Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo

During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on–off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior–posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction–diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical framework for understanding the data and in particular indicates that spatial bistability can play a central role in threshold-dependent reading mechanisms of positional information

Mathematics and biology: a Kantian view on the history of pattern formation theory

Driesch’s statement, made around 1900, that the physics and chemistry of his day were unable to explain self-regulation during embryogenesis was correct and could be extended until the year 1972. The emergence of theories of self-organisation required progress in several areas including chemistry, physics, computing and cybernetics. Two parallel lines of development can be distinguished which both culminated in the early 1970s. Firstly, physicochemical theories of self-organisation arose from theoretical (Lotka 1910–1920) and experimental work (Bray 1920; Belousov 1951) on chemical oscillations. However, this research area gained broader acceptance only after thermodynamics was extended to systems far from equilibrium (1922–1967) and the mechanism of the prime example for a chemical oscillator, the Belousov–Zhabotinski reaction, was deciphered in the early 1970s. Secondly, biological theories of self-organisation were rooted in the intellectual environment of artificial intelligence and cybernetics. Turing wrote his The chemical basis of morphogenesis (1952) after working on the construction of one of the first electronic computers. Likewise, Gierer and Meinhardt’s theory of local activation and lateral inhibition (1972) was influenced by ideas from cybernetics. The Gierer–Meinhardt theory provided an explanation for the first time of both spontaneous formation of spatial order and of self-regulation that proved to be extremely successful in elucidating a wide range of patterning processes. With the advent of developmental genetics in the 1980s, detailed molecular and functional data became available for complex developmental processes, allowing a new generation of data-driven theoretical approaches. Three examples of such approaches will be discussed. The successes and limitations of mathematical pattern formation theory throughout its history suggest a picture of the organism, which has structural similarity to views of the organic world held by the philosopher Immanuel Kant at the end of the eighteenth century

Coherence of the lattice polarization in large-polaron motion

This article was published in the journal, Physical Review B [© American Physical Society]. It is also available at: http://link.aps.org/doi/10.1103/PhysRevB.72.224303.Main problems of the large polaron theory are considered. We demonstrate that the problem of searching the ground stationary state of a system of coupled fields with translation-invariant Hamiltonian can have a solution of the form f(r−vt), v→0, i.e., the solution with the spontaneously broken translational symmetry. Such a state can be a ground state of a large polaron in case of strong electron-phonon coupling when the spontaneous break of the translational symmetry results from the phonon vacuum deformation by the electric field of the charge carrier. The correctness of the classical representation of the polarization field in the theory of a strongly coupled large polaron is proved on the base of the theory of the quantum-coherent states of the phonon field. The use of this representation has enabled us to show that extremely high losses of the electron energy in dielectric parts of cold cathodes occurring when the carrier velocity is lower than the threshold for the single-phonon radiation are due to coherent phonon radiation by polarons like Cherenkov effect. It is this radiation that results in the predicted Thornber and Feynman dependence of the carrier steady-state velocity on the applied electric field strength. The coherent phonon radiation generated by polaron current can be detected in experiments on the neutrons scattering. The primary directions of the neutrons scattering depend on the polarons steady-state velocity and, hence, on the applied field strength. The coherent phonon radiation stemming from supersonic thermal motion of polarons causes a giant increase of the resistance in a corresponding temperature interval