Biomedical subjects

N A M Monk

Publications and source records attributed to N A M Monk.

3 recordsLinked to original sources

PubMed2006

Gene expression time delays and Turing pattern formation systems.

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning.

Algorithms↗

PubMed2003

Unravelling Nature's networks.

Dramatic progress has been made recently in determining the genetic and molecular composition of cells. This has prompted the development of new approaches to the challenge of understanding how basic cellular mechanisms are coordinated to produce the dazzling complexity of living systems. To face this challenge fully, it is critical not only to know what genes and proteins are expressed in cells, but also to understand the spatiotemporal dynamics of their networks of interactions. The sheer scale and complexity of cellular interaction networks necessitates a multi-disciplinary effort in which sophisticated experimental techniques are employed in combination with computational analysis and mathematical modelling. Such approaches are beginning to provide insight into basic structures and mechanisms, and promise to become critical to the post-genomic mission of understanding the cell as a complex dynamical system.

Cells↗

PubMed2003

On the structure of protein-protein interaction networks.

We present a simple model for the underlying structure of protein-protein pairwise interaction graphs that is based on the way in which proteins attach to each other in experiments such as yeast two-hybrid assays. We show that data on the interactions of human proteins lend support to this model. The frequency of the number of connections per protein under this model does not follow a power law, in contrast to the reported behaviour of data from large-scale yeast two-hybrid screens of yeast protein-protein interactions. Sampling sub-graphs from the underlying graphs generated with our model, in a way analogous to the sampling performed in large-scale yeast two-hybrid searches, gives degree distributions that differ subtly from the power law and that fit the observed data better than the power law itself. Our results show that the observation of approximate power law behaviour in a sampled sub-graph does not imply that the underlying graph follows a power law.

Models, Theoretical↗