Membranes with the Same Ion Channel Populations but Different Excitabilities

Electrical signaling allows communication within and between different tissues and is necessary for the survival of multicellular organisms. The ionic transport that underlies transmembrane currents in cells is mediated by transporters and channels. Fast ionic transport through channels is typically modeled with a conductance-based formulation that describes current in terms of electrical drift without diffusion. In contrast, currents written in terms of drift and diffusion are not as widely used in the literature in spite of being more realistic and capable of displaying experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are mathematically related: conductance-based currents are linear approximations of drift-diffusion currents. However, conductance-based models of membrane potential are not first-order approximations of drift-diffusion models. Bifurcation analysis and numerical simulations show that the two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with drift-diffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed in response to excitatory synaptic input, and across different levels of ion channel expression. In general, the electrophysiological profiles of membranes modeled with drift-diffusion and conductance-based models having identical ion channel populations are different, potentially causing the input-output and computational properties of networks constructed with these models to be different as well. The drift-diffusion formulation is thus proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels

Modelling and analysis of neurons coupled by electrical synapses

The objective of this thesis is to analyze the role of the intrinsic properties of neurons in the communication through electrical synapses. Mesencephalic trigeminal neurons constitute an excellent experimental model to study the communication between neurons, because of its easy experimental access experimental and simple to model and analyze a biological system. Among the contributions of this thesis are: the complete modeling of the sodium currents and other ionic current (and its modulation); the explanation preference subthreshold frequency transfer between neuronfor example and its coupling. Some preliminary results of this work have been presented at international conferences.morphology. However, the analysis of real neurons is limited by experimental constraints that do not allow to explore all aspects of the model. Within the context of this thesis, a mathematical model is built, based on electrophysiological recordings made by Sebastián Curti at the School of Medicine of Universidad de la República. The model consists of a set of differential equations, which can be represented by a nonlinear electrical circuit. Some of the differential equations are obtained from literature and only some minor parameters’ adjustments are made. Moreover, during the thesis we have found that more data was needed in order to explain some of the most important features of the behavior of neurons, such as the duration of the action potential. Therefore, more experimental recordings were made, allowing to refine the model. The model allows to evaluate the response of the neuron to different stimuli (currents or voltages imposed by an electrode), making possible to make new “experiments” that are not possible in a laboratory. Alternatives models are analyzed (varying ionic currents and morphology) using experimental information to validate them. Then the model is used to understand some unusual features of the communication between neurons. First, it is studied the subthreshold transfer function (i.e. without action potentials) between neurons coupled by electrical synapses. A reduced model is used and then linearized, in order to derive an analytical expression of the transfer function, whose behaviour is consistent with experimental results. Moreover, numerical simulations are performed to analyze the rol of the intrinsic properties of neurons in their synchronization. It is shown that the same properties that determine the subthreshold behavior are relevant to improve synchronization between neurons too. Finally, this thesis contributes not only with new models and answers, but with new questions, which should be studied using experimental models as well. This thesis applies several tools used for electrical engineering (frequency response of systems, cable equation, Markov chains, evolutionary algorithms, etc.) to model and analyze a biological system. Among the contributions of this thesis are: the complete modeling of the sodium currents and other ionic current (and its modulation); the explanation preference subthreshold frequency transfer between neuronfor example and its coupling. Some preliminary results of this work have been presented at international conferences.El objetivo de esta tesis es analizar el rol de las propiedades intrínsecas de las neuronas en la comunicación a través de sinapsis eléctricas. Las neuronas del nervio trigeminal del mesencéfalo constituyen un excelente modelo experimental para estudiar la comunicación entre neuronas, debido a su fácil acceso experimental y su sencilla morfología. Sin embargo, el análisis de neuronas reales está limitado por restricciones experimentales que impiden explorar todos los aspectos del modelo. En el marco de esta tesis, se construye un modelo matemático basado en registros electrofisiológicos realizados por Sebastián Curti en la Facultad de Medicina de la Universidad de la República. El modelo consiste en un sistema de ecuaciones diferenciales, que puede ser representado por un circuito eléctrico con componentes no lineales. Algunas de las ecuaciones diferenciales son obtenidas de bibliografía y se realizan algunos ajustes menores de parámetros. Por otro lado, durante la tesis evaluamos que se necesitaba más información para reproducir algunas de las características más importantes del comportamientos de las neuronas, como la duración del potencial de acción. Por eso, se debieron realizar nuevos registros experimentales, que permitieron refinar el modelo. El modelo permite evaluar la respuesta de la neurona ante diferentes estímulos (corrientes o voltajes impuestos por un electrodo), posibilitando nuevos “experimentos” que no son posibles en un laboratorio. Se analizan diversas alternativas de modelado (variando corrientes iónicas y morfología) usando información experimental para validarlos. Luego, el modelo es utilizado para entender algunas características inusuales de la comunicación entre neuronas. En primer lugar, se estudia la transferencia subumbral (i.e.: sin potenciales de acción) entre neuronas acopladas por sinapsis eléctricas. Se utiliza un modelo reducido, que es linealizado para obtener una expresión analítica de la transferencia, cuyo comportamiento es coherente con los resultados experimentales. Asimismo, se realizan simulaciones numéricas para analizar el rol en la sincronización de las propiedades intrínsecas de las neuronas. Se muestra que las mismas propiedades que determinan el comportamiento subumbral son relevantes para mejorar la sincronización entre neuronas. Finalmente, esta tesis no sólo contribuye con nuevos modelos y respuestas, sino con nuevas preguntas, que deberán ser estudiadas usando modelos experimentales también. Esta tesis hace uso de diversas herramientas utilizadas por la ingeniería eléctrica (comportamiento en frecuencia de sistemas, ecuación del cable, cadenas de Markov, algoritmos evolutivos, etc) para modelar y analizar un sistema biológico. Se realizan diversos aportes, por ejemplo: modelado completo de las corrientes de sodio, así como de la modulación de otra corriente; explicación de la preferencia en frecuencia de la transferencia subumbral entre neuronas; estudio de la sincronización en función de las propiedades de los osciladores y de su acople. Algunos resultados preliminares de este trabajo han sido presentados en congresos internacionales

Reproducing Five Motor Behaviors in a Salamander Robot With Virtual Muscles and a Distributed CPG Controller Regulated by Drive Signals and Proprioceptive Feedback

Diverse locomotor behaviors emerge from the interactions between the spinal central pattern generator (CPG), descending brain signals and sensory feedback. Salamander motor behaviors include swimming, struggling, forward underwater stepping, and forward and backward terrestrial stepping. Electromyographic and kinematic recordings of the trunk show that each of these five behaviors is characterized by specific patterns of muscle activation and body curvature. Electrophysiological recordings in isolated spinal cords show even more diverse patterns of activity. Using numerical modeling and robotics, we explored the mechanisms through which descending brain signals and proprioceptive feedback could take advantage of the flexibility of the spinal CPG to generate different motor patterns. Adapting a previous CPG model based on abstract oscillators, we propose a model that reproduces the features of spinal cord recordings: the diversity of motor patterns, the correlation between phase lags and cycle frequencies, and the spontaneous switches between slow and fast rhythms. The five salamander behaviors were reproduced by connecting the CPG model to a mechanical simulation of the salamander with virtual muscles and local proprioceptive feedback. The main results were validated on a robot. A distributed controller was used to obtain the fast control loops necessary for implementing the virtual muscles. The distributed control is demonstrated in an experiment where the robot splits into multiple functional parts. The five salamander behaviors were emulated by regulating the CPG with two descending drives. Reproducing the kinematics of backward stepping and struggling however required stronger muscle contractions. The passive oscillations observed in the salamander's tail during forward underwater stepping could be reproduced using a third descending drive of zero to the tail oscillators. This reduced the drag on the body in our hydrodynamic simulation. We explored the effect of local proprioceptive feedback during swimming and forward terrestrial stepping. We found that feedback could replace or reduce the need for different drives in both cases. It also reduced the variability of intersegmental phase lags toward values appropriate for locomotion. Our work suggests that different motor behaviors do not require different CPG circuits: a single circuit can produce various behaviors when modulated by descending drive and sensory feedback

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane

Defining neurochemical properties and functions of primary sensory neurons in the rat trigeminal ganglion

The trigeminal ganglion (TG) is a complex sensory structure and multiple lines of evidence suggest that significant differences exist in anatomical, neurochemical and physiological properties between it and its equivalent structure in the somatosensory system, the dorsal root ganglion (DRG). This is likely to be a reflection, first on the unique areas of tissue innervation of the TG and second, on the unusual responses to injury which give rise to distinct pain symptoms such as toothache, migraine and temporomandibular joint disorders. In an attempt to address this disparity in knowledge, we have carried out an in-depth in vivo study investigating neurochemical populations and cell size distributions of sensory neurons within the rat TG. We have performed a detailed analysis of expression patterns for receptor components of important inflammatory mediators, NGF (TrkA), TNFα (p55) and IL-6 (gp130), along with the thermo-transducers TRPV1 and TRPM8. For each analysis we have compared our findings with those of the rat DRG. We have shown a significantly larger population of NF200+ neurons within the TG (51%) compared to the DRG (40%), and most interestingly, the majority of NF200+ neurons in the TG were within the small to medium cell size range, conferring a nociceptive phenotype. We have for the first time, determined expression of p55 and gp130 protein levels within neurochemically defined subpopulations of the TG. We show that a large proportion (33%) of TG neurons, in particular 27% of NF200+ neurons co-express p55, and thereby have the potential to respond directly to TNFα. Furthermore, we have observed gp130 protein expression to be ubiquitous within the TG, suggesting all neurons, including non-nociceptors, could respond to IL-6. In addition, we have utilised biochemical and electrophysiological techniques in vitro to measure the functional outcome of exposure of TG neurons to IL-6. We have demonstrated that IL-6 activates the JAK/STAT signalling pathway, preferentially within NF200+ neurons. Furthermore, we have shown that IL-6 sensitises the response of TG neurons to the TRPV1 agonist capsaicin, altering the gating properties and prolonging the opening time of the channel. Taken together, our findings support the emerging picture of a complex combinatorial pattern of co-expression of sensory neurochemicals, transducers and receptor components that help to define TG neuronal modality and function. We would advocate caution in making generalisations across sensory ganglia in particular in extrapolating data from the DRG to the trigeminal ganglion

Characterization of Social Status-Dependent Neuromodulation in Zebrafish (Danio rerio)

In zebrafish (Danio rerio), social interactions between adult males consist of a series of aggressive encounters that ultimately lead to the formation of stable hierarchies of either socially dominant or subordinate animals. Although it has been shown that social status leads to neurophysiological changes in brain structure and function, our understanding of the underlying mechanisms that control behavioral function remains limited. We show that socially dominant animals display increased swimming activity. Conversely, social Subordinates display decreased swimming activity, but an enhanced sensitivity of the C-start escape circuit. We also show that whole brain expression of dopamine transporter (DAT) was significantly up-regulated in Dominants compared to Subordinates. In addition, Dopamine 1 receptor (D1R) expression was down-regulated in Subordinates compared to Dominants, suggesting that there is a social-status dependent regulation of the dopaminergic (DA) system. Finally, we show that visual cues play an important role in regulating zebrafish dominance relationships and the prioritization of different motor outputs by using a zebrafish line lacking pigmentation. Taken together, our results reveal that neuromodulation by DA signaling and visual information provides a mechanism for the nervous system to adapt to changes in social conditions by permitting the animal to prioritize a socially appropriate behavioral response

Optimising perceptuo-motor performance and learning with EEG neurofeedback

The neurobiological functions of an organism serve to assist its adaptation to behaviourally challenging environments, which commonly involves the learning and refinement of perceptuo-motor skills. The intensity and time scale at which this occurs is critical towards survival. Previous work has observed that the neurochemical and neuroelectric (EEG) operation of specific functional systems is upregulated during so-called ‘activated’ states of behaviour. Thus it has recently been shown that artificial (i.e. exogenous) stimulation of such systems via pharmacological or electrical means can successfully modulate as well as enhance learning and associated behavioural performance. We hypothesized that neurofeedback, which is implemented through non-invasive volitional control of electrocortical rhythms (EEG), offers an alternate and natural (i.e. endogenous) way to modulate and thereby stimulate analogous systems. Study 1 shows that neurofeedback is a viable and beneficial method for improving the acquisition and performance of perceptuo-motor skills in trainee microsurgeons, when compared to a wait-list control group. With the aid of transcranial magnetic stimulation (TMS), Study 2 demonstrates for the first time that 30 minutes of a single neurofeedback session directly leads to a robust and correlated change in corticomotor plasticity which is usually associated with learning or observed after exogenous stimulation. Lastly, Study 3 investigates the short-term modulation of one session of‘excitatory’ neurofeedback on the subsequent performance of a serial reaction-time task (SRTT), an experimental paradigm widely used as a model for procedural perceptuo-motor learning. In conclusion, this thesis contributes original evidence of direct as well as long-term functional enhancements following EEG neurofeedback, and supports its use as a safe, non-invasive and natural method for improving human perceptuo-motor performance and learning.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Postnatal maturation of the opioid and endocannabinoid signalling systems within the descending pain pathway of the rat

Significant opioid- and endocannabinoid-dependent changes occur within the periaqueductal grey (PAG), rostroventral medulla (RVM) and spinal cord (DH) during postnatal development of the rat (Sprague Dawley). These changes are involved in the differential descending control of spinal excitability between young and mature rats. Microinjection of the µ-opioid receptor (MOR) agonist DAMGO (30ng) into the PAG of rats increased spinal excitability and lowered mechanical threshold to noxious stimuli in postnatal day (P)21 rats, but had inhibitory effects in adults and lacked efficacy in P10 pups. A tonic opioidergic tone within the PAG was revealed in adult rats by intra-PAG microinjection of CTOP (120ng, MOR antagonist) which lowered mechanical thresholds and increased spinal reflex excitability. Spinal adminstration of DAMGO inhibited spinal excitability in all ages yet the magnitude of this was greater in younger animals than in adults. The expression of MOR and related peptides were also investigated using TaqMan RT-PCR and immunohistochemistry. Proopiomelanocortin (POMC) peaked at P21 in the ventral-PAG, and MOR increased significantly in the DH as the animals aged. CB1/CB2 receptor activation by WIN55212 (4µg, CB1/CB2 agonist) and HU210 (4µg, CB1/CB2 receptor agonist) in the PAG, RVM and DH was anti-nociceptive in both young (P10, P21) and adult rats, but GPR55 receptor activation by LPI (12µg, endogenous GPR55 agonist) and AM251 (2.77µg, CB1 antagonist, GPR55 agonist) was exclusively inhibitory in young rats. Micro-injection of LPI into the adult RVM facilitated spinal reflex excitability, suggesting that GPR55 receptor activation in mature animals is pro-nociceptive. The expression of cannabinoid receptors and endocannabinoid-synthesising enzymes was investigated with immunohistochemical and TaqMan RT-PCR techniques. Overall the expression of CB1 receptors and the anandamide synthesising enzyme NAPE-phospholipase D (NAPE-PLD) increased within the descending pain pathway with age, whereas the expression of the 2-AG synthesising enzyme Diacylglycerol lipase α (DAGLα) decreased. These results illustrate that profound differences in the endogenous-opioidergic and endocannabinoid signalling systems occur within the descending pain pathway throughout postnatal development

Postnatal maturation of the opioid and endocannabinoid signalling systems within the descending pain pathway of the rat

Significant opioid- and endocannabinoid-dependent changes occur within the periaqueductal grey (PAG), rostroventral medulla (RVM) and spinal cord (DH) during postnatal development of the rat (Sprague Dawley). These changes are involved in the differential descending control of spinal excitability between young and mature rats. Microinjection of the µ-opioid receptor (MOR) agonist DAMGO (30ng) into the PAG of rats increased spinal excitability and lowered mechanical threshold to noxious stimuli in postnatal day (P)21 rats, but had inhibitory effects in adults and lacked efficacy in P10 pups. A tonic opioidergic tone within the PAG was revealed in adult rats by intra-PAG microinjection of CTOP (120ng, MOR antagonist) which lowered mechanical thresholds and increased spinal reflex excitability. Spinal adminstration of DAMGO inhibited spinal excitability in all ages yet the magnitude of this was greater in younger animals than in adults. The expression of MOR and related peptides were also investigated using TaqMan RT-PCR and immunohistochemistry. Proopiomelanocortin (POMC) peaked at P21 in the ventral-PAG, and MOR increased significantly in the DH as the animals aged. CB1/CB2 receptor activation by WIN55212 (4µg, CB1/CB2 agonist) and HU210 (4µg, CB1/CB2 receptor agonist) in the PAG, RVM and DH was anti-nociceptive in both young (P10, P21) and adult rats, but GPR55 receptor activation by LPI (12µg, endogenous GPR55 agonist) and AM251 (2.77µg, CB1 antagonist, GPR55 agonist) was exclusively inhibitory in young rats. Micro-injection of LPI into the adult RVM facilitated spinal reflex excitability, suggesting that GPR55 receptor activation in mature animals is pro-nociceptive. The expression of cannabinoid receptors and endocannabinoid-synthesising enzymes was investigated with immunohistochemical and TaqMan RT-PCR techniques. Overall the expression of CB1 receptors and the anandamide synthesising enzyme NAPE-phospholipase D (NAPE-PLD) increased within the descending pain pathway with age, whereas the expression of the 2-AG synthesising enzyme Diacylglycerol lipase α (DAGLα) decreased. These results illustrate that profound differences in the endogenous-opioidergic and endocannabinoid signalling systems occur within the descending pain pathway throughout postnatal development

Pacemaking Neurons in the study of Parkinson’s Disease

Parkinson’s disease is the second most common neurodegenerative disorder with a signiVcant social cost. The disease that develops over years results in signiVcant movement related problems for the aUected. The pathogenesis however is partially understood. Computational approaches are signiVcant in the analysis of events that are multi-factorial. Parkinson’s Disease results from a system failure that leads to severe degeneration in the substantia nigra , a locus in the mid-brain. Traditional approaches tend to focus on isolated sub-components of the pathogenic pathways. However, such an approach may be inadequate to describe the pathogenesis. Substantia nigra neurons function on an expensive energy budget, due to a high level of arborisation and pacemaking activity. Spontaneous oscillations of these neurons are an important feature of motor control. Pacemaking involves the L-type calcium channel, and could impose long-term accumulation of calcium within its organelles. Modelling of this activity is an important part of developing an understanding of the pathogenic process. We develop a mathematical paradigm to describe this activity with a single compartment approach. To develop the mathematical framework we initially identify the components that contribute to the process and investigate an appropriate mathematical representation for the respective components. In the next part, we bring together such representation to develop a model that can reproduce measured data. Global optimisation strategies are adopted to tune important parameters. The model explicitly describes the dynamics of the transmembrane potential with changes in the levels of important cations. The model is veriVed for two major observations in literature regarding its response in the presence of channel blockers. The model is analysed for parameter bifurcation and stability of oscillations. Finally a framework is proposed to extend the model to include aspects of calcium homeostasis