Is nuclear division in Physarum controlled by a continuous limit cycle oscillator?

A stochastic, molecular model of the fission yeast cell cycle: role of the nucleocytoplasmic ratio in cycle time regulation

We propose a stochastic version of a recently published, deterministic model of the molecular mechanism regulating the mitotic cell cycle of fission yeast, Schizosaccharomyces pombe. Stochasticity is introduced in two ways: (i) by considering the known asymmetry of cell division, which produces daughter cells of slightly different sizes; and (ii) by assuming that the nuclear volumes of the two newborn cells may also differ. In this model, the accumulation of cyclins in the nucleus is proportional to the ratio of cytoplasmic to nuclear volumes. We have simulated the cell-cycle statistics of populations of wild-type cells and of wee1(-) mutant cells. Our results are consistent with well known experimental observations.

Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions

In recent years, molecular biologists have uncovered a wealth of information about the proteins controlling cell growth and division in eukaryotes. The regulatory system is so complex that it defies understanding by verbal arguments alone. Quantitative tools are necessary to probe reliably into the details of cell cycle control. To this end, we convert hypothetical molecular mechanisms into sets of nonlinear ordinary differential equations and use standard analytical and numerical methods to study their solutions. First, we present a simple model of the antagonistic interactions between cyclin-dependent kinases and the anaphase promoting complex, which shows how progress through the cell cycle can be thought of as irreversible transitions (Start and Finish) between two stable states (G1 and S-G2-M) of the regulatory system. Then we add new pieces to the "puzzle" until we obtain reasonable models of the control systems in yeast cells, frog eggs, and cultured mammalian cells.

Coupled biological oscillators in a cave insect

Insects that live in the interior of caves show the basic internal temporal organization of coupled oscillators. An analysis is made of the coupled moulting and oviposition cycles of Folsomia candida, a cave-dwelling Collembolan, with regard to their oscillatory nature, their phase dependent responses to external perturbations, the effect of coupling on these responses, and conjecture about the link of these cycles with circadian clocks in other organisms.

A purified cellular extract accelerates the cell cycle in Physarum polycephalum

Plasmodia of the myxomycete Physarum polycephalum (strain Cl) were collected at different times during the cell cycle and extracts were prepared from homogenates using a buffer optimized for microinjection into plasmodial veins. These extracts were injected into plasmodia during the first 3 h of the cell cycle. The time of the following mitosis was monitored and compared with that of the buffer-injected controls. Extracts of plasmodia homogenized 45 min before late telophase accelerated the onset of mitosis in the injected plasmodium up to 70 min, i.e., an advance of 10-14% compared to the 8- to 10-h cell cycle duration of the controls. The accelerating activity vanished completely after heating, freezing, or protease digestion, thus indicating the peptide nature of the active agent. Purification of the active compound by means of gel filtration revealed a molecular mass of about 2500 Da. The active portion of the extract was further fractionated by HPLC and the activity determined in a single peak.

The effects of superior laryngeal nerve stimulation on the respiratory rhythm: phase-resetting and aftereffects

The effect of brief superior laryngeal nerve stimulation on the respiratory rhythm was investigated in midcollicular decerebrate, unanesthetized, artificially ventilated, paralysed, vagotomized and debuffered cats. Stimulus trains (50 ms, 200 Hz) delivered during inspiration (I) with intensities exceeding a threshold value, that was inversely related to the phase of the cycle, terminated I and shortened the following expiration (E) (irreversible I termination). Stimulus trains given during I with intensities just below this threshold value produced a transient suppression of I followed by resumption of activity, resulting in a slight prolongation of both I and the following E (reversible I termination). Stimulation during E produced a phase-dependent prolongation of E, but did not affect the next I. Phase-resetting curves were constructed by measuring the changes in respiratory cycle duration produced by stimuli given at phases throughout the cycle. A single stimulus produced aftereffects that lasted several cycles. The aftereffects were investigated by delivering stimuli at a fixed delay from cycle onset every n cycles (n is an integer). Certain combinations of delay, stimulus intensity, and n, resulted in (1) a variable combination of reversible and irreversible I terminations, rather than a consistent response, and (2) an increase in cycle duration. The stimulus aftereffects, that can last up to 9 cycles, may account for previously described unpredictability in the response of the respiratory oscillator to a given stimulus.

Quantized cell cycle times: interaction between a relaxation oscillator and ultradian clock pulses

Control of the timing of cell division is considered to result from a relaxation cell cycle oscillator: this has one slow and one rapid component and obeys a system of two ordinary differential equations. Interactions of the slow component with an ultradian oscillator leads to quantization of cell cycle times when the free parameters of the cell cycle oscillator are chosen close to its bifurcation point. This model fits the experimental results previously reported.

Unstable activator models for size control of the cell cycle

The unstable activator model of Wheals & Silverman (1982) is extended to account for the delay of nuclear division in the acellular slime mold, Physarum polycephalum, that is caused by pulse treatments with inhibitors of protein synthesis. The model is solved exactly to predict the delay as a function of the half-life of the activator. The Wheals-Silverman model is found to give results comparable, but not superior, to other unstable activator models of the cell cycle.

Clocked cell cycle clocks

The cell division cycle of both mammalian cells and microorganisms, which apparently has both deterministic and probabilistic features, is a clock of sorts in that the sequence of events that comprise it measures time under a given set of environmental conditions. The cell division cycle may itself be regulated by a programmable clock that, under certain conditions, can generate circadian periodicities by interaction with a circadian pacemaker. These clocks must insert time segments into the cell division cycle in order to generate the observed variability in cellular generation times.

A simple model for phase locking of biological oscillators

A mathematical model is presented for phase locking of a biological oscillator to a sinusoidal stimulus. Analytical, numerical and topological considerations are used to discuss the patterns of phase locking as a function of amplitude of the sinusoidal stimulus and the relative frequencies of the osillator and the sinusoidal stimulus. The sorts of experimental data which are needed to make comparisons between theory and experiment are discussed.