Biomedical subjects

E Plahte

Publications and source records attributed to E Plahte.

5 recordsLinked to original sources

PubMed2001

Pattern formation in discrete cell lattices.

In recent years, models for lattices of discrete cells have been attracting increased attention due to their greater flexibility to represent signalling and contact-dependent cell-cell interaction than conventional reaction-diffusion models. Using the almost forgotten method of Othmer and Scriven (1971) to calculate eigenvalues and eigenvectors for the Jacobian of the homogeneous state, a Turing-like linear stability analysis is carried out for diffusion-driven (DD) and signalling-driven (SD) discrete models. The method is a generalisation of the original method of Turing (1952). For two-species models it is found that there are profound differences between the two types of model when the size of the lattice increases. For DD models, the homogeneous state is typically either always stable, always unstable, or becomes unstable when the lattice gets suffficiently large. For SD models, the homogeneous state is typically unstable independent of lattice size, and stable only in a minor part of parameter space. Thus, SD models seem in general more pattern-prone than DD models. The conjecture that the linear analysis predicts the final pattern is investigated for a DD system with Thomas internal dynamics. Commonly the final pattern resembles the pattern of the initial perturbation of the homogeneous state, but this is by no means a general feature. When applied to a recent model for Delta-Notch lateral inhibition, linear analysis must be supplemented by various non-linear techniques to get a deeper insight into the patterning mechanisms. The overall conclusion is that a linear Turing analysis may be useful for predicting pattern, but when it comes to explaining patterns, non-linear analysis cannot be ignored.

Animals↗

PubMed2000

Gene regulatory networks generating the phenomena of additivity, dominance and epistasis.

We show how the phenomena of genetic dominance, overdominance, additivity, and epistasis are generic features of simple diploid gene regulatory networks. These regulatory network models are together sufficiently complex to catch most of the suggested molecular mechanisms responsible for generating dominant mutations. These include reduced gene dosage, expression or protein activity (haploinsufficiency), increased gene dosage, ectopic or temporarily altered mRNA expression, increased or constitutive protein activity, and dominant negative effects. As classical genetics regards the phenomenon of dominance to be generated by intralocus interactions, we have studied two one-locus models, one with a negative autoregulatory feedback loop, and one with a positive autoregulatory feedback loop. To include the phenomena of epistasis and downstream regulatory effects, a model of a three-locus signal transduction network is also analyzed. It is found that genetic dominance as well as overdominance may be an intra- as well as interlocus interaction phenomenon. In the latter case the dominance phenomenon is intimately connected to either feedback-mediated epistasis or downstream-mediated epistasis. It appears that in the intra- as well as the interlocus case there is considerable room for additive gene action, which may explain to some degree the predictive power of quantitative genetic theory, with its emphasis on this type of gene action. Furthermore, the results illuminate and reconcile the prevailing explanations of heterosis, and they support the old conjecture that the phenomenon of dominance may have an evolutionary explanation related to life history strategy.

Epistasis, Genetic↗

PubMed1998

Description and analysis of switchlike regulatory networks exemplified by a model of cellular iron homeostasis.

The post-transcriptional regulation of factors involved in the maintenance of cellular iron homeostasis is exerted by iron regulatory proteins (IRPs), which bind to mRNA structures known as iron regulatory elements (IREs). The IRP-IRE interactions are regulated by the intracellular iron level by affecting the binding affinity, synthesis and stability of the IRPs. A model of this homeostasis phenomenon is described and analysed within a methodological framework specifically designed for handling complex systems with steep sigmoidal input/output relationships between the state variables. According to the analysis there is only one threshold regulated homeostatic point. Approximate values for its coordinates, and the conditions ensuring its existence, may be given in terms of parameters. The analysis also provides some tentative insight into the evolution of the regulatory system. A comparison between analytical and numerical estimates of the position of the stationary point as a function of the steepness of the sigmoidal interactions show that the analytical approximations agree quite well with the numerical ones. The results show that we are able to obtain a deeper analytical insight by this methodological framework than what is achievable by most alternative approaches. We find this type of insight to be of considerable heuristic value in connection with the numerical simulation work which normally must be done to unfold the predictive potential of a complex model.

Animals↗

PubMed1998

A methodological basis for description and analysis of systems with complex switch-like interactions.

A wide range of complex systems appear to have switch-like interactions, i.e. below (or above) a certain threshold x has no or little influence on y, while above (or below) this threshold the effect of x on y saturates rapidly to a constant level. Switching functions are frequently described by sigmoid functions or combinations of these. Within the context of ordinary differential equations we present a very general methodological basis for designing and analysing models involving complicated switching functions together with any other non-linearities. A procedure to determine position and stability properties of all stationary points lying close to a threshold for one or several variables, so-called singular stationary points, is developed. Such points may represent homeostatic states in models, and are therefore of considerable interest. The analysis provides a profound insight into the generic effects of steep sigmoid interactions on the dynamics around homeostatic points. It leads to qualitative as well as quantitative predictions without using advanced mathematical methods. Thus, it may have an important heuristic function in connection with numerical simulations aimed at unfolding the predictive potential of realistic models.

Animals↗

PubMed1995

A mathematical framework for describing and analysing gene regulatory networks.

This paper presents a mathematical framework for describing and analysing gene regulatory networks by autonomous differential equations. It represents an improvement on existing frameworks in that it may handle a wider range of gene regulatory mechanisms. Gene regulatory networks are frequently threshold-dominated, i.e. genes are activated only when the concentration of certain gene products lie between definite thresholds. Here, the concept of regulatory domain is introduced to describe these regions in the phase space. To each regulatory domain is associated an indicator function whose value is 1 inside and 0 outside the domain. The indicator functions thus reflect the logical structure of the network. The sharp borders between the regulatory domains may be smoothed by replacing the logical step functions by continuous sigmoids or so-called logoid functions. A logoid function coincides with the step function outside a narrow interval around the threshold, and rises continuously from 0 to 1 inside it. Using logoids, the task of finding steady states is considerably simplified. A list of regions in phase space comprising all steady states lying close to a threshold is obtained by examining a certain type of matrix called the Logoid-Jacobian. In addition, this matrix leads to the conditions necessary for stability of the steady states. External signals may be conveniently incorporated in the form of Boolean variables. Thus the framework is well suited for studying gene regulatory networks both in single cells and multicellular systems.

Animals↗