Density dependent neurodynamics

Modeling effects of neural fluctuations and inter-scale interactions

One of the greatest challenges to science, in particular, to neuroscience, is to understand how processes at different levels of organization are related to each other. In connection with this problem is the question of the functional significance of fluctuations, noise, and chaos. This paper deals with three related issues: (1) how processes at different organizational levels of neural systems might be related, (2) the functional significance of non-linear neurodynamics, including oscillations, chaos, and noise, and (3) how computational models can serve as useful tools in elucidating these types of issues. In order to capture and describe phenomena at different micro (molecular), meso (cellular), and macro (network) scales, the computational models need to be of appropriate complexity making use of available experimental data. I exemplify by two major types of computational models, those of Hans Braun and colleagues and those of my own group, which both aim at bridging gaps between different levels of neural systems. In particular, the constructive role of noise and chaos in such systems is modelled and related to functions, such as sensation, perception, learning/memory, decision making, and transitions between different (un-)conscious states. While there is, in general, a focus on upward causation, I will also discuss downward causation, where higher level activity may affect the activity at lower levels, which should be a condition for any functional role of consciousness and free will, often considered to be problematic to science.

Uncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis in Computational Neuroscience

Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.

A cortical network model of cognitive and emotional influences in human decision making

Decision making (DM)(2) is a complex process that appears to involve several brain structures. In particular, amygdala, orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) seem to be essential in human decision making, where both emotional and cognitive aspects are taken into account. In this paper, we present a computational network model representing the neural information processing of DM, from perception to behavior. We model the population dynamics of the three neural structures (amygdala, OFC and LPFC), as well as their interaction. In our model, the neurodynamic activity of amygdala and OFC represents the neural correlates of secondary emotion, while the activity of certain neural populations in OFC alone represents the outcome expectancy of different options. The cognitive/rational aspect of DM is associated with LPFC. Our model is intended to give insights on the emotional and cognitive processes involved in DM under various internal and external contexts. Different options for actions are represented by the oscillatory activity of cell assemblies, which may change due to experience and learning. Knowledge and experience of the outcome of our decisions and actions can eventually result in changes in our neural structures, attitudes and behaviors. Simulation results may have implications for how we make decisions for our individual actions, as well as for societal choices, where we take examples from transport and its impact on CO2 emissions and climate change.

Density of voltage-gated potassium channels is a bifurcation parameter in pyramidal neurons

Several types of intrinsic dynamics have been identified in brain neurons. Type 1 excitability is characterized by a continuous frequency-stimulus relationship and, thus, an arbitrarily low frequency at threshold current. Conversely, Type 2 excitability is characterized by a discontinuous frequency-stimulus relationship and a nonzero threshold frequency. In previous theoretical work we showed that the density of Kv channels is a bifurcation parameter, such that increasing the Kv channel density in a neuron model transforms Type 1 excitability into Type 2 excitability. Here we test this finding experimentally, using the dynamic clamp technique on Type 1 pyramidal cells in rat cortex. We found that increasing the density of slow Kv channels leads to a shift from Type 1 to Type 2 threshold dynamics, i.e., a distinct onset frequency, subthreshold oscillations, and reduced latency to first spike. In addition, the action potential was resculptured, with a narrower spike width and more pronounced afterhyperpolarization. All changes could be captured with a two-dimensional model. It may seem paradoxical that an increase in slow K channel density can lead to a higher threshold firing frequency; however, this can be explained in terms of bifurcation theory. In contrast to previous work, we argue that an increased outward current leads to a change in dynamics in these neurons without a rectification of the current-voltage curve. These results demonstrate that the behavior of neurons is determined by the global interactions of their dynamical elements and not necessarily simply by individual types of ion channels.

Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and down-regulation, by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In the present investigation, we analyze how the impulse patterns are regulated by the density of voltage-gated channels in a model neuron, based on voltage clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf bifurcation threshold dynamics, respectively. Single strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The presently found relationship between channel densities and oscillatory behavior may be relevance for understanding principal spiking patterns of cortical neurons (regular firing and fast spiking). It may also be of relevance for understanding the action of pharmacological compounds on brain oscillatory activity.