T cell development in the thymus: from periodic seeding to constant output

T cell development occurs in the thymus throughout life. Recent experimental findings show that the seeding of the thymus by multi-potent stem cells from the bone marrow is periodic rather than continuous, as previously assumed. However it is well known that the output rate of cells from the thymus is relatively constant. A quantitative model is used to verify the current hypotheses regarding T cell development in the steady state mouse thymus. The results show that the thymus could be at a periodic steady state with out-of-phase thymocyte populations. Experiments to examine possible periodic fluctuations in the thymus are proposed and methods for further analysis are outlined.     

Sustained oscillations via coherence resonance in SIR

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.     

Two guard cell mitogen‐activated protein kinases,MPK9 and MPK12, function in methyl jasmonate‐induced stomatal closure in Arabidopsis thaliana

Methyl jasmonate (MeJA) and abscisic acid (ABA) signalling cascades share several signalling components in guard cells. We previously showed that two guard cell‐preferential mitogen‐activated protein kinases (MAPKs), MPK9 and MPK12, positively regulate ABA signalling in Arabidopsis thaliana. In this study, we examined whether these two MAP kinases function in MeJA signalling using genetic mutants for MPK9 and MPK12 combined with a pharmacological approach. MeJA induced stomatal closure in mpk9‐1 and mpk12‐1 single mutants as well as wild‐type plants, but not in mpk9‐1 mpk12‐1 double mutants. Consistently, the MAPKK inhibitor PD98059 inhibited the MeJA‐induced stomatal closure in wild‐type plants. MeJA elicited reactive oxygen species (ROS) production and cytosolic alkalisation in guard cells of the mpk9‐1, mpk12‐1 and mpk9‐1 mpk12‐1 mutants, as well in wild‐type plants. Furthermore, MeJA triggered elevation of cytosolic Ca²⁺ concentration ([Ca²⁺]_cyt) in the mpk9‐1 mpk12‐1 double mutant as well as wild‐type plants. Activation of S‐type anion channels by MeJA was impaired in mpk9‐1 mpk12‐1. Together, these results indicate that MPK9 and MPK12 function upstream of S‐type anion channel activation and downstream of ROS production, cytosolic alkalisation and [Ca²⁺]_cyt elevation in guard cell MeJA signalling, suggesting that MPK9 and MPK12 are key regulators mediating both ABA and MeJA signalling in guard cells.     

Transient oscillations induced by delayed growth response in the chemostat

In this paper, in order to try to account for the transient oscillations observed in chemostat experiments, we consider a model of single species growth in a chemostat that involves delayed growth response. The time delay models the lag involved in the nutrient conversion process. Both monotone response functions and nonmonotone response functions are considered. The nonmonotone response function models the inhibitory effects of growth response of certain nutrients when concentrations are too high. By applying local and global Hopf bifurcation theorems, we prove that the model has unstable periodic solutions that bifurcate from unstable nonnegative equilibria as the parameter measuring the delay passes through certain critical values and that these local periodic solutions can persist, even if the delay parameter moves far from the critical (local) bifurcation values.When there are two positive equilibria, then positive periodic solutions can exist. When there is a unique positive equilibrium, the model does not have positive periodic oscillations and the unique positive equilibrium is globally asymptotically stable. However, the model can have periodic solutions that change sign. Although these solutions are not biologically meaningful, provided the initial data starts close enough to the unstable manifold of one of these periodic solutions they may still help to account for the transient oscillations that have been frequently observed in chemostat experiments. Numerical simulations are provided to illustrate that the model has varying degrees of transient oscillatory behaviour that can be controlled by the choice of the initial data.Mathematics Subject Classification: 34D20, 34K20, 92D25Research was partially supported by NSERC of Canada.This work was partly done while this author was a postdoc at McMaster.     

Yeast glycolytic oscillations that are not controlled by a single oscillophore: a new definition of oscillophore strength

Biochemical oscillations, such as glycolytic oscillations, are often believed to be caused by a single so-called ‘oscillophore’. The main characteristics of yeast glycolytic oscillations, such as frequency and amplitude, are however controlled by several enzymes. In this paper, we develop a method to quantify to which extent any enzyme determines the occurrence of oscillations. Principles extrapolated from metabolic control analysis are applied to calculate the control exerted by individual enzymes on the real and imaginary parts of the eigenvalues of the Jacobian matrix. We propose that the control exerted by an enzyme on the real part of the smallest eigenvalue, in terms of absolute value, quantifies to which extent that enzyme contributes to the emergence of instability. Likewise the control exerted by an enzyme on the imaginary part of complex eigenvalues may serve to quantify the extent to which that enzyme contributes to the tendency of the system to oscillate. The method was applied both to a core model and to a realistic model of yeast glycolytic oscillations. Both the control over stability and the control over oscillatory tendency were distributed among several enzymes, of which glucose transport, pyruvate decarboxylase and ATP utilization were the most important. The distributions of control were different for stability and oscillatory tendency, showing that control of instability does not imply control of oscillatory tendency nor vice versa. The control coefficients summed up to 1, suggesting the existence of a new summation theorem. These results constitute proof that glycolytic oscillations in yeast are not caused by a single oscillophore and provide a new, subtle, definition for the oscillophore strength of an enzyme.     

The evolutionary ecology of masting: does the environmental prediction hypothesis also have a role in mesic temperate forests?

The evolutionary advantages of mast seeding in mesic temperate forests are reviewed with reference to the whole plants lifecycle. The aim of this article is to give attention to the environmental prediction hypothesis as an evolutionary aspect of closed-forest dynamics that need to be tested in field studies and modelling. It is suggested that the year after a period of water stress (or other suboptimal conditions for growth) trees respond with high seed production. Due to an understory environment favorable for prolific establishment of seedlings (i.e., more light at the forest floor) this may give rise to a pulse of regeneration. Thus, understanding masting may require a multi-faceted approach including the study of the ecology of the trees themselves beyond pollination and seed predation, and including gap ecology and patch dynamics with special attention to patterns of forest regeneration.     

Mammalian freeze-dried sperm can maintain their calcium oscillation-inducing ability when microinjected into mouse eggs

Mammalian freeze-dried sperm can maintain their genetic integrity and event support full development to term when microinjected into mature oocytes. However, it is unknown whether freeze-dried sperm can still maintain their calcium oscillation-inducing capability. Here, we microinjected mouse and bovine freeze-dried sperm into mouse MII oocytes and examined their calcium oscillation-inducing ability following intracytoplasmic sperm injection (ICSI). Two pieces of information are revealed. First, nearly all oocytes injected with a freeze-dried mouse sperm head or a bovine sperm showed fertilization-like calcium oscillations, indicating that freeze-drying treatment does not affect the activity of the sperm factor responsible for calcium oscillations. Second, freeze-dried sperm exhibited high resistance to external temperature increase. This is shown by the finding that the freeze-dried sperm can maintain their calcium oscillation-inducing capacity even following exposure to 100 degrees C for 3 h. We therefore conclude that mammalian sperm can maintain their calcium oscillation-inducing capability following freeze-drying, rehydration, and ICSI treatments.     

Oscillatory Activity of P-Type Membrane Adenosine Triphosphatases: a Kinetic Model

A kinetic model for membrane P-type adenosine triphosphatases is considered, the main application being to the erythrocyte Ca²⁺-ATPase. It is shown that a simple modification of the known catalytic mechanism of the ATPase by addition of a self-inhibition step and the steady calcium influx leads to damped oscillations in the system discussed. In this way, the model can explain the kinetic experimental results obtained for the purified enzyme in solution as well as for the enzyme incorporated into liposome membranes. The estimated kinetic parameters are close to the experimental ones. Alternative changes in time, demonstrated by the kinetic model for the conformational enzyme states, E₁ and E₂, confirm the model of two alternatively functioning gates in the ion pumping Ca²⁺-ATPase.__________Translated from Biokhimiya, Vol. 70, No. 4, 2005, pp. 533–538.Original Russian Text Copyright © 2005 by Goldstein, Mayevsky, Zakrjevskaya.     

Brevetoxin activation of voltage-gated sodium channels regulates Ca dynamics and ERK1/2 phosphorylation in murine neocortical neurons

Voltage-gated sodium channels (VGSC) are involved in the generation of action potentials in neurons. Brevetoxins (PbTx) are potent allosteric enhancers of VGSC function and are associated with the periodic 'red tide' blooms. Using PbTx-2 as a probe, we have characterized the effects of activation of VGSC on Ca(2+) dynamics and extracellular signal-regulated kinases 1/2 (ERK1/2) signaling in neocortical neurons. Neocortical neurons exhibit synchronized spontaneous Ca(2+) oscillations, which are mediated by glutamatergic signaling. PbTx-2 (100 nm) increased the amplitude and reduced the frequency of basal Ca(2+) oscillations. This modulatory effect on Ca(2+) oscillations produced a sustained rise in ERK1/2 activation. At 300 nm, PbTx-2 disrupted oscillatory activity leading to a sustained increase in intracellular Ca(2+) ([Ca(2+)](i)) and induced a biphasic, activation followed by dephosphorylation, regulation of ERK1/2. PbTx-2-induced ERK1/2 activation was Ca(2+) dependent and was mediated by Ca(2+) entry through manifold routes. PbTx-2 treatment also increased cAMP responsive element binding protein (CREB) phosphorylation and increased gene expression of brain-derived neurotrophic factor (BDNF). These findings indicate that brevetoxins, by influencing the activation of key signaling proteins, can alter physiologic events involved in survival in neocortical neurons, as well as forms of synaptic plasticity associated with development and learning.