Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes

We review our work on generalisations of the Becker-Doring model of cluster-formation as applied to nucleation theory, polymer growth kinetics, and the formation of upramolecular structures in colloidal chemistry. One valuable tool in analysing mathematical models of these systems has been the coarse-graining approximation which enables macroscopic models for observable quantities to be derived from microscopic ones. This permits assumptions about the detailed molecular mechanisms to be tested, and their influence on the large-scale kinetics of surfactant self-assembly to be elucidated. We also summarise our more recent results on Becker-Doring systems, notably demonstrating that cross-inhibition and autocatalysis can destabilise a uniform solution and lead to a competitive environment in which some species flourish at the expense of others, phenomena relevant in models of the origins of life.

Spatio-temporal filtering properties of a dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modeled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. In this paper we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded on a simple one-dimensional cable. In the first instance this system is shown to support saltatory waves with the same qualitative features as those observed in a model with Hodgkin-Huxley kinetics in the spine-head. Moreover, there is excellent agreement with the analytically calculated speed for a solitary saltatory pulse. Upon driving the system with time varying external input we find that the distribution of spines can play a crucial role in determining spatio-temporal filtering properties. In particular, the SDS model in response to periodic pulse train shows a positive correlation between spine density and low-pass temporal filtering that is consistent with the experimental results of Rose and Fortune [1999, Mechanisms for generating temporal filters in the electrosensory system. The Journal of Experimental Biology 202, 1281-1289]. Further, we demonstrate the robustness of observed wave properties to natural sources of noise that arise both in the cable and the spine-head, and highlight the possibility of purely noise induced waves and coherent oscillations.

Species-specific kinetics and zonation of hepatic DNA synthesis induced by ligands of PPARα

PPARα ligands evoke a profound mitogenic response in rodent liver, and the aim of this study was to characterise the kinetics of induction of DNA synthesis. The CAR ligand, 1,4-bis[2-(3,5- dichoropyridyloxy)]benzene, caused induction of hepatocyte DNA synthesis within 48 hours in 129S4/SvJae mice, but the potent PPARα ligand, ciprofibrate, induced hepatocyte DNA synthesis only after 3 or 4 days dosing; higher or lower doses did not hasten the DNA synthesis response. This contrasted with the rapid induction (24 hours) reported by Styles et al. (Carcinogenesis 9:1647-1655). C57BL/6 and DBA/2J mice showed significant induction of DNA synthesis after 4, but not 2, days ciprofibrate treatment. Alderley Park and 129S4/SvJae mice dosed with methylclofenapate induced hepatocyte DNA synthesis at 4, but not 2, days after dosing, and proved that inconsistency with prior work was not due to a difference in mouse strain or PPARα ligand. Ciprofibrate-induced liver DNA synthesis and growth was absent in PPARα- null mice, and are PPARα-dependent. In the Fisher344 rat, hepatocyte DNA synthesis was induced at 24 hours after dosing, with a second peak at 48 hours. Lobular localisation of hepatocyte DNA synthesis showed preferential periportal induction of DNA synthesis in rat, but panlobular zonation of hepatocyte DNA synthesis in mouse. These results characterise a markedly later hepatic induction of panlobular DNA synthesis by PPARα ligands in mouse, compared to rapid induction of periportal DNA synthesis in rat.