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J Schnakenberg

Publications and source records attributed to J Schnakenberg.

10 recordsLinked to original sources
PubMed2002

A stochastic model of multistable visual perception.

Multistability in vision is an intriguing phenomenon that is currently not well understood. In this paper, we present a new, stochastic model for multistable visual perception. It is based on results of time series analysis of experimental data, yielding evidence for it being a linear, stochastic process. This is the outcome of testing for unstable periodic orbits and comparing the correlation dimension of the data to that of white noise. In the model, all degrees of freedom but one can be determined by general knowledge, thus resulting in a high degree of parsimony. The remaining parameter is used to model the individual characteristics that vary between subjects. Fitting simulations to the experimental data proves the parameter to be in a physiologically highly plausible range.

Depth Perception↗
PubMed1989

Amplification and latency in photoreceptors: integrated or separated phenomena?

It is shown that the models for the transduction process in photoreceptors which treat latency and amplification as integrated phenomena ("integrated models") yield time scales for single photon signals ("quantum bumps") which distinctly conflict with the experimentally observed ones for the ventral nerve photoreceptor of Limulus: the ratio of bump duration/latency tB/tlat is predicted by integrated models to be approximately 3 in contrast to the experimental result of approximately 0.5. Moreover, integrated models lead to a predicted value of an extinction rate of approximately 50%, i.e., 50% of the absorbed photons should be expected to cause no signal in the dark adapted state of the cell. In this paper it is shown that separation of latency and amplification in such a way that the latency causing process precedes amplification in the transduction process eliminates these discrepancies. In addition, the separate modeling of latency and amplification resolves the rather large ambiguity in determining the exponent n of the initial signal current J(t) approximately tn reported in the literature to be between n approximately 2 (from noise analysis) up to n approximately 17 (from flash experiments). Two alternative models for the latency part of transduction are suggested which give a qualitatively much better agreement with the experimental histograms of latencies.

Animals↗
PubMed1988

Can quantum-bumps in photoreceptors be reconstructed from noise-data?

The method of reconstructing quantum bumps in photoreceptor cells from noise data by making use of shot noise theory is critically reviewed. The application of this method produces results irrespective of whether the conditions for reconstructing bumps by the method are satisfied or not and even irrespective of whether at high stimulus intensities quantum bumps exist or not. We argue that at high intensities the concept of quantum bumps indeed becomes physically meaningless and degenerates to a purely mathematical concept. In order to investigate the meaning of the results of the reconstruction method, we submit it to a test model for which bumps and single channel opening events can be evaluated analytically. By comparing the analytical results of the test model with that of the reconstruction method applied to the test model we find: (1) even at low intensities, the reconstructed bump values deviate from the analytical results by up to an order of magnitude due to the variability of the bumps, (2) at high intensities, the reconstruction method produces single channel opening events rather than anything like a quantum bump. We also find, however, that there is no continuous transition from a bump at low intensities to a single channel event at high intensities.

Animals↗
PubMed1985

Comparison of time constants of single channel patches, quantum bumps, and noise analysis in Limulus ventral photoreceptors.

The characteristic time constants derived from three different experimental procedures for measuring light-evoked currents in photoreceptors are compared; these procedures include single-channel patch-clamp measurements, noise analysis, and current relaxation studies. Recent patch-clamp measurements of the mean open times of single light-activated channels in the ventral photoreceptor of Limulus (Bacigalupo, J., Lisman, J.E. (1983), Nature (London) 304:268-270) yield a disagreement of the measured mean open time with the relaxation time of the falling phase of quantum bumps and with the inverse characteristic frequency of the noise power spectrum, measured by Wong (Wong, F. (1978), Nature (London) 276:76-79). We present new experimental results which show that the relaxation time of the falling phase of bumps is markedly shortened by light-adaptation. Hence the state of light-adaptation has to be taken into account when comparing different experiments. Secondly, we investigate three simple models for the mechanism of channel opening and closing, and conclude that an agreement of the mean open time of single channels, the relaxation time of the falling phase of bumps, and the inverse characteristic frequency of the noise power spectrum cannot be expected.

Acclimatization↗
PubMed1973

Physical properties of Onsager's dipole chain model for ionic transport across membranes. I. Steady-state fluxes and instabilities.

The steady-state fluxes in Onsager's model for ionic transport along a dipole chain are derived by application of Hill's diagrammatic technique for unimolecular systems. It is shown that under specific conditions the chain exhibits thermodynamic instabilities which prove to be a possible explanation for the phenomenon of electrical excitation in biological membranes.

Biological Transport↗
PubMed1972

Current-voltage curves of porous membranes in the presence of pore-blocking ions. I. Narrow pores containing no more than one moving ion.

We propose a physical model for voltage-dependent conductance changes of excitable cell membranes. It is based on competition of uni- and bivalent ions for chains of stable sites extending through the membrane. These one-dimensional pathways (pores) have different profiles of chemical potential for the two ionic species so that bivalent ions can block the passage of univalent ions at large membrane potentials. We treat the special case that each pore is either empty or, because of electrostatic repulsion, contains no more than one uni- or bivalent ion at a time. A system of linear differential equations describes the time-dependent probabilities of the various possible pore states. The states are limited by transition rate constants involving the profile of the chemical potential, the membrane voltage, the ionic concentrations in the adjacent baths, and electrostatic interactions between the ions. The steady-state solutions (Kirchhoff-Hill theorem) yield expressions for the relationship between the small signal conductance of univalent ions and the concentration of these ions in the external bathing medium (a saturation curve) and for the ionic currents and the steady-state current-voltage curve (N-shaped). From the latter curve we compute the shift of theshold potential caused by concentration changes of the external bathing medium. The model yields a number of predictions which can be tested experimentally.

Binding Sites↗