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Biomedical subjects

U an der Heiden

Publications and source records attributed to U an der Heiden.

9 recordsLinked to original sources
PubMed2006

Schizophrenia as a dynamical disease.

It is demonstrated that schizophrenia is a dynamical disease, i. e. that important aspects of schizophrenia can be understood on the basis of concepts of the theory of nonlinear dynamical systems. In particular, the gradual shift of a single parameter may result in completely different kinds of behavior of the entire system just like water can be in three qualitatively different states depending on the single parameter temperature. Transitions between these different states are called bifurcations or phase transitions. In case of schizophrenia the parameter may be the neurotransmitter dopamine (or serotonin or glutamate). With a high level of dopamine transmission the symptoms of schizophrenia appear, and with rather low levels those of Morbus Parkinson. In between a healthy state prevails. With respect to neuronal activity the effects of dopamine are demonstrated by a mathematical model which can be interpreted in two ways: on the one hand as a model of typical excitatory-inhibitory circuits in the cortex, on the other hand of a negative feedback loop between thalamus, prefrontal cortex and striatum. The model exhibits different types of firing patterns and their bifurcation, from various kinds of periodicities up to erratic or chaotic behavior, corresponding to different levels of dopamine concentration.

Animals↗
PubMed2006

Mathematical model for NF-kappaB-driven proliferation of adult neural stem cells.

Neural stem cells (NSCs) are early precursors of neuronal and glial cells. NSCs are capable of generating identical progeny through virtually unlimited numbers of cell divisions (cell proliferation), producing daughter cells committed to differentiation. Nuclear factor kappa B (NF-kappaB) is an inducible, ubiquitous transcription factor also expressed in neurones, glia and neural stem cells. Recently, several pieces of evidence have been provided for a central role of NF-kappaB in NSC proliferation control. Here, we propose a novel mathematical model for NF-kappaB-driven proliferation of NSCs. We have been able to reconstruct the molecular pathway of activation and inactivation of NF-kappaB and its influence on cell proliferation by a system of nonlinear ordinary differential equations. Then we use a combination of analytical and numerical techniques to study the model dynamics. The results obtained are illustrated by computer simulations and are, in general, in accordance with biological findings reported by several independent laboratories. The model is able to both explain and predict experimental data. Understanding of proliferation mechanisms in NSCs may provide a novel outlook in both potential use in therapeutic approaches, and basic research as well.

Adult Stem Cells↗
PubMed1997

A theoretical approach to G-protein modulation of cellular responsiveness.

Structure and function of cells often depend critically on molecular signals arriving at their surface. There are universal mechanisms of signal transduction and signal processing across cell membranes. In this paper the mechanisms involving guanine-nucleotide regulatory proteins ("G-proteins") and certain receptor-kinases are considered. On the basis of recent findings in molecular biology a mathematical model is developed taking into account all essential components in the biochemical network between first and second messenger. There are two coupled feedback loops inherent in this process. The model finally consists of three nonlinear equations, which are obtained from a system of originally ten equations by using conservation laws and quasi-steady state conditions. The second part of the paper contains a mathematical analysis of the model. Solutions describing the temporal development of the involved biochemical species are shown to be bounded, more specifically to remain, independent of the size of the input signal, in a bounded domain of the state space. For the situation of stationary input signals existence, uniqueness and asymptotic stability of steady states are derived. We also demonstrate biologically relevant stimulus-response properties like monotonicity and saturation effects. For temporally non-constant input signals we show numerically that the model is able to produce phenomena of hypersensitivity and desensitization which are important characteristics of cellular responsiveness.

Animals↗
PubMed1987

Mathematical model and simulation of retina and tectum opticum of lower vertebrates.

The processing of information within the retino-tectal visual system of amphibians is decomposed into five major operational stages, three of them taking place in the retina and two in the optic tectum. The stages in the retina involve (i) a spatially local high-pass filtering in connection to the perception of moving objects, (ii) separation of the receptor activity into ON- and OFF-channels regarding the distinction of objects on both light and dark backgrounds, (iii) spatial integration via near excitation and far-reaching inhibition. Variation of the spatial range of excitation and inhibition allows to account for typical activities observed in a variety of classes of retina ganglion cells. Mathematical description of the operations in the tectum opticum include (i) spatial summation of retinal output (mainly of class-2 and class-3 retina ganglion cells), and (ii) direct or indirect lateral inhibition between tectal cells. In the computer simulation, first the output of the mathematical retina model is computed which, then, is used as the input to the tectum model. The full spatio-temporal dynamics is taken into account. The simulations show that different combinations of strength of lateral inhibition on the one side and the response properties of the retina ganglion cells on the other side determine the response properties of tectal cell types involved in object recognition.

Amphibians↗
PubMed1985

Principles of self-generation and self-maintenance.

Living systems are characterized as self-generating and self-maintaining systems. This type of characterization allows integration of a wide variety of detailed knowledge in biology. The paper clarifies general notions such as processes, systems, and interactions. Basic properties of self-generating systems, i.e. systems which produce their own parts and hence themselves, are discussed and exemplified. This makes possible a clear distinction between living beings and ordinary machines. Stronger conditions are summarized under the concept of self-maintenance as an almost unique character of living systems. Finally, we discuss the far-reaching consequences that the principles of self-generation and self-maintenance have for the organization, structure, function, and evolution of single- and multi-cellular organisms.

Animals↗
PubMed1984

The dynamics of recurrent inhibition.

A heuristic model for the dynamics of recurrent inhibition, emphasizing non-linearities arising from the stoichiometry of transmitter-receptor interactions and time delays due to finite feedback pathway transmission times, is developed and analyzed. It is demonstrated that variation in model parameters may lead to the existence of multiple steady states, and the local stability of these are analyzed as well as the occurrence of switching behaviour between them. As an example of the applicability of this model, parameters are estimated for the hippocampal mossy fibre-CA3 pyramidal cell-basket cell complex. Numerically simulated responses of this system to alterations in presynaptic drive and titration of inhibitory transmitter receptors by penicillin are presented. Numerical simulations indicate the existence of multiple bifurcations between periodic solutions, as well as the existence of bifurcations to chaotic solutions, as presynaptic drive and receptor density are varied. It is hypothesized that the model offers insight into the sequences of events recorded in single CA3 pyramidal cells following the application of penicillin, a specific inhibitory receptor blocking agent.

Animals↗
PubMed1979

Delays in physiological systems.

In comparison to most physical or chemical systems, biological systems are of extreme complexity. In addition the time needed for transport or processing of chemical components or signals may be of considerable length. Thus temporal delays have to be incorporated into models leading to differential-difference and functional differential equations rather than ordinary differential equations. A number of examples, on different levels of biological organization, demonstrate that delays can have an influence on the qualitative behavior of biological systems: The existence or non-existence of instabilities and periodic or even chaotic oscillations can entirely depend on the presence of absence of delays with appropriate duration.

Animals↗