Resonant effects in a voltage-activated channel gating

The non-selective voltage activated cation channel from the human red cells, which is activated at depolarizing potentials, has been shown to exhibit counter-clockwise gating hysteresis. We have analyzed the phenomenon with the simplest possible phenomenological models by assuming $2\times 2$ discrete states, i.e. two normal open/closed states with two different states of ``gate tension.'' Rates of transitions between the two branches of the hysteresis curve have been modeled with single-barrier kinetics by introducing a real-valued ``reaction coordinate'' parameterizing the protein's conformational change. When described in terms of the effective potential with cyclic variations of the control parameter (an activating voltage), this model exhibits typical ``resonant effects'': synchronization, resonant activation and stochastic resonance. Occurrence of the phenomena is investigated by running the stochastic dynamics of the model and analyzing statistical properties of gating trajectories.Comment: 12 pages, 9 figure

“Calibration-on-the-spot”: How to calibrate an EMCCD camera from its images

In order to count photons with a camera, the camera must be calibrated. Photon counting is necessary, e.g., to determine the precision of localization-based super-resolution microscopy. Here we present a protocol that calibrates an EMCCD camera from information contained in isolated, diffraction-limited spots in any image taken by the camera, thus making dedicated calibration procedures redundant by enabling calibration post festum, from images filed without calibration information

Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers

Optical tweezers and AFM cantilevers are often calibrated by fitting their experimental powerspectra of Brownian motion. We demonstrate here that if this is done with typical weighted least-squares methods the result is a bias of relative size between -2/n and +1/n on the value of the fitted diffusion coefficient. Here n is the number of power-spectra averaged over, so typical calibrations contain 10-20% bias. Both the sign and the size of the bias depends on the weighting scheme applied. Hence, so do length-scale calibrations based on the diffusion coefficient. The fitted value for the characteristic frequency is not affected by this bias. For the AFM then, force measurements are not affected provided an independent length-scale calibration is available. For optical-tweezers there is no such luck, since the spring constant is found as the ratio of the characteristic frequency and the diffusion coefficient. We give analytical results for the weight-dependent bias for the wide class of systems whose dynamics is described by a linear (integro-)differential equation with additive noise, white or colored. Examples are optical tweezers with hydrodynamic self-interaction and aliasing, calibration of Ornstein-Uhlenbeck models in finance, models for cell-migration in biology, etc. Because the bias takes the form of a simple multiplicative factor on the fitted amplitude (e.g. the diffusion coefficient) it is straightforward to remove, and the user will need minimal modifications to his or her favorite least-square fitting programs. Results are demonstrated and illustrated using synthetic data, so we can compare fits with known true values. We also fit some commonly occurring power spectra once-and-for-all in the sense that we give their parameter values and associated error-bars as explicit functions of experimental power-spectral values.Comment: 20 pages, 10 figure

Intracellular signaling by diffusion: can waves of hydrogen peroxide transmit intracellular information in plant cells?

Amplitude- and frequency-modulated waves of Ca(2+) ions transmit information inside cells. Reactive Oxygen Species (ROS), specifically hydrogen peroxide, have been proposed to have a similar role in plant cells. We consider the feasibility of such an intracellular communication system in view of the physical and biochemical conditions in plant cells. As model system, we use a H(2)O(2) signal originating at the plasma membrane (PM) and spreading through the cytosol. We consider two maximally simple types of signals, isolated pulses and harmonic oscillations. First we consider the basic limits on such signals as regards signal origin, frequency, amplitude, and distance. Then we establish the impact of ROS-removing enzymes on the ability of H(2)O(2) to transmit signals. Finally, we consider to what extent cytoplasmic streaming distorts signals. This modeling allows us to predict the conditions under which diffusion-mediated signaling is possible. We show that purely diffusive transmission of intracellular information by H(2)O(2) over a distance of 1 μm (typical distance between organelles, which may function as relay stations) is possible at frequencies well above 1 Hz, which is the highest frequency observed experimentally. This allows both frequency and amplitude modulation of the signal. Signaling over a distance of 10 μm (typical distance between the PM and the nucleus) may be possible, but requires high signal amplitudes or, equivalently, a very low detection threshold. Furthermore, at this longer distance a high rate of enzymatic degradation is required to make signaling at frequencies above 0.1 Hz possible. In either case, cytoplasmic streaming does not seriously disturb signals. We conclude that although purely diffusion-mediated signaling without relaying stations is theoretically possible, it is unlikely to work in practice, since it requires a much faster enzymatic degradation and a much lower cellular background concentration of H(2)O(2) than observed experimentally