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

Abstract

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.

Keywords: consciousness; noise; non-linear feedback; randomness; readiness potentials; synchronization; volitional decisions.

FIGURE 1

Examples of experimental “patch-clamp” registrations of ion currents. (A) Single-channel currents (downward swings) through acetylcholine receptors at different temperatures [from Dilger et al. (1991) with permission by “Elsevier”]. (B) Voltage-dependent whole cell currents (top) in response to voltage steps to different membrane potentials (bottom). (C) Curve of the voltage-dependent activation of ion channels plotted as normalized conductivity (measured current related to maximum current). Mean values of repeated measurements are plotted together with the standard deviations and fitted to a Boltzmann function (solid line) [Figures 2B,C from Leitner et al. (2012) with permission by “John Wiley and Sons”].

FIGURE 2

Computer simulation of voltage-dependent opening and closing of ion channels (simplified approach according to Hodgkin and Huxley, 1952; see Tchaptchet et al., 2013). Upper diagrams: Exponential transition functions (rate constants) α and β with p = α/(α + β) leading to the well-known Boltzmann function of the opening probability (all shown in green). The black dots scattering around it in the upper left-hand diagram are obtained when the transitions are determined by drawing random numbers in comparison to the values given by α and β. Some examples of this are shown in the graphs at the bottom left (over a 60-ms time axis with a calculation step size of 0.1 ms). The curves at the bottom right are obtained by determining the opening and closing times directly from the transition functions α and β without random factors. Accordingly, all points of the opening probability lie exactly on the Boltzmann curve in the upper right diagram, which then is completely covered by the black dots.

FIGURE 3

Left: Computer simulations of the opening states of ion channels with randomly introduced variability (according to the left-hand diagrams in Figure 2), which manifests itself as noise over time. The upper diagram again shows the exponential transition functions α and β (blue) and the resulting Boltzmann function p (green). The black dots are the opening probabilities averaged over 60 ms according to the points in Figure 3 (top left), but are now determined for repeated passes with a few potentials. In addition, the fluctuations of the opening probabilities are shown as a sum of 100 ion channels over the period of 60 ms. The lower diagram shows another curve of the fluctuations at –30 mV with 100 ion channels and at a 10-fold increase to 1,000 channels. Right: Pulse sequence, interspike intervals, and interval histogram to illustrate a neuronal pulse pattern whose structure implies that the action potentials are generated by intrinsic oscillations with functionally decisive participation of random processes (noise) (Braun et al., 1994).

FIGURE 4

Extracellular registrations of action potentials from hypothalamic brain slices of the rat (nucleus paraventricularis). The figures, screenshots from the oscillograph, show the action potentials (APs) of two different neurons, which can be distinguished by their very different amplitudes (ordinate: 50 μV/Div). Groups of small action potentials are followed by a single large action potential (A, time base: 200 ms/Div). The lower traces, plotted in higher time resolution (50 ms/Div), show a burst triplet of small spikes followed by a big spike (B), whereas a big spike does not occur after a burst doublet (C).

FIGURE 5

Computer simulation of noise effects on a model neuron of subthreshold oscillations and spike generation, tuned to different steady-state potentials (A: –61 mV, B: –53 mV) and subjected to noise of increasing intensity D (D = 0 to 0.4, blue curves) Simulation time: 10 s. Arrows in (C) indicate the position of the steady-state potentials in comparison to the activation curves F(V) of the subthreshold currents (F_Nap, F_Ks) and spike generating currents (F_Na, F_K). Model equations and parameter values are given in Huber and Braun (2006).