steps used to derive the motifs, and so specifies quantitative information about their domains of validity. The template representation of a mechanism is converted to a hybrid dynamical system, which is simulated as a sequence of low-dimensional reduced models (in this example, phase plane models) with appropriate switching conditions taken from the motifs. We demonstrate the validity of the template on a detailed single neuron model of spiking taken from the literature, and show that the corresponding hybrid system simulation closely mimics the spiking dynamics of the full model.

Smoothing of, and parameter estimation from, noisy biophysical recordings

Biophysically detailed models of single cells are difficult to fit to real data. Recent advances in imaging techniques allow simultaneous access to various intracellular variables, and these data can be used to significantly facilitate the modelling task. These data, however, are noisy, and current approaches to building biophysically detailed models are not designed to deal with this. We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo ("particle filtering") methods, in combination with a detailed biophysical description of a cell, are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a non-parametric manner. Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances, and observation noise) are inferred automatically from noisy data via expectation-maximization. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise.

Experimentally guided modelling of dendritic excitability in rat neocortical pyramidal neurones

Constructing physiologically relevant compartmental models of neurones is critical for understanding neuronal activity and function. We recently suggested that measurements from multiple locations along the soma, dendrites and axon are necessary as a data set when using a genetic optimization algorithm to constrain the parameters of a compartmental model of an entire neurone. However, recordings from L5 pyramidal neurones can routinely be performed simultaneously from only two locations. Now we show that a data set recorded from the soma and apical dendrite combined with a parameter peeling procedure is sufficient to constrain a compartmental model for the apical dendrite of L5 pyramidal neurones. The peeling procedure was tested on several compartmental models showing that it avoids local minima in parameter space. Based on the requirements of this analysis procedure, we designed and performed simultaneous whole-cell recordings from the soma and apical dendrite of rat L5 pyramidal neurones. The data set obtained from these recordings allowed constraining a simplified compartmental model for the apical dendrite of L5 pyramidal neurones containing four voltage-gated conductances. In agreement with experimental findings, the optimized model predicts that the conductance density gradients of voltage-gated K(+) conductances taper rapidly proximal to the soma, while the density gradient of the voltage-gated Na(+) conductance tapers slowly along the apical dendrite. The model reproduced the back-propagation of the action potential and the modulation of the resting membrane potential along the apical dendrite. Furthermore, the optimized model provided a mechanistic explanation for the back-propagation of the action potential into the apical dendrite and the generation of dendritic Na(+) spikes.