Threshold value (development)

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A threshold is defined as a level, e.g. B. a gene expression or an enzyme from which a target product, z. B. a protein , cell status or another phenotype characteristic , no longer behaves linearly and a phase change takes place, causing a discontinuity in visible expression. Threshold behavior is a widespread phenomenon at all levels of embryonic development ( ontogenesis ).

Fig. 1 Threshold value effect on gross temperature in turtles as a variable with threshold value for sex determination.
Fig. 2 Butterfly wing pattern. Color transitions are stochastic. They obey thresholds. When enlarged, there are clear differences in the precision of the color transitions and thus differences in the threshold values
Fig. 3 Threshold effect. Projection of one or more normally distributed, continuous random variables (gene expression level or protein level) with a phenotypic characteristic expression
Fig. 4 Computer simulation of dynamic expression patterns for boundary formation in the presomitic mesoderm. The process has multiple threshold values ​​due to its repetitive, oscillating character for the formation of somites.

Examples

In general, a threshold value usually has an independent linear, but in any case continuous variable, as well as a dependent non-linear variable that forms the threshold value (Fig. 1). In one simple case, the continuous variable can be thought of as a decreasing concentration of a substance, in another case as a linearly increasing rate of gene activation. An example of threshold values ​​for color samples are color transitions on butterfly wings (Fig. 2). The boundaries between two colors can be more or less sharp or soft. The threshold value curve is always s-shaped (sigmoid); With a sharp color separation the transition curve shows a steeper one, with a softer color transition a flatter one. In any case, the sigmoid color transition is non-linear with a linear course of the gene expression level. A well-known example of the presence of a threshold in development is litter size . The number of boys is always a discrete, discontinuous quantity. It is believed to be correlated to one or more continuous variables; here it is mainly the activity of gonadotropic hormones that determines the number of ovulated eggs, as well as other hormonal factors. The sex determination of some turtles and other egg-laying reptiles obeys threshold effects that are dependent on the gross temperature (Fig. 1). In this case, the S-transition curve is very abrupt, steep, since there are only two gender forms, male and female. The formation of somites in development has long been explained and simulated with threshold value effects , first by Hans Meinhardt and, based on this, more recently also empirically substantiated with concrete gene networks (Fig. 4). Another example is the susceptibility to a disease, which can also only manifest itself discretely (sick / not sick), while the molecular biological prerequisites for this cannot be seen as discrete. One speaks therefore of a continuity with a threshold value .

Origin and properties

Fred Nijhout has analyzed that stochastic gene expressions inherently contain threshold values. According to this view, stochastics generate threshold values. Reaction-diffusion systems or activator-inhibitor systems according to Gierer - Meinhardt also imply the formation of threshold values ​​based on their mathematical logic. The patterns that such models describe are characterized by threshold values ​​at their environmental limits. The models describe mathematically how threshold values ​​arise. The Hill coefficient reflects the steepness of the transition of a threshold value . Different model parameters, such as gene activation, gene inhibition, diffusion constants, etc., or exogenous factors can determine the course. The projection of discrete values ​​into a continuous variable, which can often be assumed to be normally distributed or approximately normally distributed, allows the application of stochastic analyzes of quantitative genetics (Fig. 3).

A threshold value can be determined by the measure of an environmental factor as a continuous variable, e.g. B. Temperature. Induced heat shocks can also trigger threshold value effects. Conrad Hal Waddington was able to show for the first time that heat shocks in the pupal stage of a population of Drosophila melanogaster can lead to the elimination of the cross-bracing of wing veins (crossveinless), which is only later genetically assimilated ( genetic assimilation ).

Furthermore, a threshold value can be determined by a complex, interdependent interaction of several gene products in gene regulation , whereby the level of transcription factors is determined. An example of complex threshold mechanisms is the cat's pre-axial polydactyly . In this case, several threshold values ​​are assumed that are not known in detail in molecular biology, for example for the development of 20, 22, 24 or 26 toes of an individual (wild type: 18 toes). Inheritance does not follow the simple Mendelian rules . This becomes understandable if one takes into account that the polyphenism of the toe numbers is always genetically based on the same point mutation.

Implications for Development and Evolution

Threshold value effects can contribute to the fact that a marginal genetic change, such as a point mutation, leads to an extensive phenotypic variation , a “quantum leap” as it were. Or also: a linear gene activation rate suddenly causes a high spatial percentage of activated genes. Both considerations are fundamental to evolutionary developmental biology (Evo-Devo). In Stephen Jay Gould puts it back in 1980: ". If we do not appeal to discontinuous changes due to slight deviations from the development speed, then I do not see, in fact, like most major evolutionary transitions could ever be explained" Today we discussed in In this context, in addition to the change in the speed of development ( heterochrony ), the parameters location (heterotopy), type of gene product generated (heterotype) and increase or decrease of the gene product generated (heterometry) are the starting parameters that can trigger threshold values.

Threshold mechanisms lead to robust development. They represent constraints . Small expression changes can have no effect; they remain channeled . Threshold values ​​can then not be exceeded undesirably. One can say that the development is insensitive to the variation in this area. If a threshold value is z. B. exceeded as a result of a mutation or an environmental factor, the consequence (decanalization) is often not chaotic, contrary to expectations, but now previously hidden (cryptic), possibly multiple accumulated variations or hidden development paths can be revealed, and it can be revealed within the framework of the integrative services of development come to a considerable phenotypic variation or innovation evolutionary, through the implementation and existence of which in the population the natural selection can finally determine.

With the introduction of threshold value effects, the theory of evolution expands both Darwin's argument and that of the synthetic theory of evolution , according to which variations always run gradually in the smallest steps and thus over long evolutionary periods of time ( gradualism ). Today, evolutionary developmental biology in particular no longer sees variation as an exclusively gradual one ( Altenberg-16 ).

Individual evidence

  1. ↑ A. Lange: Darwin's legacy under construction. Königshausen & Neumann, 2012, ISBN 978-3-8260-4813-5 , p. 383.
  2. ↑ Gerd B. Müller: Epigenetic Innovation. In: Massimo Pigliucci, Gerd B. Müller: Evolution. The Extended Synthesis. MIT Press, 2010, ISBN 978-0-262-51367-8 , pp. 316f.
  3. ^ Scott F. Gilbert, David Epel: Ecological Developmental Biology. Sinauer, 2009, ISBN 978-0-87893-299-3 , p. 380.
  4. ↑ a b c d H. F. Nijhout: Stochastic Gene Expression: Dominance, Thresholds and Boundaries. In: Reiner A. Veita (Ed.): The Biology of Genetic Dominance. Eurekah.com, 2004, Chapter 8.
  5. ↑ a b H. B. Tiedemann, E. Schneltzer, S. Zeiser, B. Hoesel, J. Beckers and others: From Dynamic Expression Patterns to Boundary Formation in the Presomitic Mesoderm. In: PLoS Comput Biol. Volume 8, No. 6, 2012, p. E1002586. doi: 10.1371 / journal.pcbi.1002586 .
  6. ^ Hans Meinhardt: Models of Biological Pattern Formation. Academic Press, London 1982, ISBN 0-12-488620-5 .
  7. ^ A b Douglas S. Falconer: Introduction to Quantitative Genetics. Ulmer, Stuttgart 1984, ISBN 3-8001-2532-3 , chap. 18th
  8. ↑ Jingjing Li: The Evolutionary Implication of Gene Expression Variation in Eukaryotes: From Yeast to Human. Dissertation. 2011, ISBN 978-0-494-78260-6 , pp. 80ff.
  9. ↑ Jingjing Li: The Evolutionary Implication of Gene Expression Variation in Eukaryotes: From Yeast to Human. Dissertation. 2011, p. 6ff.
  10. ^ CH Waddington: Genetic Assimilation of an Acquired Character. In: evolution. Volume 7, 1953, pp. 118-126.
  11. ↑ Gerd B Müller: Epigenetic Innovation. In: Massimo Pigliucci, Gerd B. Müller: Evolution. The Extended Synthesis. MIT Press, 2010, p. 317.
  12. ↑ Gerd B. Müller: Epigenetic Innovation. In: Massimo Pigliucci, Gerd B. Müller: Evolution. The Extended Synthesis. MIT Press, 2010, pp. 307-332.
  13. ↑ Stephen J. Gould: The Panda's Thumb - Reflections on Natural History. Suhrkamp Taschenbuch Wissenschaft, 1989, ISBN 3-518-28389-8 , p. 302.
  14. ^ Wallace Arthur: Biased Embryos and Evolution. Cambridge University Press, 2004, ISBN 0-511-21180-5 , p. 81.
  15. ↑ Gerd B. Müller: Epigenetic Innovation. In: Massimo Pigliucci, Gerd B. Müller: Evolution. The Extended Synthesis. MIT Press, 2010, p. 316ff.