Unstable Property Research Articles

Uniqueness of the Dyer-Lashof operations

It is well known that the Steenrod operations are uniquely determined by certain of their properties, namely stability, the Cartan formula, and the unstable property. In this note we give a similar characterization of Dyer-Lashof operations.

Structural stability and model design

The paper introduces the concept of structural stability and proposes that it should be considered a necessary property of scientifically valid models. Formalization of the concept is considered in both linear and non-linear models. A strong preference in favour of the wider use of non-linear models is supported by consideration of the dangers of linearization in dynamic models. The importance of structural stability is demonstrated with reference to dynamic rational expectations models which exhibit the saddle-point property. In such cases convergence to equilibrium is shown to be a structurally unstable property which can be forced by restrictive auxillary assumptions, which are highlighted.

Apparent heterogeneity in the response of quiescent swiss 3T3 cells to serum growth factors: implications for the transition probability model and parallels with "cellular senescence" and "competence".

When subconfluent, Swiss 3T3 cells made quiescent by serum deprivation are stimulated with low concentrations of serum (ca. 1%), only a proportion of them (roughly 50%) enter S phase despite daily replacement with fresh, low-serum medium. The cells that fail to enter S phase are not incapable of doing so, since most of them initiate DNA synthesis after transfer to 10% serum. It would appear that individual cells vary in their growth factor requirements. Using time-lapse cinemicroscopy a few of the cells that respond to low serum were seen to give rise to several generations of progeny, while the majority of cells failed to divide at all, or divided once at most. Despite this, differences between cells in growth factor requirements do not seem to be heritable in the long term, since attempts to enrich for responding cells by prolonged culture in 1% serum have been unsuccessful. Rather, it would appear that the capacity to respond to low serum is an unstable property lost after a few generations in low serum. The loss of responsiveness shows parallels with "cellular senescence" and could conceivably result from decay of the platelet-derived growth factor-induced state of "competence." But regardless of why some cells respond to low serum while others do not, it is clear that the kinetics of entry into S phase after serum stimulation of quiescent 3T3 cells are not strictly first-order, since the labelling index plateaus after roughly 3 days at values substantially below 100%. As such, the kinetics, though not contradicting the transition probability model, cannot be taken to support it as was previously thought.