Fitting experimental data to models that use morphological data from public databases

Synaptic Plasticity Is Predicted by Spatiotemporal Firing Rate Patterns and Robust to In Vivo-like Variability

Synaptic plasticity, the experience-induced change in connections between neurons, underlies learning and memory in the brain. Most of our understanding of synaptic plasticity derives from in vitro experiments with precisely repeated stimulus patterns; however, neurons exhibit significant variability in vivo during repeated experiences. Further, the spatial pattern of synaptic inputs to the dendritic tree influences synaptic plasticity, yet is not considered in most synaptic plasticity rules. Here, we investigate how spatiotemporal synaptic input patterns produce plasticity with in vivo-like conditions using a data-driven computational model with a plasticity rule based on calcium dynamics. Using in vivo spike train recordings as inputs to different size clusters of spines, we show that plasticity is strongly robust to trial-to-trial variability of spike timing. In addition, we derive general synaptic plasticity rules describing how spatiotemporal patterns of synaptic inputs control the magnitude and direction of plasticity. Synapses that strongly potentiated have greater firing rates and calcium concentration later in the trial, whereas strongly depressing synapses have hiring firing rates early in the trial. The neighboring synaptic activity influences the direction and magnitude of synaptic plasticity, with small clusters of spines producing the greatest increase in synaptic strength. Together, our results reveal that calcium dynamics can unify diverse plasticity rules and reveal how spatiotemporal firing rate patterns control synaptic plasticity.

Integration of Within-Cell Experimental Data With Multi-Compartmental Modeling Predicts H-Channel Densities and Distributions in Hippocampal OLM Cells

Determining biophysical details of spatially extended neurons is a challenge that needs to be overcome if we are to understand the dynamics of brain function from cellular perspectives. Moreover, we now know that we should not average across recordings from many cells of a given cell type to obtain quantitative measures such as conductance since measures can vary multiple-fold for a given cell type. In this work we examine whether a tight combination of experimental and computational work can address this challenge. The oriens-lacunosum/moleculare (OLM) interneuron operates as a “gate” that controls incoming sensory and ongoing contextual information in the CA1 of the hippocampus, making it essential to understand how its biophysical properties contribute to memory function. OLM cells fire phase-locked to the prominent hippocampal theta rhythms, and we previously used computational models to show that OLM cells exhibit high or low theta spiking resonance frequencies that depend respectively on whether their dendrites have hyperpolarization-activated cation channels (h-channels) or not. However, whether OLM cells actually possess dendritic h-channels is unknown at present. We performed a set of whole-cell recordings of OLM cells from mouse hippocampus and constructed three multi-compartment models using morphological and electrophysiological parameters extracted from the same OLM cell, including per-cell pharmacologically isolated h-channel currents. We found that the models best matched experiments when h-channels were present in the dendrites of each of the three model cells created. This strongly suggests that h-channels must be present in OLM cell dendrites and are not localized to their somata. Importantly, this work shows that a tight integration of model and experiment can help tackle the challenge of characterizing biophysical details and distributions in spatially extended neurons. Full spiking models were built for two of the OLM cells, matching their current clamp cell-specific electrophysiological recordings. Overall, our work presents a technical advancement in modeling OLM cells. Our models are available to the community to use to gain insight into cellular dynamics underlying hippocampal function.

Parameter Optimization Using Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES), an Approach to Investigate Differences in Channel Properties Between Neuron Subtypes

Computational models in neuroscience can be used to predict causal relationships between biological mechanisms in neurons and networks, such as the effect of blocking an ion channel or synaptic connection on neuron activity. Since developing a biophysically realistic, single neuron model is exceedingly difficult, software has been developed for automatically adjusting parameters of computational neuronal models. The ideal optimization software should work with commonly used neural simulation software; thus, we present software which works with models specified in declarative format for the MOOSE simulator. Experimental data can be specified using one of two different file formats. The fitness function is customizable as a weighted combination of feature differences. The optimization itself uses the covariance matrix adaptation-evolutionary strategy, because it is robust in the face of local fluctuations of the fitness function, and deals well with a high-dimensional and discontinuous fitness landscape. We demonstrate the versatility of the software by creating several model examples of each of four types of neurons (two subtypes of spiny projection neurons and two subtypes of globus pallidus neurons) by tuning to current clamp data. Optimizations reached convergence within 1,600-4,000 model evaluations (200-500 generations × population size of 8). Analysis of the parameters of the best fitting models revealed differences between neuron subtypes, which are consistent with prior experimental results. Overall our results suggest that this easy-to-use, automatic approach for finding neuron channel parameters may be applied to current clamp recordings from neurons exhibiting different biochemical markers to help characterize ionic differences between other neuron subtypes.

Optimizing computer models of corticospinal neurons to replicate in vitro dynamics

Corticospinal neurons (SPI), thick-tufted pyramidal neurons in motor cortex layer 5B that project caudally via the medullary pyramids, display distinct class-specific electrophysiological properties in vitro: strong sag with hyperpolarization, lack of adaptation, and a nearly linear frequency-current (F-I) relationship. We used our electrophysiological data to produce a pair of large archives of SPI neuron computer models in two model classes: 1) detailed models with full reconstruction; and 2) simplified models with six compartments. We used a PRAXIS and an evolutionary multiobjective optimization (EMO) in sequence to determine ion channel conductances. EMO selected good models from each of the two model classes to form the two model archives. Archived models showed tradeoffs across fitness functions. For example, parameters that produced excellent F-I fit produced a less-optimal fit for interspike voltage trajectory. Because of these tradeoffs, there was no single best model but rather models that would be best for particular usages for either single neuron or network explorations. Further exploration of exemplar models with strong F-I fit demonstrated that both the detailed and simple models produced excellent matches to the experimental data. Although dendritic ion identities and densities cannot yet be fully determined experimentally, we explored the consequences of a demonstrated proximal to distal density gradient of I_h, demonstrating that this would lead to a gradient of resonance properties with increased resonant frequencies more distally. We suggest that this dynamical feature could serve to make the cell particularly responsive to major frequency bands that differ by cortical layer.

NEW & NOTEWORTHY

We developed models of motor cortex corticospinal neurons that replicate in vitro dynamics, including hyperpolarization-induced sag and realistic firing patterns. Models demonstrated resonance in response to synaptic stimulation, with resonance frequency increasing in apical dendrites with increasing distance from soma, matching the increasing oscillation frequencies spanning deep to superficial cortical layers. This gradient may enable specific corticospinal neuron dendrites to entrain to relevant oscillations in different cortical layers, contributing to appropriate motor output commands.

Dendritic diameters affect the spatial variability of intracellular calcium dynamics in computer models

There is growing interest in understanding calcium dynamics in dendrites, both experimentally and computationally. Many processes influence these dynamics, but in dendrites there is a strong contribution of morphology because the peak calcium levels are strongly determined by the surface to volume ratio (SVR) of each branch, which is inversely related to branch diameter. In this study we explore the predicted variance of dendritic calcium concentrations due to local changes in dendrite diameter and how this is affected by the modeling approach used. We investigate this in a model of dendritic calcium spiking in different reconstructions of cerebellar Purkinje cells and in morphological analysis of neocortical and hippocampal pyramidal neurons. We report that many published models neglect diameter-dependent effects on calcium concentration and show how to implement this correctly in the NEURON simulator, both for phenomenological pool based models and for implementations using radial 1D diffusion. More detailed modeling requires simulation of 3D diffusion and we demonstrate that this does not dissipate the local concentration variance due to changes of dendritic diameter. In many cases 1D diffusion of models of calcium buffering give a good approximation provided an increased morphological resolution is implemented.

Quantifying altered long-term potentiation in the CA1 hippocampus

Long-term potentiation (LTP) of synaptic transmission is a widely accepted model of learning and memory. In vitro brain slice techniques were used to investigate the effects of cortical-spreading depression and picrotoxin, an antagonist of the gamma-aminobutyric acid A (GABA(A)) receptor, on the tetanus-induced long-term potentiation of field excitatory postsynaptic potentials. Cortical-spreading depression is involved in glutamate desensitization; on the other hand, GABA(A) antagonists could increase postsynaptic excitability. This study shows that picrotoxin effectively induced long-term potentiation with 142.25 ± 4.18% of the baseline in the picrotoxin group (n = 8) versus 134.36 ± 2.35% of the baseline in the control group (n = 10). In group with picrotoxin applied to CSD, we obtained the smallest magnitude of LTP (120.15 ± 3.73% of the baseline, n = 8). These results suggest that picrotoxin could increase hippocampal activity and LTP; on the contrary, CSD reduced LTP magnitude. In addition, the results also suggest that the decay rate of post-tetanic potentiation has a direct relationship with LTP. Moreover, data were interpreted by nonlinear least squares quantifying, and LTP could also be quantified. The nonlinear attribute of LTP had an influence on the fitting, with respect to increasing the accuracy of the parameters and the compatibility of combination of stimuli that produce LTP.

A computer model of unitary responses from associational/commissural and perforant path synapses in hippocampal CA3 pyramidal cells

Despite the central position of CA3 pyramidal cells in the hippocampal circuit, the experimental investigation of their synaptic properties has been limited. Recent slice experiments from adult rats characterized AMPA and NMDA receptor unitary synaptic responses in CA3b pyramidal cells. Here, excitatory synaptic activation is modeled to infer biophysical parameters, aid analysis interpretation, explore mechanisms, and formulate predictions by contrasting simulated somatic recordings with experimental data. Reconstructed CA3b pyramidal cells from the public repository NeuroMorpho.Org were used to allow for cell-specific morphological variation. For each cell, synaptic responses were simulated for perforant pathway and associational/commissural synapses. Means and variability for peak amplitude, time-to-peak, and half-height width in these responses were compared with equivalent statistics from experimental recordings. Synaptic responses mediated by AMPA receptors are best fit with properties typical of previously characterized glutamatergic receptors where perforant path synapses have conductances twice that of associational/commissural synapses (0.9 vs. 0.5 nS) and more rapid peak times (1.0 vs. 3.3 ms). Reanalysis of passive-cell experimental traces using the model shows no evidence of a CA1-like increase of associational/commissural AMPA receptor conductance with increasing distance from the soma. Synaptic responses mediated by NMDA receptors are best fit with rapid kinetics, suggestive of NR2A subunits as expected in mature animals. Predictions were made for passive-cell current clamp recordings, combined AMPA and NMDA receptor responses, and local dendritic depolarization in response to unitary stimulations. Models of synaptic responses in active cells suggest altered axial resistivity and the presence of synaptically activated potassium channels in spines.

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.

Automated neuron model optimization techniques: a review

The increase in complexity of computational neuron models makes the hand tuning of model parameters more difficult than ever. Fortunately, the parallel increase in computer power allows scientists to automate this tuning. Optimization algorithms need two essential components. The first one is a function that measures the difference between the output of the model with a given set of parameter and the data. This error function or fitness function makes the ranking of different parameter sets possible. The second component is a search algorithm that explores the parameter space to find the best parameter set in a minimal amount of time. In this review we distinguish three types of error functions: feature-based ones, point-by-point comparison of voltage traces and multi-objective functions. We then detail several popular search algorithms, including brute-force methods, simulated annealing, genetic algorithms, evolution strategies, differential evolution and particle-swarm optimization. Last, we shortly describe Neurofitter, a free software package that combines a phase-plane trajectory density fitness function with several search algorithms.

Minimal Hodgkin-Huxley type models for different classes of cortical and thalamic neurons

We review here the development of Hodgkin-Huxley (HH) type models of cerebral cortex and thalamic neurons for network simulations. The intrinsic electrophysiological properties of cortical neurons were analyzed from several preparations, and we selected the four most prominent electrophysiological classes of neurons. These four classes are "fast spiking", "regular spiking", "intrinsically bursting" and "low-threshold spike" cells. For each class, we fit "minimal" HH type models to experimental data. The models contain the minimal set of voltage-dependent currents to account for the data. To obtain models as generic as possible, we used data from different preparations in vivo and in vitro, such as rat somatosensory cortex and thalamus, guinea-pig visual and frontal cortex, ferret visual cortex, cat visual cortex and cat association cortex. For two cell classes, we used automatic fitting procedures applied to several cells, which revealed substantial cell-to-cell variability within each class. The selection of such cellular models constitutes a necessary step towards building network simulations of the thalamocortical system with realistic cellular dynamical properties.

Successes and rewards in sharing digital reconstructions of neuronal morphology

The computer-assisted three-dimensional reconstruction of neuronal morphology is becoming an increasingly popular technique to quantify the arborization patterns of dendrites and axons. The resulting digital files are suitable for comprehensive morphometric analyses as well as for building anatomically realistic compartmental models of membrane biophysics and neuronal electrophysiology. The digital tracings acquired in a lab for a specific purpose can be often re-used by a different research group to address a completely unrelated scientific question, if the original investigators are willing to share the data. Since reconstructing neuronal morphology is a labor-intensive process, data sharing and re-analysis is particularly advantageous for the neuroscience and biomedical communities. Here we present numerous cases of "success stories" in which digital reconstructions of neuronal morphology were shared and re-used, leading to additional, independent discoveries and publications, and thus amplifying the impact of the "source" study for which the data set was first collected. In particular, we overview four main applications of this kind of data: comparative morphometric analyses, statistical estimation of potential synaptic connectivity, morphologically accurate electrophysiological simulations, and computational models of neuronal shape and development.

MorphML: level 1 of the NeuroML standards for neuronal morphology data and model specification

Quantitative neuroanatomical data are important for the study of many areas of neuroscience, and the complexity of problems associated with neuronal structure requires that research from multiple groups across many disciplines be combined. However, existing neuron-tracing systems, simulation environments, and tools for the visualization and analysis of neuronal morphology data use a variety of data formats, making it difficult to exchange data in a readily usable way. The NeuroML project was initiated to address these issues, and here we describe an extensible markup language standard, MorphML, which defines a common data format for neuronal morphology data and associated metadata to facilitate data and model exchange, database creation, model publication, and data archiving. We describe the elements of the standard in detail and outline the mappings between this format and those used by a number of popular applications for reconstruction, simulation, and visualization of neuronal morphology.

Contribution of morphology and membrane resistance to integration of fast synaptic signals in two thalamic cell types

Thalamocortical cells (TCs) and interneurons (INs) in the lateral geniculate nucleus process visual information from the retina. The TCs have many short dendrites, whereas the INs have fewer and longer dendrites. Because of these morphological differences, it has been suggested that transmission of synaptic signals from dendritic synapses to soma is more efficient in TCs than in INs. However, a higher membrane resistance (R(m)) for the INs could, in theory, compensate for the attenuating effect of their long dendrites and allow distal synaptic inputs to significantly depolarize the soma. Compartmental models were made from biocytin filled TCs (n = 15) and INs (n = 3) and adjusted to fit the current- and voltage-clamp recordings from the individual cells. The confidence limits for the passive electrical parameters were explored by simulating the influence of noise, morphometric errors and non-uniform and active conductances. One of the useful findings was that R(m) was accurately estimated despite realistic levels of active conductance. Simulations to explore the somatic influence of dendritic synapses showed that a small (0.5 nS) excitatory synapse placed at different dendritic positions gave similar somatic potentials in the individual TCs, within the TC population and also between TCs and INs. A linear increase in the conductance of the synapse gave increases in somatic potentials that were more sublinear in INs than TCs. However, when the total synaptic conductance was increased by simultaneously activating many small, spatially distributed synapses, the INs converted the synaptic signals to soma potentials almost as efficiently as the TCs. Thus, INs can transfer fast synaptic signals to soma as efficiently as TCs except when the focal conductance is large.

Quantifying the magnitude of changes in synaptic level parameters with long-term potentiation

Experimental evidence supports a number of mechanisms for the synaptic change that occurs with long-term potentiation (LTP) including insertion of AMPA receptors, an increase in AMPA receptor single channel conductance, unmasking silent synapses, and increases in vesicle release probability. Here we combine experimental and modeling studies to quantify the magnitude of the change needed at the synaptic level to explain LTP with these proposed mechanisms. Whole cell patch recordings were used to measure excitatory postsynaptic potential (EPSP) amplitude in response to near minimal afferent stimulation before and after LTP induction in CA1 pyramidal cells. Detailed neuron and synapse level models were constructed to estimate quantitatively the changes needed to explain the experimental results. For cells in normal artificial cerebrospinal fluid (ACSF), we found a 60% average increase in EPSP amplitude with LTP. This was explained in the models by a 63% increase in the number of activated synapses, a 64% increase in the AMPA receptor single channel conductance, or a 73% increase in the number of AMPA receptors per potentiated synapse. When the percentage LTP was above the average, the required increases through the proposed mechanisms became nonlinear, particularly for increases in the number of receptors. Given constraints from other experimental studies, our quantification suggests that neither unmasking silent synapses nor increasing the numbers of AMPA receptors at synapses is sufficient to explain the magnitude of LTP we observed, but increasing AMPA single channel conductance or vesicle release probability can be sufficient. Our results are most compatible with a combination of mechanisms producing LTP.