Mathematical model of bursting in dissociated Purkinje neurons

In vitro, Purkinje cell behaviour is sometimes studied in a dissociated soma preparation in which the dendritic projection has been cleaved. A fraction of these dissociated somas spontaneously burst. The mechanism of this bursting is incompletely understood. We have constructed a biophysical Purkinje soma model, guided and constrained by experimental reports in the literature, that can replicate the somatically driven bursting pattern and which hypothesises Persistent Na+ current (INaP) to be its burst initiator and SK K+ current (ISK) to be its burst terminator

The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na+/K+ pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. The model can replicate these recordings. We propose that Na+/K+ pump activity controls the intrinsic firing mode of cerbellar Purkinje cells

Simulation of alcohol action upon a detailed Purkinje neuron model and a simpler surrogate model that runs >400 times faster

Background: An approach to investigate brain function/dysfunction is to simulate neuron circuits on a computer. A problem, however, is that detailed neuron descriptions are computationally expensive and this handicaps the pursuit of realistic network investigations, where many neurons need to be simulated. Results: We confront this issue; we employ a novel reduction algorithm to produce a 2 compartment model of the cerebellar Purkinje neuron from a previously published, 1089 compartment model. It runs more than 400 times faster and retains the electrical behavior of the full model. So, it is more suitable for inclusion in large network models, where computational power is a limiting issue. We show the utility of this reduced model by demonstrating that it can replicate the full model’s response to alcohol, which can in turn reproduce experimental recordings from Purkinje neurons following alcohol application. Conclusions: We show that alcohol may modulate Purkinje neuron firing by an inhibition of their sodium-potassium pumps. We suggest that this action, upon cerebellar Purkinje neurons, is how alcohol ingestion can corrupt motor co-ordination. In this way, we relate events on the molecular scale to the level of behavior

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

Binary Associative Memories as a Benchmark for Spiking Neuromorphic Hardware

Stöckel A, Jenzen C, Thies M, Rückert U. Binary Associative Memories as a Benchmark for Spiking Neuromorphic Hardware. Frontiers in Computational Neuroscience. 2017;11: 71.Large-scale neuromorphic hardware platforms, specialized computer systems for energy efficient simulation of spiking neural networks, are being developed around the world, for example as part of the European Human Brain Project (HBP). Due to conceptual differences, a universal performance analysis of these systems in terms of runtime, accuracy and energy efficiency is non-trivial, yet indispensable for further hard- and software development. In this paper we describe a scalable benchmark based on a spiking neural network implementation of the binary neural associative memory. We treat neuromorphic hardware and software simulators as black-boxes and execute exactly the same network description across all devices. Experiments on the HBP platforms under varying configurations of the associative memory show that the presented method allows to test the quality of the neuron model implementation, and to explain significant deviations from the expected reference output

Action selection in the rhythmic brain: The role of the basal ganglia and tremor.

Low-frequency oscillatory activity has been the target of extensive research both in cortical structures and in the basal ganglia (BG), due to numerous reports of associations with brain disorders and the normal functioning of the brain. Additionally, a plethora of evidence and theoretical work indicates that the BG might be the locus where conflicts between prospective actions are being resolved. Whereas a number of computational models of the BG investigate these phenomena, these models tend to focus on intrinsic oscillatory mechanisms, neglecting evidence that points to the cortex as the origin of this oscillatory behaviour. In this thesis, we construct a detailed neural model of the complete BG circuit based on fine-tuned spiking neurons, with both electrical and chemical synapses as well as short-term plasticity between structures. To do so, we build a complete suite of computational tools for the design, optimization and simulation of spiking neural networks. Our model successfully reproduces firing and oscillatory behaviour found in both the healthy and Parkinsonian BG, and it was used to make a number of biologically-plausible predictions. First, we investigate the influence of various cortical frequency bands on the intrinsic effective connectivity of the BG, as well as the role of the latter in regulating cortical behaviour. We found that, indeed, effective connectivity changes dramatically for different cortical frequency bands and phase offsets, which are able to modulate (or even block) information flow in the three major BG pathways. Our results indicate the existence of a multimodal gating mechanism at the level of the BG that can be entirely controlled by cortical oscillations, and provide evidence for the hypothesis of cortically-entrained but locally-generated subthalamic beta activity. Next, we explore the relationship of wave properties of entrained cortical inputs, dopamine and the transient effectiveness of the BG, when viewed as an action selection device. We found that cortical frequency, phase, dopamine and the examined time scale, all have a very important impact on the ability of our model to select. Our simulations resulted in a canonical profile of selectivity, which we termed selectivity portraits. Taking together, our results suggest that the cortex is the structure that determines whether action selection will be performed and what strategy will be utilized while the role of the BG is to perform this selection. Some frequency ranges promote the exploitation of actions of whom the outcome is known, others promote the exploration of new actions with high uncertainty while the remaining frequencies simply deactivate selection. Based on this behaviour, we propose a metaphor according to which, the basal ganglia can be viewed as the ''gearbox" of the cortex. Coalitions of rhythmic cortical areas are able to switch between a repertoire of available BG modes which, in turn, change the course of information flow back to and within the cortex. In the same context, dopamine can be likened to the ''control pedals" of action selection that either stop or initiate a decision. Finally, the frequency of active cortical areas that project to the BG acts as a gear lever, that instead of controlling the type and direction of thrust that the throttle provides to an automobile, it dictates the extent to which dopamine can trigger a decision, as well as what type of decision this will be. Finally, we identify a selection cycle with a period of around 200 ms, which was used to assess the biological plausibility of the most popular architectures in cognitive science. Using extensions of the BG model, we further propose novel mechanisms that provide explanations for (1) the two distinctive dynamical behaviours of neurons in globus pallidus external, and (2) the generation of resting tremor in Parkinson's disease. Our findings agree well with experimental observations, suggest new insights into the pathophysiology of specific BG disorders, provide new justifications for oscillatory phenomena related to decision making and reaffirm the role of the BG as the selection centre of the brain.Open Acces

Dynamic Modeling and Parameter Identification of a Plug-in Hybrid Electric Vehicle

In recent times, mechanical systems in an automobile are largely controlled by embedded systems, called micro-controllers. These automobiles, installed with micro-controllers, run complex embedded code to improve the efficiency and performance of the targeted mechanical systems. Developing and testing these control algorithms using the concept of model based design (MBD) is a cost-efficient and time-saving approach. MBD employs vehicle system models throughout the design process and offers superior understanding of the system behaviour than a traditional hardware prototype based testing. Consequently, accurate system identification constitutes an important aspect in MBD. The main focus of this thesis is to develop a validated vehicle dynamics model of a Toyota Prius Plug-in hybrid vehicle. This model plays a crucial role in achieving better fuel economy by assisting in the development process of various controller designs such as energy management system, co-operative adaptive cruise control system, and trip planning module. In this work, initially a longitudinal vehicle dynamics model was developed in MapleSim that utilizes acausal modeling techniques and symbolic code generation to create models that are capable of real-time simulation. Here, the motion in longitudinal direction was given importance as it is the crucial degree of freedom (DOF) for determining the fuel consumption. Besides, the generic and full-fledged vehicle dynamics model in Simulink-based Automotive Simulation Models (ASM) software was also modified to create a validated model of the Prius. This software specifically facilitates the implementation of the model for virtual data collection using a driving simulator. Both vehicle models were verified by studying their simulation results at every stage of the development process. Once the vehicle models were fully functional, the accurate and reliable parameters that control the vehicle motion were estimated. For this purpose, experimental data was acquired from the on-road and rolling dynamometer testing of the Prius. During these tests, the vehicle was instrumented with a vehicle measurement system (VMS), global-positioning system (GPS), and inertial measurement unit (IMU) to collect synchronized vehicle dynamics data. Parameters were identified by choosing a local optimization algorithm that minimizes the difference between simulated and experimental results. Homotopy, a global optimization technique was also investigated to check the influence of optimization algorithms on the suspension parameters. This method of parameter estimation from on-road data is highly flexible and economical. Comparison with the parameters obtained from 4-Post testing, a standardized test method, shows that the proposed methods can estimate parameters with an accuracy of 90%. Moreover, the longitudinal and lateral dynamics exhibited by the developed vehicle models are in accordance with the experimental data from on-road testing. The full vehicle simulations suggest that these validated models can be successfully used to evaluate the performance of controllers in real time

Design space exploration of associative memories using spiking neurons with respect to neuromorphic hardware implementations

Stöckel A. Design space exploration of associative memories using spiking neurons with respect to neuromorphic hardware implementations. Bielefeld: Universität Bielefeld; 2016.Artificial neural networks are well-established models for key functions of biological brains, such as low-level sensory processing and memory. In particular, networks of artificial spiking neurons emulate the time dynamics, high parallelisation and asynchronicity of their biological counterparts. Large scale hardware simulators for such networks – _neuromorphic_ computers – are developed as part of the Human Brain Project, with the ultimate goal to gain insights regarding the neural foundations of cognitive processes. In this thesis, we focus on one key cognitive function of biological brains, associative memory. We implement the well-understood Willshaw model for artificial spiking neural networks, thoroughly explore the design space for the implementation, provide fast design space exploration software and evaluate our implementation in software simulation as well as neuromorphic hardware. Thereby we provide an approach to manually or automatically infer viable parameters for an associative memory on different hardware and software platforms. The performance of the associative memory was found to vary significantly between individual neuromorphic hardware platforms and numerical simulations. The network is thus a suitable benchmark for neuromorphic systems