Oscillations of the energy gap for the initial electron-transfer step in bacterial reaction centers

Oscillations in the electrostatic energy gap [V_elec(t)] for electron transfer from the primary electron donor (P) to the adjacent bacteriochlorophyll (B) in photosynthetic bacterial reaction centers are examined by molecular-dynamics simulations. Autocorrelation functions of V_elec in the reactant state (PB) include prominent oscillations with an energy of 17 cm^–1. This feature is much weaker if the trajectory is propagated in the product state P⁺B^–. The autocorrelation functions also include oscillations in the regions of 5, 80 and 390 cm^–1 in both states, and near 25 and 48 cm^–1 in P⁺B^–. The strong 17-cm^–1 oscillation could involve motions that modulate the distance between P and B, because a similar oscillation occurs in the direct electrostatic interactions between the electron carriers.     

COMT polymorphism modulates the resting‐state EEG alpha oscillatory response to acute nicotine in male non‐smokers

Performance improvements in cognitive tasks requiring executive functions are evident with nicotinic acetylcholine receptor (nAChR) agonists, and activation of the underlying neural circuitry supporting these cognitive effects is thought to involve dopamine neurotransmission. As individual difference in response to nicotine may be related to a functional polymorphism in the gene encoding catechol‐O‐methyltransferase (COMT), an enzyme that strongly influences cortical dopamine metabolism, this study examined the modulatory effects of the COMT Val158Met polymorphism on the neural response to acute nicotine as measured with resting‐state electroencephalographic (EEG) oscillations. In a sample of 62 healthy non‐smoking adult males, a single dose (6 mg) of nicotine gum administered in a randomized, double‐blind, placebo‐controlled design was shown to affect α oscillatory activity, increasing power of upper α oscillations in frontocentral regions of Met/Met homozygotes and in parietal/occipital regions of Val/Met heterozygotes. Peak α frequency was also found to be faster with nicotine (vs. placebo) treatment in Val/Met heterozygotes, who exhibited a slower α frequency compared to Val/Val homozygotes. The data tentatively suggest that interindividual differences in brain α oscillations and their response to nicotinic agonist treatment are influenced by genetic mechanisms involving COMT.     

Developmental instability: measures of resistance and resilience using pumpkin (Cucurbita pepo L.)

Fluctuating asymmetry measures random deviations from bilateral symmetry, and thus estimates developmental instability, the loss of ability by an organism to regulate its development. There have been few rigorous tests of this proposition. Regulation of bilateral symmetry must involve either feedback between the sides or independent regulation toward a symmetric set point. Either kind of regulation should decrease asymmetry over time, but only right–left feedback produces compensatory growth across sides, seen as antipersistent growth following perturbation. Here, we describe the developmental trajectories of perturbed and unperturbed leaves of pumpkin, Cucurbita pepo L., grown at three densities. Covering one side of a leaf with aluminium foil for 24 h perturbed leaf growth. Reduced growth on the perturbed side caused leaves to become more asymmetrical than unperturbed controls. After the treatment the size-corrected asymmetry decreased over time. In addition, rescaled range analysis showed that asymmetry was antipersistent rather than random, i.e. fluctuation in one direction was likely to be followed by fluctuations in the opposite direction. Development involves right–left feedback. This feedback reduced size-corrected asymmetry over time most strongly in the lowest density treatment suggesting that developmental instability results from a lack of resilience rather than resistance.   © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 78, 27–41.     

A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle

We have developed a quantitative model for the creation of cytoplasmic Ca²⁺ gradients near the inner surface of the plasma membrane (PM). In particular we simulated the refilling of the sarcoplasmic reticulum (SR) via PM–SR junctions during asynchronous [Ca²⁺]_i oscillations in smooth muscle cells of the rabbit inferior vena cava. We have combined confocal microscopy data on the [Ca²⁺]_i oscillations, force transduction data from cell contraction studies and electron microscopic images to build a basis for computational simulations that model the transport of calcium ions from Na⁺/Ca²⁺ exchangers (NCX) on the PM to sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase (SERCA) pumps on the SR as a three-dimensional random walk through the PM–SR junctional cytoplasmic spaces. Electron microscopic ultrastructural images of the smooth muscle cells were elaborated with software algorithms to produce a very clear and dimensionally accurate picture of the PM–SR junctions. From this study, we conclude that it is plausible and possible for enough Ca²⁺ to pass through the PM–SR junctions to replete the SR during the regenerative Ca²⁺ release, which underlies agonist induced asynchronous Ca²⁺ oscillations in vascular smooth muscle.     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

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.