Christian Finke

Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations

We have examined the effects of current and conductance noise in a single-neuron model which can generate a variety of physiologically important impulse patterns. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Additive Gaussian white noise which is implemented as conductance noise appears in the voltage equations as an additive and a multiplicative term. Moreover, the originally white noise is turned into colored noise. The noise correlation time is a function of the systems control parameters which may explain the different effects of current and conductance noise in different dynamic states. We have found the most significant, qualitative differences between different noise implementations in a pacemaker-like, tonic firing regime at the transition to chaotic burst discharges. This reflects a dynamic state of high physiological relevance.

Generalized synchronization in relay systems with instantaneous coupling.

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

On the role of subthreshold currents in the Huber–Braun cold receptor model

We study the role of the strength of subthreshold currents in a four-dimensional Hodgkin-Huxley-type model of mammalian cold receptors. Since a total diminution of subthreshold activity corresponds to a decomposition of the model into a slow, subthreshold, and a fast, spiking subsystem, we first elucidate their respective dynamics separately and draw conclusions about their role for the generation of different spiking patterns. These results motivate a numerical bifurcation analysis of the effect of varying the strength of subthreshold currents, which is done by varying a suitable control parameter. We work out the key mechanisms which can be attributed to subthreshold activity and furthermore elucidate the dynamical backbone of different activity patterns generated by this model.

Temperature-dependent stochastic dynamics of the Huber-Braun neuron model

The response of a four-dimensional mammalian cold receptor model to different implementations of noise is studied across a wide temperature range. It is observed that for noisy activation kinetics, the parameter range decomposes into two regions in which the system reacts qualitatively completely different to small perturbations through noise, and these regions are separated by a homoclinic bifurcation. Noise implemented as an additional current yields a substantially different system response at low temperature values, while the response at high temperatures is comparable to activation-kinetic noise. We elucidate how this phenomenon can be understood in terms of state space dynamics and gives quantitative results on the statistics of interspike interval distributions across the relevant parameter range.

Conductance-Based Models for the Evaluation of Brain Functions, Disorders, and Drug Effects

Neurological and psychiatric disorders such as Parkinson’s disease and clinical depression are diseases of the nervous system. Disorders of different autonomic functions, including disturbances of sleep, energy balance, and hormonal secretion also have their origin in brain dysfunctions. However, while diseases associated with energy control or hormonal secretion can be diagnosed by measuring specific parameters (so-called biomarkers) such as blood glucose or hormone concentration, diagnosis is much more difficult for psychiatric disorders including clinical depression or manic-depressive states, also known as unipolar and bipolar disorders.

The role of intrinsic dynamics and noise for neural encoding and synchronization

Transitions from tonic firing (single spikes) to burst discharges (impulse groups) play an important role for neuronal information processing (sensory encoding, information binding) and are closely associated with neuronal synchronization in many physiological processes (hormone release, sleep-wake cycles) as well as in disease (Parkinson, epilepsy). Synchronization is typically considered to depend on the network connectivity. The intrinsic dynamics of individual neurons are mostly neglected. However, in computer simulations we have seen that transitions from tonic firing to burst discharges can significantly facilitate synchronization without any changes of the coupling strength [1,2]. Thereby, it is not really surprising that periodically bursting neurons synchronize. The more interesting question is why the same neurons need much higher coupling strengths for synchronization when they are operating in a likewise periodic but tonic firing mode. Remarkably, the tonic firing mode also appeared to be much more sensitive to noise [3] which, in terms of phase space, can be related to deviations of the trajectories in the vicinity of a saddle point [4]. Our study shall help to understand under which conditions these particular features appear. We have used a simplified Hodgkin-Huxley-type approach to implement different types of model neurons for the examination of their synchronization properties especially in the tonic firing mode. Starting point was a four-dimensional model neuron for spike-generation with subthreshold oscillations which can be tuned to a diversity of impulse pattern [5] and which exhibits the above described features. For comparison, we have examined HH-type model neurons without subthreshold oscillations but pacemaker properties. When two identical, periodically firing neurons in the same dynamic state are connected via gap junctions (diffusive coupling) it should be expected that they are synchronizing at infinitely low coupling strengths in all periodically firing regimes. Indeed, this is the case in the examined model neurons – with only one exception as mentioned above. The subthreshold currents of the oscillatory subsystem, although not recognisable in the tonic firing regime, are introducing a dynamic instability on which the particular noise sensitivity is built up and which likewise prevents immediate synchronization. The input from neighboured neurons can be considered as a disturbance which rather induces random phase fluctuations than in-phase synchronisation. The interdependencies between subthreshold and spike generating currents and their different time scales seem to be the necessary conditions for this behaviour but only the overlapping of their activation range, bringing the trajectories close to a saddle point, provides sufficient conditions.