Modeling neuronal activity in relation to experimental voltage-/patch-clamp recordings

Stochasticity Versus Determinacy in Neurobiology: From Ion Channels to the Question of the "Free Will"

If one accepts that decisions are made by the brain and that neuronal mechanisms obey deterministic physical laws, it is hard to deny what some brain researchers postulate, such as "We do not do what we want, but we want what we do" and "We should stop talking about freedom. Our actions are determined by physical laws." This point of view has been substantially supported by spectacular neurophysiological experiments demonstrating action-related brain activity (readiness potentials, blood oxygen level-dependent signals) occurring up to several seconds before an individual becomes aware of his/her decision to perform the action. This report aims to counter the deterministic argument for the absence of free will by using experimental data, supplemented by computer simulations, to demonstrate that biological systems, specifically brain functions, are built on principle randomness, which is introduced already at the lowest level of neuronal information processing, the opening and closing of ion channels. Switching between open and closed states follows physiological laws but also makes use of randomness, which is apparently introduced by Brownian motion - principally unavoidable under all life-compatible conditions. Ion-channel stochasticity, manifested as noise, function is not smoothed out toward higher functional levels but can even be amplified by appropriate adjustment of the system's non-linearities. Examples shall be given to illustrate how stochasticity can propagate from ion channels to single neuron action potentials to neuronal network dynamics to the interactions between different brain nuclei up to the control of autonomic functions. It is proposed that this intrinsic stochasticity helps to keep the brain in a flexible state to explore diverse alternatives as a prerequisite of free decision-making.

Automata complete computation with Hodgkin-Huxley neural networks composed of synfire rings

Synfire rings are neural circuits capable of conveying synchronous, temporally precise and self-sustained activities in a robust manner. We propose a cell assembly based paradigm for abstract neural computation centered on the concept of synfire rings. More precisely, we empirically show that Hodgkin-Huxley neural networks modularly composed of synfire rings are automata complete. We provide an algorithmic construction which, starting from any given finite state automaton, builds a corresponding Hodgkin-Huxley neural network modularly composed of synfire rings and capable of simulating it. We illustrate the correctness of the construction on two specific examples. We further analyze the stability and robustness of the construction as a function of changes in the ring topologies as well as with respect to cell death and synaptic failure mechanisms, respectively. These results establish the possibility of achieving abstract computation with bio-inspired neural networks. They might constitute a theoretical ground for the realization of biological neural computers.

Activity patterns with silent states in a heterogeneous network of gap-junction coupled Huber-Braun model neurons

A mathematical model of a network of nearest neighbor gap-junction coupled neurons has been used to examine the impact of neuronal heterogeneity on the networks' activity during increasing coupling strength. Heterogeneity has been introduced by Huber-Braun model neurons with randomization of the temperature as a scaling factor. This leads to neurons of an enormous diversity of impulse pattern, including burst discharges, chaotic activity, and two different types of tonic firing-all of them experimentally observed in the peripheral as well as central nervous system. When the network is composed of all these types of neurons, randomly selected, a particular phenomenon can be observed. At a certain coupling strength, the network goes into a completely silent state. Examination of voltage traces and inter-spike intervals of individual neurons suggests that all neurons, irrespective of their original pattern, go through a well-known bifurcation scenario, resembling those of single neurons especially on external current injection. All the originally spontaneously firing neurons can achieve constant membrane potentials at which all intrinsic and gap-junction currents are balanced. With limited diversity, i.e., taking out neurons of specific patterns from the lower and upper temperature range, spontaneous firing can be reinstalled with further increasing coupling strength, especially when the tonic firing regimes are missing. Reinstalled firing develops from slowly increasing subthreshold oscillations leading to tonic firing activity with already fairly well synchronized action potentials, while the subthreshold potentials can still be significantly different. Full in phase synchronization is not achieved. Additional studies are needed elucidating the underlying mechanisms and the conditions under which such particular transitions can appear.