Environmental Noise and Nonlinear Relaxation in Biological Systems

Abstract

We analyse the effects of environmental noise in three different biological systems: (i) mating behaviour of individuals of 'Nezara viridula' (L.) (Heteroptera Pentatomidae); (ii) polymer translocation in crowded solution; (iii) an ecosystem described by a Verhulst model with a multiplicative Lèvy noise. Specifically, we report on experiments on the behavioural response of 'N. viridula' individuals to sub-threshold deterministic signals in the presence of noise. We analyse the insect response by directionality tests performed on a group of male individuals at different noise intensities. The percentage of insects which react to the sub-threshold signal shows a non-monotonic behavior, characterized by the presence of a maximum, for increasing values of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a "hard" threshold model we find that the maximum of the signal-to-noise ratio occurs in the same range of noise intensity values for which the behavioral activation shows a maximum. In the second system, the noise driven translocation of short polymers in crowded solutions is analyzed. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics, by taking into account both the interactions between adjacent monomers and introducing a Lennard-Jones potential between non-adjacent beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion. Thermal fluctuations are taken into account by introducing a Gaussian uncorrelated noise. The mean first translocation time of the polymer center of inertia shows a minimum as a function of the frequency of the oscillating forcing field. In the third ecosystem, the transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Lèvy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise, (ii) noise with a probability density of increments expressed in terms of Gamma function, and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induced by the multiplicative Lèvy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity.