Simulation of mRNA diffusion in the nuclear environment.

A mathematical model is devised to study the diffusion of mRNA in the nucleus from the site of synthesis to a nuclear pore where it is exported to the cytoplasm. This study examines the role that nuclear structure can play in determining the kinetics of export by considering models in which elements of the nuclear skeleton and confinement by chromatin direct the mRNA movement. As a rule, a dense chromatin layer favours rapid export by reducing the effective volume for diffusion. However, it may also result in a heavy tail in the export time distribution because of the low mobility of molecules that accidentally find their way deep into the dense layer. An anisotropic solid-state transport system can also assist export. There exist both an optimal ratio of the anisotropy and an optimal depth of the solid-state transport layer that favour rapid export.

Synchronization by irregular inactivation.

Many natural and technological systems have on/off switches. For instance, mitosis can be halted by biochemical switches which act through the phosphorylation state of a complex called mitosis promoting factor. If switching between the on and off states is periodic, chaos is observed over a substantial portion of the on/off time parameter plane. However, we have discovered that the chaotic state is fragile with respect to random fluctuations in the on time. In the presence of such fluctuations, two uncoupled copies of the system (e.g., two cells) controlled by the same switch rapidly synchronize.

Modeling the differential fitness of cyanobacterial strains whose circadian oscillators have different free-running periods: comparing the mutual inhibition and substrate depletion hypotheses.

In a recent experimental study, Ouyang et al. (1998, Proc. Natl. Acad. Sci. U.S.A.95, 8660-8664) have shown that, in direct competition, cyanobacterial strains whose circadian clocks have free-running periods (FRPs) which match the period of an imposed light/dark (LD) cycle exclude strains whose FRPs are out of resonance with the LD cycle. These differences in competitive fitness are observed despite the lack of measurable differences in monoculture growth rates between the strains. Here we show that the experimental results are consistent with a mathematical model in which cells rhythmically produce a metabolic inhibitor to which they display a sensitivity modulated by their circadian rhythm. We argue that models in which there is a circadian modulation of nutrient uptake kinetics cannot account for the results of these experiments. We discuss possible experiments to further characterize this phenomenon. The experimental protocol we propose can be used to distinguish between mutual inhibition and substrate depletion as underlying causes of the competitive advantage of circadian resonance.

An autonomous cell-cycle oscillator involved in the coordination of G1 events.

In early embryonic development, the cell cycle is paced by a biochemical oscillator involving cyclins and cyclin-dependent kinases (cdks). Essentially the same machinery operates in all eukaryotic cells, although after the first few divisions various braking mechanisms (the so-called checkpoints) become significant. Haase and Reed have recently shown that yeast cells have a second, independent oscillator which coordinates some of the events of the G1 phase of the cell cycle.(1) Although the biochemical nature of this oscillator is not known,it seems unlikely to be a redundant cyclin/cdk system. BioEssays 22:3-5, 2000.

A new class of biochemical oscillator models based on competitive binding.

It has been noted that single-enzyme systems can undergo strongly damped transient oscillations. In this paper, we present a nonlinear dynamics analysis of oscillations in undriven chemical systems. This analysis allows us to classify transient oscillations into two groups. In the first group, oscillations arise from rapid oscillatory relaxation to a slower transient relaxation mode. These oscillations are always strongly damped. In the second group, it is the slowest relaxation mode which is implicated in the oscillations so these can be very lightly damped. This second class of oscillations has not previously been studied in enzymology. We show that a remarkably simple single-enzyme system, namely competitive inhibition with substrate flow, generates transient oscillations which belong to the second class. In an attempt to design an experimentally realizable version of this model, we then discovered a system which is capable of sustained oscillations. In this experimentally realizable model, two substrates compete to bind to a macromolecule. The flow of one substrate is controlled by a simple feedback device. Sustained oscillations are observed over a very wide range of parameters. In both models, oscillations are favored by a wide disparity in rates of binding and dissociation of the two substrates to the macromolecule.