Stochastic resonance as a possible amplification mechanism
of weak external signals in cellular systems
C.E. Wagner and F. Kaiser
Institute of Applied Physics, Theory,
Nonlinear Dynamics,
Technical University of Darmstadt,
Hochschulstr. 4a, 64289 Darmstadt, FRG
The question of whether or not non-thermal and non-ionizing
electromagnetic fields (EMFs) affect the function of biological systems is
currently the subject of controverse discussions. In recent years, a
number of experimental studies have provided evidence that weak,
low-frequency EMFs influence biological systems on the cellular level.
However, not much is known about the specific bio-physical interaction
mechanisms and the corresponding interaction sites[1]. In particular, one
open question is how such weak EMFs may influence biological systems
in spite of the ever present noise. In order to elucidate this question,
we discuss stochastic resonance (SR) as a possible amplification
mechanism.
In view of experiments with T-lymphocytes which showed a significant
modification of calcium influx when exposed to non-thermal
extremely-low-frequency EMFs we focus our interest on the calcium
metabolism of non-excitable cells. Many non-excitable cell
types, including lymphocytes, respond to an external biochemical
stimulation with an oscillation of the intracellular calcium
concentration. Signal transduction of the external stimulus into the
cell takes place via a complex reaction chain. Since calcium is one
of the few second-messengers and therefore responsible for the onset
of various cell functions interaction of EMFs within the signaling
pathway might induce significant field effects through modification of
the calcium dynamics.
In order to demonstrate that stochastic resonance might be relevant
for the amplification of weak EMFs on the cellular level, we extend
the model of intracellular calcium oscillations proposed by Goldbeter,
Dupont and Berridge (GDB)[2]. The GDB-model is a two-dimensional
relaxation oscillator. With the background of experiments which
indicate that interaction of EMFs with the cell takes place at the
cell membrane we couple a bistable passive oscillator to the
GDB-model. This is done in a way to account for bistability of the
G-proteins located at the inner side of the cell membrane. The
G-proteins play a key role in the transduction of external biochemical
stimuli into the cell. When driven by noise and a weak periodic
signal, the bistable membrane oscillator shows stochastic resonance
phenomena, that is, an increasing resonance-like
Signal-to-Noise-Ratio (SNR) or amplification factor ( 
) with
growing noise strength.
We compare the amplification factor of the membrane oscillator,
considered as input, with the amplification factor of the calcium
oscillator (GDB-model), considered as output.
Depending on both, frequency and strength of the periodic signal,
the active calcium oscillator takes over the amplification of the
coherently and noisy driven membrane oscillator or even further
amplifies the original signal.
oscillations and for
their frequency encoding through protein phosphorylation,
Proc. Natl. Acad. Sci. USA 87 (1990) 1461.