Biomedical subjects

Lutz Schimansky-Geier

Publications and source records attributed to Lutz Schimansky-Geier.

11 recordsLinked to original sources

PubMed2006

New species in evolving networks--stochastic theory of sensitive networks and applications on the metaphorical level.

In this paper we develop a theory to describe stochastic influences on the fate of new species with non-linear growth rates in evolutionary processes. We develop a theoretical framework based on notions of species, network, innovation, competition, survival and fitness. We introduce a stochastic picture describing the role of fluctuations in the survival of new species in non-linear systems. In particular we consider the fate of new species with non-linear growth. As an application of the general model framework we consider the fate of 'rare species' in early biological evolution. We show that hypercycle systems do not represent the end of the evolutionary process as they may evolve further in small niches. This has implications for different types of applications ranging from biological systems on one level to socio-technological systems on a more metaphoric level.

Biological Evolution↗

PubMed2005

Information processing in noisy burster models of sensory neurons.

Processing of external stimuli by sensory neurons often involves bursting, when epochs of fast firing alternate with intervals of quiescence. In particular, sensory neurons of electroreceptors in paddlefish (Polyodon spathula) undergo bursting when stimulated externally with broad-band noise, but otherwise fire spontaneously in a quasiperiodic tonic manner. We use a simple phenomenological model for noise-induced bursting to quantify analytically, by means of the Kullback entropy and Fisher information, the gain in information transfer and electroreceptor sensitivity for external noisy stimuli. A good agreement between theoretical predictions, numerical simulations and experimental data is shown.

Animals↗

PubMed2004

Stochastic resonance in biological nonlinear evolution models.

We investigate stochastic resonance in the nonlinear, one-dimensional Fisher-Eigen model (FEM), which represents an archetypal model for biological evolution based on a global coupling scheme. In doing so we consider different periodically driven fitness functions which govern the evolution of a biological phenotype population. For the case of a simple harmonic fitness function we are able to derive the exact analytic solution for the asymptotic probability density. A distinct feature of this solution is a phase lag between the driving signal and the linear response of the system. Furthermore, for more complex systems a general perturbation theory (linear response approximation) is put forward. Using the latter approach, we investigate stochastic resonance in terms of the spectral amplification measure for a quadratic, a quartic single-peaked, and for a bistable fitness function. Our analytical results are also compared with those of detailed numerical simulations. Our findings vindicate that stochastic resonance does occur in these nonlinear, globally coupled biological systems.

Journal Article↗

PubMed2004

Exact solutions for evolutionary strategies on harmonic landscapes.

In this paper two different evolutionary strategies are tested by means of harmonic landscapes. Both strategies are based on ensembles of searchers, spreading over the search space according to laws inspired by nature. The main difference between the two prototypes is given by the underlying selection mechanism, governing the increase or decrease of the local population of searchers in certain regions of the search space. More precisely, we compare a thermodynamic strategy, which is based on a physically motivated local selection criterion, with a biologically motivated strategy, which features a global selection scheme (i.e., global coupling of the searchers). Confining ourselves to a special class of initial conditions, we show that, in the simple case of harmonic test potentials, both strategies possess particular analytical solutions of the same type. By means of these special solutions, the velocities of the two strategies can be compared exactly. In the last part of the paper, we extend the scope of our discussion to a mixed strategy, combining local and global selection.

Biological Evolution↗

PubMed2003

Frequency and phase synchronization in stochastic systems.

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention paid to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by Rice the related phase velocity is termed the Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.

Models, Theoretical↗

PubMed2002

Analytic description of stochastic calcium-signaling periodicity.

Calcium release is an important tool for cellular signaling processes where chemical signals are converted into spatio-temporal variations of intracellular calcium concentration. We investigated the temporal behavior of a single cluster of inositol-(1,4,5)-triphosphate receptor (IP3R)-I channels and will present an analytic approach to obtain the spectrum of the calcium signal within the cluster. We compare these results with stochastic simulations and obtain an intermediate number of channels per cluster for optimal signaling periodicity.

Biophysical Phenomena↗

PubMed2002

Noise-induced transport with low randomness.

We study the transport of overdamped Brownian particles in periodic potentials subject to a spatially modulated Gaussian white noise. We derive an analytical expression for the diffusion coefficient of particles. By means of velocity, diffusion coefficient, and their ratio (Péclet number) we discuss (a) symmetric potential and modulation of noise intensity and (b) a ratchet profile with strong noise modulation. It is shown that state dependent fluctuations may not only induce directed transport, but also a pronounced coherence of transport if the potential exhibits a strong asymmetry.

Journal Article↗

PubMed2002

Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model.

We study noise-induced resonance effects in the leaky integrate-and-fire neuron model with absolute refractory period, driven by a Gaussian white noise. It is demonstrated that a finite noise level may either maximize or minimize the regularity of the spike train. We also partition the parameter space into regimes where either or both of these effects occur. It is shown that the coherence minimization at moderate noise results in a flat spectral response with respect to periodic stimulation in contrast to sharp resonances that are observed for both small and large noise intensities.

Journal Article↗

PubMed2002

Stochastic resonance for motion of flexible macromolecules in solution.

We consider a dilute or semidilute polymer solution with localized attracting centers near a flat phase boundary and assume it driven by both stochastic and periodic forces. The attracting inhomogeneities restrict the free motion of macromolecules and play the role of fixed pinning centers. The flat boundary is modeled by a bistable potential whose minima attract the movable polymer segments between neighboring pinning points. We study the motion of these segments. The stochastic forces lead to stochastic oscillations of the polymer parts between the two potential wells near the phase boundary. Application of a small temporal periodic force can synchronize these oscillations and leads to the phenomenon of stochastic resonance for a nonvanishing noise intensity. As an outcome of our theory in agreement with numerical simulations, the resonance is stronger for wider and/or less deep potentials and observed at smaller values of the noise intensity. Additionally, we discuss under what conditions doubly stochastic resonance of the macromolecular motion occurs, that is, if bistability of the potential near the boundary originates in the action of multiplicative noise.

Journal Article↗

PubMed2002

Oscillatory systems driven by noise: frequency and phase synchronization.

The phenomenon of effective phase synchronization in stochastic oscillatory systems can be quantified by an average frequency and a phase diffusion coefficient. A different approach to compute the noise-averaged frequency is put forward. The method is based on a threshold crossing rate pioneered by Rice. After the introduction of the Rice frequency for noisy systems we compare this quantifier with those obtained in the context of other phase concepts, such as the natural and the Hilbert phase, respectively. It is demonstrated that the average Rice frequency R typically supersedes the Hilbert frequency H, i.e. R > or = H. We investigate next the Rice frequency for the harmonic and the damped, bistable Kramers oscillator, both without and with external periodic driving. Exact and approximative analytic results are corroborated by numerical simulation results. Our results complement and extend previous findings for the case of noise-driven inertial systems.

Journal Article↗

PubMed2002

Behavioral stochastic resonance: how the noise from a Daphnia swarm enhances individual prey capture by juvenile paddlefish.

Zooplankton emit weak electric fields into the surrounding water that originate from their own muscular activities associated with swimming and feeding. Juvenile paddlefish prey upon single zooplankton by detecting and tracking these weak electric signatures. The passive electric sense in this fish is provided by an elaborate array of electroreceptors, Ampullae of Lorenzini, spread over the surface of an elongated rostrum. We have previously shown that the fish use stochastic resonance to enhance prey capture near the detection threshold of their sensory system. However, stochastic resonance requires an external source of electrical noise in order to function. A swarm of plankton, for example Daphnia, can provide the required noise. We hypothesize that juvenile paddlefish can detect and attack single Daphnia as outliers in the vicinity of the swarm by using noise from the swarm itself. From the power spectral density of the noise plus the weak signal from a single Daphnia, we calculate the signal-to-noise ratio, Fisher information and discriminability at the surface of the paddlefish's rostrum. The results predict a specific attack pattern for the paddlefish that appears to be experimentally testable.

Animals↗