Modeling the Influence of Ion Channels on Neuron Dynamics in Drosophila

abstract: Voltage gated ion channels play a major role in determining a neuron's firing behavior, resulting in the specific processing of synaptic input patterns. Drosophila and other invertebrates provide valuable model systems for investigating ion channel kinetics and their impact on firing properties. Despite the increasing importance of Drosophila as a model system, few computational models of its ion channel kinetics have been developed. In this study, experimentally observed biophysical properties of voltage gated ion channels from the fruitfly Drosophila melanogaster are used to develop a minimal, conductance based neuron model. We investigate the impact of the densities of these channels on the excitability of the model neuron. Changing the channel densities reproduces different in situ observed firing patterns and induces a switch from integrator to resonator properties. Further, we analyze the preference to input frequency and how it depends on the channel densities and the resulting bifurcation type the system undergoes. An extension to a three dimensional model demonstrates that the inactivation kinetics of the sodium channels play an important role, allowing for firing patterns with a delayed first spike and subsequent high frequency firing as often observed in invertebrates, without altering the kinetics of the delayed rectifier current.View the article as published at http://journal.frontiersin.org/article/10.3389/fncom.2015.00139/ful

Ion channel degeneracy enables robust and tunable neuronal firing rates.

Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.This is the author accepted manuscript. The final version is available from National Academy of Sciences via http://dx.doi.org/10.1073/pnas.1516400112

Computational models in the age of large datasets.

Technological advances in experimental neuroscience are generating vast quantities of data, from the dynamics of single molecules to the structure and activity patterns of large networks of neurons. How do we make sense of these voluminous, complex, disparate and often incomplete data? How do we find general principles in the morass of detail? Computational models are invaluable and necessary in this task and yield insights that cannot otherwise be obtained. However, building and interpreting good computational models is a substantial challenge, especially so in the era of large datasets. Fitting detailed models to experimental data is difficult and often requires onerous assumptions, while more loosely constrained conceptual models that explore broad hypotheses and principles can yield more useful insights.Charles A King TrustThis is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.conb.2015.01.00

Neuroanatomical and Morphological Properties of Neurons that Generate Inspiratory Related Breathing Rhythm and Influence Respiratory Motor Pattern in Mice

The relationship between neuron morphology and function is a perennial issue in neuroscience. Information about synaptic integration, network connectivity, and the specific roles of neuronal subpopulations can be obtained through morphological analysis of key neurons within any given microcircuit. Breathing is essential behavior for humans and all mammals, yet the neural microcircuit that governs respiration is not completely understood. The respiratory neural microcircuit resides within the ventral respiratory column located in the medulla. Within the respiratory column, the site of respiratory rhythm generation is the bilaterally distributed preBötzinger complex (preBötC). Rhythm-generating neurons in the preBötC are derived from a single genetic line, i.e., precursor cells expressing the transcription factor Developing brain homeobox-1 (Dbx1). An analysis of over 40 dendritic morphological features of rhythmogenic Dbx1 preBötC neurons and putatively premotor Dbx1 neurons in the intermediate reticular formation, revealed these two populations are similar except reticular neurons have a larger dendritic diameter, which may contribute to a greater passive transmembrane conductance. Both populations showed commissural axon projections and reticular formation neurons show premotor-like projections to the XII motor nucleus. These morphological data provide additional evidence supporting bilateral synchronization the preBötC through Dbx1 neurons, and demonstrate that Dbx1 preBötC neuron connectivity includes recurrent interconnections. On the molecular level, the ion channels that mediate rhythm-generating whole-cell ion currents have not been not identified, and were investigated using principally an anatomical approach. The nonspecific cation current, ICAN, underlies robust inspiratory drive potentials in the preBötC and the persistent sodium current, INaP may play a role in the production of robust bursts when respiration is challenged in such cases as anoxia or hypoxia. The leading candidate for ion channels that contribute to ICAN belong to the transient membrane receptor (Trp) ion channel superfamily and the leading ion channel candidate for INaP is Nav1.6. I determined the presence of Trpc3 ion channels and Nav1.6 ion channels on Dbx1 preBötC neurons (as well as their expression in neighboring non-Dbx1 preBötC neurons). Finally, breathing behavior involves periodic sighs, which are slower than normal eupneic breathing but critical for lung function. I examined receptor expression for bomebsin-like peptides neuromedin B (NMB) and gastrin releasing peptide (GRP), which are important for sigh behavior. I show that NMB and GRP receptors are expressed in Dbx1 preBötC neurons and are not expressed by glia in the preBötC, as posited by some because of the low frequency of sigh breaths. These advances in morphological and anatomical knowledge can be used to design targeted in vitro and in vivo experiments to further explore their role in respiratory rhythm and pattern generation

Correlations in ion channel expression emerge from homeostatic tuning rules.

Experimental observations reveal that the expression levels of different ion channels vary across neurons of a defined type, even when these neurons exhibit stereotyped electrical properties. However, there are robust correlations between different ion channel expression levels, although the mechanisms that determine these correlations are unknown. Using generic model neurons, we show that correlated conductance expression can emerge from simple homeostatic control mechanisms that couple expression rates of individual conductances to cellular readouts of activity. The correlations depend on the relative rates of expression of different conductances. Thus, variability is consistent with homeostatic regulation and the structure of this variability reveals quantitative relations between regulation dynamics of different conductances. Furthermore, we show that homeostatic regulation is remarkably insensitive to the details that couple the regulation of a given conductance to overall neuronal activity because of degeneracy in the function of multiple conductances and can be robust to "antihomeostatic" regulation of a subset of conductances expressed in a cell.Swartz FoundationThis is the final version of the article. It first appeared from National Academy of Sciences via http://dx.doi.org/10.1073/pnas.1309966110

Hopf bifurcation analysis and control of three-dimensional Prescott neuron model

Neurons generate different firing patterns because of different bifurcations in the dynamical viewpoint. Various nerve diseases are relevant to the bifurcation of nervous system. Therefore, it is vital to control bifurcation since it may be potential ways of treating nerve diseases. This paper focuses on the critical Hopf bifurcation analysis and the problem of Hopf bifurcation control. We investigate the effects of key parameters on critical Hopf bifurcation and obtain the Hopf bifurcation occurrence region on parameter plane. With the theory of high-dimensional Hopf bifurcation, we analytically deduce the judgement criteria of Hopf bifurcation type for the three-dimensional models and judge the Hopf bifurcation type of Prescott model by using it. With application of the Washout filter, the subcritical Hopf bifurcation of Prescott model is controlled and converted to supercritical Hopf bifurcation. In addition, we make some discussions on Hopf bifurcation analysis of a coupled neural network. The results provided in this paper could bring new ways to controlling neurological diseases

Frequency preference and reliability of signal integration

Die Eigenschaften einzelner Nervenzellen sind von grundlegender Bedeutung für die Verarbeitung von Informationen im Nervensystem. Neuronen antworten auf Eingangsreize durch Veränderung der elektrischen Spannung über die Zellmembran. Die Spannungsantwort wird dabei durch die Dynamik der Ionenkanäle in der Zellmembran bestimmt. In dieser Arbeit untersuche ich anhand von leitfähigkeits-basierten Modellneuronen den Einfluss von Ionenkanälen auf zwei Aspekte der Signalverarbeitung: die Frequenz-Selektivität sowie die Zuverlässigkeit und zeitliche Präzision von Aktionspotentialen. Zunächst werden die zell-intrinsischen Mechanismen identifiziert, welche the Frequenz-Selektivität und die Zuverlässigkeit bestimmen. Weiterhin wird untersucht, wie Ionenkanäle diese Mechanismen modulieren können, um die Integration von Signalen zu optimieren. Im ersten Teil der Arbeit wird demonstriert, dass der Mechanismus der unterschwelligen Resonanz, so wie er bisher für periodische Signale beobachtet wurde, auch auf nicht-periodische Signale anwendbar ist und sich ebenfalls in den Feuerraten niederschlägt. Im zweiten Teil wird gezeigt, dass zeitliche Präzision und Zuverlässigkeit von Aktionspotentialen mit der Stimulusfrequenz variieren und dass, in Abhängigkeit davon, ob das Stimulusmittel über- oder unterhalb der Feuerschwelle liegt, zwei Stimulusregime unterschieden werden müssen. In beiden Regimen existiert eine bevorzugte Stimulusfrequenz, welche durch die Gesamtleitfähigkeit und die Dynamik spezifischer Ionenkanäle moduliert werden kann. Im dritten Teil wird belegt, dass Ionenkanäle die Zuverlässigkeit auch direkt über eine Veränderung der Sensitivität einer Zelle gegenüber neuronalem Rauschen bestimmen können. Die Ergebnisse der Arbeit lassen auf eine wichtige Rolle der dynamischen Regulierung der Ionenkanäle für die Frequenz-Selektivität und die zeitliche Präzision und Zuverlässigkeit der Spannungsantworten schließen.The properties of individual neurons are of fundamental importance for the processing of information in the nervous system. The generation of voltage responses to input signals, in particular, depends on the properties of ion channels in the cell membrane. Within this thesis, I employ conductance-based model neurons to investigate the effect of ionic conductances and their dynamics on two aspects of signal processing: frequency-selectivity and temporal precision and reliability of spikes. First, the cell-intrinsic mechanisms that determine frequency selectivity and spike timing reliability are identified on the basis of conductance-based model neurons. Second, it is analyzed how ionic conductances can serve to modulate these mechanisms in order to optimize signal integration. In the first part, the frequency selectivity of subthreshold response amplitudes previously observed for periodic stimuli is proven to extend to nonperiodic stimuli and to translate into firing rates. In the second part, it is demonstrated that spike timing reliability is frequency-selective and that two different stimulus regimes have to be distinguished, depending on whether the stimulus mean is below or above threshold. In both cases, resonance effects determine the most reliable stimulus frequency. It is shown that this frequency preference can be modulated by the peak conductance and dynamics of specific ion channels. In the third part, evidence is provided that ionic conductances determine spike timing reliability beyond changes in the preferred frequency. It is demonstrated that ionic conductances also exert a direct influence on the sensitivity of the timing of spikes to neuronal noise. The findings suggest an important role for dynamic neuromodulation of ion channels with regard to frequency selectivity and spike timing reliability

Stochastic neural network dynamics: synchronisation and control

Biological brains exhibit many interesting and complex behaviours. Understanding of the mechanisms behind brain behaviours is critical for continuing advancement in fields of research such as artificial intelligence and medicine. In particular, synchronisation of neuronal firing is associated with both improvements to and degeneration of the brain’s performance; increased synchronisation can lead to enhanced information-processing or neurological disorders such as epilepsy and Parkinson’s disease. As a result, it is desirable to research under which conditions synchronisation arises in neural networks and the possibility of controlling its prevalence. Stochastic ensembles of FitzHugh-Nagumo elements are used to model neural networks for numerical simulations and bifurcation analysis. The FitzHugh-Nagumo model is employed because of its realistic representation of the flow of sodium and potassium ions in addition to its advantageous property of allowing phase plane dynamics to be observed. Network characteristics such as connectivity, configuration and size are explored to determine their influences on global synchronisation generation in their respective systems. Oscillations in the mean-field are used to detect the presence of synchronisation over a range of coupling strength values. To ensure simulation efficiency, coupling strengths between neurons that are identical and fixed with time are investigated initially. Such networks where the interaction strengths are fixed are referred to as homogeneously coupled. The capacity of controlling and altering behaviours produced by homogeneously coupled networks is assessed through the application of weak and strong delayed feedback independently with various time delays. To imitate learning, the coupling strengths later deviate from one another and evolve with time in networks that are referred to as heterogeneously coupled. The intensity of coupling strength fluctuations and the rate at which coupling strengths converge to a desired mean value are studied to determine their impact upon synchronisation performance. The stochastic delay differential equations governing the numerically simulated networks are then converted into a finite set of deterministic cumulant equations by virtue of the Gaussian approximation method. Cumulant equations for maximal and sub-maximal connectivity are used to generate two-parameter bifurcation diagrams on the noise intensity and coupling strength plane, which provides qualitative agreement with numerical simulations. Analysis of artificial brain networks, in respect to biological brain networks, are discussed in light of recent research in sleep theor