Communication: how to generate and measure anomalous diffusion in simple systems.

It is shown that in systems with time-dependent and/or spatially nonuniform temperature T(t, r), the diffusion (Brownian motion) is anomalous (AD). A few examples of simple arrangements, easy for experimental realization, are discussed in detail. Proposed measurements will enable also the observation of transitions from normal to anomalous diffusion. New effects are predicted: (i) zero-mean oscillations of T(t) accelerate AD (pumping effect), (ii) the combination of temporal and spatial variations of temperature may lead to superballistic AD, (iii) various forms of T(t, r) may result in non-algebraic AD including exponential diffusion. One can expect similar effects in inflationary systems with time-dependent metric and in expanding/contracting gases.

Anomalous diffusion and weak nonergodicity.

Ergodic behavior of the class of G processes G(t)=∫(t(m))(t)du K(t,u)ξ(u)-∫(t(m))(0)du K(0,u)ξ(u), (ξ(t))=0, (ξ(t)ξ(s))=ϕ(|t-s|) is examined. Ergodicproperties are only G extensions of normal diffusion (K=1) and of Mandelbrot-Van Ness fractional diffusion [K(t,u)=K(t-u), t(m)→-∞]. Any deviation from these two types results in weak ergodicity breaking which thus is neither exceptional nor limited to some specific events but is typical for much wider class of processes. G processes driven by ξ(t) with nonvanishing correlations are important for describing transport in strongly nonequilibrium systems and may be responsible for peculiarities of diffusion found in biological, glassy, and nanoscale systems.

Asymmetric nanodiffusion.

The asymmetric diffusion through conical nanopores is described by the diffusional model. Diffusion is several times faster; when the concentration gradient points from the wide towards the narrow opening of the cone than in the opposite direction. The asymmetric diffusion appears either when the diffusion coefficient depends on the concentration or when the diffusing substances interact with the channel (i.e., ions moving through channels with charged walls). These results suggest that asymmetric nanopores can act as molecular (ionic) filters which could be used for retrieving the molecules of a given component from solutions in which its concentration fluctuates strongly, and only occasionally attains high values.

Asymmetric diffusion through synthetic nanopores.

We show that diffusion currents for a membrane containing a single conical nanopore with a fixed surface charge and small enough opening diameter depend on the concentration gradient direction. We interpret the results based on the effect of salt concentration on the thickness of the electrical double layer within the nanopore associated with the nanopore's surface charge and the distribution of electric fields inside the pore. The experimental observations are described by a diffusional model based on the Smoluchowski-Nernst-Planck equation.

Fabrication of a synthetic nanopore ion pump.

We present a synthetic nanodevice, which transports potassium ions against their concentration gradient if stimulated with external field fluctuations. It consists of a single, conical pore, created in a thin polyethylene terephthalate film. The pumping mechanism is similar to one of longitudinally oscillating deterministic ratchets.

Origin of 1/f(alpha) noise in membrane channel currents.

The transport characteristics of nanofabricated synthetic pores of similar dimensions to those of biological channels is reported. By comparison of the ion current through single synthetic and biological channels we show that the 1/f(alpha) noise indeed originates from the channel's opening-closing process. Strong evidence has been provided that the latter is related to the underlying motions of channel wall constituents.

Constructive role of noise in signal transmissions by biomembrane proteins.

We discuss new examples of the constructive role of environmental fluctuations in biophysical processes, namely quantitative enhancement and qualitative sharpening of the outgoing signal in the intercellular signal transduction, e.g., in the synaptic links. An experimental check in a chemical flow reactor is suggested.

Barrier fluctuations and stochastic resonance in membrane transport.

The role of barrier fluctuations in membrane enzymatic processes, in particular in the active transport of ions through cell membranes, is examined. For enzymes embedded in the cell membrane the role of the barrier height (activation energy) is played by the membrane electric potential. This barrier height can be modulated either by internal fluctuations or by external electrical fields, either random or periodic. Existing experimental data on active transport of Na(+) and Rb(+) in human erythrocytes (catalyzed by Na(+)-K(+)-ATPase) can be interpreted as evidence of stochastic resonance between the external ac field and the fluctuations of the membrane potential. The obtained results suggest that the significant part of these fluctuations is supplied by the stimulated action of neighbor voltage-gated ionic channels. This supports the idea that intrinsic noise plays a constructive role in one of most important and most frequent biophysical processs, viz. ion transmission through cell membranes. Means of further experimental verification of this conjecture are proposed. (c) 1998 American Institute of Physics.