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

Long-term xylem pressure measurements in the liana Tetrastigma voinierianum by means of the xylem pressure probe

Diurnal changes of xylem pressure in the liana Tetrastigma voinierianum have been measured under greenhouse conditions by means of the recently developed xylem pressure probe. During the early morning hours, tensions in the vessels developed more or less rapidly with time, depending on light intensity. On sunny days, absolute negative pressures down to about -0.4 MPa (atmospheric = 0.1 MPa) were recorded around noon in petiolar or stem xylem vessels, whereas on rainy or cloudy days the xylem pressure remained in the positive sub-atmospheric or slightly negative pressure range. Towards the evening the tension in the vessels always decreased, i.e. the xylem pressure shifted to about atmospheric, or even above-atmospheric, values during the night. Simultaneous xylem pressure recordings at heights of 1 and 5 m frequently yielded either no gradient in tension at all, or far less than expected from the Cohesion Theory. Occasionally, tension gradients were even opposite to those predicted by this theory. Stem-toleaves pressure gradients in accord with the Cohesion Theory were recorded only when tension had been developed during sunny days in the upper branches of the liana, because increases in tension were not immediately propagated to the xylem of the leaves at ground level, as would be expected from a strictly coupled hydraulic system. Parallel recordings of the ldquoxylem tensionrdquo using the pressure chamber yielded rather variable values ranging from 0.1 to 1 MPa; diurnal pressure changes could not be detected at all. The data are discussed on the basis of the equation for the chemical activity of water. They strongly suggest that the xylem tension induced by transpiration is not the sole force for water ascent. Other forces, such as osmotic pressure or convectional and interfacial forces, which to a remarkable extent have already been postulated for decades, seem to be equally important