Concept Of Positional Information Research Articles

A Julia set model of field-directed morphogenesis: developmental biology and artificial life.

One paradigm used in understanding the control of morphogenetic events is the concept of positional information, where sub-organismic components (such as cells) act in response to positional cues. It is important to determine what kinds of spatiotemporal patterns may be obtained by such a method, and what the characteristics of such a morphogenetic process might be. This paper presents a computer model of morphogenesis based on gene activity driven by interpreting a positional information field. In this model, the interactions of mutually regulating developmental genes are viewed as a map from R2 to R2, and are modeled by the complex number algebra. Functions in complex variables are used to simulate genetic interactions resulting in position-dependent differentiation. This is shown to be equivalent to computing modified Julia sets, and is seen to be sufficient to produce a very rich set of morphologies which are similar in appearance and several important characteristics to those of real organisms. The properties of this model can be used to study the potential role of fields and positional information as guiding factors in morphogenesis, as the model facilitates the study of static images, time-series (movies) and experimental alterations of the developmental process. It is thus shown that gene interactions can be modeled as a multi-dimensional algebra, and that only two interacting genes are sufficient for (i) complex pattern formation, (ii) chaotic differentiation behavior, and (iii) production of sharp edges from a continuous positional information field. This model is meant to elucidate the properties of the process of positional information-guided biomorphogenesis, not to serve as a simulation of any particular organism's development. Good quantitative data are not currently available on the interplay of gene products in morphogenesis. Thus, no attempt is made to link the images produced with actual pictures of any particular real organism. A brief introduction to top-down models and positional information is followed by the formal definition of the model. Then, the implications of the resulting morphologies to biological development are discussed, in terms of static shapes, parametrization studies, time series (movies made from individual frames), and behavior of the model in light of experimental perturbations. All figures (in grayscale), formulas and parameter values needed to re-create the figures and movies are included.

The effect of scale changes on repetitive patterns: Influence of 6-aminonicotinamide on feather germ number

There are many examples of patterned developing systems which are size invariant: if the total size of the system is reduced, then the pattern responds by changing its scale in such a way that the number of pattern elements remains constant. This phenomenon is one of the bases which underaly the formulation of the concept of positional information, one of the great unifying ideas in developmental biology. However, there are less common examples of patterns which are size dependent. In these, alterations of overall size lead to a reduction in pattern elements. Such size-dependent patterns are therefore of theoretical interest. Here we describe how the number of feather germs along the wing bud of the developing chick embryo responds to shortening of the limb, and consider the implications of these observations.

A non-linear field model of pattern formation: Intercalation in morphalactic regulation

Useful insights into pattern formation problems in regulating biological systems have been gained from the concept of positional information . In particular, the polar co-ordinate model of positional information ( French et al. , 1976 , Science 193 , 969–981) and its relatives (e.g. Bryant et al. , 1981 , Science 212 , 993–1002; Lewis, 1981 , J. theor. Biol. 88 , 371–392; Mitthenthal, 1981 , Dev. Biol. 88 , 15–26; Winfree, 1980 , The Geometry of Biological Time . New York: Springer) have helped to provide a qualitative framework for understanding epimorphic regulation, which involves localized growth and pattern formation at a discontinuity (e.g. at a cut surface). On the other hand, these models lack the formal structure to deal quantitatively with regulation; in particular, they are inadequate to treat morphallactic regulation, in which reorganization of the biological system occurs as a consequence of, e.g. changes in its size, rather than a distinct “discontinuity in the positional values”. To overcome this limitation, we propose a morphogenetic field model of pattern formation. We define a simple vector field (morphogenetic field) with generative dynamics arising from the minimization of a non-linear energy functional based on the positional information idea of an “optimal spacing of positional values” and an additional “smoothness” condition. As the system size is changed, transitions to solutions with pattern reversal regions take place, suggesting how reverse intercalation phenomena can arise in morphallactic regulation even without the presence of a discontinuity, as is observed in Tetrahymena doublets regulating to singlets ( Nelsen & Frankel, 1986 , Dev. Biol. 114 , 53–71; Brandts & Trainor, 1990 , J. theor. Biol. 146 , 57–86). We view the success of our model as support for the unification of the formalism, phenomenology and concepts of physical theory with the foundations of theory in biology.

Wound healing in Sharks

Pieces of skin together with scales measuring 7×7 mm were removed from a mature Nurse Shark and a mature Leopard Shark. In the following 2 weeks the wound area secreted mucus, later it contracted and the epidermis regenerated, then it expanded again and newly formed scales erupted. Most of the scar area was covered with scales after 4 months. In the regenerated dermal skeleton the scales show a high degree of variability in that they are much larger and much more complex than the scales of control areas. The repair scales are no longer arranged in diagonal rows and are not so perfectly oriented in a caudal direction as the control scales. Wolpert's concept of positional information in pattern formation can explain this type of regeneration behaviour. The fact that regeneration of the dermal skeleton is not perfect leads to the assumption that the flow of positional information was temporarily inhibited by the surgery.

Positional information in the amphibian limb.

(1) The concept of positional information is applied to a large amount of data obtained previously in experiments on developing and regenerating amphibian limbs. Only the proximo-distal axis of the limb is considered. It is shown that the concept provides a simple, unitary hypothesis which satisfactorily accounts for the experimental data, and may moreover suggest meaningful new approaches. (2) It is suggested that the boundaries of the bipolar limb system lie in the girdle skeleton and at the distal end of the limb, respectively, and that it is the apical epidermis of the growing or regenerating limb which defines the distal boundary conditions. A relatively stable gradient of positional information is assumed to be set up in the mesoderm (or mesenchyme). It is further shown that the differentiated limb retains its positional information and upon amputation imparts it to the base of the blastema. (3) To explain an apparent discrepancy between the developing and the regenerating limb, it is proposed that dedifferentiation of mesodermal limb tissues upon amputation entails a change os positional value in the mesenchyme. Consequently, the amputation level does not once and for all specify the positional value at the proximal end of a mass of blastemal mesenchyme, particularly when the mesenchyme is transplanted in such a way that its linear size decreases (regression) or increases (furion of several blastemas).