Non-Markovian Stochastic Resonance

The phenomenological linear response theory of non-Markovian Stochastic Resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e. the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.Comment: 4 pages, 1 figur

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signalled by the dramatic enhancement of the net particle current. Magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict

Toolbox for analyzing finite two-state trajectories

In many experiments, the aim is to deduce an underlying multi-substate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory. However, the mapping of a KS into a two-state trajectory leads to the loss of information about the KS, and so, in many cases, more than one KS can be associated with the data. We recently showed that the optimal way to solve this problem is to use canonical forms of reduced dimensions (RD). RD forms are on-off networks with connections only between substates of different states, where the connections can have non-exponential waiting time probability density functions (WT-PDFs). In theory, only a single RD form can be associated with the data. To utilize RD forms in the analysis of the data, a RD form should be associated with the data. Here, we give a toolbox for building a RD form from a finite two-state trajectory. The methods in the toolbox are based on known statistical methods in data analysis, combined with statistical methods and numerical algorithms designed specifically for the current problem. Our toolbox is self-contained - it builds a mechanism based only on the information it extracts from the data, and its implementation on the data is fast (analyzing a 10^6 cycle trajectory from a thirty-parameter mechanism takes a couple of hours on a PC with a 2.66 GHz processor). The toolbox is automated and is freely available for academic research upon electronic request

A continuous process for the biological treatment of heavy metal contaminated acid mine water

Alkaline precipitation of heavy metals from acidic water streams is a popular and long standing treatment process. While this process is efficient it requires the continuous addition of an alkaline material, such as lime. In the long term or when treating large volumes of effluent this process becomes expensive, with costs in the mining sector routinely exceeding millions of rands annually. The process described below utilises alkalinity generated by the alga Spirulina sp., in a continuous system to precipitate heavy metals. The design of the system separates the algal component from the metal containing stream to overcome metal toxicity. The primary treatment process consistently removed over 99% of the iron (98.9 mg/l) and between 80 and 95% of the zinc (7.16 mg/l) and lead (2.35 mg/l) over a 14-day period (20 l effluent treated). In addition the pH of the raw effluent was increased from 1.8 to over 7 in the post-treatment stream. Secondary treatment and polishing steps depend on the nature of the effluent treated. In the case of the high sulphate effluent the treated stream was passed into an anaerobic digester at a rate of 4 l/day. The combination of the primary and secondary treatments effected a removal of over 95% of all metals tested for as well as a 90% reduction in the sulphate load. The running cost of such a process would be low as the salinity and nutrient requirements for the algal culture could be provided by using tannery effluent or a combination of saline water and sewage. This would have the additional benefit of treating either a tannery or sewage effluent as part of an integrated process

Entropic Stochastic Resonance

We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. This Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single-molecules and nano-devices.Comment: 4 pages, 3 figure

Stochastic resonance as a collective property of ion channel assemblies

By use of a stochastic generalization of the Hodgkin-Huxley model we investigate both the phenomena of stochastic resonance (SR) and coherence resonance (CR) in variable size patches of an excitable cell membrane. Our focus is on the challenge how internal noise stemming from individual ion channels does affect collective properties of the whole ensemble. We investigate both an unperturbed situation with no applied stimuli and one in which the membrane is stimulated externally by a periodic signal and additional external noise. For the nondriven case, we demonstrate the existence of an optimal size of the membrane patch for which the internal noise causes a most regular spike activity. This phenomenon shall be termed intrinsic CR. In presence of an applied periodic stimulus we demonstrate that the signal-to-noise ratio (SNR) exhibits SR vs. decreasing patch size, or vs. increasing internal noise strength, respectively. Moreover, we demonstrate that conventional SR vs. the external noise intensity occurs only for sufficiently large membrane patches, when the intensity of internal noise is below its optimal level. Thus, biological SR seemingly is rooted in the collective properties of large ion channel ensembles rather than in the individual stochastic dynamics of single ion channels.Comment: 9 pages, 2 figure

Effective zero-thickness model for a conductive membrane driven by an electric field

The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Non-equilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.Comment: 14 pages, 5 figure

Soft disks in a narrow channel

The pressure components of "soft" disks in a two dimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the two-body potential, u(r), is singular at some distance r_0, the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r_0. In channels with periodic boundary conditions and for potentials which are discontinuous at r_0, the transverse and longitudinal pressure components exhibit a 1/2 and 3/2 singularity, respectively. Continuous potentials with a power law singularity result in weaker singularities of the pressure components. In channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries

Ion exchange phase transitions in "doped" water--filled channels

Ion transport through narrow water--filled channels is impeded by a high electrostatic barrier. The latter originates from the large ratio of the dielectric constants of the water and a surrounding media. We show that ``doping'', i.e. immobile charges attached to the walls of the channel, substantially reduces the barrier. This explains why most of the biological ion channels are ``doped''. We show that at rather generic conditions the channels may undergo ion exchange phase transitions (typically of the first order). Upon such a transition a finite latent concentration of ions may either enter or leave the channel, or be exchanged between the ions of different valences. We discuss possible implications of these transitions for the Ca-vs.-Na selectivity of biological Ca channels. We also show that transport of divalent Ca ions is assisted by their fractionalization into two separate excitations.Comment: 16 pages, 27 figure

Enhanced production of propionic acid through acidic hydrolysis by choice of inoculum

BACKGROUND In this study, the enhancement of propionic acid production from a model feedstock mimicking kitchen waste was investigated. For that purpose, two operational runs of a semicontinuous anaerobic hydrolysis reactor were carried out at pH 6.0 ± 0.1 and mesophilic (30 °C) temperature. Two different types of inocula, a mixed microbial culture selected over 24 months for growth on cellulose and a culture contained in goat cheese were compared. RESULTS The results show that the goat cheese inoculum was significantly more efficient for propionic acid (PA) production. The highest propionic acid concentration achieved amounted to 139 mmol L−1 at a yield of 23.3 mg g−1 volatile solids (VS), which was 55% greater than what was achieved with the mixed culture. Furthermore, it was observed that propionic acid production was enhanced by a combination of high hydraulic retention time (HRT) with low organic loading rate (OLR), ensuring sufficient time for complete processing of the complex organic substrates. The fermentation could be kept in a stable process of propionic acid production at HRT of 20 days and a rather low OLR of 11.1 g L−1 day−1 VS. CONCLUSION Our results give a better understanding of PA production in semicontinuous mode, applying optimized process parameters and selecting the adequate microbial community for inoculation. This study provides important information for the improvement of PA production from complex substrates for future industrial application. © 2020 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI)