Probing the dynamics of identified neurons with a data-driven modeling approach

In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach

Data-true Characterization Of Neuronal Models

In this thesis, a weighted least squares approach is initially presented to estimate the parameters of an adaptive quadratic neuronal model. By casting the discontinuities in the state variables at the spiking instants as an impulse train driving the system dynamics, the neuronal output is represented as a linearly parameterized model that depends on filtered versions of the input current and the output voltage at the cell membrane. A prediction errorbased weighted least squares method is formulated for the model. This method allows for rapid estimation of model parameters under a persistently exciting input current injection. Simulation results show the feasibility of this approach to predict multiple neuronal firing patterns. Results of the method using data from a detailed ion-channel based model showed issues that served as the basis for the more robust resonate-and-fire model presented. A second method is proposed to overcome some of the issues found in the adaptive quadratic model presented. The original quadratic model is replaced by a linear resonateand-fire model -with stochastic threshold- that is both computational efficient and suitable for larger network simulations. The parameter estimation method presented here consists of different stages where the set of parameters is divided in to two. The first set of parameters is assumed to represent the subthreshold dynamics of the model, and it is estimated using a nonlinear least squares algorithm, while the second set is associated with the threshold and iii reset parameters as its estimated using maximum likelihood formulations. The validity of the estimation method is then tested using detailed Hodgkin-Huxley model data as well as experimental voltage recordings from rat motoneurons

The quantitative single-neuron modeling competition

As large-scale, detailed network modeling projects are flourishing in the field of computational neuroscience, it is more and more important to design single neuron models that not only capture qualitative features of real neurons but are quantitatively accurate in silico representations of those. Recent years have seen substantial effort being put in the development of algorithms for the systematic evaluation and optimization of neuron models with respect to electrophysiological data. It is however difficult to compare these methods because of the lack of appropriate benchmark tests. Here, we describe one such effort of providing the community with a standardized set of tests to quantify the performances of single neuron models. Our effort takes the form of a yearly challenge similar to the ones which have been present in the machine learning community for some time. This paper gives an account of the first two challenges which took place in 2007 and 2008 and discusses future directions. The results of the competition suggest that best performance on data obtained from single or double electrode current or conductance injection is achieved by models that combine features of standard leaky integrate-and-fire models with a second variable reflecting adaptation, refractoriness, or a dynamic threshold

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system

Statistical Optimizations of Muscle Action Potentials Based on Modeling and Analysis of Ion Channel Dynamics

An Electromyogram (EMG) is an electrical signal, which is measured from a skeletal muscle during voluntary and involuntary contractions. EMGs are useful in interpreting pathological states of the musculoskeletal system. In particular, EMGs offer valuable information concerning the timing of muscular activity and its relative intensity. Various EMG models have developed with many different purposes from a pure mathematical model to a pattern structure model [17,46]. Sophisticated EMG models are necessary to examine the effects of small changes in muscular morphology and activities [46]. Due to the crucial importance of EMG models, all factors in the model should be precise and accurate. Especially, an intracellular action potential (IAP) model, the starting point of an EMG model, should be precisely generated because of its importance as the main component for an EMG model. Generally, the Rosenfalck IAP model [75,89] has been used because of its computational simplicity [59,72,77]. However, the Rosenfalck IAP model oversimplifies a real IAP, which has been experimentally measured, and it results in mismatching amplitudes and time duration between a real and modeled IAP. This research proposes a mathematical IAP model using a series of modified gamma and erlang probability density functions. The optimization of the proposed IAP model was conducted by several different numerical methods, namely Gauss-Newton, Steepest Descent, and Conjugate Gradient methods. These optimizing methods for the proposed muscle IAP model were validated by applying them to the experimental results of the Hudgkin and Huxley neuron action potential [11]. Due to the similarity in the mechanism of both nerve and muscle IAP generations, the validation shows that the methods and results are reasonably applied and obtained in the proposed muscle model, which for the first time incorporates properties that explain ion channel behavior in IAP generation

Biophysical Characterization and Simulation of Neocortical Layer 2/3 Pyramidal Neurons during Postnatal Development

Pyramidal neurons in layer 2/3 of the mammalian neocortex constitute the most abundant neocortical cell type, yet their biophysical properties are still poorly understood. In this thesis, fundamental properties of layer 2/3 pyramidal neurons of 1-to-6-weeks old rats were investigated with an approach combining in vitro electrophysiological characterization, reconstruction of cell morphologies, and numerical computer simulations. A specific goal was to identify ion channel mechanisms underlying the sub-threshold integrative properties of these cells and to reveal the developmental profile of channel expression. A simulated annealing algorithm was employed to numerically simulate layer 2/3 neurons and to generate valid models of varying complexity and constrained by experimental data. At all ages, layer 2/3 pyramidal neurons showed prominent anomalous rectification which could be attributed to inward-rectifier potassium (KIR) channels based both on pharmacological experiments and modeling. In contrast to other types of pyramidal neurons little hyperpolarization-activated current (Ih) was found. While morphological development essentially was complete at postnatal week 2, biophysical properties continued to change until week 4-6. In particular, input resistance strongly decreased with age, rendering the cells less excitable as the cortical network matures. Computer simulations showed that these properties will have a large impact on the integration of synaptic inputs during ongoing spontaneous activity in vivo. It is concluded, that layer 2/3 pyramidal neurons possess biophysical properties distinct from other pyramidal cells and that the prolonged postnatal development is critical for shaping synaptic integration and neocortical circuit activity in vivo