Parameter estimation for bursting neural models

Estimation of the Motor Threshold for Near-Rectangular Stimuli Using the Hodgkin-Huxley Model

The motor threshold measurement is a standard in preintervention probing in TMS experiments. We aim to predict the motor threshold for near-rectangular stimuli to efficiently determine the motor threshold size before any experiments take place. Estimating the behavior of large-scale networks requires dynamically accurate and efficient modeling. We utilized a Hodgkin-Huxley (HH) type model to evaluate motor threshold values and computationally validated its function with known true threshold data from 50 participants trials from state-of-the-art published datasets. For monophasic, bidirectional, and unidirectional rectangular stimuli in posterior-anterior or anterior-posterior directions as generated by the cTMS device, computational modeling of the HH model captured the experimentally measured population-averaged motor threshold values at high precision (maximum error ≤ 8%). The convergence of our biophysically based modeling study with experimental data in humans reveals that the effect of the stimulus shape is strongly correlated with the activation kinetics of the voltage-gated ion channels. The proposed method can reliably predict motor threshold size using the conductance-based neuronal models and could therefore be embedded in new generation neurostimulators. Advancements in neural modeling will make it possible to enhance treatment procedures by reducing the number of delivered magnetic stimuli to participants.

Dynamic Redistribution of Plasticity in a Cerebellar Spiking Neural Network Reproducing an Associative Learning Task Perturbed by TMS

During natural learning, synaptic plasticity is thought to evolve dynamically and redistribute within and among subcircuits. This process should emerge in plastic neural networks evolving under behavioral feedback and should involve changes distributed across multiple synaptic sites. In eyeblink classical conditioning (EBCC), the cerebellum learns to predict the precise timing between two stimuli, hence EBCC represents an elementary yet meaningful paradigm to investigate the cerebellar network functioning. We have simulated EBCC mechanisms by reconstructing a realistic cerebellar microcircuit model and embedding multiple plasticity rules imitating those revealed experimentally. The model was tuned to fit experimental EBCC human data, estimating the underlying learning time-constants. Learning started rapidly with plastic changes in the cerebellar cortex followed by slower changes in the deep cerebellar nuclei. This process was characterized by differential development of long-term potentiation and depression at individual synapses, with a progressive accumulation of plasticity distributed over the whole network. The experimental data included two EBCC sessions interleaved by a trans-cranial magnetic stimulation (TMS). The experimental and the model response data were not significantly different in each learning phase, and the model goodness-of-fit was [Formula: see text] for all the experimental conditions. The models fitted on TMS data revealed a slowed down re-acquisition (sessions-2) compared to the control condition ([Formula: see text]). The plasticity parameters characterizing each model significantly differ among conditions, and thus mechanistically explain these response changes. Importantly, the model was able to capture the alteration in EBCC consolidation caused by TMS and showed that TMS affected plasticity at cortical synapses thereby altering the fast learning phase. This, secondarily, also affected plasticity in deep cerebellar nuclei altering learning dynamics in the entire sensory-motor loop. This observation reveals dynamic redistribution of changes over the entire network and suggests how TMS affects local circuit computation and memory processing in the cerebellum.

Computational Neuroscience: Mathematical and Statistical Perspectives

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm.

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.

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.

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.