Numerische Implementierung neuronaler Diversität im Hinblick auf ein realitätsnäheres Computermodell für Forschung und Lehre

The aim of this work was to create a mathematical neuron model whose structure can take the physiological diversity into account, and can be converted, as close to the reality as possible, into computer models not only of single neuron but also of neuronal networks. Considering the mechanism-based approach, the starting point was the model published by Hodgkin and Huxley in 1952 on neuronal excitation based on potential- and time-dependent ion currents. For these investigations, however, a simplified form adapted to the current requirements of electrophysiological measurement technology was used. Their comparability with the original model is documented in detail and an important advantage, especially for experimental physiologists, has been identified (3.1). This consists in the fact that the results of experimental measurements can be directly assigned to the model parameters. For this purpose, the unit neuron of such computer models, otherwise related to 1 cm2 membrane area, also had to be broken down to realistic neuron sizes (3.2). In addition, the model was extended by physiologically and clinically important parameters such as ion concentrations and separate leakage conductivities (3.3), also in terms of practical usability. With these adaptations of the model structure to experimentally measurable quantities, the basis was also created to randomize the different model parameters regarding a physiologically plausible diversity of neurons. The basic model presented here, like the original Hodgkin-Huxley model, has four simple first-order differential equations. In addition to the four variables, the model has 18 parameters. Most of these parameters, especially those newly introduced here, represent physiologically and metrologically important parameters, but are as usual only indirectly included in the model calculations, i.e. in combination with other parameters. For example, the leakage conductivity of the membrane is composed of two different parameters and the voltage-dependent ion currents still result, despite simplification, from three different parameters each, which interact in a rather complex form. It therefore seemed justified to use the advantages of simple equal distributions in parameter randomization which consist among other things in the fact that the distribution limits are clearly defined and physiologically absurd values such as negative ion concentrations are avoided. How physiologically meaningful distribution forms result under these conditions despite simple equal distributions is described in detail (3.4). The distribution of the equilibrium potentials resulting from equally distributed ion concentrations via the Nernst equation, which corresponds approximately to a lognormal distribution, is particularly noteworthy. As briefly outlined in the discussion, a fundamentally new approach for the numerical implementation of lognormal distributions and various other forms of distribution can be developed from this. The problem of the numerical implementation of lognormally distributed neuron sizes could thus be solved in a quite elegant way for the present work. Another rather extensive part of this work deals with the effects of the randomization of certain parameters on neuronal excitability. It turned out that about 80% of the neurons randomized in this way have a stable resting potential, while the remaining 20% are spontaneously active pacemaker cells, i.e. generate action potentials from their intrinsic properties. For many neuron populations, this ratio should correspond quite well to reality. The changes in the ratio of spontaneously active to stable neurons were therefore taken as an easy-to-grasp measure for altered excitability by randomization of certain membrane parameters. As expected, some membrane parameters had a particularly strong influence on excitability, such as the shift of the Na+ half-activation potential. But again, it is not so much the individual parameter but the combination of parameters that determines the excitability. Thus, not only the position of the Na+ half-activation but even more its distance from the equilibrium potential becomes noticeable. Such findings have also been incorporated into some practical applications, as they are briefly outlined in the discussion. This includes the SimNeuron learning program from the Virtual Physiology series. Here, randomized neurons are made available to students for examination in virtual current and voltage/patch clamp laboratories (4.1). For didactic reasons, however, these neurons should initially have a stable resting potential, i.e. show no spontaneous activity. This was achieved by introducing some restrictions on randomization based on the findings of this work. Finally, some preliminary results on the synchronization of neuronal networks are presented, which are composed of neurons with randomized parameters, including pacemaker cells (4.2). The sometimes very surprising and impressive results compared to conventional simulations with homogeneous networks provide further insight into the importance of neuronal diversity regarding the neuronal network activity. The work is concluded with a corresponding outlook (4.3), also with regard to various extensions.