BDNF boosts spike fidelity in chaotic neural oscillations

Abstract

Oscillatory activity and its nonlinear dynamics are of fundamental importance for information processing in the central nervous system. Here we show that in aperiodic oscillations, brain-derived neurotrophic factor (BDNF), a member of the neurotrophin family, enhances the accuracy of action potentials in terms of spike reliability and temporal precision. Cultured hippocampal neurons displayed irregular oscillations of membrane potential in response to sinusoidal 20-Hz somatic current injection, yielding wobbly orbits in the phase space, i.e., a strange attractor. Brief application of BDNF suppressed this unpredictable dynamics and stabilized membrane potential fluctuations, leading to rhythmical firing. Even in complex oscillations induced by external stimuli of 40 Hz (gamma) on a 5-Hz (theta) carrier, BDNF-treated neurons generated more precisely timed spikes, i.e., phase-locked firing, coupled with theta-phase precession. These phenomena were sensitive to K252a, an inhibitor of tyrosine receptor kinases and appeared attributable to BDNF-evoked Na(+) current. The data are the first indication of pharmacological control of endogenous chaos. BDNF diminishes the ambiguity of spike time jitter and thereby might assure neural encoding, such as spike timing-dependent synaptic plasticity.

FIGURE 1

Frequency-dependent transition between periodic and chaotic oscillations. Left panels indicate representative traces of membrane potential (top) in response to sinusoidal somatic current injection (bottom) at frequencies of 1 (B), 2 (C), 4 (D), 10 (E), and 20 Hz (F) with an amplitude of 25 pA. Zero hertz (A) indicates no current injection (free run). The responses were analyzed by reconstructing the phase spaces of V versus dV/dt (middle) and stroboscopic return maps obtained from Poincaré cross sections at sinusoidal phase 144°, at which the Lyapunov exponent of the 20-Hz oscillations rendered the maximal value (right). The return map for 0 Hz was reconstructed by a 164-ms separation. The neuron displayed harmonic spikes with 6:1, 3:1, 2:1, and 1:1 entrainments onto exterior 1-Hz, 2-Hz, 4-Hz, and 10-Hz oscillators, respectively, whereas at 20 Hz, it responded chaotically.

FIGURE 2

Frequency- and amplitude-dependent transition between periodic and chaotic oscillations. The max-plus Lyapunov exponents of membrane potential in response to sinusoidal somatic current injection are plotted against both frequency (1, 5, 10, 15, and 20 Hz) and amplitude (10–50 pA). The insets show the phase portraits of membrane potential versus its temporal derivative (a, 25 pA at 20 Hz; b, 35 pA at 10 Hz).

FIGURE 3

BDNF reduces chaotic neural activity. (A and B) Representative waveforms (left top) of membrane potential in response to sinusoidal current injection (20 Hz, 25 pA, left bottom), and the corresponding stroboscopic portraits of membrane potential versus its temporal derivative (right) immediately before (A) and 5 min after 50 ng/ml BDNF application (B). (C) Average max-plus Lyapunov exponents in control (open bars) and BDNF-treated neurons (solid bars) in the absence (N = 8) and presence of 20 μM CNQX, 50 μM AP5, and 20 μM picrotoxin (PTX) (N = 9) or 200 nM K252a (N = 4). In each experiment, the driving current was adjusted to the amplitude that produced the largest chaotic response before drug application (usually 20–40 pA). ^*P < 0.05 versus control; t-test. Data are mean ± SE of N cases.

FIGURE 4

BDNF narrows the time window of spike events and shifts spike timing relative to θ-phases. Synchronized oscillations of membrane potential (left top) in response to complex current consisting of a combination of sinusoidal θ-like (5 Hz, 20 pA) and γ-like (40 Hz, 10 pA) rhythm (left bottom) immediately before (A) and 5 min after treatment with 50 ng/ml BDNF (B). The number of spikes was normalized to the total number for 25 s and plotted against the phase of a 5-Hz sinusoid (right). In this neuron, the average phases of spike events were 114.2 ± 28.9° in control and 78.5 ± 13.3° in BDNF (mean ± SE, P < 0.01, Student's t-test), which indicates that BDNF induced forward phase precession in spike timing. The CV values of the spike timing in phase were 28.3% in control and 19.2% in BDNF (P < 0.01, F-test), which means that BDNF-treated neurons fired with more precise timing. See text for data of the other neurons.

FIGURE 5

BDNF immobilizes spike patterns in random aperiodic drive. Reliability of firing pattern (top subpanels) evoked by repeated stimulation with Gaussian white noise current (bottom subpanels; μ_s = 50 pA, σ_s = 10 pA, τ_s = 3 ms) immediately before (A) and 5 min after treatment with 50 ng/ml BDNF (B). The middle subpanels indicate eight superimposed voltage traces. In this neuron, the average CV of spike timing was 72.8 ± 28.4 ms (mean ± SD of eight successive trials) in control and 32.4 ± 15.6 ms in BDNF (P < 0.05, t-test), which means that BDNF-treated neurons fired with more precise timing. See text for data of the other neurons.

FIGURE 6

Increasing Na_V1.9-like conductance induces chaos stabilization and phase precession in a Hodgkin-Huxley model neuron. (A and B) Voltage-insensitive Na⁺ conductance (g_{Na_VI}) reduces chaotic activities. The phase portraits indicate membrane potential versus its temporal derivative in response to sinusoidal current injection (150 Hz, 50.4 μA/cm²) before (A) and after addition of 0.01 mS/cm² g_{Na_VI} (B). (C–H) Summary of the effects of g_{Na_VI} (C and D), (E and F), and (G and H) on the largest Lyapunov exponents (C, E, and G) and firing phase (D, F, and H). In the simulation of phase advancement (D, F, and H), we used stimulating current consisting of a combination of sinusoidal 5-Hz (2.5 μA/cm²) and 40-Hz (0.05 μA/cm²) cycles, and the spike phases in the 5-Hz cycle are plotted against changes in each conductance.